Sivak, D. | bioRxiv Science

bioRxiv2018

Using a System’s Equilibrium Behavior to Reduce Its Energy Dissipation in Non-Equilibrium Processes

Cells must operate far from equilibrium1, utilizing and dissipating energy continuously to maintain their organization and to avoid stasis and death. However, they must also avoid unnecessary waste of energy2. Recent studies have revealed that molecular machines are extremely efficient thermodynamically when compared to their macroscopic counterparts3,4. There are also tantalizing hints of molecular machines conserving energy while operating out of equilibrium5,6. However, the principles governing the efficient out-of-equilibrium operation of molecular machines remain a mystery. A theoretical framework has been recently formulated in which a generalized friction coefficient quantifies the energetic efficiency in non-equilibrium processes7,8. Moreover, it posits that to minimize energy dissipation, external control should drive the system along the reaction coordinate with a speed inversely proportional to the square root of that friction coefficient. Here, we test and validate the predictions of this theory by probing the non-equilibrium energetic efficiency of a single DNA hairpin subjected to unfolding and refolding protocols using a dual-trap optical tweezers.

biophysics↗

bioRxiv2018

Quantifying configuration-sampling error in Langevin simulations of complex molecular systems

While Langevin integrators are popular in the study of equilibrium properties of complex systems, it is challenging to estimate the timestep-induced discretization error: the degree to which the sampled phase-space or configuration-space probability density departs from the desired target density due to the use of a finite integration timestep. In [1], Sivak et al. introduced a convenient approach to approximating a natural measure of error between the sampled density and the target equilibrium density, the KL divergence, in phase space, but did not specifically address the issue of configuration-space properties, which are much more commonly of interest in molecular simulations. Here, we introduce a variant of this near-equilibrium estimator capable of measuring the error in the configuration-space marginal density, validating it against a complex but exact nested Monte Carlo estimator to show that it reproduces the KL divergence with high fidelity. To illustrate its utility, we employ this new near-equilibrium estimator to assess a claim that a recently proposed Langevin integrator introduces extremely small configuration-space density errors up to the stability limit at no extra computational expense. Finally, we show how this approach to quantifying sampling bias can be applied to a wide variety of stochastic integrators by following a straightforward procedure to compute the appropriate shadow work, and describe how it can be extended to quantify the error in arbitrary marginal or conditional distributions of interest.

biophysics↗