Biological Uncertainty Principle

arXiv:0902.0490v2 [q-bio.OT] 4 Feb 2009

Existen e of biologi al un ertainty prin iple implies that we an never nd 'THE' measure for biologi al omplexity. Anirban Banerji Bioinformati s Centre, University of Pune Pune-411007, Maharashtra, India anirbanbioinfo.ernet.in, anirbanabgmail. om July 4, 2009

There are innumerable 'biologi al omplexity measure's. While some of these measures ontradi t ea h other, general patterns emerge from other attempts to represent biologi al omplexity. Nevertheless, a single measure to en ompass the seemingly ountless features of biologi al systems, still eludes the students of Biology. It is the pursuit of this paper to dis uss the feasibility of nding one

omplete and obje tive measure for biologi al omplexity.

A theoreti al on-

stru t (the 'Thread-Mesh model') is proposed here to des ribe biologi al reality. It segments the entire biologi al spa e-time in a series of dierent biologi al organizations before modeling the property spa e of ea h of these organizations with omputational and topologi al onstru ts. A knowledging emergen e as a key biologi al property, it has been proved here that the quest for an obje tive and all-en ompassing biologi al omplexity measure would ne essarily end up

1

in failure. Sin e any study of biologi al omplexity is rooted in the knowledge of biologi al reality, an expression for possible limit of human knowledge about ontologi al biologi al reality, in the form of an un ertainty prin iple, is proposed here. Two theorems are proposed to model the fundamental limitation, owing to observer dependent nature of des ription of biologi al reality. They explain the reasons behind failures to onstru t a single and omplete biologi al omplexity measure. This model nds support in various experimental results and therefore provides a reliable and general way to study biologi al omplexity and biologi al reality.

Keywords : Biologi al threshold levels; thread-mesh model; biologi al spa e-time; biologi al un ertainty prin iple; observer-dependent biologi al reality. 1

Introdu tion :

Biologi al omplexity measures are many [Edmonds, 1999℄. While all these measures are useful (be ause they quantify ertain aspe ts of the biologi al systems), in many of the ases, they tend not to onsider the gamut of properties that a omplex system is known to possess in general (emergen e, near-neighbor intera tions, non-linear fun tional dependen ies, feedba k loops - to name a few) [Hazen et al., 2007℄.

The words ' omplexity measure' or ' omplexity in-

dex' have be ome almost synonymous with some kind of marker for the omplex system under observation [Chiappini et al., 2005, Banerji and Yeragani, 2003℄. Although a review of all the methodologies proposed for the studies of biologi al omplexity is not the obje tive behind this work, it assumes importan e to

apture a glimpse of the spe trum of signi ant outlooks prevalent in ontemporary studies on the subje t. Su h glimpse exposes us to the glaring nature of

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ontradi tions among the existing omplexity measures.

Des ription length, in some way or other, forms the basis of most of the omplexity measures [Lofgren, 1977℄. The stri t and lassi al measure of omplexity, namely the KCS denition [Kolmogorov, 1965, Chaitin, 1966, Solomono, 1964℄ states that for a universal Turing Ma hine, the KCS omplexity of a string of

hara ters des ribing it will be given by the length of the shortest program running on it that generates the des ription.

However, apart from the the-

oreti al problem of being non- omputable to obtain any reasonable pra ti al estimate[Badii and Politi, 1997℄; the impli ation of KCS omplexity measure, namely, to ontain maximum information the sequen e on erned should be absolutely random[Gellmann, 1994℄, ontradi ts the nature of biologi al organizations ompletely. The ase of one[Hinegardner and Engelberg, 1983℄ measure of (stru tural) omplexity, whi h builds upon the KCS paradigm and ounts the number of dierent parts that a system ontains, highlights the aforesaid

ontradi tion. The riti isms to this measure are threefold; rst, it is di ult to identify the "parts"; se ond, the so- alled 'C value paradox'[Thomas, 1971℄ and third, ambiguous results originating from ' oding-non- oding ratio'. To elaborate a little, C value paradox suggests an absen e of orrelation between phenotypi omplexity with total size of the genome (even though the plant

nudum

P silotum

is widely viewed as easy to understand than the plant Arabidopsis,

the former has 3000 times as mu h DNA; similarly the phenotypi omplexity of a lungsh(C

∽ 1.4 × 1011

base-pairs), has been ounted to be higher than

phenotypi omplexity of us, the

Homo Sapiens(C ∽ 3.4 × 109

base-pairs)).

On the other hand, onfounding results arise out of ' oding-non- oding ratio' too. The use of the number of protein- oding gene as a measure of biologi al

omplexity would make uro hordates and inse ts less omplex than nematodes;

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and alsos, humans less omplex than ri e.

The inadequa y of applying this

s hool of thought to ompute biologi al omplexity is dis ussed by Szathmary [Szathmary et al., 2001℄.

From the paradigm of DNA base-pairs to the realm of e ology, the theme of

onstru tion of a omplexity measure for biologi al systems, only to be regarded subsequently as either erroneous or ill-suited for biologi al onsiderations, appears re urrent. One approa h [Uso et al., 2000℄ had measured e ologi al omplexity by ounting number of synonyms for a parti ular pro ess, omparing between models that des ribe same set of exe uted behaviors. However, it was re ognized very soon [Barnstad et al., 2001℄ that not only the information regarding who is intera ting with whom but also the information related to the strength of various (time-dependent) oupling s hemes is what should be taken into a

ount.

Soon after, still another approa h bearing a distin t similarity

with Hinegardner's philosophy [Anand and Tu ker, 2003℄ surfa ed and asked the question "if diversity is a part of omplexity, then should not biodiversity be a part of bio omplexity?".

Evolution of these ideas learly demonstrate

that while none of the proposed omplexity measures might be wrong, none of them an en ompass all the aspe ts pertinent to the system under onsideration.

In ompleteness of a omplexity measure and subsequent renun iation of it ( ontradi ted by another omplexity measure or otherwise) is nowhere more prominent than in the paradigm of biologi al sequen e related omplexity measures. Even a eeting glimpse at the linguisti approa hes enables us to appre iate the extent of dis ord between them.

From the rather simple and parti ular

model of alphabet symbol frequen ies [Wootton and Federhen, 1996℄ to general algorithm on erning lustering hara teristi s of rypti ally simple sequen es

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[Alba et al., 2002℄, from popular approa hes for evaluation of the alphabet apa ity with the help of ombinatorial omplexity and linguisti omplexity [Milosavljevi and Jurka, 1993, Gabrielian and Bolshoy, 1999℄ to a omplexity measure based on text segmentation by Lempel and Ziv [Lempel and Ziv, 1976℄ and subsequent modi ations [Gusev et al., 1999, Chen et al., 1999℄, from studies in sto hasti omplexity [Orlov et al., 2002℄ to approa hes related to grammati al omplexity [Jimenez et al., 2002℄; numerous approa hes of linguisti

omplexity with potential relevan e to biologi al systems have been explored. With a dierent onus, identi ation and hara terization of low text omplexity regions that might be fun tionally important, was studied by many [Han o k, 2002, Wan and Wootton, 2000, Chuzhanova et al., 2000℄, where low omplexity regions have been identied as regions of biased omposition ontaining simple sequen e repeats [Han o k, 2002, Tautz et al., 1986℄. But even in the sphere of this sub-approa h, several dieren es of opinions prevail. Cox and Mirkin [Cox and Mirkin, 1997℄ diers from Tautz [Tautz et al., 1986℄ in asserting that the stret hes of sequen es having imperfe t dire t and inverted repeats should be also onsidered as the sequen e with low omplexity. A review of many of these methodologies that had attempted to onstru t omplexity measure for sequen e level biology an be found in a re ent work [Abel and Trevor, 2005℄.

Other than the linguisti framework, the information theoreti and graph theoreti approa hes are also used extensively to address the notion of biologi al

omplexity. When the former relied prin ipally upon the notion of ompositional diversity; the later, oupled with ontrol theoreti tool-set, ould investigate stru tural or topologi al omplexity of many dynami systems. To provide some

hara teristi examples, at the level of networks, Palsson [Papin et al., 2002℄ dened a pertinent algebrai stru ture, the 'extreme pathway', to hara terize its

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length as the size ( omplexity marker) of the orresponding ux distribution map. Considering topologi al "diversity" of the assigned graphs as fun tional exibility of network on erned, Hildegard Meyer-Ortmanns [Hildegard, 2003℄ had proposed another useful omplexity measure. On a rm graph theoreti note Bon hev [Bon hev, 2003℄ has identied some signi ant omplexity markers by

hara terizing the networks with respe t to onne tedness, subgraph ount, total walk ount, vertex a

essibility, et .; before observing that the information theoreti index an also serve to assess the ompositional omplexity of a network.

However, innovative as they are, none of these measures have found

onsistent usage in the biologi al treatise; hinting perhaps at their limitations with respe t to general appli ability in biologi al realm.

Apart from these, the other omplexity measures with a distin t ba kground of Physi s, have also been proposed.

Bennett [Bennett, 1988℄ wanted to ir-

umvent the problems asso iated with KCS s hool of omplexity measures by dening a measure based on the degree to whi h the information has been organized in a parti ular obje t.

This method named 'logi al depth' had at-

tempted to measure the time needed to de ode the optimal ompression of the observed data.

However this was bounded from below by the magnitude

of another omplexity measure[Grassberger, 1986℄ whi h quanties the minimal information one needs to extra t from the past in order to provide optimal predi tion.

The omplexity measure due to Wolpert and Ma Ready

[Wolpert and Ma Ready, 1997℄, namely 'self dis-similarity', had attempted to fuse information theory with statisti al inferen e.

It wanted to attribute the

variation of spatio-temporal signatures of systems at dierent s ales (instead of mere ardinality of them) to the omplexity marker for it.

But regardless

of their theoreti al elegan e, none of these aforementioned measures have been

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onsidered by the biologist fraternity for mu h pra ti al appli ability, whi h tends to suggest that all these measures have (probably) failed to distinguish between general biologi al ases beyond some simple ones.

A omplexity measure proposed in re ent past by Hazen [Hazen et al., 2007℄ presents itself as one that respe ts the entanglements of biologi al systemi features seriously. This attempt revolves around the measurement of omplexity of a system in terms of the 'fun tional information'; in other words, measurement of the information required by the system to en ode a spe i fun tion. It appears to share similar mathemati al philosophy as another sequen e-based omplexity measure, namely the T- omplexity [Ebeling et al., 2001℄. The T- omplexity works by ounting the numbers of steps required by an alphabet set to onstru t a string. However, it has been proved on lusively [Fei and Adjeroh, 2004℄ that T- omplexity is rather ine ient to des ribe the biologi al omplexity, even when viewed at one-dimensional sequen e level merely.

The dis ussion of above helps us to identify two signi ant problems with the

onstru tion of omplexity measures in many ases. First, the ontext dependent nature of biologi al systems is addressed rather in ompletely in many of the omplexity measures and se ond, many of these measures are onstru ted on the basis of observer dependent des ription of biologi al reality. Although it is widely agreed upon [Mahner and Kary, 1997, Kaneko, 1998, Andrianantoandro et al., 2006, Marguet et al., 2007℄ that there an't be a biologi al omplexity measure without onsideration of the ontext dependen e (be ause fun tion of any biologi al system itself is ontext dependent), many measures do not take it into a

ount [Hinegardner and Engelberg, 1983℄. The se ond problem on erns the fa t that denition of many of the omplexity measures seem to arise from

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the observer's hoi e of, what he onsiders, important properties of the system [Flu kiger, 1995℄. These predile tions of observer [Corna

hio, 1977, Bar-Yam, 2004℄ often revolve around des ription of systemi property under onsideration from the referen e frame of an observer and not from the referen e frame of the system itself. Consequently, the dened omplexity measure tends not to be intrinsi to the system being studied but depends on extrinsi state (properties) of the observer, as well as on his preferen es to study ertain aspe ts of system on erned.

These two extremely important aspe ts of

context dependence and observer dependence

were however not entirely unaddressed. Gellmann [Gellmann and Lloyd, 1996℄ argued that the des ription of the ensemble is also determined by a number of external fa tors; whi h depend on who (the observer) is des ribing.

From

a dierent perspe tive Adami [Adami, 2002℄ had noted that many of the abstra t measures for biologi al omplexity "do not appear satisfa tory from an intuitive point of view" and proposed a measure ('physi al omplexity') that owes it's root to the automata theory but is smart enough to bypass the problems of KCS measure of omplexity by identifying genomi omplexity with the amount of information a sequen e stores about it's environment. The ontext dependen e of this measure is its most interesting feature. The impli it starting point of Adami's work is to re ognize that there an be no su h thing as biologi al omplexity in the absen e of ontext (whi h in identally is in ontradi tion to the views expressed in the onstru tion of another omplexity measure [Roman et al., 1998℄), be ause biologi al fun tion itself tends to be ontext dependent.

It has been shown re ently that 'physi al omplexity' an estimate

both stru tural and fun tional omplexity too, at least for some parti ular biologi al ma romole ules [Carothers et al., 2004℄.

However, as has been noted

by Seth [Seth, 2000℄, in Adami's measure the observer of omplexity be omes

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the environment itself and therefore enables the measure to assert that it is a measure of the information about the environment, that is oded in the one dimensional biologi al reality, viz. the sequen e. The problem with su h assertion has been dis ussed in details by Seth [Seth, 2000℄. Furthermore, although being biologi ally more relevant than many other suggested omplexity measures, 'physi al omplexity' has been found to be di ult to evaluate in general pra ti e ex ept for some parti ular ases. Thus, although theoreti ally impressive, this measure too has not found widespread use amongst the biologist fraternity.

Hen e it an be learly seen that even after exhaustive resear h from various perspe tives, no lear denition of biologi al omplexity measure has emerged hitherto; as have been admitted in some re ent works [Hazen et al., 2007, Hulata et al., 2005, Bialek et al., 2001℄. In fa t, as it is evident from the dis ussions above, the entire eld is burdened by numerous ounter laims and possible sour es of ontradi tions. Sin e biologi al omplexity measures try to represent biologi al reality, a

loser examination of these ontradi tory nature omplexity measures reveal the

ontradi tory nature of biologi al reality, as per eived by observers. Examples of su h ontradi tions about biologi al reality are provided later (Se tion 2.4.3), with (possible) reasons behind su h ontradi tions.

But before delving into

those details, we an note that there are exists two lear lusters of biologi al

omplexity measures in the onfusing ensemble of them. One luster omprises of omplexity measures that re ognize emergen e as a property of biologi al systems and the other whi h do not. Sin e emergen e has been on lusively proved to be an unmistakable feature of any omplex adaptive system (true hara terization of biologi al systems) [Hazen et al., 2007, Bar-Yam, 2004, Ri ard, 2004, Gellmann, 1994℄; we an, from now on, justiably limit ourselves to only the set

9

of omplexity measures that pay adequate importan e to biologi al emergen e.

A knowledging emergen e as an important biologi al property, a toy model (the 'Thread-Mesh model') to des ribe biologi al reality is proposed here. With the help of this model it has been proved here (algorithmi ally and topologi ally) that the nature of biologi al reality is observer-dependent, time-dependent and

ontext-spe i . Sin e any biologi al omplexity measure attempts ne essarily to depi t the biologi al reality (in some way or other), the Thread-Mesh model proves that no biologi al omplexity measure an be onstru ted that is obje tive and omplete in its des ription of biologi al reality. Furthermore, it proves that the reason for having so many biologi al omplexity measures and so many (possible) ontradi tions in them is due to the subje tive and in omplete views of biologi al reality, as aptured by the observers.

2. Des ription of biologi al reality with the Thread-Mesh model : Thread-Mesh model (TM model) segments the biologi al spa e-time into a series of dierent biologi al organizations, viz. the nu leotides; amino a ids; ma romole ules (proteins, sugar polymers, gly oproteins); bio hemi al networks; biologi al ell; tissue; organs; organisms; so iety and e osystem; where these organizational s hemes are alled threshold levels. Emergen e of a single biologi al property ( ompositional or fun tional) reates a new biologi al threshold level

th biologi al threshold level

in the TM model. Thus, if any arbitrarily hosen i is denoted as that

THi

TH THi+1 i,

didn't possess.

will be ontaining at least one biologi al property

Somewhat similar s hemes of identi ation of bio-

logi al threshold levels is neither new [Testa and Kier, 2000, Dhar, 2007℄ nor

10

unique and there an be many other intermediary threshold levels too ( onsidering the fa t that existen e of one emergent thread distinguishes

THi

THi+1

from

). For example, at high resolution one an onsider the se ondary, tertiary,

quaternary stru tures too as separate threshold levels that exist between amino a ids and the proteins. The basi prin iples for subsequent dis ourse, however, are general and an be applied to any threshold level. Every possible property that a threshold level is endowed with, is represented by a 'thread' in the TM model.

Thus an environmental property will be alled as an 'environmental

thread' in the present parlan e.

Threads an be ompositional, stru tural or

fun tional. For example, for the biologi al threshold level orresponding to the enzymes (threshold level representing the ma romole ules), one of the ompositional threads is the amino a id sequen e; whereas the radius of gyration, the resultant ba kbone dipole moment and ea h of the bond lengths, bond angles, torsion angles are some examples of stru tural threads and the values for Km , Vmax , K at are some examples of it's fun tional threads.

2.1) Components of TM model : Any biologi al system to be studied and the observer who is interested to study some properties of that system, both ontribute to the formation of the thread mesh. Threads in the thread-mesh spa e of any threshold level an be lassied in 3 types : Type 1) The systemi threads, whi h represent the ompositional, stru tural and fun tional properties of any threshold level of only the biologi al system under onsideration (ex luding the pertinent environmental features that might intera t with the treshold under onsideration); Type 2) The environmental threads, whi h represent all the relevant properties of environment (stru tural and/or fun tional) that an potentially intera t

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with the systemi threads belonging ea h and every threshold level, exhaustively. It is purely biologi al to expe t that dierent subsets of the gamut of environmental threads will be relevant for operations with dierent threshold levels of the biologi al system under onsideration (an environmental thread that is important for helping ertain operations at the threshold level of tissues, might not be relevant at the threshold level of nu leotides and so on ..) and Type 3) The observer threads, representing the observer (along with his observational (experimental) tool-set). Although the observer himself is represented by the threshold level of an individual organism, the entire set of observer threads an intera t with thread set representing any threshold level of the biologi al system. It is easy to see that a partial symmetry results when (in the spe ial ase), the observer observes the 'organismi ' threshold level, be ause the observer himself exists at the 'organismi ' threshold level ( ons iousness of tissue or proteins haven't been reported hitherto). However even this symmetry will not be omplete, be ause the type-3 threads will be hara terized by threads emanating from experimental tool-sets too, whi h the type-1 threads are devoid of. The myriad possible intera tions between rst and se ond type of threads in thread-mesh spa e, a

ount for the ontext spe i nature of biologi al reality to a great extent. The other kind of ontext dependen e obviously originates from the nature of intera tions between type 1 threads only. The relevant question at this point might be : "what is the general nature of properties that we an measure on entrating on any one threshold level?" Only the threads representing strong emergent patterns would be more probable to intera t with observer's thread set and thus will make their presen e felt to the observer. As a result, only some of the properties for a parti ular threshold level

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will be noti ed while some other subdued systemi features will not be known to us.

2.2) Assumptions of Thread-Mesh model : Assumption 1)

The systemi properties will be onserved; that is, no systemi

thread an be found that destroys itself without any tra e at the higher threshold levels. In other words, the TM model states that a systemi thread (a systemi property, stru tural or fun tional) representing biologi al threshold level either preserve itself as it is at the threshold level

THi+1

THi

should

, or it will merge with

some other thread (systemi property or environmental property) representing

THi

, to onstru t systemi property representing

property an vanish from the thread-mesh spa e.

THi+1

.

But no biologi al

On the other hand, a new

systemi thread an always emerge at any threshold level

THi+1

as an entirely

novel one. But on e present, the lineage of the property an always be per eived on the higher threshold levels.

Assumption 2)

The systemi thread set representing any threshold level is

onstant, but the observer thread set intera ting with it varies with time and

ontext. In other words, the total number of threads that dene any threshold level say

N

THx

,

(all possible ompositional and fun tional threads of the system along

with all possible environmental threads that have a probability to intera t with the systemi threads, under all possible ontexts that the biologi al threshold might experien e); must be time-invariant for that parti ular threshold level. This implies that the volume of the thread-spa e representing any biologi al

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threshold-level will be onstant. Observer's thread set that an intera t with

N N

, in ontrast, is variable. More intera tion of the observer's thread set with will a

ount for more ompleteness of our knowledge about

intera tion of the observer's thread set with of our knowledge about

N

N

N

, similarly less

will a

ount for less ompleteness

.

This assumption of TM model an thus be stated otherwise as, the interse tion between observer's thread-set and systemi thread-set is not invariant but is a fun tion of prevailing ontext and time.

In other words, if the interse -

tion between observer's thread-set and systemi thread-set under any given

ontext at any instan e of time t1 onstitutes a set

At1

; and the interse tion

between observer's thread-set and systemi thread-set under the same ontext at any other instan e of time t2 onstitutes another set

|At1 | = 6 |At2 |.

At2

; then in general,

However the assumption asserts further that even if

it is not probable that their thread-set.

At1

and

At2

|At1 | = |At2 |,

will be having identi al ompositions of

These dierent interse tions ( ontext-dependent and time-

dependent) between observer's thread-set and systemi thread-set are the ones that ause the subje tive and ontradi tory inferen es about biologi al systems. Examples of how dierent experimentalists (dierent observers) an interfere with biologi al reality to draw dierent inferen es about it, is provided in a re ent work [Xu et al., 2006℄ at the ellular threshold level and by another study [Moen et al., 2005℄ at the organismi threshold level. It is due to this subje tive nature of our a quired knowledge about biologi al reality that we annot have a general and omplete measure for biologi al omplexity; but rather will only have to be ontent with numerous threshold spe i ontext-dependent omplexity measures.

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Indeed the re ent studies [Dokholyan and Shakhnovi h, 2001℄, [Ding and Dokholyan, 2006℄ tend to vindi ate the assumption of thread-intera tions being ontext-dependent and time-dependent. A software, 'Medusa' [Ding and Dokholyan, 2006℄ attempts to explore the evolution of a protein fold family in a dynami manner; that is, by monitoring the time-dependent hanges in sequen e and stru ture upon random mutations of amino a ids. This means, the software attempts to learn about the nature of fun tional threads generated by intera tions between three types of threads (rst, the thread-set representing omplete amino a id sequen e alongside several windows of varying lengths of that same sequen e, se ond, threads representing every stru tural features and third, the ompositional threads representing the random mutations of the amino a ids) in a time-variant manner. The same study nds that a "subtle" hange in the ompositional nature of a subset of thread-set representing amino a id level of biologi al threshold, result in "distin t pa king of the protein ore and, thus, novel ompositions of ore residues"; depi ting how a hange in ertain set of threads at a parti ular time and under appropriate ontext, an hange the entire s heme of intera tions and a

ount for the emergen e of one parti ular property (novel ore residues) at the next level of biologi al threshold from a pool of possible properties.

Assumption 3)

The thread-mesh for any threshold level is onstituted of all

the threads representing the systemi properties, environmental properties and observer (observational me hanisms) properties and will have a bounded geometry typi al of that threshold level. This assumption points to the denite yet distin tly dierent existen es of biologi al organizations. It implies that the pattern of intera tions between biologi al properties prevalent in any threshold level must be following a denite pattern that is dierent (either subtly or markedly) from the pattern of intera tions between biologi al properties in an-

15

other threshold level. However as the threads(properties) of any threshold level are related to those of other threshold levels and the thread-mesh for ea h of these threshold levels have unique bounded geometries, intera tion between two threads in any threshold level an potentially inuen e the thread intera tions in some other threshold level too.

2.3) Properties of Thread-Mesh model : Property 1) : THi THi+1 THi THi THi-1 THi+1 THi

If the emergent thread that separates threshold level

from

is not a ase of 'strong emergen e' [Crut held, 1994, Ri ard, 2004℄,

the entire thread set of

said about

THi+1

and

is produ ed from

, and so on). However, although the ompositional

lineage exists, the thread set of

tion of thread set of

(the same an obviously be

is independent in its fun tion from fun -

. This fun tional dieren e originates due to the exis-

ten e of dierent set of pertinent biologi al ontexts for the threshold levels. For

THi

example, although originating from the genes (

THi+1

), the proteins (

) an

undergo independent ontext driven operations (enzymati leavage, aggregation with other mole ules, phosphorylation, gly osylation et ...), whi h are ompletely dierent from the ontext-driven operations relevant at the nu leotide level (for example, due to alternative spli ing (a ontext-spe i operation), almost one third of DNA produ es dierent proteins; - an operation only pertinent at the nu leotide level). In fa t, as noted re ently [Cohen and Atlan, 2006℄, a protein gly eraldehyde-3-phosphate dehydrogenase, dis overed as an enzyme, has now been identied to have a fun tion in membrane fusion, mi ro-tubule bundling, RNA export, DNA repli ation and repair, apoptosis, an er, viral infe tion and neural degeneration; whi h would have been impossible if dierent

ontextual onstraints for ma romole ular threshold level were not in pla e.

16

Property 2) :

Although in ertain ases the absolute number of threads repre-

senting threshold level

THi+1

might be less than that of

THi

(a pro ess referred

to as 'integration' in a previous study [Ri ard, 2004℄); a ontext-spe i de omposition that respe ts ompositional lineage of thread-set representing will reveal that

(|T Hi+1 | − |T Hi |) > 1.

THi+1

It is important to note that this inequal-

ity expresses an innate fa t about behavior of the systemi threads between biologi al threshold level and doesn't involve observer thread set at all. This inequality

(|T Hi+1 | − |T Hi |) > 1

tends to suggest a deeper biologi al fa t;

that is, even in the absen e of an observer, the biologi al reality an only be talked about in a threshold-dependent manner. That is, even with the omplete knowledge of the thread-set ( ompositional, stru tural, fun tional) of

THi

un-

der every possible ontext, the omplete set of biologi al properties representing

THi+1

won't be known to us. In fa t, the possible limit of knowledge about

biologi al properties about

THi+1

derived from

THi

will always follow the in-

equality

[(f (T Hi+1 ) − f (T Hi)) > 1]

(1)

Some related works exemplify the impossibility to a quire knowledge about

omplete thread-set of representing

THi

.

THi+1

, from the knowledge of omplete set of threads

These studies learly point to the fa t that to represent

the ontextual onstraints typi al of any

THi+1

, novel threads ( ompositional

and/or stru tural) are required. The nature of su h novel threads representing the typi al ontextual ( ompositional and/or stru tural threads) onstraints of

THi+1 THi

an not be predi ted from the knowledge of thread-set representing

. For example, based upon theoreti al al ulations that takes into a

ount

the ompositional and stru tural threads in the forms of exa t magnitudes of an individual protein's mole ular weight, solute radius and solvent molar volumes along with appropriate intera tion fa tors (Wilke-Chang equation and

17

Stokes-Einstein equation), an estimate of diusion fa tors for the proteins was

onstru ted[Rangamani and Iyengar, 2007℄. However the study nds that su h estimates were inadequate when des ribing the protein's property spa e when it is undergoing intera tions with other ma romole ules in ytoplasm. The ontext of ytoplasmi reality demands "appropriate orre tion fa tors" that suitably

onsiders ytoplasmi vis osity, drag and mole ular rowding (all being ompositional and stru tural threads representing ellular reality). The exa t nature of parameter set representing this "appropriate orre tion fa tors" at any

an never be as ertained from the knowledge of

THi

THi+1

,

. From a dierent stand-

point, another study [Hut et al., 2000℄ had also established the impossibility to

reate a biologi al ell on the basis of di ulty to ensure "intrinsi oheren e" (the parameter set representing ontextual onstraints at

THi

physi al studies between mole ular level entities (

THi+1

) obtained from

). These laims tend to

vindi ate the se ond property of TM model.

Findings of

eq n − 1

an be expressed in more formal and general term with the

a theorem, on the nature of a quired knowledge about any threshold level of any biologi al system. It an be stated as :

Theorem-1 : The very nature of biologi al reality makes it impossible for any observer to a quire omplete knowledge about the mutual intera tion of biologi al properties between any two adja ent biologi al threshold levels, representing any part of biologi al spa e-time. Proof : Let us denote any parti ular biologi al property ( ompositional or stru tural or

THi

fun tional) of any arbitrarily hosen biologi al threshold level (

thi .

) by thread

Similarly let us denote the lineage of that parti ular biologi al property,

18

viz.

thi ,

THi+1

in the adja ent biologi al threshold level (

(Examples of su h lineages are many. At

TH

) by thread

thi+1 .

protein , many proteins are found

with unfavorable hydrophobi and/or non-polar residues on their surfa e. But su h unexpe ted stru tural feature only makes sense when one observes that it is those hydrophobi residues on the surfa e of the protein that serve as hotspots for other proteins to bind [Lijnzaad and Argos,1997℄, and subsequently that protein-protein intera tion forms a part of some bio hemi al pathway at the next biologi al threshold level, namely at

TH

pathway ).

Sin e every biologi al property operates within a spe ied bound of magnitude (referred to as 'u tuation' in an earlier study [Testa and Kier, 2000℄) we des ribe the range of magnitude that

thi

an assume by its inherent en-

pi log p1i ; (pi = P r (α = αi ), 0 ≤ pi ≤ 1

tropy

S (thi ),

where

Pr

p = 1).

Similarly we des ribe the range of magnitude that the lineage of

i=1

S (thi ) =

P

TH

i

and

thi+1 , in ( i+1 ) an assume by its inherent entropy S (thi+1 ), where
P Ps S thj=(i+1) = j qj log q1j ; (qj = P r (β = βj ), 0 ≤ qj ≤ 1 and j=1 q = 1). thi ,

viz.

To des ribe the extent of ee t

thi

has on

thi+1 ,

we resort to onditional prob-

ability. Denoting the entire expe ted extent of the ee t of

thi

as

Γj ,

a part of the same as

a

ounts for

βj

as

αi ((

S (thi |βj ) =

P

i

X

βj

P

j

αi thi = σi ),

where

P r (αi |βj ) log

i

The parameter

Qij

βj thj = Γj

due to entire

, and the part of

a

ounts for

THi+1

thi+1

thi+1

Γj );

thi ,

that is ausing

thi+1

that

we have :

(2)

) when it is aware that

βj

is operative, but does not possess the entire infor-

mation ontent about the qualitative and quantitative nature about of

thi

X 1 1 Qij log = P r (αi |βj ) Qij i

represents the state of (

extent of the property

σi



αi

extent

to behave in the way it is doing. Similarly, by

19

Pij ,

THi

we an des ribe state of ( operative in ausing

βj

THi

) when (

extent of ee t on

αi

) is aware that

thi+1 ,

extent of

THi+1

n Eq -2, by itself, des ribes the un ertainty in (

thi .

is

but does not possess the en-

tire information ontent about the qualitative and quantitative nature of

and quantitative nature of

thi

thi+1 .

) about the qualitative

Jij ,

The joint probabilities, say

des ribing the

state of an observer (obviously not a part of the system), attempting to know the qualitative and quantitative extent of both

αi

and

βj

an be des ribed by

simple Bayesian stru ture as :

∀ i, j :

pi Pij = P r (αi ) P r (βj |αi ) = P r (αi , βj ) = P r (βj ) P r (αi |βj ) =

qj Qij = Jij , hen e

Qij =

On averaging over all the for equivo ation of




S thi |thj=(i+1) =

thi

βj s

w.r.t

X

and using

thj=(i+1)

qj S (thi |βj ) =

j

pi Pij qj

(3)

qj Qij = Jij ,

we derive the expression

:

X

X

qj

i

j

THi+1

n Eq -4 des ribes the average un ertainty in (

!

1 Qij log Qij

) about

=

thi

XX i

Jij log

j

when

1 Qij

(4)

thi+1

is

operative.

THi+1

n n The set of argument des ribed by eq -2 and eq -4 w.r.t (

THi

as mirror image w.r.t (

) holds true

) and an be des ribed as eq-5 and eq-6, respe tively

as:

20


X P r (βj |αi ) log S thj=(i+1) |αi = j

αi s

and averaging over all the sion for equivo ation of




S thj=(i+1) |thi =

X

and using

thj=(i+1)

w.r.t

pi S (thj |αi ) =

thi

X i

i

X 1 1 Pij log = P r (βj |αi ) Pij j

pi Pij = Jij ,

(5)

we derive the expres-

as :



pi 

X j

 1 1  XX Jij log Pij log = Pij Pij i j (6)

An observation pro ess that attempts to retrieve qualitative and quantitative information regarding the lineage of the properties under onsideration, will hen eforth be subje ted to an average un ertainty given by the joint entropy :

S (thi , thj ) =

XX i

P r (αi , βj ) log

j

XX 1 1 Jij log = P r (αi , βj ) Jij i j

(7)

Sin e the mode of information ex hange between any two arbitrarily hosen biologi al threshold levels inependent, using

thi

pi Pij = Jij ,

S (thi , thj ) =

and

P

j

Jij = pi ∀i,

(and vi e-versa), is farthest from being

we arrive at :

XX i

∵

thj

Jij log

j

hen e

21

XX 1 1 Jij log + pi Pij i j

(8)

S (thi , thj ) =

X i

pi log

XX 1 1 Jij log + = S (thi ) + S (thj |thi ) pi Pij i j

Neither the information regarding the magnitude of the parameter

(9)

S (thj |thi )

nor the same about the qualitative nature of it an be retrieved by studying the

THi

entire thread-set of either (

THi+1

) or (

), exhaustively.

Q.E.D

Hen e the proof.

Property 3) : THi

The mapping between threads representing

with that of another threshold level

THi+r

ith

threshold level

follows a many-to-many map-

ping s heme. For example, the mapping from genotype (DNA) to phenotype (organism) is marked with signi ant redundan y from either side.

Dierent

genotypes an map to the same phenotype; for example, dierent odons (DNA nu leotide triplets, representing threads of the nu leotide threshold level) an

ode for the same amino a id; ensuring that the genotype an hange (a nu leotide an mutate) without hanging the phenotype.

On the other hand,

the same genotype an result in dierent phenotypes, due to dierent environmental onditions during development (dierent time-variant and ontextdependent intera tions between systemi and environmental threads). It should be mentioned here that a ase of one-to-many mapping s heme an also take pla e in ertain situations (intera tion-dependent dierentiation rules for stem ell[Furusawa et al., 1995℄); however that will only be a spe ial ase of manyto-many mapping.

22

Property 4) :

For any threshold level, only a subset of possible thread inter-

a tions (between systemi and environmental threads) an give rise to emergent threads at the higher threshold levels. In other words, the geometry of thread asso iation denes the produ tion of an emergent thread. For example, it has been found that from a superset of possible intera tions amongst threads representing biologi al threshold of amino a ids, only a ertain subset an give rise to stable se ondary stru tures and tertiary symmetries [Li et al., 1996℄.

This

is a lear a t of emergen e, where the emergent threads are that of ele trostati and thermodynami stability of the stru tures.

The relevan e of this

property an be vindi ated by its top-down ounterpart drawn from a study [Laughlin and Pines, 2000℄ of physi al laws; although the bottom-up approa h involving biologi al ausality was not mentioned there.

2.4) E ient des riptions with TM Model 2.4.1) Des ription of ontext-dependen e and time-dependen e in biologi al systems : Time dependen e and ontext dependen e do not mean the same; while timedependen e attempts to apture the observed ee t due to same biologi al ontext at dierent instan es of time, ontext-dependen e attempts to represent the relevant biologi al ontext used for the des ription of biologi al pro ess under onsideration.

The level of antibody produ tion and ell proliferation

of animals treated with 6-hydroxydopamine serves as an interesting example [Kohm and Sanders, 1999℄ of how the a quired knowledge of biologi al reality

an hange as a result of time-dependent and ontext-dependent intera tions between systemi threads and observer threads. In this ase [Kohm and Sanders, 1999℄, involvement of various biologi al threshold levels under observation had re-

23

sulted in produ ing very many types of ontexts.

In fa t, the patterns seen

from the observed fa ts reveal numerous s hemes of dierent interse tions between intera ting thread sets.

While some studies [Besedovsky et al., 1979,

Williams et al., 1981, Kruszewska et al., 1995℄, have reported enhan ement in antibody produ tion and ell proliferation, another group of ndings tends to reveal a suppression [Hall et al., 1982, Livnat et al., 1985, Madden et al., 1989℄ of the same; while still another experiment [Miles et al., 1981℄ reports "no hange" in the level of antibody produ tion. Assuming none of the results were wrong, reasons behind obtaining su h ontradi tory results an be understood by TM model.

Although the biologi al system (and possibly the environment) was

kept invariant, the diering results have originated due to observer's reading of subtle hanges in the omposite biologi al ontexts. Ea h of these dierent

ontexts had provided the favorable onditions of it's own for dierent subsets of threads to intera t. In order to study the ee t on the threads of any threshold level

THi

involved in the pro ess in a minimal two- ontext s enario,

we onsider ontexti1 as one whi h provides suitable ondition for thread-set

THi1x

to intera t; and ontexti2 , as one whi h provides suitable ondition for

thread-set

THi2x

THi1x

to intera t. Both

and

thread-sets and are independent of observer.

THi1x

and

THi2x

THi2x

represent the systemi

Sin e neither the ardinality of

, nor the omposition of them are guaranteed to mat h, dif-

ferent s heme of intera tions, even in the absen e of the observer, will a

ount for emergen e of dierent threads in intera ting with either of

THi1x

THi+1 THi2x

. The observer thread-set, whenever

and

will produ e dierent interse tions,

and in general, these interse tions will neither have their ardinality mat hed, nor will there be a onsensus in their omposition. Sin e it is not probable to have a mat h between two-step interse tions (rst, between

THi1x

and

THi2x

and se ond, between either of them and the observer), we will always a quire

24

(potentially) ontradi tory knowledge about biologi al systems. Thus, even in the ase where all the observations (experiments) are orre t, the disparity in observed patterns (experimental results) will be present, as have been proved in an exhaustive experimental work [Wahlsten et al., 2003℄. Due to this subtle (or overt) intera tion with the observer thread-set, the systemi thread-set will only be per eived by dierent interse tions between the two and therefore the obje tive biologi al reality will not be known.

2.4.2) Des ription of biologi al emergen e : Due to its ar hite tural hara teristi s, the TM model explains emergen e naturally. It an easily dierentiate between two broad kinds of emergen es as mentioned in some previous studies [Bedau, 1997, Bar-Yam, 2004℄. The weak emer-

THi+1 THi THi-1 THi-2

gen e is exemplied by threads (biologi al properties) that represent who arise from the intera tions of the threads present at

,

,

, ,

and so on, [Odell, 2002℄. There an as well be strong emergen e, exemplied by novel threads at

THi+1

that are neither predi table nor dedu ible from threads

representing pre eding threshold levels

THi THi-1 THi-2 ,

,

[Crut held, 1994,

Ri ard, 2004℄. The TM model states that there should be at least one emergent thread (emergent property, be it an example of week emergen e or strong emergen e) to distinguish any

THi+1

from

THi

. For example, protein fold family

formation [Ding and Dokholyan, 2006℄ an be re ognized as a ase of weak emergen e (be ause time-dependent thread intera tions between stru tural threads

THi

at protein(

) level and ompositional threads representing (randomly mu-

tated) amino a ids(

THi-1

) level are responsible for emergen e of a ertain pro-

tein fold at the threshold level representing various protein-folds(

THi+1

)). Due

to extreme ontext-dependen e and nonlinearity in the thread intera tions, at times a ause initiated at any

THi-r

an exhibit pronoun ed weak-emergen e at

25

any higher order threshold level. For example, the triggering of the e losion hormone (intera tion of some fun tional thread at

THproteins

) had been reported

to initiate a sequen e of events, whi h ultimately results in the emergen e of

THorganism

the moth (

) from the pupal exuviae [Truman, 1973℄. On the other

hand, the formation of fun tional bio hemi al network in several bran hes of mole ular ell physiology an be identied to exemplify the strong emergen e [Boogerd et al.(2005)℄.

However, it might not always be easy to identify the emergent threads, be ause of the low resolution viewing of the threshold level. For example, it was

THCell

known that during ell y le (

) the G1 to S transition, under any given

growth ondition, is hara terized by a requirement of a spe i and riti al

ell size, PS. However, it has been found re ently [Barberis et al., 2007℄ that the reation of PS is itself an emergent property, where the onstraints on ell size only serve as the lower bound of ardinality of ompositional thread set ne essary to reate the emergent phase PS.

Sin e biologi al systems are open systems, many (but not all) biologi al threshold levels intera t with environment. In fa t, environmental threads that inuen e systemi threads for any threshold level, form a part of biologi al ontext. An example of how environmental threads at on the

THCell

THNu leotide

an ause emergen e

an be found in re ent literature [Bar ellos-Ho, 2008℄; where it

has been shown that an er in an organism an be onsidered as an emergent phenomenon of genotype (viz., DNA) perturbed through radiation exposure. Similar observation has been made elsewhere too [Glade et al., 2004℄; where it has been found that "under appropriate in vitro onditions" (whi h implies, only in the presen e of ertain environmental threads) mi rotubules (represented by

26

thread set belonging to the threshold level sub- ellular ma romole ular omplex) form dissipative stru tures that not only shows self-organization but also displays emergent phenomena.

Although it is di ult to estimate the number of intera ting threads to a hieve emergen e, in some of the ases, it has been al ulated. For example, based on Landauer's prin iple it has been al ulated[Landauer, 1967, Davies, 2004℄ that to ensure the onset of emergen e of fun tional proteins (ea h aspe t of protein fun tionality denotes one fun tional thread at

THi+1

) from an ensemble

of amino a ids (ea h amino a id onstitutes a stru tural thread at

THi

), the

inequality 60 < n < 92 should hold, where n denotes the number of amino a ids. A similar al ulation argues that there should be at least 200 base-pairs (i.e.; 200 stru tural threads at the nu leotide threshold level) to ensure the emergent features of a fun tional gene [Davies, 2004℄.

2.4.3) Des ription of observer-dependent nature of biologi al reality : There are myriad examples of ontradi tions about a quired knowledge of biologi al systems, studied under the same biologi al ontexts. Here we will enlist only some of them to highlight the in omplete, subje tive and observerdependent nature of a quired knowledge about biologi al reality.

Ex.1)

In a study [Lev henko et al., 1997℄ involving Clp family of haperones,

the presen e of PDZ-like domains in the arboxy-terminal region of ClpX was reported. However, another study [Neuwald et al., 1999℄ within a few days, had not only reported the absen e of that entire PDZ-like domain, but also failed to nd any signi ant similarity to multiple alignment prole of PDZ domains. The ause for this ontradi tion an be attributed to dierent (almost mutually ex lusive) ompositions of sets of interse tions

27

between observer's thread set with the systemi thread set.

Ex.2)

The msx homeodomain protein is a known downstream trans ription

fa tor of the bone morphogeneti protein (BMP-4) signal besides being an important regulator for neural tissue dierentiation.

A re ent study

[Ishimura et al., 2000℄ has reported that both BMP-4 and Xmsx-1 have failed to inhibit the neurulation of e todermal tissue that was ombined with prospe tive dorsal mesoderm; although the amount of inje ted RNA was su ient for inhibiting neurulation in the single ap assay. This result is in dire t ontradi tion with the results obtained from some other studies about the same biologi al pro ess involving the same biologi al entities and the same systemi ontexts. These studies have reported that the BMP-4 signal is su ient for the determination of neural ell fate [Sasai et al., 1995, Suzuki et al., 1995, Wilson and Hemmati, 1995, Xu et al., 1995℄. The ause behind this subje tivity, therefore, an solely be attributed to dierent ompositions for sets of interse tions between observer's thread set with the systemi thread set.

Ex.3)

In the eld of determination of phylogeny of Rhizobium galegae by genome

sequen ing (nu leotide threshold level), an interesting ase an be observed. Upon sequen ing 260 bp of the 16S gene, two independent reports [Young et al., 1991, Nour et al., 1994℄ had inferred that Rhizobium galegae is losely related to mesorhizobia. However, upon examining 800 bp (instead of 260 bp), another study [Terefework et al., 1998℄ had inferred that the previous assertion regarding phylogeneti proling of Rhizobium galegae, was wrong. Su h subje tive knowledge about biologi al reality is a quired be ause the possible s opes of intera tion of observer's thread set with the systemi threads were dierent. In one ase the observer's thread set ould intera t with 800 bp (representing a part of systemi thread set

28

of ompositional nature) whereas in the other ase, the possibility of intera tions were limited by a small number of systemi thread set ( ompositional), viz. 260 bp. The qualitative hanges in biologi al ontext due to the presen e of 540 bp (800 bp - 260 bp) ould not obviously be taken are of by two previous studies [Young et al., 1991, Nour et al., 1994℄. As a result of a squeezed systemi spa e with merely 260 ompositional threads and the orresponding fun tional threads, possibility of intera tion with observer's thread set was redu ed substantially, leading to a ontradi tion.

While this example demonstrates learly that onstri tion of the systemi thread spa e under observation (a pro ess represented by the observer thread set) redu es the probability of the intera tion and an eventually lead to wrong inferen es about biologi al reality, it is lear that the same logi holds for an expanded systemi thread spa e under observation too. In fa t, to observe any biologi al pro ess of interest, experiments are arefully designed to ensure the presen e of ertain systemi threads and not others. The experimental design ensures a suitable size of the systemi thread spa e; whi h, when intera ting with the observer's thread spa e, reveals ertain fa ets of a biologi al pro ess. Although a squeezed or expanded systemi thread set might not hange the underlying biologi al pro ess under observation (intera tion of systemi threads with the observer's thread set under a given ontext), it an a

ount for less or more bulk of information than the observer an handle. Thus, the pro ess of observation an always be onsidered subje tive and in omplete; be ause the set representing interse tion of systemi thread set and observer thread set will always be dierent (with respe t to ardinality of the set, as well as with respe t to omposition of the set), even under the same ontext.

29

2.5) Mathemati al framework of TM model : Despite the fa t that there have been attempts to develop mathemati al models to des ribe emergen e [Rasmussen and Barrett, 1995, Bonabeau and Dessalles, 1997, Bar-Yam, 2004, Ri ard, 2004℄; an universally a

epted mathemati al model to des ribe biologi al emergen e has still not been found [Cohen and Atlan, 2006℄. Here with the TM model we propose a mathemati al template that attempts to suitably des ribe biologi al emergen e. More importantly, it is proved here that the nature of biologi al reality is observer-dependent (hen e subje tive). Owing to this inherent observer-dependent knowledge of biologi al reality, ontradi tions arise in the des riptions of it and it is due to the observer predile tion that there are so many omplexity measures to des ribe the biologi al reality. Further, it is due to this innate nature of biologi al reality that it will not be possible to onstru t a biologi al omplexity measure that is obje tive.

Se tion : 2.5.1) Let us dene :

(Defn :1) T

: The superset of all the threads ( ompositional, stru tural and

fun tional properties) that ompletely represent ea h of systemi features, environmental features and observer (features of observational me hanism that intera ts with the biologi al system) at any threshold level

(Defn :2) τ : {τ }

i=1 where

τ ∈ T;

i=1 where

o ∈ T;

THi

.

are the threads representing properties of the

observer (and observational me hanisms) at with

.

are the threads representing all the systemi -

environmental (systemi and environmental) properties at

(Defn :3) o : {o}

THi

THi

, that an possibly intera t

τ.

Thus the intera tion between observer and systemi -environmental thread-set

an be des ribed in the broadest terms with the entire spe trum of threads that represent them as :

30

Ω1 (τ )∪Ω2 (o) , where both Ω1 and Ω2 are ontext-dependent and time-dependent fun tions that model the favorable onditions for the observer threads to intera t with the systemi -environmental threads.

(Defn :4) MI

: An index set of mutually intera ting pair of threads (mutually

intera ting biologi al properties).

The elements of this set; viz.

the pair of

threads, are not pairwise disjoint at any instan e of time.

|M I| = ξ

Hen e formally, if

and for ea h

i ∈ MI

let

λi

be a minimally intera t-

ing set, then :

{λi : ∀i ∈ M I}, λi =ξ C2

and

∀λi , |λi | = 2

Sin e the thread-mesh for any threshold level is bounded in its geometry (by assumption), any hange of thread oordinate will denitely inuen e oordinate of other threads (either subtly or markedly). Biologi ally this implies that every biologi al property ( ompositional, stru tural, fun tional) has some inuen e (however subtle or pronoun ed) on all the other biologi al properties of the same threshold level and potentially on some properties belonging to other threshold levels too. Thus the threads an not be pairwise disjoint and we have : For a general ase, we'll have : where

η = η (time,

(Defn :5) τ

+

λi =ξ Cη , η > 2

and

biologi al ontext) and learly

and

τ −: τ + ⊂ M I,

∩ λi 6= φ

i∈MI

η −→ ξ ;

|λi | > 2.

represents the set of ( ontext-dependent)

intera ting thread-pairs that help the formation of an emergent thread (this emergen e, obviously, is an example of weak emergen e; strong emergen e does not result from a ausal lineage [Crut held, 1994, Bar-Yam, 2004℄). The where

τ − ⊂ M I,

τ −,

represents the set of ( ontext-dependent) intera ting thread-

pairs that do not ontribute to the emergen e of that parti ular thread. Sin e

τ+

and

τ−

are ontext-dependent and time-dependent,

τ + ∩ τ − 6= φ;

whi h

makes perfe t biologi al sense. For example, roughness of the pat hes of protein

31

surfa e might not have a great dependen e on resultant dipole moment of the protein arising out of its main- hain and vi e versa. Therefore the threads representing these two properties might not always intera t. However under ertain

onditions, say in a highly polar environment with low diele tri onstant, the dipole moment of the protein ba kbone might inuen e the surfa e geometry and hen eforth the ner aspe ts of surfa e topology too, and in su h a ase the threads of the aforementioned properties will intera t with ea h other. while

τ+

and

τ−

Thus

an not be regarded as mutually ex lusive, their (possible)

interse tion depends on parti ular biologi al ontexts. If we dene

|τ + |time,context = ω ,

the quantitative hange in the intera t-

ing thread population that ause weak emergen e an then be represented as:

d + dt (τ )

= ωf (ω),

where any suitably found

f (ω)

will represent the fun -

tional hara teristi s of time-dependent, ontext-spe i population of intera ting threads, su h that

∀ω1 , ω2 ; ω1 < ω2 ⇒ f (ω1 ) < f (ω2 ).

This is biologi ally appropriate stru ture.

For example, it has been found in

the ase of spatio-temporal ytoplasmi organization that an in rease or de rease of the gly olyti ux is indu ed by an in rease or de rease of polymeri mi rotubular proteins, as instan es of emergen e within a metaboli network [Aon et al., 2004℄. If

d | dt (τ + )| > 0

d + , we denote dt (τ ) as

H

. However, even if

H

exists, the ne es-

sary ondition for weak emergen e for the intera ting threads representing is satised only when

THi+1

THi

holds at least 1 thread (a property, be it om-

positional, stru tural or fun tional) present in

H.

In that ase the inequality

n n of (eq -1) will be satised. This inequality (along with eq -9) suggests a possible limit of our knowledge of biologi al properties representing any biologi al threshold level

THi+1

, even if we (ideally) know the omplete set of biologi al

properties that hara terize

THi

.

32

We an now pro eed to prove that nature of biologi al reality is observerdependent. However before than that it is important to derive an idea of the topologi al nature of biologi al spa e with the help of TM model.

Se tion : 2.5.2) 2.5.2.1) Topologi al nature of biologi al spa e : Biologi al spa e an be des ribed in terms of the generalized oordinates of 'systemi ' properties ( ompositional, stru tural and fun tional) of the biologi al system under onsideration along with the relevant set of property of the environment, that exerts denite inuen e on the systemi properties. Ea h one of these properties (systemi and environmental) an be represented by stru tures alled 'threads'. Hen e an ensemble of intera tive biologi al properties will give rise to a mesh of threads, the 'thread-mesh'. Su h des ription of biologi al spa e is abstra t but is advantageous in its being independent of any parti ular

oordinate system. Furthermore, it des ribes ompletely what a system is omprised of ( ompositional and stru tural threads) and what the system is apable of performing (fun tional threads) and how (intera tions amongst the pertinent threads). The topologi al properties of thread-mesh spa e for any biologi al threshold level oer interesting insights. The two omponents of su h spa e an be identied as, rst, the 'biologi al-system thread-mesh' (exhaustive set of ompositional, stru tural and fun tional properties, des ribing any arbitrarily hosen biologi al threshold level, say

Thi

ith

; in luding the relevant environmental prop-

erties) and se ond, the 'observer thread-mesh' (exhaustive set of ompositional, stru tural and fun tional properties of the observer, whi h in ludes the subset of properties required to study

Thi

). We assume that ea h of these biologi al

33

properties an be represented by some suitable mathemati al fun tions.

Resorting to fun tional analysis, if we tend to represent these fun tions by ve tors; we arrive at an abstra t ve tor spa e to represent biologi al properties at any biologi al threshold level. Su h representation of biologi al property spa e (thread-mesh) enables us to dene a "distan e" between two fun tions (any two biologi al properties) by

d(p1 , p2 ) = ||p1 − p2 ||.

This distan e will orrespond to

the dieren e between the nature of biologi al properties, when these properties are represented by threads. Two losely related biologi al properties will have a small distan e between them in the abstra t thread-mesh oordinate spa e. For example, for

THprotein

, the distan e between the thread representing interior

diele tri onstant and the thread representing probability of interior salt-bridge formation will always be less than the distan e between the thread representing interior diele tri onstant of proteins and the thread representing the shape of the proteins. The distan e between two threads an always be measured and sin e any biologi al property is dependent upon other biologi al properties, the distan e level

d(p1 , p2 )

between any two biologi al properties of the same threshold

(d(p1 , p2 ) = ||p1 − p2 ||)

an be onsidered omplete. This turns the thread

spa e (biologi al property spa e) representing

THi

, into a metri spa e. Also

sin e the threads, who are fun tions that represent biologi al properties, an be asso iated with their respe tive lengths (norms); the abstra t ve tor spa e of thread-mesh an be onsidered as a normed ve tor spa e. The ee t of any external inuen e on a ve tor (biologi al property) of this normed ve tor spa e an be represented by addition and multipli ation of a s alar variable to that ve tor. A s aler addition or multipli ation s heme in reases or de reases the weightage of a thread in any thread-intera tion.

This is ne essary, be ause all the bio-

logi al properties assume weightages with respe t to the hanging ontexts and

34

an't be onsidered as having invariant importan e under all ir umstan es. Thus we noti e that :

1)

any biologi al property representing any biologi al threshold level is depen-

dent on all the other properties representing the same threshold level. Whi h implies inner-produ ts an be dened on all the threads (biologi al properties),

2)

ontext-dependent importan e of any property (a biologi al property mod-

eled as a ve tor in the normed abstra t ve tor spa e) an be modeled by addition and multipli ation by a s alar, and

3)

Cau hy onvergen e exists amongst the properties representing any thresh-

I

old level (for example, the ele trostati intera tions ( ) between ma romole ules in ytoplasm an be broadly modeled as intera tions between set of relevant

V th2

threads (

harges;

th1

), given by :

, a thread that represents intera tions between

, thread that represents intera tions between dipoles(for mole ules

without inversion enter);

th3

, representing intera tions between quadrupoles(for

mole ules with symmetry lower than ubi ); tween permanent multipoles;

th5

th4

, representing intera tions be-

, thread representing indu tion(between a per-

manent multipole on one mole ule with an indu ed multipole on another); that represents London dispersion for es and

th7

th6

,

, a thread that represents ele -

trostati repulsions(to prevent ma romole ular ollapse). If we onsider a lo al base

L

for the thread-set of ele trostati intera tions

I

about any suitably ho-

sen entral point (say, 0); then for sequen e of threads

V L th of

-

, for some number

m is an element of

V

ε,

whenever any

n, m > ε;

for all the threads

it will be ensured that

thn

. Whi h is pre isely what the Hilbert spa e riterion

for Cau hy sequen e is. In other words, even if from onsiderations of

ths

I th2 th4 ;

,

and

th

35

th1 th th5 th7 I ,

3,

6 will be parts of

,

.

are omitted

Hen e, the thread-mesh representing any biologi al threshold level an be onsidered as a Hilbert spa e. This is supported from other aspe ts of thread-mesh also. For example, any thread (a biologi al property modeled as fun tion) is a real-valued fun tion and on the biologi ally relevant interval of this fun tion, the integral of the square of its absolute value (over that interval) will ne essarily be nite (no biologi al property has ever been reported to assume a non-nite magnitude during its existen e). This implies that the threads (biologi al properties)

an be represented by measurable and square integrable fun tions and su h a

hara teristi is a hallmark of Hilbert spa e (or putting in other way,

L2 spa e

).

A areful observation topology of thread-mesh (abstra t normed ve tor spa e representing biologi al properties of any biologi al threshold level) reveals several other interesting hara teristi s of it :

2.5.2.2) Additional topologi al hara teristi of thread-mesh - 01) Geometry of the thread-mesh spa e resembles that of a real ve tor bundle, where we dene a ve tor bundle as a geometri onstru t whi h makes pre ise the idea of a family of ve tor spa es parametrized by another spa e X. Here X an be a topologi al spa e, a manifold, or a pertinent algebrai onstru t. The denition demands that if, to every point x of the spa e X we an asso iate a ve tor spa e V(x) in su h a way that these ve tor spa es t together to form another spa e of the same kind as X (e.g. a topologi al spa e, manifold, or a pertinent algebrai

onstru t), it an then be alled a ve tor bundle over X. Sin e, the nature of thread-mesh in either 'biologi al-system' set or observer spa e does not dier, we an safely represent the thread-mesh spa e by a real ve tor bundle. Thus it

an be said that : 1) V

* (spa e representing the observer thread-mesh spa e) and V (spa e repre-

senting systemi thread-mesh spa e) are nite-dimensional.

36

2) V

* has the same dimensions as V.

Assumption (2) of TM model states that only a subset of the entire set of observer properties an intera t with the 'Biol-System Thread-Mesh'(BSTM). We denote this subset of observer properties as the 'preferen e' of the observer. In a more formal representation, if

(e1 , ..., en )

forms the basis of V (the ve tor

spa e representing systemi thread-mesh spa e); then the asso iated basis for

*

V (the ve tor spa e representing observer thread-mesh spa e) an be written as

(e1 , ..., en ) ei (ej ) = 1

where : if

i=j

(observer preferen es are apable of observing BSTM),

if

i 6= j

(observer preferen es are not apable of observing BSTM).

and

ei (ej ) = 0

The apability of observer to observe any biologi al phenomenon stems from

ompatibility between thread-set representing observational me hanism and BSTM. For example, to obtain a measure of stru tural onstraints of an enzyme, the observer thread-set should ne essarily intera t with only ertain threads of BSTM (for example, the permitted ranges of bond lengths and bond angles, omega angle restraints, side hain planarity, proline pu kering, B-fa tor distribution, rotamer distribution, Rama handran plot hara teristi s et .). If the observational me hanism gathers information about the asso iated pathways, atalyti sites of the enzyme, its ellular lo ation, or about its fun tional domains; they will be in ompatible with the systemi properties of interest and thus will not be

apable to obtain a measure of stru tural onstraints of an enzyme). To elaborate a little, if the systemi thread-mesh spa e were a simple 2 dimensional spa e,

R2

, its basis B would have been given by :

B = e1 = (1, 0), e2 = (0, 1). Then,

e1

and

e2

an be alled one-forms (fun tions whi h map a ve tor to a

s alar),

37

su h that

: e1 (e1 ) = 1, e1 (e2 ) = 0, e2 (e1 ) = 0

and

e2 (e2 ) = 1

(10)

2.5.2.3) Additional topologi al hara teristi of thread-mesh - 02) Thi X The BSTM representing any

, (say

), is a topologi al ve tor spa e.

Let x and y be the oordinates of any two threads (biologi al properties) in

X

.

Although the biologi al properties are losely dependent upon one another, they are distin t in their fun tionality (for example, for the biologi al threshold level of proteins, a thread representing interior mass distribution of a protein may be having a lose orrelation with another thread representing interior hydrophobi ity distribution of the same protein; but these threads are indeed dierent). Thus in the ontext of geometry of thread-mesh we an say that x and y an be separated by neighborhoods if there exists a neighborhood (innitesimal or not) N1 of x and N2 of y, su h that N1 and N2 are disjoint, property, viz. any two distin t points of

X

(N1 ∩ N2 = 0).

This

an be separated by neighborhoods,

suggests that the biologi al thread-mesh (X) under onsideration an be alled a

T2

spa e (Hausdor spa e).

2.6) Insights into the thread dynami s : If a parti ular thread denoting property p and oordinate x within biologi al spa e (BSTM, in terms of generalized oordinate), have a potential V to be part of an intera tion; then at any instan e of time t, we an quantify the a tion A (in Lagrangian formulation as) :

38

 A[x]

=

L [x(t), x(t)] ˙ dt



=

(

(11)

pX 2 x˙i − V (x(t)))dt 2

Here we note that while x (generalized oordinate for any arbitrarily hosen biologi al property p of

THi

) has an expli it dependen e on time (sin e biolog-

i al properties are time-varying); owing to the symmetry of thread lo ations in the thread-mesh for any

THi

, V does not. Sin e xi stands for the generalized

oordinate of any thread p (biologi al property; be it ompositional, stru tural or fun tional) within any arbitrarily hosen threshold level

THi

,

x˙

represents

hange of position of the thread p; whi h implies intera tion between threads. More magnitude of

Thus, denoting

Q[L] = p If we set

P i

x˙

implies more intera tion between biologi al properties.

Q=

∂ ∂t (so that

x¨ ˙x −

P ∂V (x) i

∂xi

Q[x(t)] = x˙

x˙ =

d p dt [ 2

K =[

P i

)

x˙ 2 − V (x)]

pX 2 x˙ − V (x)] 2 i

then

z

=

X ∂L

Q[xi ] − K ∂ x˙ X pX 2 = p x˙ 2 − [ x˙ − V (x)] 2 i i pX 2 = [ x˙ + V (x)] 2 i

i

39

(12)

The

eqn-12

, des ribes total energy of BSTM for any arbitrarily hosen

and owing to the presen e of symmetri al potential V(x),

eqn-12

THi

des ribes a

onservation of z. Sin e we know that the onservation of energy is the dire t

onsequen e of the translational symmetry of the quantity onjugate to energy, namely time; an appli ation of Noether's theorem suggests

z˙ = 0.

that the prin iple of onservation of thread-mesh energy for any

This implies

THi

is a on-

sequen e of invarian e under translation through time.

The onforman e to Noether's theorem dire tly suggests that if the pro ess of observation (over any interval of time), is represented by an one-dimensional manifold, the systemi thread-mesh spa e ( omprised of system's properties and pertinent environmental properties) an be onsidered as a target manifold of the it. Under su h ir umstan es one an atta h to every point x of a smooth (or dierentiable) manifold, a ve tor spa e alled the otangent spa e at x. Typi ally, this otangent spa e an be dened as the dual spa e of the tangent spa e at x. Hen e the thread-mesh an be thought of as the otangent bundle of spa e of generalized positions of threads, with respe t to the observation manifold.

Sin e otangent bundle of a smooth manifold an as well be onsidered as the ve tor bundle of all the otangent spa es at every point in the manifold, we an assert that observer properties that are ompatible with some systemi property and is apable of measuring it, must be sharing a anoni al relationship with ea h other. Reasons behind su h argument follow from the spe ial set of attributes that oordinates on the otangent bundle of a manifold satisfy. Thus, if 'q's denote the oordinates on the underlying manifold (systemi thread-mesh spa e) and the 'p's denote their onjugate oordinates (observer thread-mesh spa e) then they an be written as a set of

40

(q i , pj )

too.

If C denotes the onguration spa e of smooth fun tions between thread-mesh manifold M to the observation manifold O, then the a tion A (aforementioned)

an be hara terized pre isely as a fun tional,

A : C −→ O.

The biologi al properties are fun tions of many inuen ing fa tors. Hen e fun tional A an be pre isely des ribed as a fun tion that takes fun tions as its argument (from the thread-mesh manifold) and returns a real number to be per eived by the observer at a given instan e of time (observation manifold).

2.7) Un ertainty in observation of biologi al phenomenon : The ma ros opi observable nature of biologi al properties ome to existen e due to frequen y of intera tions amongst many biologi al properties belonging to biologi al system or the environment or both. An individual intera tion between two biologi al entities does not a

ount for an observable biologi al property, but signi ant frequen y of same type of intera tions within some dened set of biologi al entities do produ e a biologi al property. A series of very re ent ndings tend to vindi ate this assertion. For example, a signi ant frequen y of Brownian ollisions between parts of protein mole ules (not a single ollision) within ytoplasm is what has been suggested to ause aggregation [Chang et al., 2005℄; similarly it is found that the signi ant frequen y (and not a single intera tion) with whi h the an er proteins parti ipate in various intera tions is what attributes them their unique nature [Jonsson et al., 2006℄. The importan e of frequen y of biomole ular ollisions between ma romole ules (representing

THbiol-ma romole ules

) within the ytoplasm, whi h auses weak

emergen e at the next threshold level (viz.

THbio hemi al pathways

in details by Alsallaq [Alsallaq and Zhou, 2007℄.

) is dis ussed

From a ompletely dierent

paradigm, the signi an e of frequen y of intera tions on the e ologi al om-

41

munities have been reported by Tylianakis [Tylianakis, 2008℄.

The ee ts of

all these intera tions, viz. measurable biologi al properties, are observed in the time domain by the observer.

Hen e while the pro ess of observation of any

biologi al property takes pla e in the time domain, the ma ros opi observable nature of biologi al property omes to being due to signi ant frequen y of thread intera tions in the thread-mesh spa e. Sin e, rst, any arbitrarily hosen biologi al property an be des ribed in the relevant biologi al frequen y domain in the thread-mesh spa e, when its observation takes pla e on the the time domain and se ond, the thread-mesh manifold has been proved to be residing on the otangent bundle of the observation manifold; the entire arrangement an be des ribed in terms of a Fourier transform pair in the observation (time) domain. Thus, if any arbitrarily hosen biologi al property is observed to be represented as an waveform with basis element b(t) (that is, in the observation domain) with its Fourier transform

B(Ω)

(in the

thread-mesh domain); we an dene the energy of the waveform to be E; so that (by Parseval's theorem) :

∞

1 (|b(t)|) dt = 2π

∞

2

E= −∞

(|B(Ω)|)2 dΩ

(13)

−∞

Sin e every biologi al property operates within a spe ied bound of magnitude, something that has been referred to as 'u tuation' in an earlier study [Testa and Kier, 2000℄ the fun tions that represent them will also be bounded in their ranges.

Examples for su h u tuation are many; in

THCell

, for the

mitogen-a tivated protein kinase as ade studies, the total on entrations of MKKK, MKK and MAPK have been found to be in the range 101000 nm and the estimates for the k at values of the protein kinases and phosphatases

-1 [Kholodenko, 2000℄. Similarly, for

have been found to range from 0.01 to 1 s

42

THbiol-ma romole ules

the proteins (

), the mass fra tal dimension representing

ompa tness of the protein has been found to be in the range of 2.22 to 2.69 [Enright and Leitner, 2005℄.

Thus for any arbitrarily hosen biologi al prop-

erty we an identify a enter of the waveform representing the property

t

and

Ωc (observed mean magnitude that the property an be asso iated to) along with

orresponding widths

∆t

and∆Ω (the permissible limits that the magnitude of

the observed property an approa h, of t and

Ω).

∆2t

2

and∆Ω an be interpreted as varian es

Sin e biologi al properties are represented by threads in the TM

model, we an interpret tc and

Ωc as the mean oordinates for the lo ation of the

threads in thread-spa e, with the varian e sible range of variability around tc and more varian e than a thread by the thread

Th1

Th2

∆t

and∆Ω representing their permis-

Ωc , respe tively.

Any thread

Th1

having

will imply the biologi al property represented

is more apable to intera t (and inuen e) with other bio-

logi al properties than the property represented by

Th2 Th1 .

biologi al property represented by than the property represented by

Th2

; or in other words, the

is more spe i in its mode of working

Hen e, 1) for entral measures of the fun tions representing biologi al properties, we have :

1 t = E

∞

t(|b(t)|)2 dt

(14)

Ω(|B(Ω)|)2 dΩ

(15)

−∞

1 Ω = 2πE

∞ −∞

Sin e both

1 1 2 2 E (|b(t)|) and 2πE (|B(Ω)|) are non-negative and both of them

integrate to 1, they satisfy the requirements of probability density fun tions for random variables t and

Ω,

with t and

43

Ω denoting

their respe tive means.

Su h probabilisti interpretation of the fun tioning of biologi al properties an be immensely helpful in des ribing any biologi al phenomenon, be ause in many of the ases, a deterministi knowledge about the extent of involvement of any biologi al property in a pro ess is found absent.

2) for the deviations (widths) of the fun tions representing biologi al properties, we have :

v u ∞ u1 u 2 2 ∆t = t (t − tc ) (|b(t)|) dt E

(16)

−∞

v u u 1 ∞ u ∆Ω = t (Ω − Ω )2 (|B(Ω)|)2 dΩ 2πE

(17)

−∞

We an now attempt to prove that the nature of biologi al reality as observed by any observer sharing the same biologi al spa e-time as the system under onsideration, will always be subje tive in nature. Whi h follows from the fa t that there will always be an un ertainty in observer's measurement of any biologi al system that he studies. This un ertainty will be inherent to the pro ess of observation, be ause the observer is a part of the biologi al spa e-time that he wishes to observe; therefore his mere presen e is going to disturb the biologi al spa e-time (that in ludes geometry of thread-mesh) in some denite manner. Hen e a super-observer, who is not a part of biologi al spa e-time, will be able to noti e that the more an observer (everyone of us) attempts to lo ate a threadmesh property under observation (say, signal) in the time-domain for a pre ise measurement; the less would he able to lo ate it's nature in the systemi threadmesh domain. Be ause for a very short duration of observation, the observer

an only, at best, hope to apture a mere snap-shot of the thread dependen-

44

ies and a snap-shot of ausality behind thread intera tion behind the observed biologi al phenomenon. Although this snap-shot of these dependen ies an be obtained in a pre ise manner, it will not be able to provide any insight about either the ause of these dependen ies (between biologi al properties) or evolution of the dependen ies (between biologi al properties). Therefore an attempt to lo ate a signal in the time-domain (pre iseness in the observation manifold) will result in obtaining an inherently in omplete and inadequate des ription of the biologi al pro ess under onsideration.

On the other hand, if the obser-

vation pro ess is arried out over a long duration of time, only the statisti al nature of thread intera tions (statisti al nature of biologi al properties) an be measured and not the pre ise ausalities and time-variant dependen ies behind thread intera tions. Thus even in this ase also, only an in omplete idea of biologi al reality an be found with un ertainty about the pre ise biologi al auses and time-variant pre ise dependen ies (between biologi al properties) behind the pro ess.

2.8) Un ertainty relationship for Biology : The anoni al onjuga y between variables hosen from thread-mesh spa e and observation manifold an be expressed in the form of an un ertainty prin iple for biology. This fundamental un ertainty in observation of any biologi al property

an be mathemati ally expressed as :

Theorem-2 : If p|t|b(t) → 0 as |t| → ∞ then

t Ω ≥

1 2

and the equality holds only if b(t) is of the form b(t) = CeProof :

αt2

The Cau hy-S hwarz inequality for any square integrable fun tions z(x)

and w(x) dened on the interval [a,b℄ states,

45

2 b  b b 2 z(x)w(x)dx ≤ |z(x)| dx |w(x)|2 dx a

a

(18)

a

Sin e b(t) is real for the biologi al properties, an appli ation of last equation yields

2 ∞  ∞ ∞ db db 2 2 tb dt ≤ t b dt | |2 dt dt dt −∞

let

−∞

∞ tb

A =

(19)

−∞

db dt dt

−∞



= =

t

d(b2 /2) dt dt

b2 t |∞ −∞ − | 2{z } α

In the limit, Furthermore

∞

b2 dt 2 −∞ | {z } β

p |t|b → 0 ⇒ |t|b2 → 0 ⇒ tb2 = 0. β = E/2

(from

eqn-13

Thus

α = 0.

) ; and so

A = −E/2 d Re alling that dt b(t)

↔ jΩ B(Ω),

∞

by Parseval's theorem we have :

eqn-20

∞

1 db | |2 dt = dt 2π

−∞ Substituting (

(20)

Ω2 |B(Ω)|dΩ

−∞

eqn-21

) and (

eqn -19

) into (

46

) we obtain :

(21)

∞

E | − |2 2

=

|

tb

−∞ ∞

≤ −∞

|

db 2 dt| dt

∞

1 t b dt × Ω2 (|B(Ω)|)2 dΩ 2π −∞ {z } | {z } 2 2

Et2

eqn -24

(23)

EΩ2

⇒ tc Ω c ≥

In the spe ial ase, if (

(22)

1 2

(24)

eqn 19

) is an equality, then (

-

) must be also; whi h

is possible only if

d dt b(t) = k t b(t) 2 ⇒b(t) = Ce-αt (a Gaussian waveform).

Q.E.D

3. Experimental works that report observer-dependen e in understanding biologi al reality : The inherent onstraint of observer dependen e in knowing biologi al reality, as

eqn -24

have been proved (

) with the TM model, e hoes (mathemati ally) the

ndings of many previous studies. The propheti views of Ashby [Ashby, 1973℄ had stressed on the importan e of a knowledging observer-dependen e, so did Kay [Kay, 1984℄ in his assessment of s ope of appli ation of information theory to biologi al systems, and so did a list of works who had tou hed upon the role of observer-dependen e in the studies of emergen e and omplexity

47

[Casti, 1986, Cariani, 1991, Baas, 1994, Brandts, 1997℄.

To onsider parti u-

lar examples, how the studies on p53 gene mutation and/or p53 protein expression an be observer-dependent (owing to the innate nature of immunohisto hemi al te hniques [Feil henfeldt et al., 2003℄) and how therefore, they report dierent views of biologi al reality, have been do umented in a review [Ishii and Tribolet, 1998℄. From a ompletely dierent paradigm of studies involving erebral ortex, the ytoar hite toni al distin tions are also reported to suer from observer-dependen e, resulting in several denitions of orti al areas [Kotter et al., 2001℄.

From using immuno ytology as an observer-

dependent standard method for tumour ell dete tion [Benoy et al., 2004℄, to observer-dependent te hniques involving immuno yto hemistry in attempting to quantify neurodegeneration in animal models [Petzold et al., 2003℄; from pro edures of ell- ounting in epidemiologi al studies [Araujo et al., 2004℄, to ways of noninvasive assessments of endothelial fun tion that usually relies on postis haemi dilation of forearm vessels and use of ow-mediated dilation measurements of bra hial artery [Lee et al., 2002℄; from aspe ts of immunouores en e testing [Meda et al., 2008℄ to methods involving positron emission tomography in the realm of radiotherapy [Jarritt et al., 2006℄ - observer-dependen e in as ertaining the biologi al reality is well do umented in myriad ontexts.

The

diversity of biologi al realms that report observer-dependen e, tend to point to the universal presen e of it in our (observer's) attempts to know biologi al reality.

From the ase of so alled bystander ee t, where nanoparti le

mediated ell transfe tion study was reported to suer from observer ee t [Zhang et al., 2007℄; to studies involving tumor peripheries in the ontext of breast tumors [Preda et al., 2005℄; experimental biology is replete with reports of observer dependen e in understanding biologi al reality.

48

Some of the most startling studies in this regard prove unmistakably that observer's mere presen e perturbs the biologi al reality.

This happens be ause

ondu ting an experiment on some system residing within biologi al spa e-time

orresponds to an a tive perturbation of the thread-mesh by the observer. However, sin e the observer is always a part of the thread-mesh (regardless of his being an experimentor or not), his sheer presen e is going to perturb the threadmesh geometry in some passively subtle, yet denite manner. The existen e of the observer in the biologi al spa e-time implies that he (observer) extra ts ne essary energy for his survival from the same pool of available energy, whi h the biologi al system under onsideration is also using to derive energy from. Hen e this a t of sharing the available (solar) energy between the biologi al system and the observer ensures that the presen e of observer perturbs the biologi al reality, a ross all threshold levels.

This point is proved in a re ent

experimental work [De Boe k et al., 2008℄ where the authors refute the notion of possible existen e of any benign observer.

The perturbation of biologi-

al reality by the very existen e of the observer has been strongly reported in many other experimental works too [Almeida et al., 2006, Siegfried, 2006, Lay et al., 1999, Wahlsten et al., 2003, Hik et al., 2003℄. Even the possibility of an un ertainty relationship arising out of observer's interferen e with biologi al reality in the realm of e ology was dis ussed in systemati well-do umented manner by Cahill [Cahill et al., 2001℄ and (in philosophi al terms) in another

eqn-24

work [Regan and Burgman, 2002℄. However the un ertainty relation (

)

is signi ant be ause it mathemati ally proves that for any super-observer (who is not a part of biologi al spa e-time) it will be lear that during any observation pro ess (passive/a tive), an attempt to measure any biologi al property exa tly(typi ally in the time-domain, be ause evolution of biologi al properties are observed over relevant time-s ales) will not be able to apture the omplete

49

information of the same in biologi ally fun tional spa e. This is be ause pre ise measurements will only apture a snap-shot of the property-dependen ies prevalent in the system under onsideration; whereas a biologi al meaningful

omplete des ription of these time-dependent and ontext-dependent propertydependen ies an only be provided if the measurement is ondu ted over a long period of time; whi h on the other hand, due to its innate statisti al nature, smoothen out the ner aspe ts of phenomenon under onsideration. Hen e, it is in the very nature of biologi al reality that it would not be observed in an obje tive way.

4. Con lusion : A des ription-oriented theoreti al toy model to study the nature of biologi al reality, the `thread-mesh model', has been proposed.

The ne essity to on-

stru t this model originated from the realization that issues related to biologi al omplexity an honestly be answered only when the nature of biologi al reality an be obje tively des ribed, qualitatively and quantitatively. The TM model attempts to mimi biologi al reality by, rst, splitting the entire biologi al universe into a series of biologi al threshold levels (dierent biologi al organization) and se ond; by des ribing the ompositional, stru tural and fun tional features of these biologi al threshold levels (with their spe i environmental onstraints).

The proposed model used a linear algebrai framework

to des ribe biologi al omplexity a knowledging emergen e. It ould des ribe and explain the ontext-dependent nature of biologi al behaviors. The role of observer in measuring a biologi al property is exhaustively examined in the proposed thread-mesh paradigm and it has been proved here that nature of biologi al reality is observer dependent. Taking a note of anoni al onjuga y between variables hosen from biologi al property manifold and observation manifold, an

50

un ertainty relationship for biology has been suggested too, whi h proved that there annot be an obje tive des ription of biologi al reality and therefore an obje tive and omplete omplexity measure an not exist for biologi al systems. The nature of biologi al omplexity measures an only be subje tive (to varying extent) and an only be relevant when the s ope of them (biologi al threshold level) is mentioned.

A knowledgment

This work was supported by COE-DBT (Department of

Biote hnology, Government of India) s holarship. The author wants to thank professor Indira Ghosh, former Dire tor, Bioinformati s entre, University of Pune along with Dr.

Urmila Kulkarni-Kale, the

present Dire tor, Bioinformati s entre, University of Pune for providing him with an opportunity to work on a problem that has got nothing to do with his PhD degree.

Referen es [Abel and Trevor, 2005℄

Abel, D.L, Trevors, J.T., 2005. Three subsets of sequen e omplexity and their relevan e to biopolymeri information. Theor. Biol. and Med. Modelling. 2, 29.

[Adami, 2002℄

Adami,

C.,

2002. What is omplexity?

BioEssays. 24, 10851094.

[Alba et al., 2002℄

Alba, M.M., Laskowski, R.A., Han o k, J.M., 2002. Dete ting rypti ally simple protein sequen es using the SIMPLE algorithm. Bioinformati s.18, 672-678.

51

[Almeida et al., 2006℄

Almeida, M., Paula, H., Tavora, R., 2006. Observer ee ts on the behavior of nonhabituated wild living Marmosets (Callithrix ja

hus); Revista de Etologia. 8(2), 81-87.

[Alsallaq and Zhou, 2007℄

Alsallaq,

R.,

Zhou,

H.X.,

2007,

En-

ergy Lands ape and Transition State of Protein-Protein Asso iation, Biophys. J., 92, 1486-1502.

[Anand and Tu ker, 2003℄

Anand, M., Tu ker, B.C., 2003. Dening bio omplexity:

an e ologi al perspe tive;

Comm. Theor. Biol. 8, 497-510.

[Andrianantoandro et al., 2006℄

Andrianantoandro, E., Basu, S., Karig, D.K., Weiss, R., 2006. Syntheti biology: new engineering rules for an emerging dis ipline; Mol. Syst. Biol. 2, 0028.

[Aon et al., 2004℄

Aon, M.A., O'Rourke, B., Cortassa, S., 2004. The fra tal ar hite ture of ytoplasmi organization: emergen e in

S aling, kineti s and

metaboli networks. Mol.

Cell. Bio hem. 256-257: 169184.

[Araujo et al., 2004℄

Araujo, R., Rodrigues, A.G., Pina-Vaz, C., 2004. A fast, pra ti al and reprodu ible pro edure for the standardization of the

ell density of an Aspergillus suspension. J. Med. Mi robiol. 53, 783-786.

52

[Ashby, 1973℄

Ashby,

W.,

1973. Some pe uliarities of

omplex systems. Cyberneti s Med. 9, 18.

[Baas, 1994℄

Baas, N., 1994. Emergen e, Hierar hies, and Hyperstru tures. In: Langton C. G., (Ed.) Art. life III, Santa Fe Inst. Studies in the S ien es of Complexity Pro . Redwood City, Calif. Addison-Wesley. Vol. XVII., pp.515-537.

[Badii and Politi, 1997℄

Badii, ity:

R.,

Politi,

A.,

1997.

Complex-

Hierar hi al Stru tures and S aling

in Physi s; Cambridge University Press, Cambridge, UK.

[Banerji and Yeragani, 2003℄

Banerji,

A.,

Yeragani,

V.K.,

2003.

A

new measure to quantify the omplexity of phase data (PhaseCmp) from rossspe tral

analysis.

Cardiovas ular

Eng.

3(4), 149-154.

[Barberis et al., 2007℄

Barberis, M., Klipp, E., Vanoni, M., Alberghina, L., 2007. Cell Size at S Phase Initiation: An Emergent Property of the G1/S Network. PLoS Comp. Biol. 3(4), e64.

[Bar ellos-Ho, 2008℄

Bar ellos-Ho, M.,

2008. Can er as an

emergent phenomenon in systems radia-

53

tion biology;

Radiat. Environ. Biophys.

47(1), 33-38.

[Barnstad et al., 2001℄

Bjørnstad,

O.N.,

Sait

S.M.,

Stenseth,

N.C., Thompson, D.J., Begon, M., 2001. The impa t of spe ialized enemies on the dimensionality of host dynami s. Nature. 409, 1001-1006.

[Bar-Yam, 1997℄

Bar-Yam., Y., 1997. Dynami s of Complex Systems, hapter 0, Overview:

The Dy-

nami s of Complex Systems - examples, questions, methods and on epts. Studies in Nonlinearity. Westview Press.

[Bar-Yam, 2004℄

Bar-Yam, Y., 2004. Multis ale omplexity/entropy; Adv. in Complex Sys. 7(1), 4763.

[Bedau, 1997℄

Bedau, M., 1997. Weak emergen e. Phil. Perspe tives. 11, 375399.

[Bennett, 1988℄

Bennett, C., 1988. Logi al depth and physi al omplexity. In: Herken R. (Ed.), Universal Turing Ma hine, A Half-Century Survey, Oxford University Press, Oxford, pp 227257.

[Benoy et al., 2004℄

Benoy, I.H., Elst, H., Van der Auwera, I., Van Laere, S., van Dam P., Van Mar k, E.,S harpé,

54

S.,

Vermeulen

P.B.,

Dirix

L.Y., 2004. Real-time RTPCR orrelates with immuno yto hemistry for the dete tion of disseminated epithelial ells in bone marrow aspirates of patients with breast

an er; Brit. J. Can er. 91, 18131820.

[Besedovsky et al., 1979℄

Besedovsky, H.O., del Rey, A., E.,

Da Prada, M.,

Sorkin,

Keller, H.H.,

1979.

Immunoregulation mediated by the sympatheti nervous system. Cell Immunol., 48(2), 346-55.

[Bialek et al., 2001℄

Bialek, W., Nemenman, I., Tishby, N., 2001.

Predi tability,

Complexity,

and

Learning; Neural Comp. 13, 2409-2463.

[Bonabeau and Dessalles, 1997℄

Bonabeau, E., Dessalles, J.L., 1997. Dete tion and emergen e. Intelle ti a. 25, 89-94.

[Bon hev, 2003℄

Bon hev

D.,

2003. On

the

omplexity

of dire ted biologi al networks. SAR and QSAR in Env. Res. 14(3), 199-214.

[Boogerd et al.(2005)℄

Boogerd, F., Bruggeman, F., Ri hardson, R.,

Stephan,

A.,

Westerho,

H.,

2005.

Emergen e and its pla e in nature: a ase study of bio hemi al networks. Synthese. 145, 131-164.

[Brandts, 1997℄

Brandts, W.A.M., 1997. Complexity: pluralisti approa h. In:

55

a

Lumsden, C.J.,

Brandts,

W.A.,

Trainor,

L.E.H. (Eds.)

Physi al theory in biology. Foundations and explorations. Singapore: World S ienti . pp. 45-68.

[Cahill et al., 2001℄

Cahill, J.F.Jr., Castelli, J.P., Casper, B.B., 2001. The herbivory un ertainty prin iple: visiting plants an alter herbivory. E ology. 82(2), 307-312.

[Cariani, 1991℄

Cariani, P., 1991. Emergen e and Arti ial Life. In:

Langton C. G., Taylor C.,

Farmer J. D., Rasmussen S., (Eds.) Art. Life II. Santa Fe Inst. Studies in the S ien es of Complexity Pro . Redwood City, Calif. Addison-Wesley. Vol.X, pp.775-797.

[Carothers et al., 2004℄

Carothers, J.M., Oestrei h, S.C., Davis, J.H., Szostak, J.W., 2004. Informational

omplexity and fun tional a tivity of RNA stru tures; J. Am. Chem. So . 126, 51305137.

[Casti, 1986℄

Casti, J., 1986. On system omplexity: identi ation, measurement, and management.

In:

Casti

J.

L.,

Karlqvist

A.,

(Eds.), Complexity, Language, and Life: mathemati al approa hes (Biomathemati s vol.16). Berlin: 146-173.

56

Springer-Verlag. pp.

[Chaitin, 1966℄

Chaitin,

G.J.,

1966. On the length of

programs for omputing nite binary sequen es. Journal of the ACM (JACM). 13, 547-569.

[Chang et al., 2005℄

Chang, C., Lina P., Yeh X., Deng K., Ho Y., Kan L., 2005. Protein folding stabilizing time measurement:

A dire t fold-

ing pro ess and three-dimensional random walk simulation. Bio hem. Biophys. Res. Comm. 328, 845-850.

[Chen et al., 1999℄

Chen, X., Kwong, S., Li, M., 1999. Compression algorithm for DNA sequen es and its

appli ations in

genome

omparison.

Genome Inform. Ser. Workshop Genome Inform. 10, 51-61.

[Chiappini et al., 2005℄

Chiappini E., Galli L., Tovo P., Gabiano C., Martino M., Th antatae Ita antatalian Register for HIV Infe tion in Children, 2005. Persistently high IgA serum levels are a marker of immunologi al or virologi al failure of ombined antiretroviral therapy in hildren with perinatal HIV-1 infe tion. Clin Exp Immunol. 140(2), 320324.

[Chuzhanova et al., 2000℄

Chuzhanova,

N.A.,

Anassis,

E.J.,

Ball,

E.V., Kraw zak, M., Cooper, D.N., 2000. Meta-analysis of indels ausing human ge-

57

neti disease: me hanisms of mutagenesis and the role of lo al DNA sequen e omplexity. Hum. Mutation. 21, 28-44.

[Cohen and Atlan, 2006℄

Cohen, I., Atlan, H., 2006. Geneti s as explanation:

Limits to the human genome

proje t. En y lopedia of Life S i., 2006, John Wiley & Sons, Ltd., 1-7.

[Corna

hio, 1977℄

Corna

hio, J., 1977. Maximum-entropy

omplexity measures, Int. J. Gen. Sys., 3, 215225.

[Cox and Mirkin, 1997℄

Cox, R., Mirkin, S.M., 1997. Chara teristi enri hment of DNA repeats in dierent genomes. Pro . Natl. A ad. S i. USA. 94, 5237-5242.

[Crut held, 1994℄

Crut held,

J.,

1994. Is anything ever

new? Considering emergen e. Working paper, Santa Fe Institute. 94-03-011.

[Crux et al., 1997℄

Cruz, X., Mahoney, M., Lee, B., 1997. Dis rete representations of the protein Cα

hain. Folding and Design. 2, 223234.

[Davies, 2004℄

Davies, P.C.W., 2004. Emergent biologi al prin iples and the omputational properties of the universe. Complexity. 10(2), 1115.

58

[De Boe k et al., 2008℄

De Boe k, H., Liberloo, M., Gielen, B., Nijs, I., Ceulemans, R., 2008. The observer ee t in plant s ien e. New Phytologist, 177, 579583.

[Dhar, 2007℄

Dhar, P., 2007. The next step in biology: A periodi table? J. Bios i. 32, 10051008.

[Ding and Dokholyan, 2006℄

Ding, F., Dokholyan, N.V., 2006. Emergen e of protein fold families through rational design. PloS Comp. Biol. 2, 725-733.

[Dokholyan and Shakhnovi h, 2001℄ Dokholyan, N.V., Shakhnovi h, E.I., 2001. Understanding hierar hi al protein evolution from rst prin iples. J. Mol. Biol. 312, 289-307.

[Ebeling et al., 2001℄

Ebeling, W., Steuer, R., Tit hener, M.R., 2001. Partition-based entropies of deterministi and sto hasti maps. Sto hasti s and Dyn. 1(1), 117.

[Edmonds, 1999℄

Edmonds, B., 1999. Synta ti measures of omplexity. PhD thesis, University of Man hester.

[Enright and Leitner, 2005℄

Enright, M.B., Leitner, D.M., 2005. Mass fra tal dimension and the ompa tness of proteins. Phys. Rev. E., 71, 011912.

[Feil henfeldt et al., 2003℄

Feil henfeldt, J., Töts h, M., Sheu, S.Y., Robert, J., Spiliopoulos, A., Frilling, A.,

59

S hmid, K.W., Meier, C.A., 2003. Expression of gale tin-3 in normal and malignant thyroid tissue by quantitative PCR and immunohisto hemistry. Mod. Pathol. 16(11), 11171123.

[Fei and Adjeroh, 2004℄

Fei, N., Adjeroh, D.A., 2004. On omplexity measures for biologi al sequen es. Computational

Systems

Bioinformati s

Conferen e, 2004. CSB 2004. Pro eedings. 2004 IEEE. 522-526.

[Flu kiger, 1995℄

Flü kiger, D.F., 1995. Contributions towards a unied on ept of information. PhD thesis; University of Berne.

[Furusawa et al., 1995℄

Furusawa, C., Kaneko, K., 1998. Emergen e of rules in ell so iety: dierentiation, hierar hy and stability. Bull. Math. Biol. 60(4), 659-87.

[Gabrielian and Bolshoy, 1999℄

Gabrielian, A.E., Bolshoy, A., 1999 . Sequen e omplexity and DNA urvature. Comput. Chem. 23, 263-274.

[Gellmann, 1994℄

Gell-mann, M., 1994. The Quark and the Jaguar (W.H. Freeman and Co.).

[Gellmann and Lloyd, 1996℄

Gell-mann, mation

M.,

Lloyd,

measures,

S.,

ee tive

1996. Infor omplexity,

and total information. Complexity. 1(1), 4452.

60

[Glade et al., 2004℄

Glade, 2004.

N.,

Demongeot,

Mi rotubule

J., Tabony,

J.,

self-organisation

by

rea tion-diusion pro esses auses olle tive transport and organisation of ellular parti les. BMC Cell Biol. 5, 23.

[Grassberger, 1986℄

Grassberger P., 1986. Toward a quantitative theory of selfgenerated omplexity. Int. J. Theor. Phys. 25, 907938.

[Gusev et al., 1999℄

Gusev,

V.D.,

Chuzhanova, plexity

Nemytikova,

N.A.,

measures

of

L.A.,

1999. On the omgeneti

sequen es.

Bioinformati s. 15, 994-999.

[Hall et al., 1982℄

Hall, N.R., M Clure, J.E., Hu, S.K., Tare, N.S., Seals, C.M., Goldstein, A.L., 1982. Ee ts of 6-hydroxydopamine upon primary and se ondary thymus dependent immune responses. Immunopharma ology. 5(1), 3948.

[Han o k, 2002℄

Han o k, J.M., 2002. Genome size and the a

umulation of simple sequen e repeats: impli ations of new data from genome sequen ing proje ts. Geneti a. 115, 93-103.

[Hazen et al., 2007℄

Hazen,

R.M.,

Grin,

P.L.,

Carothers,

J.M., Szostak, J.W., 2007. Fun tional information and the emergen e of bio om-

61

plexity. Pro . Natl. A ad. S . USA, 104, 85748581.

[Hik et al., 2003℄

Hik, D., Brown, M., Dabros, A., Weir, J., Cahill, J.Jr., 2003. Prevalen e and predi tability of handling ee ts in eld studies :

results from eld experiments and

a meta-analysis. Am. J. Botany. 90(2), 270277.

[Hildegard, 2003℄

Hildegard,

M.,

2003.

omplexity

measure

for

Fun tional networks;

arXiv: ond-mat/0311109

[Hinegardner and Engelberg, 1983℄

Hinegardner, R., Engelberg, H., 1983. Biologi al omplexity. J. Theor. Biol. 104, 720.

[Hulata et al., 2005℄

Hulata, E., Volman, V., Ben-Ja ob, E., 2005. Self-regulated omplexity in neural networks. Natural Comp. 4, 363386.

[Hut et al., 2000℄

Hut, P., Goodwin, B., Kauman, S., 2000. Complexity and fun tionality: a sear h for the where, the when, and the how. Pro . Int. Conf. on Complex Sys. Nashua. New Hampshire, USA. 259-268.

[Ishii and Tribolet, 1998℄

Ishii, N., Tribolet, N., 1998. Are p53 mutations and p53 overexpression prognosti fa tors for astro yti tumors? Neurosurg. 8, 269274.

62

Crit. Rev.

[Ishimura et al., 2000℄

Ishimura,

A.,

Maeda,

R.,

Takeda,

M.,

Kikkawa,

M.,

Daar,

I.O.,

Maéno.

M.,

2000. Involvement of BMP-4/msx-1 and FGF pathways in neural indu tion in the Xenopus embryo. Dev. Growth Dier. 42, 307316.

[Rangamani and Iyengar, 2007℄

Rangamani, P., Iyengar, R., 2007. Modelling spatio-temporal intera tions within the ell. J. Bios i. Ind. A ad. S i. 32(1), 157167.

[Jarritt et al., 2006℄

Jarritt, P.H., Carson, K.J., Hounsell, A.R., Visvikis, D., 2006. The role of PET/CT s anning in radiotherapy planning. The Brit. J. Radiol. 79, S27S35.

[Jimenez et al., 2002℄

Jiménez-Montaño,

M.A.,

Ebeling,

W.,

Pohl, T., Rapp, P.E., 2002. Entropy and

omplexity of nite sequen es as u tuating quantities. Biosystems. 64, 23-32.

[Jonsson et al., 2006℄

Jonsson, P.F.,

Bates P.A, 2006. Global

topologi al features of an er proteins in the human intera tome;

Bioinformati s.

22, 22912297.

[Kaneko, 1998℄

Kaneko, K., 1998. Life as omplex systems: Viewpoint from intra-inter dynami s. Complexity. 3(6), 53-60.

63

[Kay, 1984℄

Kay, J., 1984. Self-organization in living systems. Chap.3, PhD thesis. University of Waterloo.

[Kholodenko, 2000℄

Kholodenko, B., 2000. Negative feedba k and ultrasensitivity an bring about os illations in the mitogen-a tivated protein kinase as ades. Eur. J. Bio hem. 267(6), 15831588.

[Kohm and Sanders, 1999℄

Kohm, A.P., Sanders, V.M., 1999. Suppression

of

antigen-spe i

Th2

ell-

dependent IgM and IgG1 produ tion following norepinephrine depletion in vivo. J. Immunol. 162, 52995308.

[Kolmogorov, 1965℄

Kolmogorov, A., 1965. Three approa hes to the quantitative denition of information. Problems of Inf. Transmission. 1, 117.

[Kotter et al., 2001℄

Kötter,

R.,

Stephan,

K.E.,

Palomero-

Gallagher, N., Geyer, S., S hlei her, A., Zilles, K., 2001. Multimodal hara terisation of orti al areas by multivariate analyses of re eptor binding and onne tivity data. Anat. Embryol. 204, 333350.

[Kruszewska et al., 1995℄

Kruszewska,

B.,

Felten,

S.,

Moynihan,

J.A., 1995. Alterations in ytokine and antibody produ tion following hemi al sym-

64

pathe tomy in two strains of mi e. J. Immunol. 155(10). 4613-4620.

[Landauer, 1967℄

Landauer, R., 1967. Wanted: a physi ally possible theory of physi s;

IEEE Spe -

trum. 4, 105109.

[Laughlin and Pines, 2000℄

Laughlin, R., Pines, D., 2000. The Theory of Everything. Pro . Natl. A ad. S i. USA. 97, 28-31.

[Lay et al., 1999℄

Lay,

D.C. Jr.,

Bu hanan, H.S.,

Hauss-

mann, M.F., 1999. A note on simulating the

`observer

photoperiod Animal

ee t'

on

Behav.

using

nursery S .

onstant

pigs.

63(4),

Appl.

301-309.

doi:10.1016/S0168-1591(99)00018-0

[Lee et al., 2002℄

Lee,

K.W,

Felmeden,

D.C,

Lip,

G.Y.,

2002. Statins and the assessment of endothelial fun tion. J. Internal Med. 251, 452454.

[Lempel and Ziv, 1976℄

Lempel, A., Ziv, J., 1976. On the omplexity of nite sequen es. IEEE Trans. Inf. Theory. 22, 75-81.

[Lev henko et al., 1997℄

Lev henko, I., Smith, C.K., Walsh, N.P., Sauer,

R.T.,

Baker,

T.A.,

1997. PDZ-

like domains mediate binding spe i ity in the Clp/Hsp100 family of haperones

65

and protease regulatory subunits. Cell. 91, 939947.

[Li et al., 1996℄

Li H., Helling R., Tang C., Wingreen N., 1996. Emergen e of preferred stru tures in a simple model of protein folding. S ien e. 273(5275), 666-669.

[Lijnzaad and Argos,1997℄

Lijnzaad P., Argos P., 1997. Hydrophobi pat hes on protein subunit interfa es:

hara teristi s and predi tion. Proteins: Stru . Fun . Genet. 28, 333343.

[Livnat et al., 1985℄

Livnat,

S.,

Felten,

Bellinger, D.L.,

S.Y.,

Felten,

Carlson, S.L.,

D.L.,

1985. In-

volvement of peripheral and entral ate holamine systems in neural-immune intera tions. J. Neuroimmunol. 10(1), 5-30.

[Lofgren, 1977℄

Lofgren, L., 1977. Complexity of des riptions of systems: a foundational study. Int. J. General Sys. 3, 197214.

[Madden et al., 1989℄

Madden, K., Felten, S., Felten, D., Sundaresan, P., Livnat, S., 1989. Sympatheti neural modulation of the immune system. I. Depression of T ell immunity in vivo and in vitro following hemi al sympathe tomy. Brain Behav. Immun. 3, 72-89.

[Mahner and Kary, 1997℄

Mahner, M., Kary, M., 1997. What exa tly are genomes, genotypes and phenotypes?

66

And what about phenomes?

J. Theor.

Biol. 186, 55-63.doi:10.1006/jtbi.1996.0335

[Marguet et al., 2007℄

Marguet, P., Balagadde, F., Tan, C., You, L., 2007. Biology by design: redu tion and synthesis of ellular omponents and behaviour. J. R. So . Interfa e. 22, 4(15), 607-623.

[Meda et al., 2008℄

Meda, F., Zuin, M., Invernizzi, P., Vergani, D., Selmi, C., 2008. Serum autoantibodies: A road map for the lini al hepatologist. Autoimmunity, 41(1), 2734.

[Miles et al., 1981℄

Miles, K., Quintáns, J., Chelmi ka-S horr, E., Arnason, B.G., 1981. The sympatheti nervous system modulates antibody response to thymus-independent antigens. J. Neuroimmunol. 1, 101-105.

[Milosavljevi and Jurka, 1993℄

Milosavljevi , A., Jurka, J., 1993. Dis overing simple DNA sequen es by the algorithmi signi an e method. Comput. Appl. Bios i. 9(4),407-411.

[Moen et al., 2005℄

Moen, D., Winne, C., Reed, R., 2005. Habitat-mediated shifts and plasti ity in the evaporative water loss rates of two ongeneri pit vipers (Squamata, Viperidae, Agkistrodon). Evol. E ol. Res. 7, 759766.

67

[Neuwald et al., 1999℄

Neuwald, A.F., Aravind, L., Spouge, J.L., Koonin, E.V., 1999. AAA+:

A Class of

Chaperone-Like ATPases Asso iated with the Assembly, Operation, and Disassembly of Protein Complexes. Genome Res. 9,2743.

[Nour et al., 1994℄

Nour, S., Fernandez, M., Normand, P., Clayet-Marel, J., 1994. Rhizobium i eri sp. nov., onsisting strains that nodulate

hi kpeas (Ci er artenium L.). Int. J. Syst. Ba teriol. 44, 511522.

[Odell, 2002℄

Odell, J., 2002. Agents and Complex Systems. J. Obj. Te h. 1, 3545.

[Orlov et al., 2002℄

Orlov,

Y.L.,

Filippov,

V.P.,

Potapov,

V.N., Kol hanov, N.A., 2002. Constru tion of sto hasti ontext trees for geneti texts. In Sili o Biology. 2, 233-247.

[Papin et al., 2002℄

Papin, J.A., Pri e, N.D., Palsson, B.Ø., 2002.

Extreme

rea tion

pathway

parti ipation

metaboli

networks.

lengths

in

and

genome-s ale

Genome

Res.

12,

1889-1900.

[Petzold et al., 2003℄

Petzold, A., Baker, D., Pry e, G., Keir, G.,

Thompson,

2003.

E.J.,

Quanti ation

Giovannoni, of

G.,

neurodegenera-

tion by measurement of brain-spe i pro-

68

teins. J. Neuroimmunology. 138(1),

45-

48.doi:10.1016/j.jneumeth.2007.01.001

[Preda et al., 2005℄

Preda,

A.,

Floyd,

E.,

Turets hek, Viktor,

K.,

N.,

Heike,

Shames,

D., D.,

Roberts, T., Carter, W.O., Bras h, R., 2005. The Choi e of Region of Interest Measures in Contrast-Enhan ed Magneti Resonan e Image Chara terization of Experimental Breast Tumors. Investigative Radiology. Breast Imaging Part 1. 40(6), 349-354.

[Rasmussen and Barrett, 1995℄

Rasmussen,

S.,

ements

a

of

Barrett, Theory

C., of

1995. ElSimulation.

arXiv:adap-org/9504003v1.

[Regan and Burgman, 2002℄

Regan, H., Colyvan, M., Burgman, M., 2002. A taxonomy and treatment of un ertainty for e ology and onservation biology. E ol. Appl. 12(2), 618628.

[Ri ard, 2004℄

Ri ard, J., 2004. Redu tion, integration and emergen e in bio hemi al networks. Biol. of the Cell. 96, 719725.

[Roman et al., 1998℄

Roman-Roldan, R., Bernaola-Galvan, P., Oliver, J., 1998. Sequen e ompositional

omplexity of DNA through an entropi segmentation method. Phys. Rev. Lett. 80(6), 1344-1347.

69

[Sasai et al., 1995℄

Sasai, Y, Lu, B, Steinbeisser, H, De Robertis, E.M., 1995. Regulation of neural indu tion by the hd and Bmp-4 antagonisti patterning signals in Xenopus. Nature. 376, 333336.

[Seth, 2000℄

Seth, A., 2000. On the relations between behaviour, me hanism and environment : explorations in arti ial evolution. D. Phil. thesis, University of Sussex.

[Siegfried, 2006℄

Siegfried, K., 2006. Fishery management in data-limited situations :

appli ations

to sto k assessment, marine reserve design and sh by at h poli y; PhD Thesis, University of California, Santa Cruz.

[Solomono, 1964℄

Solomono, R., 1964. A Formal theory of Indu tive Inferen e. Information and Control. 7, 1-22, 224-54.

[Suzuki et al., 1995℄

Suzuki, A., Shioda, N., Ueno, N., 1995. Bone morphogeni protein a ts as a ventral mesoderm modier in early Xenopus embryos. Develop. Growth Dier. 37, 581588.

[Szathmary et al., 2001℄

Szathmáry, E., Jordán, F., Pál, C., 2001. Can Genes Explain Biologi al Complexity? S ien e. 292(5520), 1315-1316.

70

[Tautz et al., 1986℄

Tautz, D, Tri k, M, Dover, G.A., 1986. Crypti simpli ity in DNA

is a major

sour e of geneti variation. Nature. 322, 652-656.

[Terefework et al., 1998℄

Terefework, Z.,

Ni k,

G.,

Suomalainen,

S., Paulin, L., Lindstrom, K., 1998. Phylogeny of Rhizobium galegae with respe t to other rhizobia and agroba teria. Int. J. Syst. Ba teriol. 48, 349356.

[Testa and Kier, 2000℄

Testa,

B.,

Kier,

L.,

2000.

Emergen e

and Dissolven e in the Self-organisation of Complex Systems. Entropy. 2, 1-25.

[Thomas, 1971℄

Thomas, C., 1971. The geneti organization of hromosomes. Ann. Rev. Geneti s. 5, 237256.

[Truman, 1973℄

Truman, J., 1973. Physiobiology of inse t e dysis III. Relationship between the hormonal ontrol of e losion and of tanning in the toba

o hornworm mandu a sexta; J.Exp. Biol. 58, 821-829.

[Tylianakis, 2008℄

Tylianakis, J.M., 2008. Understanding the Web of Life: The Birds, the Bees, and Sex with Aliens. PLoS Biol. 6(2): e47.

[Uso et al., 2000℄

Uso-Domene h, J., Villa ampa-Esteve, Y., Mateu-Mahiques, J., Sastre-Vazquez, P.,

71

2000. Un ertainty and omplementarity prin iples in e ologi al models. Cyberneti s and Systems. 31(2), 137-159.

[Wahlsten et al., 2003℄

Wahlsten, D., Metten, P., Phillips, T.J., Boehm,

S.L.

2nd,

Burkhart-Kas h,

Dorow, J., Doerksen, S.,

S.,

Downing, C.,

Fogarty, J., Rodd-Henri ks, K., Hen, R., M Kinnon, C.S., Merrill, C.M., Nolte, C., S halomon, M., S hlumbohm, J.P., Sibert,

J.R.,

Wenger,

C.D.,

Dudek,

B.C.,

Crabbe, J.C., 2003. Dierent data from dierent labs:

Lessons from studies of

gene-environment intera tion. J. Neurobiol. 54, 283-311.

[Wan and Wootton, 2000℄

Wan,

H.,

Wootton,

J.,

2000. A global

ompositional omplexity measure for biologi al sequen es: genomes

en ode

AT-ri h and GC-ri h

less

omplex

proteins.

Comput. Chem. 24, 71-94.

[Williams et al., 1981℄

Williams,

J.M.,

Peterson,

R.G.,

Shea,

P.A., S hmedtje, J.F., Bauer, D.C., Felten, D.L., 1981. Sympatheti innervation of murine thymus and spleen: eviden e for a fun tional link between the nervous and immune systems. Brain Res. Bull. 6, 83-94.

72

[Wilson and Hemmati, 1995℄

Wilson, P., Hemmati-Brivanlou, A., 1995. Indu tion

of

epidermis

and

inhibition

of neural fate by Bmp-4. Nature. 376, 331333.

[Wolpert and Ma Ready, 1997℄

Wolpert, D., Ma Ready, W., 1997. Selfdissimilarity:

omplexity.

An empiri al measure of Working

Paper

97-12-087,

Sante Fe Inst.

[Wootton and Federhen, 1996℄

Wootton, J., Federhen, S., 1996. Analysis of ompositionally biased regions in sequen e databases. Methods Enzymol. 266, 554-571.

[Xu et al., 2006℄

Xu, F., Xu, J., Tse, F., Tse, A., 2006. Adenosine stimulates depolarization and rise in ytoplasmi Ca2+ on entration in type I ells of rat arotid bodies. Am. J. Physiol. Cell Physiol. 290, C1592-C1598.

[Xu et al., 1995℄

Xu, R.H., Kim, J., Taira, M., Zhan, S., Sredni, D., Kung, H.F., 1995. A dominant negative bone morphogeneti protein 4 re eptor auses neuralization in Xenopus e toderm. Bio hem. Biophys. Res. Comm. 212, 212219.

[Young et al., 1991℄

Young,

J.P.W.,

Downer,

H.L.,

Eardly,

B.D.,1991. Phylogeny of the phototropi rhizobium strain BTAi1 by polymerase

73

hain rea tion-based sequen ing of a 16S rRNA gene segment. J. Ba teriol. 173, 22712277. .

[Zhang et al., 2007℄

Zhang, Y., Zhang, Y., Chen, J., Zhang, B.,

Pan,

Y.,

Ren,

L.,

Zhao,

J.,

Luo,

Y., Zhai, D., Wang, S., Wang, J., 2007. Polybutyl yanoa rylate novel

ve tors

in

nanoparti les

an er

gene

as

therapy.

Nanomedi ine: Nanote h., Biol., and Med. 3, 144153.20324.

74