Ch/APh2 Bioenergetics Section Lecture of May 19, 2009 Introduction to bioenergetics. The thermodynamics of biological energy production. Kinetic aspects of bioenergetic processes. Energy transfer Electron transfer The molecular and cellular organization of bioenergetic systems. Membrane transport Ion Channels, transporters Photosynthesis Respiration and ATP synthesis Haber-Bosch process and biological nitrogen fixation

Kinetics of Bioenergetics

light energy transfer

electron transfer

diffusion

distance, time and driving force dependences

Dutton et al. Adv. Prot. Chem. 63 (2003)

Photon absorption and de-excitation

phosphorescence

time scale ~sec

fluorescence

time scale ~ ns

radiationless transfer

time scale ~ ns

absorption and fluorescence of bacteriochlorophyll

Qy

Qx

light (resonance) energy transfer

Donor absorbs at higher energy (shorter ) than Acceptor.

rate of transfer ~ (R0/R)6

R0 depends on spectral overlap and quantum yields; typically ~ 10 - 50+ Å

basis of “spectroscopic ruler”

acceptor donor

Fluorescence resonance energy transfer (FRET)

measure fluorescence yield of the donor in the absence and presence of the acceptor:

efficiency = Ro6/(Ro

6 + R6)

R0 ~ 34Å

energy transfer in bacterial RC/LHC complexes

Sundstrom et al. JPC B103, 2327 (1999)

(RC absorbs ~ 870 nm)

photosynthetic systems have a common core structure

bacterial

plants: PSI and PSII

Dutton et al. Adv. Prot. Chem. 63, 71 (2003)

bacterial photosynthetic reaction center (RC)

three subunits: L, M and H

A

BCD

E

A’

B’

C’

D’

E’

PDB IDs 2PRC; 1AIJ

view down membrane normalview in plane of membrane

organization of cofactors in the RC

Bchl2

BchlChl

BphBph

Bchl2

QBQA

B branchA branch

carotenoid

photosynthesis - the reaction center

membrane

Bchl2

QA QB

Bchl

Bph

h

Bchl -chlorophyll

Bph - bacteriopheophytin

Q - quinone

Fe

QuickTime™ and aQuickDraw decompressor

are needed to see this picture.

(Bchl)2

Bph

Bchl

QAQBFe

5 Å

10 Å

5 Å

13 Å10 Å

5 Å

5 Å

why is the B branch so much slower than the A branch?

why is the back reaction (to (Bchl)2+) so unfavorable?

Bph

Bchl

Incident solar radiation ~1 photon/RC/sec

Cycling time for the RC is ~ 10-3 sec;

Use light harvesting/antennae complexes to transfer light energy to RC

Mechanism of light energy transfer is not quantitatively understood:

After absorption of a photon, the excited state likely becomes delocalized around the electronically coupled chromophores.

http://www.chem.gla.ac.uk/protein/LH2/migrate.html

h

Electron Transfer Kinetics: classical Marcus theory

(Marcus and Sutin, BBA 811, 265 (1985))www.nobel.se/chemistry/laureates/1992/marcus-lecture.html

activation energy for exchange reaction (ET rate)

kET = A e-(∆G*/RT)

http://iriaxp.iri.tudelft.nl/~scwww/candeias/bio-et/kinetic.html

calculation of activation energy - classical model

∆G* = (1+∆G˚/ )2/4

kET = Ae-(∆G*/RT)

max. rate when ∆G˚= -

Gray & Winkler Ann. Rev. Biochem. 65, 537 (1996)

= energy to distort reactant into product geometry

the inverted region

distance dependence of electron transfer kinetics

kET = A(r) e-(∆G*)/RT

Tunneling timetable for ET in Ru-modified proteins (open symbols), water (light blue, = 1.61-1.75 Å1), and vacuum (dark blue, = 3.0-4.0 Å1) (adapted from ref. 36). Most coupling-limited electron tunneling times in proteins [cyt c (); azurin (); cyt b562 (); myoglobin (); and high-potential iron-sulfur protein ()] fall in the 1.0- to 1.2-Å1 wedge (pale blue solid lines; pale blue dashed line is the average of 1.1 Å1). Colored circles (*Zn-cyt c Fe(III)-cyt c, green and Fe(II)-cytc Zn-cyt c+, red) are interprotein time constants.

Tezcan et al. PNAS 98, 5002 (2001)

distance dependence of electron transfer A(r) ~ 1013 e-r s-1

= 1.1 Å-1

Page et al. Nature 402, 47 (1999)hopping vs jumping…

Using ~ 1.1 Å-1, ket for electron transfer over 10 Å, 15 Å, 20 Å, 25 Å, and 30 Å, are calculatedto be approximately 8.8 x 109, 3.6x107, 1.5x105, 6.0x102, 2.5 sec-1, respectively. From thesevalues, the time required for electron transfer over 30 Å by either hopping in three 10 Å steps, orby tunneling directly, are calculated to be:

t1 / 2 , hopping ~ 18.8109 ln 2 (31) 3.11010 sec

t1/ 2, tunneling ~1

2.5ln 2 (11) 0.28 sec

kET = 1013 e-r e-(∆G*)/RT s-1

Kinetic aspects of getting a molecule or ion across a membrane

Thermodynamic driving forces:concentration gradientsmembrane potential (charged species)

Pore geometry (radius, length, electrostatics)

kinetics are governed by fundamental empirical laws that relate fluxes (flows) to driving forces

Ohm’s law relates forces (V) and flows (I) of electrical current

I = (1/R) V

Fick’s laws of diffusion relate forces and flows of particles

In general, the flux is proportional to the driving force

J = L F

J L

and J = L F

L F = c v

F = (c/L) v f v f = frictional coefficient

ie at steady state, F ~ velocity, not acceleration!

J = particles/unit area/unit time = molecules cm-2 sec-1

= concentration x velocity = c v

total current = J x Area

Basic equations of microscopic diffusion: Fick’s First Law

The basic diffusion equation may be derived from random walk considerations

area = AN(x) N(x+)

Consider how many particles will move across from point x to point x+ per unitarea per unit time - ie, what is the net flux J in the x direction?

For a random walk, where N(x) is the number of particles at x,during the next step

(1/2)N(x) will move from x to x+(1/2)N(x+) will move from x+ to x(1/2)[N(x)-N(x+)] will be the net movement from x to x+

= -(1/2)[N(x+)-N(x)]

cellular and molecular architecture of bioenergetic systems

(sub)cellular organization

Buchanan, Gruissem, JonesBiochemistry and Molecular Biology of Plants

organization of phospholipid membranes

S.J. Singer’s fluid mosaic model Science 175, 720 (1972)

phospholipids assemble into a bilayer through the “hydrophobic effect”; the apolar interior of the membrane is largely impermeable to water, ions and other polar molecules. Membrane proteins are required for transport of these species into and out of cells

Chandler, Nature 417, 491 (2002)

• Mitochondria: respiratory organelle, generates ~body weight of ATP daily

• Contains an outer membrane and a highly convoluted inner membrane with respiratory complexes

• Total surface area of inner membranes in humans is estimated to be 14,000 m2. (Rich, Nature 421, 583 (2003)

E. coli has two cell membranes

membrane spanning

polypeptide conformations

Looking at Macromolecular Structures

Viewer

SwissPDB

Rasmol

iMol

PyMOL

etc….

Coordinates

PDB - the Protein Data Bank - operated by the Research Collaboratory for Structural Bioinformatics

http://www.rcsb.org/pdb

Rich, Nature 421, 583 (2003)

Abeles, Nature 420, 27 (2002)

If N(x) N(x ) , then there will be a net flux through an area elementperpendicular to x between x and x+ that is given by Fick’s first law.

J D dcdx

; if dcdx

constant, J = constant

Cb

ba

Ca

there is a next flux from right to left, simply because there are more particles onthe right than on the left.

This flux depends only on the gradient, and not the value of c. This drive towardsequalizing the concentrations (chemical potential) will tend to flatten allconcentration gradients, and is principally entropic in origin.

Just as Newton’s laws give forces are derivatives of energy, the force from aconcentration gradient can be expressed as a derivative of the chemicalpotential.

Looking at Macromolecular Structures

Viewer

SwissPDB

PyMOL

etc….

Coordinates

PDB - the Protein Data Bank - operated by the Research Collaboratory for Structural Bioinformatics

http://www.rcsb.org/pdb

membrane spanning

polypeptide conformations

electron transfer complexestransporterschannels

matter, energy, information

inside

outside

Membrane proteins are the basic circuit elements of bioenergetic processes

∆µ

KcsA potassium channel

Doyle et al. Science 280, 69 (1998)

PDB ID: 1BL8

tetramer

K+ ion coordination. Zhou et al. Nature 414, 43 (2000).

PDB ID 1K4C

potassium permeation pathway

Morais-Cabral et al. Nature 414, 317 (2001)

mechanism of K+ permeation: conduction state diagram

MthK channel

Ca+2 mediated gating through a K+ channel

Jiang et al.Nature 417, 505 (2002)

PDB ID 1LNQ

Voltage gating in Kv potassium channels

opening and closing the channel in response to changes in membrane potential: the charged S4 helix

“voltage sensor paddles operate somewhat like hydrophobic cations attached to levers, enabling the membrane electric field to open and close the pore”

Jiang et al. Nature 423, 33; 42 (2003)

closed open

mechanosensitive channel of small conductance MscS

3.9 Å resolutionBass et al. Science 298, 1582 (2002)

membrane spanning domain

cytoplasmic domain

L105L109

N-terminal

C-terminal

TM1

TM2

TM3

middle

C-terminaldomain

MscS gating mechanismmechanosensitivity - open state has larger cross-sectional area

voltage sensitivity - open state has (+) charges moving away from cytoplasm

TM1 and TM2 likely serve as coupled tension and voltage sensorsTM3 forms the pore

R46

R74

R88

conformational variability in TM region of MscS

coloring by B factor (low to high)

How are concentration gradients generated in the first place?

Alberts et al. Essential Cell Biology

Na+,K+ ATPase

Two gate mechanism of pumps

ABC transporters andthe ATP-binding cassette:

importers and exporters of a diverseset of substrates

contain two copies each ofconserved ABC domainsmembrane spanning domains (diverse)

The Escherichia coli B12 uptake system Btu

Experimentalelectron density

3.5 Å resolutioncontour level=1

BtuCD architecture

cytoplasm

BtuC BtuC

BtuD BtuD3.2 Å resolutionLocher et al. Science 296, 1091 (2002)

periplasm

exit pathway

gate

translocation pathway

membrane spanning BtuC subunits

BtuCD structural organization

mechanistic issues• consequences of ATP binding and hydrolysis? • coupling of ABC and TM domains?• role of binding protein BtuF?

ATP-binding cassettes (BtuD subunits)

ABC signature motif

Walker-B

P-loops (Walker-A)

Proposed B12 transport mechanism

BtuF-B12

BtuCD

“alternating access” or “airlock” model

Channels and Transporters - summary

channels and transporters have common architectural features, namely:

translocation pathwayclosed with either one gate (channels) or two (transporters)

specificity elements (eg selectivity filter/binding proteins)

gating sensors