Absorption Spectroscopy/Protein Function

Topic 4 Part 2Biophysics

Chemical KineticsZero Order

• Rate independent of concentrations• -dC/dt = k • C(t) = C0 – kt

C

t

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

1.40E+00

450 500 550 600 650 700

Wavelength (nm)

Abs

orpt

ion

AB

Reaction of nitrite with deoxyhemoglobin

Chemical KineticsFirst Order

• -dCA/dt = kCA , CA = CA0 e-kt

• t1/2 = ln(2)/k; = 1/k = lifetime

ln(CA)

t

NO binding to Hb

ZA k

Chemical KineticsSecond Order

• -dCA/dt = -dCB/dt = kCACB

• Make one species in excess so get pseudofirst order kinetics, kobs = kCB so

CA = CA0 exp(-kobst)

0B

0A0

B0A

B

A

CClnktCC

CCln

oductsPrBA k

Hemoglobin

Cooperative Binding of Oxygen

Linked to quaternary structure

Explained by MWC Model

On the Nature of Allosteric Transitions:

A Plausible ModelJacques Monod, Jeffries Wyman,

Jean-Pierre ChanguxJ. Mol. Biol. 1965

“Molecular Amplifiers”

ATCase

The goal is control – want a switch. “Indirect interactions between distinct specific binding sites (allosteric

effects)”

Definitions and Generalizations• Homotrophic effects – identical ligands (eg. for

Hb: O2, CO, NO)• Heterotrophic effects –different ligands (eg. for

Hb: DPG, IHP, Cl-, NO as SNO, NEM)• Most allosteric proteins are oligomers (several

subunits or protomers)• Allosteric changes often involve quaternary

stucture• Heterotrophic - positive or negative,

Homotrophic – only positive (exception of Hg reductase?)

Model in English

1. Allosteric proteins are oligomers where the protomers are arranged symmetrically

2. There is one and only one identical ligand-binding site on each protomer

3. Tertiary structure of protomers affected by quaternary structure

4. There are two quaternary states (R and T) which dictate ligand affinities on all protomers

5. Transitions between states preserve symmetry

Model in Math

• T0 = L R0, , L is the allosteric constant, (Big L = Big allostery)

• Only also define

RT

R

KFc

KK

c defines relative affinities of quaternary states and defines absolute affinity of one

When L is smalln

n

F LY

)1()1( 1

Compare Hill Equation

n

n

F LY

)1()1( 1

n

n

Q

YFvs

Q is a constant, n is the number of ligand sites, n is Hill coefficient

Hb, L, c …

Hb Sigmoidal

See satsimple.mw and sat.mw

Heterotrophic effectorsAffect L

Activators decrease L (push to R) and

Inhibitors increase it

AIn

n

n

n

F

KA

KILL

LY

, ,)1()1('

)1(')1(

1

See sat.mw

Hb – microstate predictions (vs sequential)

Unlike in sequential model, no R2 or T2 – see states.mw

ATCase and inhibitor

• At low concentrations of substrate, low concentrations of analogue activate (by promoting R-state) upper curve

• Desensitized enzyme (quaternary interactions suppressed) shows no increase in activity by analoque (maleate)

• Generally, desensitized enzymes lose cooperativity. Hb dimers are R-state like and like Mb. Homotrophic ligands promote tetramer stabilization (hard to dissociate oxyHb), as predicted

Activators can decrease cooperativity

Fig 6a is theoretical (see yf.mw )

Fig 6b and c show activations in real systems

Confirmations of MWCATCase

• Model predicts fraction in R-state > fraction ligand bound. Schachman lab (1966) shows this using sedimentation to examine quaternary state (size) and spectroscopy for ligation.

• They also showed (like Gerhart lab) low concentration of inhibitor activate ATCase

Confirmations - Hb• MWC’s prediction of concomitant changes in tertiary

structure in protomers with known symmetry of tetramer confirmed by more refined X-ray structures.

• Perutz provides mechanism of allosteric transitions• Szabo and Karplus show quantitative agreement of

MWC/perutz model with equilibrium data (Eg Lc4 constant after all salt bridges broken).

• Equilibrium oxygen binding to Hb trapped in T-state crystal non-cooperative (Eaton lab).

• CO rebinding following photolysis of HbCO (R-state) much faster than CO binding to Hb (T-state) – Gibson.