Internal energy and information flows mediate input and output power in bipartite molecular machines.

Microscopic biological systems operate far from equilibrium, are subject to strong fluctuations, and are composed of many coupled components with interactions varying in nature and strength. Researchers are actively investigating the general design principles governing how biomolecular machines achieve effective free-energy transduction in light of these challenges. We use a model of two strongly coupled stochastic rotary motors to explore the effect of coupling strength between components of a molecular machine. We observe prominent thermodynamic characteristics at intermediate coupling strength, near that which maximizes output power: a maximum in power and information transduced from the upstream to the downstream system, and equal subsystem entropy production rates. These observations are unified through a bound on the machine's input and output power, which accounts for both the energy and information transduced between subsystems.

Nonequilibrium Energy Transduction in Stochastic Strongly Coupled Rotary Motors.

Living systems at the molecular scale are composed of many constituents with strong and heterogeneous interactions, operating far from equilibrium, and subject to strong fluctuations. These conditions pose significant challenges to efficient, precise, and rapid free energy transduction, yet nature has evolved numerous molecular machines that do just this. Using a simple model of the ingenious rotary machine FoF1-ATP synthase, we investigate the interplay between nonequilibrium driving forces, thermal fluctuations, and interactions between strongly coupled subsystems. This model reveals design principles for effective free energy transduction. Most notably, while tight coupling is intuitively appealing, we find that output power is maximized at intermediate-strength coupling, which permits lubrication by stochastic fluctuations with only minimal slippage.

Diffusion and interactions of interstitials in hard-sphere interstitial solid solutions.

Using computer simulations, we study the dynamics and interactions of interstitial particles in hard-sphere interstitial solid solutions. We calculate the free-energy barriers associated with their diffusion for a range of size ratios and densities. By applying classical transition state theory to these free-energy barriers, we predict the diffusion coefficients, which we find to be in good agreement with diffusion coefficients as measured using event-driven molecular dynamics simulations. These results highlight that transition state theory can capture the interstitial dynamics in the hard-sphere model system. Additionally, we quantify the interactions between the interstitials. We find that, apart from excluded volume interactions, the interstitial-interstitial interactions are almost ideal in our system. Lastly, we show that the interstitial diffusivity can be inferred from the large-particle fluctuations alone, thus providing an empirical relationship between the large-particle fluctuations and the interstitial diffusivity.

When memory pays: Discord in hidden Markov models.

When is keeping a memory of observations worthwhile? We use hidden Markov models to look at phase transitions that emerge when comparing state estimates in systems with discrete states and noisy observations. We infer the underlying state of the hidden Markov models from the observations in two ways: through naive observations, which take into account only the current observation, and through Bayesian filtering, which takes the history of observations into account. Defining a discord order parameter to distinguish between the different state estimates, we explore hidden Markov models with various numbers of states and symbols and varying transition-matrix symmetry. All behave similarly. We calculate analytically the critical point where keeping a memory of observations starts to pay off. A mapping between hidden Markov models and Ising models gives added insight into the associated phase transitions.