Making ATP

Abstract

We present a mesoscopic model for ATP synthesis by F1Fo ATPase. The model combines the existing experimental knowledge of the F1 enzyme into a consistent mathematical model that illuminates how the stages in synthesis are related to the protein structure. For example, the model illuminates how specific interactions between the ␥, , and ␣3␤3 subunits couple the Fo motor to events at the catalytic sites. The model also elucidates the origin of ADP inhibition of F1 in its hydrolysis mode. The methodology we develop for constructing the structure-based model should prove useful in modeling other protein motors.ATP synthase ͉ ATP synthesis ͉ F1Fo ATPase M echanochemical proteins convert the energy of chemical bonds into mechanical forces and, in the case of one ancient protein, vice versa. ATP synthase (also called F 1 F o ATPase) uses the energy stored in a transmembrane electrochemical gradient to synthesize ATP. ATP synthase is unique in combining two rotary molecular motors in one protein so that the assembly can either synthesize ATP or pump ions across a membrane, depending on which motor dominates. The F 1 F o system has been studied extensively both experimentally and theoretically, so the basic operating principles of both the F o and F 1 motors are understood at near molecular detail (e.g. refs. 1-5).Modeling of mechanoenzymes takes three general approaches. Molecular dynamics (MD) attempts to account for the motion of every atom, and sometimes the surrounding water and other chemical species. Kinetic models represent the transitions between small numbers of chemical (Markov) states. Markov-FokkerPlanck (MFP) models lie somewhere between the atomic detail of MD and the phenomenology of kinetic models (6). These models describe the geometric motion along a few ''collective coordinates'' that describe the protein's major conformational movements. Motion is driven by forces derived from a set of potential functions assigned to each coordinate, with Markov jumps between the potentials corresponding to chemical transitions. MFP models generalize kinetic models by replacing the discrete kinetic states with potential functions representing collective spatial coordinates. The distinctions between, and relative advantages of, each of these models have been discussed in detail elsewhere (6). A prominent feature of MFP models is that structural and dynamical information can be included in the models without the computational load of MD models. In this work, we take this approach. We emphasize that MFP models complement MD and kinetic models; each has its proper place in understanding a mechanochemical system as complex as a protein motor.In constructing an MFP model, the central step is to identify the important degrees of freedom that must be treated explicitly, and construct a set of free energy potential surfaces with these degrees of freedom as geometrical coordinates. Identification of the collective coordinates can often be inferred from the protein structure and its biochemistry (7). Normal mode analysis also c...

Biophysical comparison of ATP synthesis mechanisms shows a kinetic advantage for the rotary process

“…Previous modeling studies of the F-ATPase have addressed structural and mechanistic questions about the rotary mechanism (e.g., refs. [11][12][13][14][15][16][17][18][19][20], but not the metaissue of the mechanism itself compared with alternatives.…”

Extending the absorbing boundary method to fit dwell-time distributions of molecular motors with complex kinetic pathways

“…The dynamics of an enzyme's activity can be modeled as a number of kinetic states using kinetic equations (3) or mechanical coordinates using diffusion-based (Fokker-Planck) equations (4). For questions addressed in this study, models of kinetic equations were appropriate.…”

δ-Free FoF1-ATPase, Nanomachine and Biosensor

“…Some work focused on the hydrolysis or synthesis of F 1 . For example, Oster et al constructed a 4 3 states model for the couplings among three catalytic sites and provided a physical view of the dynamics (Sun et al, 2004;Xing et al, 2005). However, the model is too sophisticated to be investigated analytically.…”