# ๐ Krab 2011

Explaining the enigmatic KMfor oxygen in cytochrome c oxidase: A kinetic model

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## Introduction

Complex IV (cytochrome c oxidase) reaction: 4cytc2+ + 8H_M+ + O2 โ 4cytc3+ + 4H_C+ + 2H2O

Apparent high affinity (low Km,app) for oxygen (<1ฮผM). But the dissociation constant is 0.28mM?! => fast trapping of the already bound O2

High pmf or low c2+/c3+: higher Km,app = 1~10 ฮผM

Kinetic models for this enzyme that incorporate all features of

*Gibbs energy transduction*are scarce

## The model

### The reaction cycle

- The number of charges transported across the inner mitochondrial membrane is given in parentheses.
- Division of reaction 5, the O to E transition, into 6 steps to describe the proton pumping mechanism
- 6-fold divisions of reactions 3, 4 and 6 are also modelled on this

### Values of model parameters

### Variables in the model

- fractions for cytc2+ vs cytc3+
- free proton concentrations at the C-side and M-side
- transmembrane electric potential difference (C-side minus M-side): membrane potential dependence of both kinetic constants is equal but opposite
$$
k_{\text { forward }}=k_{\text { forward }}^{\circ} \cdot e^{\frac{-q \cdot F \cdot \Delta \psi}{2 R \cdot T}}
$$
$$
k_{\mathrm{backward}}=k_{\mathrm{backward}}^{\circ} \cdot e^{\frac{q F \Delta \psi}{2 R T}}
$$
- q2 = 0.33, q3 = 0.67

### Calculation of steady state

- King and Altman method
- 26 * 26 matrix for transitions rates

### Calculation of the KM for O2

R00 -> A00 is proportional to [O2]

cycle flux to [O2] $$ v=\frac{\alpha \cdot\left[O_{2}\right]-\beta}{\gamma \cdot\left[O_{2}\right]+\delta} $$

ฮฒ « ฮฑ โ [O2] $$ v \approx \frac{V_{\max } \cdot\left[O_{2}\right]}{\left[O_{2}\right]+K_{\mathrm{M}}} $$

$$ V_{\max }=\frac{\alpha}{\gamma} \quad K_{\mathrm{M}}=\frac{\delta}{\gamma} $$

### Control coef fi cients

$$ C_{i}^{Z}=\frac{\partial \ln Z}{\partial \ln \lambda_{i}} $$

- ฮป_i is the factor by which both forward and backward rate constant of step i are changed simultaneously
- this modulation does not alter the ฮ G0

## Results and discussion

### Rate and enzyme states as a function of the energy state of the membrane

- state E04 accumulates (especially under low energy conditions)

- depends on pmf, absolute H+, ฮpH, cytochrome c redox state

### Energy state and KM for O2

- KM values are less than 1 ฮผM at lower values of ฮฮผH+, increase into the micromolar range when ฮฮผH+ is increased
- a lower reduction level of cytochrome c brings about an increase in KM
- as in experiments

### Control of cycle flux and kinetic properties by individual steps in the mechanism

- there is no individual step limiting turnover
- the same steps (13, 14, 17, 19, 25 and 26) contribute signi fi cantly to control of all three of these entities,

- 8 main contributions (control values > 0.05) to control of KMas a function of energy state ( ฮฮผH+)

- Apart from the R00โ A00and A00โ P00transitions, all these steps are electrogenic proton movements

### Sensitivity of KMincrease to arbitrarily chosen parameters

- The main prediction of our model is the increase of KMfor oxygen upon energisation
- A number of parameters in the model (midpoint potentials of heme a3 in the P, F, E states, pKaof protonation of the Fe-ligand in the F, E states and 6 bias factors) have arbitrarily assigned values.
- explored how dependent the KMchange predicted by the model is on the values of these parameters, and on the charge separation parameters q2and q3
- these small variations of the parameter values did not abolish the KMdifference

### Utility of the model

- dependence of the electron transport rate through cytochrome oxidase on
**membrane energisation**is modelled realistically and explicitly. - analysis and prediction of the separate effects of membrane potential, matrix pH and intermembrane space pH on the rate
- Not included: branches of catalytic function (slips), dimerization, regulations
- It is possible to use this model to calculate transient kinetics of the enzyme

## Reference

Krab K, Kempe H, Wikstrรถm M. Explaining the enigmatic K(M) for oxygen in cytochrome c oxidase: a kinetic model. Biochim. Biophys. Acta 2011;1807(3):348-358. doi:10.1016/j.bbabio.2010.12.015. ↩︎