Transport Energetics

The energetics of transport across membranes Dr. Denice Bay

Transport across membranes H2O, CH3CH2OH, CH3Cl

Ions, Metals, Large molecules

membrane

Passive Diffusion •  4 types of passive diffusion: 1. Simple diffusion 2. Facilitated Diffusion 3. Filtration 4. Osmosis

Energy

Active Transport •  2 types of active transport: 1.  Primary  ATP driven 3.  Secondary  electrochemical chemical gradient driven

Passive Diffusion 1. Simple Diffusion - Solute fluxed directly through the membrane

2. Facilitated Diffusion - Solute flux is facilitated by transport through protein channels / pores

3. Filtration - Solute flux occurs based on its size through a porous membrane

4. Osmosis - Solute flux occurs based on the concentration gradients

The energetics of Passive Diffusion •  The flux of all molecules across a membrane is highly influenced by its preexisting concentration gradient If Sin > Sout  active transport

out

[ Soluteout ]

in [ Solutein ]

If Sin < Sout  passive transport If Sin = Sout  equilibrium (DEAD?)

Fick’s first law of passive diffusion Adolf Fick (1829-1901)

Fick’s laws of Diffusion from a biological membrane perspective:

J = - P • A • ΔC

(1)

J is the solute flux or the rate of change (dQ/ dt) in solute quantity (Q) over time (t)  also represented as “J” P is the permeability co-efficient of the membrane (m • sec-1)  this value is negative due to solute movement towards low [Solute] A is the surface area (m2) of the membrane where the solute flux is occuring

ΔC is the difference in the concentration across the membrane

Cout

Surface area (A)

Difference in molecule concentration ΔC

Cin

dQuantity (mol) / time (sec) = Permeability (P)

Thermodynamics of Passive Diffusion Fick’s law doesn’t allow a quantitative consideration of the energetic requirements that exist during transport. For an uncharged solute the chemical potential (µ = free energy (G) per mole) can be represented by the following: Walther Nernst (1864-1941)

Modified Nernst equation

µ = µo + RT • lnC

(2)

Where, µ = chemical potential (G) of the solute

µo = standard state chemical potential R = gas constant (8.3 J • mol-1 • deg-1) T = temperature degrees Kelvin (273 oK) lnC = log base e of [solute]

•  Hence, the difference of µ (Δµ) between two points in space or (more importantly for biologists) two molecules in space separated by a membrane is given by: Δµout-in = (µoout + RT• lnCout)-( µoin + RT• lnCin) (3)

•  Since µoout = µoin are equal the equation simplifies to: Δµout-in = RT•ln (Cout/Cin)

(4)



This is an extention of both the van’t Hoff and Gibbs free energy equations.

For uncharged molecules: Cout = 500 mM ethanol Temp = 20 oC

Cin = 50 mM ethanol

Δµout-in = RT (lnCout/Cin)

Δµout-in = (8.3 J•mol-1•K-1) (293oK) (ln 500 mM Cout/ 50 mM Cin) Δµout-in = (2432 J•mol-1) • (2.3)

Δµout-in = + 5600 J/ mol

Positive value indicates that the free energy of ethanol inside is lower than outside

 passive transport

What about charged molecules? Δµ = RT ln(ΔC) - zF(ΔE)

(6)

ΔE= Δψ

Where: z = charge of the solute

F = Faraday constant (96.5 J•mol-1•mV-1) E = (ψ) electrical (redox) potential of the solute (mV) [Mg2+]out +

outside

Δψ = ψout – ψin = difference in redox potential across the mb z = +2 +

inside [Mg2+]in

[Mg2+]out = 1 mM oC Temp = 20 Δψ = +200 mV outside

z = +2 +

inside [Mg2+]in= 150 mM

Δµout-in = (RT ln Cout/Cin) - zF(Δψ) Δµout-in = (8.3 J•mol-1K-1)•(293 K)• ln(1 mM/ 150 mM) – (+2)(96.5 J•mol-1•mV-1)(+200 mV) Δµout-in = (2432 J•mol-1) (- 5.01) - (+38600 J•mol-1) Δµout-in = -12185 J•mol-1 - 38600 J• mol-1 The free energy required to Δµout-in = - 50.7 kJ/ mol

transport of Mg2+ inside is energetically unfavorable (negative)  ACTIVELY TRANSPORTED

Thermodynamics of Osmosis

Jacobus H. van 't Hoff (1852-1911)

•  The diffusion of solutes across semi-permeable membranes is also influenced by the pressure within the liquid solution across the membrane •  van’t Hoff determined that differences in [solute] flowed differently across the membrane when pressure varied

Note similarity to Pascal’s ideal gas law

π = - c • RT

(7)

c = [solute] (in M) ψπ = osmotic potential (atm or Mpa) R = gas constant (8.31 L kPa K-1 mol-1) T = temperature (Kelvin)

Osmotic potential (ψπ)

•  Theory of ψπ

–  Pure H2O has no solutes thus ψπ = 0  this explains why ψπ will always be negative (solutes displace H2O molecules thereby lowering the osmotic potential) –  Higher [solute] result in more negative ψπ values

A

Net solvent movement from BA

A[solute] > B[solute] B

ψπA < ψπB

Hypertonic  low ψπ values;[solute]↑ Hypotonic  high ψπ values;[solute]↓ Isotonic  difference ψπ is approaching 0

A[solute] > B[solute] A B

Semi- permeable membrane

ΔP

ψπA = ψπB

Water potential (Ψw) •  Water potential (Ψw) is the algebraic sum of pressure P and the osmotic potential (ψπ)

Ψw = P + ψπ (8) •  Ψw is essentially describing the free energy (G) in a mass of water which relates how much energy is involved in its movement  The Gwater is related in terms of pressure rather than by J/mol simply based on convention

Ψw = G / Vw

Where, Vw = 18 × 10−6 m3 mol−1

Knowing equations of Ψw and ψπ, we can calculate the osmotic potential of solute movement occurring across the membrane. 20oC

[solutein] = 0.3 M

Flaccid Plant cell

ψπ = -C RT ψπ = -(0.3 M) (8.3 L kPa mol-1 K-1) (293 K) = - 730 kPa or - 0.730 MPa Since the cell wall of the plant cell exerts no net pressure on the cell contents P = 0 Ψw = P + ψπ Ψw = 0 – 0.73 MPa = - 0.73 MPa

If we place the cell in 0.1 M sucrose? ψπ = - 0.24 MPa  ψπ of sucrose outside cell ΔΨw = (- 0.24 MPa)out – (- 0.73 MPa)in ΔΨw = + 0.49 MPa Cell is becoming hypotonic

H 2O

Summary of Passive Transport •  4 types of passive transport •  Diffusion of any molecule across a membrane is influenced by –  [solute] inside and outside the membrane –  the potential both chemical and electrical that resides on the given membrane

•  The free energy required by the electrochemical potential of the membrane will dictate the type of transport (passive or active) needed to transport it –  Positive = passive diffusion –  Negative = active transport

•  Osmotic transport energetics are influenced by both solute concentration and solvent pressure that exist across the membrane –  Osmotic potential (ψπ) is expressed as a unit of pressure –  The additive effect of both ψπ and pressure (P) combine to give water potential (Ψw) which relates the free energy involvement in H2O movement across the membrane –  If ΔΨw > 0  hypotonic ΔΨw < 0  hypertonic ΔΨw = 0  isotonic

Active Transport H+

ΔµH+

ΔµH+

ADP + Pi

ATP

Primary Transport

Δψ

H+

Secondary Transport

Primary (ATP driven) Transport •  ATP hydrolysis provides energy for the movement solutes across membranes under energetically unfavourable conditions •  ATP synthesis is linked to the utilization of the proton electrochemical gradient across the membrane ATP + H2O + nH+n  ADP + Pi + nH+p H+p = positive side of the membrane (µH+) H+n = negative side of the membrane

•  Knowing the standard free energy (ΔGo) of ATP hydrolysis permits the calculation of energy available for molecule transport across the membrane ATP + H2O  ADP + Pi

ΔGo = -31 kJ/ mol

[ATP] = 5 mM , [ADP] = 0.3 mM, [Pi] = 90 mM

ΔµATP = ΔGo + RT • lnΔC (10) Δµ = -3.1x104 J mol-1+(8.3 J mol-1 K-1)•(298 K) • ln [ADP] [Pi] [ATP] Δµ = -3.1 x104 J mol-1+2.47 J mol-1 • ln [3.0 x10-4 M] [9.0 x10-2 M] [5 x10-3 M]

ΔµATP = -4.4 x104 J/mol or - 44 kJ/mol

Chemiosmotic Hypothesis

Peter D. Mitchell 1920-1992

• 

States that ATP synthesis is driven by ΔµH+

• 

This means: 1.  Membranes must be vesicular, sealed and impermeable to H+ except pathways and proteins involved in H+/ redox generation

2. Energy is stored in a ΔpH gradient or Δµ equivalent to ΔµH+ 3. ΔµH+ is formed vectorially by alternating H+ and e- carriers in the electron transport chain  transport of e- permit the extrusion of H+ (Hence the ratio of H+/ e- = 1) Actually, H+/ e> 1 due to the activities of the “Q-cycle”

4. H+ flux is coupled to F0F1 ATPase activity driven by ΔµH+   from the (+) side of the membrane (p-side) = ATP synthesis   the reverse reaction drives H+ translocation to the (-) side (n-side) = ATP hydrolysis (n-side) NADH 2H+

NAD+

2e-

3H+ ADP + Pi

ATP F0F1 ATPase

nH+

ETC

4OH-

ΔµH+ 2H+

2H+

2e2e-

4H2O

H 2O 2H+ + ½ O2

3H+

p-side

nH+

n-side

Secondary Transport •  Proton motive force (Δp) is the combination of H+ and voltage/ electrical potential (ψ) that is generated across a membrane Δp = Δψ - 2.3 RT • ΔpH = ΔµH+ F F

(11)

This equation takes into consideration changes in [H+] across the membrane (ΔpH). Since pH = - log10 [H+] , then ΔpH = pHin – pHout or ΔpH = pHp- pHn

Δp = F•Δψ - 2.3 RT • log10 [H+out] [H+in]

(12)

H+

ΔµH+ and Δp required to pump out a single H + from the E. coli plasma membrane at 25 oC

E. coli inner membrane

Δψ = 140 mV

Δp = ? n-side  p-side ΔµH+= ? So, we can calculate

ΔpH = - 0.5

ΔµH+ = + F • Δp H+ ΔµH+ = F • Δψ – 2.3 RT • ΔpH = (96.5 kJ mol-1 V-1) (0.14 V) – (0.059 kJ mol-1) (-0.5) = + 16.4 kJ/ mol In this case Δp can be expressed in mV only: Δp = Δψ – 59 • ΔpH = 140 mV –59 (-0.5) = 170 mV

E. coli inner membrane

Free energy is released

p-side  n-side

3H+

[ATP] = 5.0 mM 3H+

What about pumping in a single H+ across the E. coli plasma membrane at 25 oC?

ΔµH+ = - F • Δp [ADP] = 0.3 mM [Pi] = 15.0 mM

ATP + H2O + nH+n ADP + Pi + nH+p

ΔµH+ = + 48 kJ/ mol

3H+p  3H+n ΔµH+ = - 3F • Δp = -3 (96.5) (16.3) = - 49 kJ/ mol ADP + Pi + 3H+p  ATP + H2O + 3H+n - 1 kJ/ mol

ΔµH+ linked active transport •  What about the transport of solutes across the membrane driven by ΔµH+? •  3 Different mechanisms exist to accomplish solute transport: cation+

anion- H+ H+ OH-

symport

solute

H+

H+ Na+ H+

H+

OH-

uniport

anion-

OH-

antiport

solute

H+

•  If all the free energy available in ΔµH+ is stored in the electrochemical potential of the substrate (Δµs ) then the solute accumulation occurs via each of these 3 mechanisms based on z and n. Δµs = 2.3 RT log10 [Sin+z] + zF • Δψ [Sout+z]

(13)

Where z = charge on the solute n = number of protons used for transport

2.3RT log10 [Sin+z] + zF • Δψ = 2.3RT • nΔpH - nFΔψ [Sout+z] log10 [Sin+z] = n • ΔpH – (n + z) • Δψ (14) [Sout+z] 2.3 RT

anion- H+ H+ OH-

If n > 0 and z > 0, then the transport can be driven by symport according to the equation:

symport

solute

log10 [Sin+z] = n • ΔpH – (n + z) • Δψ [Sout+z] 2.3 RT

H+

cation+ H+ OH-

uniport

anion-

On rare occasions n = 0, then the transport is driven by uniport. n is removed from the equation since no protons are spent. z is the critical factor in the equation.

log10 [Sin+z] = - z • Δψ (16) [Sout+z] 2.3 RT

H+ Na+ H+ OH-

antiport

solute

H+

During antiport the initial state of the solute in and the final state is out, then the signs are reversed from the symport equation and becomes:

log10 [Sin+z] = (n - z)• Δψ – n • ΔpH [Sout+z] 2.3 RT

In some cases, n = z. Solute transport is also driven by antiport but z movement would be neutral and Δψ can be removed altogether. (18)

log10 [Sin+z] = n • ΔpH [Sout+z]

Other methods to generate Δµ •  Bacteria and Eukaryotes can produce Δµ and Δψ using various ions driving the evolution of different electron transport chain components, motility systems, and ATPases •  Na+ and K+ are asymmetrically distributed across membranes due to the activity of Na+, K+ ATPase  osmoregulation & cell signalling •  Halophilic microorganisms often use Na+ and K+ in lieu of H+ due to the energetic constraints of their environment  costs ATP  free energy per mole of Na+ (ΔµNa+)

ΔµNa+ = F • Δψ - 2.3 RT • log10 [Na+out] [Na+in]

(19)

•  Ca2+ can also drive ΔµCa2+ through the activity of the Ca2+ ATPase in primarily eukaryotes •  ATPases maintain electrochemical gradients by transporting cations (such as Mg2+, Cu2+, Fe3+ etc.) and anions (Cl-, PO43-, etc.) 3H+

1ATP

1K+

3Na+ 2K+

ADP + Pi

F0F1 ATPase

ADP + Pi

1ATP

Na+, K+ ATPase

1Ca2+

ADP + Pi

1H+

1ATP

Ca2+ ATPase

ADP + Pi

1ATP

H+, K+ ATPase

•  Bacteriorhodopsin, from the Archaea Halobacterium salinarium purple membranes pumps H+ across the membrane generating ΔµH + using energy provided by light Light

retinal

Summary of Active Transport •  Active transport requires an input of energy derived from either ATP hydrolysis (primary) or from Δp (secondary) •  Primary transport results in a high yield of free energy available from ATP + H2O  ADP + Pi to transport an energetically prohibited molecule against Δµ of the membrane •  Secondary transport provides energy for primary transport activities (ATP synthesis) as well as for Δp driven reactions –  Secondary transport pumps ions (H+) against its natural gradient to generate energy in the form of an electrochemical potential that facilitates the transport of molecules incapable of energetically diffusing across the membrane –  the solute chemical gradient across a membrane will dictate the type of transport method that can be used ie. symport, uniport, and antiport –  This process is also essential for osmoregulation of other compounds by pumping ions other than H+ across the membrane such as Na+, K+, Ca2+