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Gaussian fluctuations and linear response in an electron transfer protein.

ABSTRACT: In response to charge separation or transfer, polar liquids respond in a simple linear fashion. A similar linear response for proteins might be expected from the central limit theorem and is postulated in widely used theories of protein electrostatics, including the Marcus electron transfer theory and dielectric continuum theories. Although these theories are supported by a variety of experimental data, the exact validity of a linear protein dielectric response has been difficult to determine. Molecular dynamics simulations are presented that establish a linear dielectric response of both protein and surrounding solvent over the course of a biologically relevant electron transfer reaction: oxido-reduction of yeast cytochrome c in solution. Using an umbrella-sampling free energy approach with long simulations, an accurate treatment of long-range electrostatics and both classical and quantum models of the heme, good agreement is obtained with experiment for the redox potential relative to a heme-octapeptide complex. We obtain a reorganization free energy that is only half that for heme-octapeptide and is reproduced with a dielectric continuum model where the heme vicinity has a dielectric constant of only 1.1. This value implies that the contribution of protein reorganization to the electron transfer free energy barrier is reduced almost to the theoretical limit (a dielectric of one), and that the fluctuations of the electrostatic potential on the heme have a simple harmonic form, in accord with Marcus theory, even though the fluctuations of many individual protein groups (especially at the protein surface) are anharmonic.

SUBMITTER: Simonson T

PROVIDER: S-EPMC124439 | biostudies-literature | 2002 May

REPOSITORIES: biostudies-literature

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Gaussian fluctuations and linear response in an electron transfer protein.

Simonson Thomas T

Proceedings of the National Academy of Sciences of the United States of America 20020501 10

In response to charge separation or transfer, polar liquids respond in a simple linear fashion. A similar linear response for proteins might be expected from the central limit theorem and is postulated in widely used theories of protein electrostatics, including the Marcus electron transfer theory and dielectric continuum theories. Although these theories are supported by a variety of experimental data, the exact validity of a linear protein dielectric response has been difficult to determine. M ...[more]

PMID: 12011418

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Project description:Electron transfer reactions are essential for life because they underpin oxidative phosphorylation and photosynthesis, processes leading to the generation of ATP, and are involved in many reactions of intermediary metabolism. Key to these roles is the formation of transient inter-protein electron transfer complexes. The structural basis for the control of specificity between partner proteins is lacking because these weak transient complexes have remained largely intractable for crystallographic studies. Inter-protein electron transfer processes are central to all of the key steps of denitrification, an alternative form of respiration in which bacteria reduce nitrate or nitrite to N2 through the gaseous intermediates nitric oxide (NO) and nitrous oxide (N2O) when oxygen concentrations are limiting. The one-electron reduction of nitrite to NO, a precursor to N2O, is performed by either a haem- or copper-containing nitrite reductase (CuNiR) where they receive an electron from redox partner proteins a cupredoxin or a c-type cytochrome. Here we report the structures of the newly characterized three-domain haem-c-Cu nitrite reductase from Ralstonia pickettii (RpNiR) at 1.01 Å resolution and its M92A and P93A mutants. Very high resolution provides the first view of the atomic detail of the interface between the core trimeric cupredoxin structure of CuNiR and the tethered cytochrome c domain that allows the enzyme to function as an effective self-electron transfer system where the donor and acceptor proteins are fused together by genomic acquisition for functional advantage. Comparison of RpNiR with the binary complex of a CuNiR with a donor protein, AxNiR-cytc551 (ref. 6), and mutagenesis studies provide direct evidence for the importance of a hydrogen-bonded water at the interface in electron transfer. The structure also provides an explanation for the preferential binding of nitrite to the reduced copper ion at the active site in RpNiR, in contrast to other CuNiRs where reductive inactivation occurs, preventing substrate binding.

Project description:BackgroundStochastic fluctuations in molecular numbers have been in many cases shown to be crucial for the understanding of biochemical systems. However, the systematic study of these fluctuations is severely hindered by the high computational demand of stochastic simulation algorithms. This is particularly problematic when, as is often the case, some or many model parameters are not well known. Here, we propose a solution to this problem, namely a combination of the linear noise approximation with optimisation methods. The linear noise approximation is used to efficiently estimate the covariances of particle numbers in the system. Combining it with optimisation methods in a closed-loop to find extrema of covariances within a possibly high-dimensional parameter space allows us to answer various questions. Examples are, what is the lowest amplitude of stochastic fluctuations possible within given parameter ranges? Or, which specific changes of parameter values lead to the increase of the correlation between certain chemical species? Unlike stochastic simulation methods, this has no requirement for small numbers of molecules and thus can be applied to cases where stochastic simulation is prohibitive.ResultsWe implemented our strategy in the software COPASI and show its applicability on two different models of mitogen-activated kinases (MAPK) signalling -- one generic model of extracellular signal-regulated kinases (ERK) and one model of signalling via p38 MAPK. Using our method we were able to quickly find local maxima of covariances between particle numbers in the ERK model depending on the activities of phospho-MKKK and its corresponding phosphatase. With the p38 MAPK model our method was able to efficiently find conditions under which the coefficient of variation of the output of the signalling system, namely the particle number of Hsp27, could be minimised. We also investigated correlations between the two parallel signalling branches (MKK3 and MKK6) in this model.ConclusionsOur strategy is a practical method for the efficient investigation of fluctuations in biochemical models even when some or many of the model parameters have not yet been fully characterised.

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Gaussian fluctuations and linear response in an electron transfer protein.

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Gaussian fluctuations and linear response in an electron transfer protein.

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