Lecture 2' - Cellular Environments

Lecture 2 – Cellular Environments

The Cellular Environment Environment plays a large role in determining macromolecular structure. 

The strength of long range interactions: 



Is inversely proportional to the dielectric constant, κ.

Also: potential for direct interaction with solvent molecules.

There are number of distinct cellular environments… 

These are divisible into two categories:  Aqueous (Aq) Environment: 



dominant, since the cell is ~ 70% H20.

Also many Non-aqueous Environments:   

interior of membranes; interfaces between folded structures; interior of folded proteins.

The Structure of Water First, we consider the Aqueous (Aq) environment:  

the dominant cellular environment. our focus: an understanding of water structure.

Water exhibits structure at several levels: 

Individual H20 molecule: 



particular interest: gross electronic structure.

Structures adopted by interacting H20 molecules:  

ice – well-characterized crystalline structure; liquid water – also generally well-organized.

Water structure has profound implications for the behavior of dissolved substances. 

including biological macromolecules.

The H20 Molecule In liquid water, H20 is roughly tetrahedral (pyramid-like) 

central, sp3-hybridized Oxygen.



two sp3 orbitals bonded to Hydrogen atoms.  angle b/w O-H bonds: ~104.5o.



two sp3 orbitals hold non-bonding e- pairs.  slightly greater repulsion than O-H bonds.



Note: In a H-bonded network, all 4 nearly identical.

H20 is a Polar Molecule H20 contains 4 permanent dipoles… 

Generally, a dipole is formed by charge separation:  two small, opposite charges of the same

strength… 

δ- to δ+ , are separated by a distance, d.

 Dipoles like to interact with charges, each

other…

Water has one dipole per pyramid apex: 

Each O-H bond is polarized, since O is much more electronegative than H.  e- are localized around the Oxygen.  Result: permanent dipole moment, µ 

directed from δ- to δ+ (O to H).

H20 is also Highly Polarizable The strength, |µ| of each of H20’s dipole moments is highly variable. 

|µ| tends to increase around charges, or other dipoles:  Isolated H20 molecule: |µ| = q*d = 1.855 debye.  In a cluster of 6 or more: |µ| = 2.6 debye.  In Ice: |µ| = 3.0 debye.



this tendency to change, based on environment is referred to as polarizability.

H20 is thus both polar and highly polarizable: 

very high dielectric constant (κ ≅ 80).

Interaction b/w 2 H20 Molecules Dominated by an interaction between dipoles:  

The dipole moment of the O-H bond of the first H20; -

The dipole moment of the non-bonding e pair of the 2nd H20.

This dipole-dipole interaction: 

aligns these two dipoles head-to-tail, to be co-linear.



brings the associated O and H atoms closer than the sum of their Van der Waals radii…  forming the water-water Hydrogen Bond (‘H-bond’).  O-H is the H-bond donor.  non-bonding e- pair of the Oxygen is the H-bond acceptor.

H-Bonded Pairs in Biopolymers There are many types of H-bonds… 

Several contribute greatly to the structure of biopolymers.

Same basic character:  

the 2 dipoles are co-linear. nearly the same strength…  Note: relative strengths determined

by bond-length…

 shorter is stronger.

Note that in Aq. solution: 

Intra-molecular H-bonds must compete with H20.

Water can form a H-bonded Network Each H20 can participate in 4 H-bonds: 

twice as a donor (2 O-H bonds).



twice as an acceptor (2 unbonded e- pairs).

Normal, frozen water (0oC, 1 Atm pressure): 

forms a hexagonal H-bonded lattice.  Oxygens fixed…but, the protons (Hydrogens) rather

disordered. 

This form of ice is ‘Ice I’.

Other Forms of Ice Removing the proton disorder requires work: 



lower T; much higher pressure (P > 20 kbars ≅ 20,000 atm). the resulting hexagonal lattice is ‘Ice VIII’.

Various other forms of ice also exist… 

note Ice IX forms a pentagonal structure.

The Structure of Liquid Water Structure of pure liquid water quite similar to Ice I.  

also an H-bonded network. H20 molecules well-organized at the air-water interface…  highly cohesive network.  A similar interface forms at the ‘surface’ of dissolved

molecules.

However, structure much more dynamic than ice. 



the pattern of H-bonding changes about every picosecond. results in a net dissociation of H20 into [H30+] and [OH-]:

Interaction of Dissolved Molecules with Water When a molecule is placed in water: 

a water envelope forms around the molecule,  whether it is polar or not.



envelope is very similar to the air-water interface.  well-organized structure (∆Senvo < 0).  Formation thus unfavorable:

∆Genvo = -T∆Senvo > 0. 

Around ions, the envelope forms a cage-like, clathrate structure:  regular hexagonal and pentagonal

faces (see right).

The solubility of a dissolved molecule… 

depends on its ability to overcome this entropic penalty…

Hydrophilic Compounds For water-soluble compounds: 

the net interaction with water molecules (∆Ginto)…  overcomes the negative ∆Senvo of forming the H20

envelope:

∆Gneto = ∆Genvo + ∆Ginto < 0. 

termed ‘hydrophilic’ (from the Greek ‘philos’ = love).

Note: Waters around hydrophilic substances… 

typically form arrays of 6 and 7 H20s.

Examples: 

Salts – interact by dissociating into pairs of charged ions.  e.g.: NaCl Na+ + Cl-.  interaction b/w water and the charged ions highly

favorable. 

ions are thus highly water-soluble.

Hydrophobic Compounds Substances that are neither charged nor polar in solution: 

do not interact appreciably with H20, and thus…  cannot overcome the entropic penalty of the water

envelope.  Are pushed out of solution (insoluble); 

Waters form rigid ice-like cages, with pentagonal faces  very low in entropy (similar to Ice IX).





Termed ‘hydrophobic’ (from the Greek, phobos = fear). e.g., Hydrocarbons, such as methane.

In contrast, Hydrophobic compounds quite soluble in organic solvents (e.g., chloroform).  

due to van der Waals interaction (with solvent). while hydrophilic compounds prefer to aggregate

Amphipathic Molecules Some molecules are hydrophobic and hydrophilic.  

referred to as amphipathic. e.g., a phospholipid molecule:  Head: phosphatidyl Choline

(hydrophilic); 

Two charged groups: PO4- + N(CH3)3+

 Tail: long hydrocarbon chains

(hydrophobic).

In water, these form aggregates… 

so that each region may interact with other groups of its own type:  hydrophilic head: groups with H20.  hydrophobic tails: interact with air…

or

Structures Formed by Amphipathic Molecules Several types of structures may form, depending on:  

type of amphipathic molecules; concentration, temperature, etc.

Typical structures: 

Lipid monolayer:  forms at air-water interface.



Globular micelles:  dilute phospholipid dispersions.  internal hydrophobic environment.



Bilayer vesicles:  define 2 hydrophilic environments.  separated by 1 hydrophobic environment.  useful for establishing cell, organelle boundaries.

Biopolymers also Amphipathic Proteins:  

a mixture of polar and nonpolar amino acid residues. fold into structures resembling micelles:  basically globular.  hydrophilic residues displayed on the surface.  hydrophobic residues buried in the interior.

Nucleic Acids:  



nitrogenous bases (hydrophobic rings). negatively charged sugar-phosphate backbone (hydrophilic). Bases pair and fold into the nucleic acid ‘interior’.  e.g., in B-DNA (two aggregated DNA chains).

This is the basic principle of the hydrophobic effect…

Non-aqueous Environments of Biopolymers Many biomolecules exist in non-aqueous environments: 

mostly, these are proteins found in lipid bilayers.  reside amongst the hydrophobic tails.

Such molecules display an inverted topology:  

hydrophobic groups: exposed on the surface; hydrophilic groups: sequestered in the center.

Example: Gramicidin 



left-handed, anti-parallel double helix. polar groups line the center…  mimic the polar, water solvent;



allows ions to pass an otherwise impermeable bilayer.  ion channel (monovalent cations).

Membrane Impermeable to Ions Hydrocarbon tails are much less polar than H20. 

κ in the membrane lower by a factor of 40.  κmembrane ≅ 2 vs. κw ≅ 80.  long-range interactions (b/w charges, dipoles) 40x

stronger.

The Self-Energy of a singly-charged ion, q: 2

Es = q /(8πκεοrs) ; rs = Stoke’s radius  

again…κ-dependent: ionic self-energy also 40x greater. Relative probabilities of existing in and out of the membrane  Given by a ratio of ‘Gibbs factors’

P(in)/P(out) ≅ exp[- Es(in)/RT]/exp[- Es(out)/RT]

≅ e-54 ≅ 3.5 x 10-24.  Thus, membrane virtually impermeable to ions…

Diffusion in Membranes is 2-Dimensional In membranes, molecules must travel in 2 dimensions. 

strong implications for chemistry, diffusion-controlled kinetics.

Concentrations within membranes must be redefined: 



moles/area (M/mm2) used, instead of moles/volume (M/mm3). For instance, for a sphere… a 2-fold radius increase accompanied by:  an 8-fold dilution in concentration, for molecules in the

volume. 

since V = 4/3 πr3

 but only a 4-fold dilution, for molecules constrained to the

The Interior of Globular Proteins Another important non-polar environment is the interior of a globular protein.  

primarily amino acids with non-polar side chains. highly non-polar (typically, κ ≅ 2.5).

Charged ions will tend to avoid such environments,  

due to an increased self-energy. energetically difficult to bury an ion within a protein.

In addition, amino acid residues which carry a charge:  (+) Lysine, Arginine;  (-) Aspartic acid, Glutamic acid. 

will tend to be uncharged, within the interior…

pKa Values of Buried Residues Tendency of charged amino acids to adopt the uncharged form in a protein interior: 



will be reflected by a pKa change for these side chains. lower pKa’s = an increased tendency to dissociate.

For positively charged (basic) side-chains:  

Arginine (Arg), Lysine (Lys). pKa will be lower…increased tendency for the ‘extra’ H+ to dissociate from the residue.

For negatively charged (acidic) side-chains:  

Glutamic acid (Glu), Aspartic acid (Asp). pKa will be higher…increased tendency for the residue to neutralize by gaining an H+.

Conclusion In this Lecture, we have discussed: 

The various Cellular Environments:  The Aqueous environment and Water Structure, 

The impact of water structure on the solubility of dissolved substances.

 Non-Aqueous environments, 

Such as the interior of lipid aggregates and proteins.

…and discussed the impact of differences in medium polarity/polarizability (κ).

In the next Lecture, we begin our discussion of symmetry:  

Various types of simple symmetry. Its use in simplifying the description of biopolymer structure;