Mechanisms for achieving high speed and efficiency in biomolecular machines

Abstract

How does a biomolecular machine achieve high speed at high efficiency? We explore optimization principles using a simple twostate dynamical model. With this model, we establish physical principles-such as the optimal way to distribute free-energy changes and barriers across the machine cycle-and connect them to biological mechanisms. We find that a machine can achieve high speed without sacrificing efficiency by varying its conformational free energy to directly link the downhill, chemical energy to the uphill, mechanical work and by splitting a large work step into more numerous, smaller substeps. Experimental evidence suggests that these mechanisms are commonly used by biomolecular machines. This model is useful for exploring questions of evolution and optimization in molecular machines. molecular machines | evolution | nonequilibrium steady state | kinetic optimization | free-energy landscape W e are interested in how biomolecular machines can be optimized for speed and efficiency. Some such machines achieve both speed and efficiency. For example, on an average day a person synthesizes, uses, and recycles his or her body weight in ATP (1, 2). All of this ATP is synthesized by the motor FoF1-ATPase, which achieves these results with high turnover rates [hundreds of ATPs per second per motor (3)] at high thermodynamic efficiency [∼90% in animal mitochondria (4)].For a particular machine with a fixed mechanism, going faster comes at the expense of efficiency. However, through evolution, a machine can develop mechanisms that optimize the entire speed-efficiency curve; they increase speed at no cost to efficiency or vice versa. What are these mechanisms that biomolecular machines have evolved to be both fast and efficient?Previous studies have identified some specific mechanisms that optimize speed, such as a constant torque generation over the angular coordinate of a rotary motor (5), the evolutionary preference for a rotary mechanism in FoF1-ATPase (6), and a transition-state location close to the initial state of a machine's mechanical step (7-9). Other studies have found more general principles-how to best distribute the barrier heights and free-energy drops across a cyclic free-energy landscape both for molecular machines (10, 11) and for maximizing the catalytic efficiency of enzymes (12, 13). Our work is consistent with and builds on these previous results to identify the essential mechanisms for optimizing speed in molecular machines. We explore in particular how a machine can link a large downhill chemical energy to a large uphill mechanical work using intermediate conformational changes, the role of the transition-state location, and the kinetic advantage of splitting a single large work step into smaller "chunks" or substeps. A Two-State Model of a Molecular MachineWe model how a machine converts the free energy that is put into the system, ∆µ ≥ 0, into the work performed by the sys-tem, w ≥ 0 (Fig. 1). We divide machine actions into two steps, a nonmechanical transition (Aj → Bj ), which may include che...

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