The energetics of transport across membranes

Dr. Denice Bay

Transport across membranes

Passive Diffusion •  4 types of passive

diffusion: 1. Simple diffusion 2. Facilitated Diffusion 3. Filtration 4. Osmosis

Active Transport •  2 types of active

transport: 1.  Primary ATP

driven 3.  Secondary

electrochemical chemical gradient driven

H2O, CH3CH2OH, CH3Cl Ions, Metals, Large molecules

Energy membrane

Passive Diffusion 1. Simple Diffusion

2. Facilitated Diffusion

- Solute flux is facilitated by transport through protein channels / pores

- Solute fluxed directly through the membrane

3. Filtration

4. Osmosis

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

- 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 pre-existing concentration gradient

[ Solutein ]

out

in

[ Soluteout ]

If Sin > Sout active transport

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

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

(1)

Surface area (A)

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

Difference in molecule

concentration ΔC

Cout

Cin

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:

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]

µ = µo + RT • lnC Where,

(2) Modified Nernst equation Walther Nernst

(1864-1941)

•  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:

•  Since µoout = µo

in are equal the equation simplifies to:

Δµout-in = (µoout + RT• lnCout)-( µo

in + RT• lnCin) (3)

Δµout-in = RT•ln (Cout/Cin) (4)

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

Cout = 500 mM ethanol

Cin = 50 mM ethanol

For uncharged molecules:

Temp = 20 oC

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)

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)

+

+ Δψ = ψout – ψin = difference in redox potential across

the mb z = +2

[Mg2+]out

[Mg2+]in

ΔE= Δψ

inside outside

+

Δψ = +200 mV

z = +2

[Mg2+]out = 1 mM

[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

Δµout-in = - 50.7 kJ/ mol The free energy required to transport of Mg2+ inside is energetically unfavorable (negative) ACTIVELY TRANSPORTED

Temp = 20oC

inside

outside

Thermodynamics of Osmosis •  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 Jacobus H. van 't Hoff

(1852-1911)

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)

Note similarity to Pascal’s ideal gas law

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

Semi- permeable membrane

A B B A

ΔP

A[solute] > B[solute]

ψπA = ψπB ψπA < ψπB

A[solute] > B[solute]

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

Net

sol

vent

m

ovem

ent f

rom

B

A

Water potential (Ψw) •  Water potential (Ψw) is the algebraic sum of

pressure P and the osmotic potential (ψπ)

•  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 = P + ψπ

Ψw = G / Vw Where, Vw = 18 × 10−6 m3 mol−1

(8)

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

[solutein] = 0.3 M

Flaccid Plant cell

Ψw = P + ψπ Ψw = 0 – 0.73 MPa = - 0.73 MPa

ψπ = -C RT ψπ = -(0.3 M) (8.3 L kPa mol-1 K-1) (293 K) = - 730 kPa or - 0.730 MPa

20oC

Since the cell wall of the plant cell exerts no net pressure on the cell contents P = 0

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

H2O

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

Primary Transport

Secondary Transport

ATP ADP + Pi

H+

H+

Δψ ΔµH+ ΔµH+

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

ΔµATP = ΔGo + RT • lnΔC

•  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

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

(10)

Chemiosmotic Hypothesis •  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

Peter D. Mitchell 1920-1992

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

4OH- 2H+

2H+

2H+

2e-

2e-

2e-

ATP

ADP + Pi

3H+

3H+

F0F1 ATPase

ΔµH+

nH+

nH+

ETC NAD+

4H2O

2H+ + ½ O2

H2O p-side

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)

Δψ = 140 mV

H+

H+ ΔpH = - 0.5

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

Δp = ? ΔµH+= ?

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. c

oli i

nner

m

embr

ane

ΔµH+ = + F • Δp

n-side p-side

3H+

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

E. c

oli i

nner

m

embr

ane

3H+

ΔµH+ = - F • Δp

Free energy is released

ATP + H2O + nH+n ADP + Pi + nH+

p

p-side n-side

[ATP] = 5.0 mM [ADP] = 0.3 mM [Pi] = 15.0 mM

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+ = + 48 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: anion- H+

solute H+

OH- H+

symport uniport

cation+

anion-

OH- H+

H+ Na+

antiport

solute H+

OH- 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)

2.3RT log10 [Sin+z] + zF • Δψ = 2.3RT • nΔpH - nFΔψ

[Sout+z]

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

[Sout+z] 2.3 RT

(14)

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

anion- H+

solute H+

OH- H+

symport

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

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

[Sout+z] 2.3 RT

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

[Sout+z] 2.3 RT

uniport

cation+

anion-

OH- H+

(16)

H+ Na+

antiport

solute H+

OH- H+

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

log10 [Sin+z] = (n - z)• Δψ – n • ΔpH

[Sout+z] 2.3 RT

log10 [Sin+z] = n • ΔpH

[Sout+z]

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:

(18)

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.)

ADP + Pi

1ATP 1ATP ADP + Pi

1ATP ADP + Pi

3H+ 3Na+

2K+ 1Ca2+

1ATP ADP + Pi

1H+ 1K+

F0F1 ATPase Na+, K+ ATPase

Ca2+

ATPase H+, K+

ATPase

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

retinal Light

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+