A general efficiency relation for molecular machines

Living systems efficiently use chemical fuel to do work, process information, and assemble patterns despite thermal noise. Whether high efficiency arises from general principles or specific fine-tuning is unknown. Here, applying a recent mapping from nonequilibrium systems to battery-resistor circuits, I derive an analytic expression for the efficiency of any dissipative molecular machine driven by one or a series of chemical potential differences. This expression disentangles the chemical potential from the machine's details, whose effect on the efficiency is fully specified by a constant called the load resistance. The efficiency passes through a switch-like inflection point if the balance between chemical potential and load resistance exceeds thermal noise. Therefore, dissipative chemical engines qualitatively differ from heat engines, which lack threshold behavior. This explains all-or-none dynein stepping with increasing ATP concentration observed in single-molecule experiments. These results indicate that biomolecular energy transduction is efficient not because of idosyncratic optimization of the biomolecules themselves, but rather because the concentration of chemical fuel is kept above a threshold level within cells

Structural ultrafast dynamics of macromolecules: diffraction of free DNA and effect of hydration

Of special interest in molecular biology is the study of structural and conformational changes which are free of the additional effects of the environment. In the present contribution, we report on the ultrafast unfolding dynamics of a large DNA macromolecular ensemble in vacuo for a number of temperature jumps, and make a comparison with the unfolding dynamics of the DNA in aqueous solution. A number of coarse-graining approaches, such as kinetic intermediate structure (KIS) model and ensemble-averaged radial distribution functions, are used to account for the transitional dynamics of the DNA without sacrificing the structural resolution. The studied ensembles of DNA macromolecules were generated using distributed molecular dynamics (MD) simulations, and the ensemble convergence was ensured by monitoring the ensemble-averaged radial distribution functions and KIS unfolding trajectories. Because the order–disorder transition in free DNA implies unzipping, coiling, and strand-separation processes which occur consecutively or competitively depending on the initial and final temperature of the ensemble, DNA order–disorder transition in vacuo cannot be described as a two-state (un)folding process

Structural Dynamics of Free Proteins in Diffraction

Among the macromolecular patterns of biological significance, right-handed α-helices are perhaps the most abundant structural motifs. Here, guided by experimental findings, we discuss both ultrafast initial steps and longer-time-scale structural dynamics of helix-coil transitions induced by a range of temperature jumps in large, isolated macromolecular ensembles of an α-helical protein segment thymosin β_9 (Tβ_9), and elucidate the comprehensive picture of (un)folding. In continuation of an earlier theoretical work from this laboratory that utilized a simplistic structure-scrambling algorithm combined with a variety of self-avoidance thresholds to approximately model helix-coil transitions in Tβ_9, in the present contribution we focus on the actual dynamics of unfolding as obtained from massively distributed ensemble-convergent MD simulations which provide an unprecedented scope of information on the nature of transient macromolecular structures, and with atomic-scale spatiotemporal resolution. In addition to the use of radial distribution functions of ultrafast electron diffraction (UED) simulations in gaining an insight into the elementary steps of conformational interconversions, we also investigate the structural dynamics of the protein via the native (α-helical) hydrogen bonding contact metric which is an intuitive coarse graining approach. Importantly, the decay of α-helical motifs and the (globular) conformational annealing in Tβ_9 occur consecutively or competitively, depending on the magnitude of temperature jump

Conformations and coherences in structure determination by ultrafast electron diffraction

In this article we consider consequences of spatial coherences and conformations in diffraction of (macro)molecules with different potential energy landscapes. The emphasis is on using this understanding to extract structural and temporal information from diffraction experiments. The theoretical analysis of structural interconversions spans an increased range of complexity, from small hydrocarbons to proteins. For each molecule considered, we construct the potential energy landscape and assess the characteristic conformational states available. For molecules that are quasiharmonic in the vicinity of energy minima, we find that the distinct conformer model is sufficient even at high temperatures. If, however, the energy surface is either locally flat around the minima or the molecule includes many degrees of conformational freedom, a Boltzmann ensemble must be used, in what we define as the pseudoconformer approach, to reproduce the diffraction. For macromolecules with numerous energy minima, the ensemble of hundreds of structures is considered, but we also utilize the concept of the persistence length to provide information on orientational coherence and its use to assess the degree of resonance contribution to diffraction. It is shown that the erosion of the resonant features in diffraction which are characteristic of some quasiperiodic structural motifs can be exploited in experimental studies of conformational interconversions triggered by a laser-induced temperature jump

Thermodynamic force thresholds biomolecular behavior

In living systems, collective molecular behavior is driven by thermodynamic forces in the form of chemical gradients. Leveraging recent advances in the field of nonequilibrium physics, I show that increasing the thermodynamic force alone can induce qualitatively new behavior. To demonstrate this principle, general equations governing kinetic proofreading and microtubule assembly are derived. These equations show that new capabilities, including catalytic regulation of steady-state behavior and exponential enhancement of molecular discrimination, are only possible if the system is driven sufficiently far from equilibrium, and can emerge sharply at a threshold force. Regardless of design parameters, these results reveal that the thermodynamic force sets fundamental performance limits on tuning sensitivity, error, and waste. Experimental data show that these biomolecular processes operate at the limits allowed by theory

Paradigms for computational nucleic acid design

The design of DNA and RNA sequences is critical for many endeavors, from DNA nanotechnology, to PCR‐based applications, to DNA hybridization arrays. Results in the literature rely on a wide variety of design criteria adapted to the particular requirements of each application. Using an extensively studied thermodynamic model, we perform a detailed study of several criteria for designing sequences intended to adopt a target secondary structure. We conclude that superior design methods should explicitly implement both a positive design paradigm (optimize affinity for the target structure) and a negative design paradigm (optimize specificity for the target structure). The commonly used approaches of sequence symmetry minimization and minimum free‐energy satisfaction primarily implement negative design and can be strengthened by introducing a positive design component. Surprisingly, our findings hold for a wide range of secondary structures and are robust to modest perturbation of the thermodynamic parameters used for evaluating sequence quality, suggesting the feasibility and ongoing utility of a unified approach to nucleic acid design as parameter sets are refined further. Finally, we observe that designing for thermodynamic stability does not determine folding kinetics, emphasizing the opportunity for extending design criteria to target kinetic features of the energy landscape

Hydrophobic forces and the length limit of foldable protein domains

To find the native conformation (fold), proteins sample a subspace that is typically hundreds of orders of magnitude smaller than their full conformational space. Whether such fast folding is intrinsic or the result of natural selection, and what is the longest foldable protein, are open questions. Here, we derive the average conformational degeneracy of a lattice polypeptide chain in water and quantitatively show that the constraints associated with hydrophobic forces are themselves sufficient to reduce the effective conformational space to a size compatible with the folding of proteins up to approximately 200 amino acids long within a biologically reasonable amount of time. This size range is in general agreement with the experimental protein domain length distribution obtained from approximately 1,200 proteins. Molecular dynamics simulations of the Trp-cage protein confirm this picture on the free energy landscape. Our analytical and computational results are consistent with a model in which the length and time scales of protein folding, as well as the modular nature of large proteins, are dictated primarily by inherent physical forces, whereas natural selection determines the native state

Dominance of misfolded intermediates in the dynamics of α-helix folding

Helices are the “hydrogen atoms” of biomolecular complexity; the DNA/RNA double hairpin and protein α-helix ubiquitously form the building blocks of life’s constituents at the nanometer scale. Nevertheless, the formation processes of these structures, especially the dynamical pathways and rates, remain challenging to predict and control. Here, we present a general analytical method for constructing dynamical free-energy landscapes of helices. Such landscapes contain information about the thermodynamic stabilities of the possible macromolecular conformations, as well as about the dynamic connectivity, thus enabling the visualization and computation of folding pathways and timescales. We elucidate the methodology using the folding of polyalanine, and demonstrate that its α-helix folding kinetics is dominated by misfolded intermediates. At the physiological temperature of T = 298 K and midfolding time t = 250 ns, the fraction of structures in the native-state (α-helical) basin equals 22%, which is in good agreement with time-resolved experiments and massively distributed, ensemble-convergent molecular-dynamics simulations. We discuss the prominent role of β-strand–like intermediates in flight toward the native fold, and in relation to the primary conformational change precipitating aggregation in some neurodegenerative diseases