Fluctuation as a tool of biological molecular machines

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.

Dynamics of a polymer in a Brownian ratchet

We have used Brownian dynamics simulations to study the dynamics of a bead-and-spring polymer subject to a flashing ratchet potential. To elucidate the role of hydrodynamic (HD) interactions, simulations were carried out for the cases where HD interactions are present and when they are absent. The average speed of the polymer and its conformational properties were examined upon variation in the polymer length, N, and the ratchet spatial period, L. Two distinct dynamical regimes were evident. In the low-N/high-L regime, the velocity decreases with increasing N, and center-of-mass diffusion is a key part of the motional mechanism. By contrast, in the high-N /low-L regime, the velocity is insensitive to variation in N, and motion is achieved via the coupling of internal modes to the cycling of the ratchet potential. The location of the regimes is correlated with the average conformational state of the polymer. Incorporating HD interactions increases the average polymer velocity for all polymer lengths and ratchet spatial periods considered. The dynamical behavior of polymers in the low-N/high-L regime can be understood using simple a theoretical model that yields quantitatively reasonable predictions of the polymer velocity.

A hypothesis for bacteriophage DNA packaging motors

The hypothesis is presented that bacteriophage DNA packaging motors have a cycle comprised of bind/release thermal ratcheting with release-associated DNA pushing via ATP-dependent protein folding. The proposed protein folding occurs in crystallographically observed peptide segments that project into an axial channel of a protein 12-mer (connector) that serves, together with a coaxial ATPase multimer, as the entry portal. The proposed cycle begins when reverse thermal motion causes the connector’s peptide segments to signal the ATPase multimer to bind both ATP and the DNA molecule, thereby producing a dwell phase recently demonstrated by single-molecule procedures. The connector-associated peptide segments activate by transfer of energy from ATP during the dwell. The proposed function of connector/ATPase symmetry mismatches is to reduce thermal noise-induced signaling errors. After a dwell, ATP is cleaved and the DNA molecule released. The activated peptide segments push the released DNA molecule, thereby producing a burst phase recently shown to consist of four mini-bursts. The constraint of four mini-bursts is met by proposing that each mini-burst occurs via pushing by three of the 12 subunits of the connector. If all four mini-bursts occur, the cycle repeats. If the mini-bursts are not completed, a second cycle is superimposed on the first cycle. The existence of the second cycle is based on data recently obtained with bacteriophage T3. When both cycles stall, energy is diverted to expose the DNA molecule to maturation cleavage.