Structure-function relations and kinetic principles underlying multiscale electron transfer in biology

Abstract

Electron transfer (ET) is a fundamental process in biology, driving the core biochemical reactions of respiration, photosynthesis, redox catalysis, and cellular signaling. Biological ET systems achieve remarkable efficiency and control through finely tuned structure–function relations and kinetics. The aim of this dissertation is to understand the fundamental principles that govern nanometer to micrometer scale ET and free energy transduction in biological systems, using the methods and theories of molecular biophysics, quantum chemistry, and statistical mechanics. While nanometer scale ET reactions are relatively well understood, the conceptual and theoretical framework required to describe micrometer scale ET is only beginning to emerge. Our goal is to leverage our understanding of nanometer scale ET to elucidate the mechanisms ofmicrometer scale ET and understand how structure, ET dynamics, and biological functions are interrelated in protein assemblies.My projects focus on two major topics. The first topic is long-range extracellular ET (Chapter 2), where I investigated the ET mechanisms and the physical origins of anomalous temperature dependencies in bacterial nanowires. Extracellular ET reactions through bacterial nanowires support anaerobic metabolism by electrically connecting microbes and minerals. Bacterial nanowires are thus novel forms of sustainable conducting materials that provide access to new bioinspired technologies. Protein-mediated electron transfer reactions in biological redox chains typically obey the Arrhenius law, with rates that increase as the temperature grows. Surprisingly, bacterial nanowire proteins exhibit an anti-Arrhenius behavior: experiments find that Geobacter nanowire conductivity decreases by about 10% as the temperature changes from 275 to 340 K. This observed temperature dependence is inconsistent with the generally accepted thermally activated multi-step hopping mechanism in structures of protein-mediated ET. Instead, anti-Arrhenius transport is characteristic of metallic-like transport. We simulated electron transport in a one-dimensional OmcS nanowire from 275 K to 375 K, using an electrostatic model based on OmcS structures simulated with molecular dynamics. Our results reveal a non-linear but monotonic increase in the effective electron transport rate with temperature. While the experimentally observed anti-Arrhenius behavior is not reproduced, our simulations show a softer rate acceleration than predicted by the Arrhenius law in the 300–375 K range. The softer acceleration is primarily attributed to temperature-dependent changes in the reaction free energies.Our findings suggest that electrostatic effects alone are insufficient to account for the experimentally observed anti-Arrhenius behavior. Instead, the physical origin likely involves more complex structural or dynamical factors, beyond electrostatics, that modulate electron transfer in bacterial nanowires.The second topic is free energy transduction by nanoscale molecular machines (Chapters 3, 4, 5, and 6). Living systems use nanoscale molecular machines, which are protein complexes that convert between different forms of energy via free energy transduction. Free energy transduction is a process in which exergonic reactions are leveraged to drive endergonic reactions. Reaction cycles that only perform exergonic processes without driving endergonic processes are known as slippage, which must be suppressed for successful free energy transduction. In chapter 3, I investigated the validity of a many-particle transport model that are often used to study energy processing systems in biology. The full description of many-particle transport requires the model to include all statistical correlations among particle site occupancies. Yet, neglecting statistical correlations is a widely used approach since the computational cost of solving the model including full correlations grows exponentially with system size. However, it is challenging to anticipate when the statistical correlations among site occupancies strongly influence biological function, and we studied this issue in the context of nanoscale molecular machines. We studied whether statistical correlations among site occupancies are required to describe the energy transducing function of electron bifurcation (EB), a reaction that plays a vital role in processes such as the Q-cycle of respiration and nitrogen fixation. We compared the efficiency of energy transduction by EB computed by the full master equation (includes all correlations) with the mean-field model (neglects all correlations). The results indicated that the mean-field model predicts rampant slippage while the full master equation describes efficient free energy transduction by EB. We find that at least some of the neglected correlations were essential to describe the energy transducing function of EB enzymes. The necessity of a fully correlated description of many-particle transport is potentially a general feature of any energy transducing complexes. Our study introduces a new concept: the biological function of a system may constrain the kinds of theoretical models required to study that system. We find this concept of functional constraints on physical models to be essential for modeling and understanding free energy transduction by nanoscale molecular machines.In chapter 4, I explored different reservoir models that describe open-system many-particle transport. Biological charge transport chains typically direct charge flow between reservoirs that are linked by charge-hopping chains. Models of electron transport chains linked to reservoirs are often framed with infinite reservoir models. For example, earlier models of electron bifurcation, including the studies in chapter 3, used infinite reservoirs. The reservoir species in the infinite reservoir are degenerate and weakly interact with each other (i.e. “narrow band” limit). Transport has also been modeled in a wide-band reservoir limit, where the infinite reservoir is described with a uniform density of electronic states and Fermi-Dirac statistics, suitable for describing bulk electrodes. Many in vivo redox reactions occur in confined spaces that are nano- to micrometer scale, such as mitochondrial membranes, peroxisomes, lysosome vesicles, or endosomes, and the number of carrier storing molecules can be small. In the case of EB, the one- and two-electron redox pool concentrations may be far from an “infinite” reservoir regime. Typical redox substrates in biological ET, such as NADH, NADPH, O2, quinones, and cytochromes, do not form band structures, so the narrow-band model seems to be an appropriate starting point to model biological charge transport. We therefore developed a finite narrow-band reservoir model that captures the essential features of redox chains that operate in confined spaces or with low substrate concentrations. We studied multi-particle transport kinetics through a linear hopping chain that links two finite reservoirs, and analyzed the finite-size and initial-state effects on the kinetics. The infinite narrow- and wide-band models both produce one unique steady-state transport regime, which persists because of the infinite source of particles. The steady state is reached independent of the initial particle configuration of the chain. The finite narrow-band reservoir model, in contrast, returns to equilibrium and may or may not produce a steady-state regime on its path to equilibrium. The time-evolution of the finite narrow-band reservoir model depends strongly on the initial particle configuration and the total number of particles in the system. Indeed, the initial particle configuration and the total particlenumber determines whether or not a steady-state regime is accessed. Chapter \ref{chap:finiteres_EB} describes the application of the finite narrow-band reservoir model to simulate the steady state of EB networks.In chapter 5, I studied the functional role of inverted potentials at the bifurcating site of an EB enzyme. EB provides a scheme to generate strongly reducing redox species in living systems, on demand, from a two-electron source. EB enzymes typically contain a two-electron site, which serves as the bifurcating site, and a network of redox active cofactors that electrons transport through. A two-electron donor substrate reduces the bifurcating site by two electrons, and the electrons transport through a network of redox active cofactors to reduce the high- and low-potential electron acceptor substrates. The bifurcating site of an EB enzyme is known to have inverted potentials. A two-electron site having inverted potentials means that its first reduction potential is larger than its second reduction potential. Despite the ubiquity of inverted potentials in EB enzymes, the possible advantages afforded by inverted potentials remain unclear, as earlier studies on idealized free energy landscapes found that both normal and inverted potentials support efficient bifurcation at steady state. Here, we investigated the influence of potential inversion on pre-steady-state bifurcation kinetics and find that inverted potentials suppress pre-steady state short-circuiting, providing a possible functional advantage. We also examine the pre-steady state kinetics for a model of the Nfn1 enzyme, that inverted potentials on this landscape also increase efficiency in the pre-steady-state regime. Living systems may therefore benefit from recruiting inverted potentials at the bifurcation site, especially if the organisms frequently switch between bifurcation and confurcation modes of transport.Together, this dissertation provides new insights into how biological ET systems achieve efficiency and control, emphasizing the role of physical constraints, correlations, and structural dynamics.