We explore the dynamical large-deviations of a lattice heteropolymer model of a protein by means of path sampling of trajectories. We uncover the existence of non-equilibrium dynamical phase-transitions in ensembles of trajectories between active and
inactive dynamical phases, whose nature depends on properties of the interaction potential. When the full heterogeneity of interactions due to the amino-acid sequence is preserved, as in a fully interacting model or in a heterogeneous version of the G={o} model where only native interactions are considered, the transition is between the equilibrium native state and a highly native but kinetically trapped state. In contrast, for the homogeneous G={o} model, where there is a single native energy and the sequence plays no role, the dynamical transition is a direct consequence of the static bi-stability between unfolded and native states. In the heterogeneous case the native-active and native-inactive states, despite their static similarity, have widely varying dynamical properties, and the transition between them occurs even in lattice proteins whose sequences are designed to make them optimal folders.
Elastic systems that are spatially heterogeneous in their mechanical response pose special challenges for molecular simulations. Standard methods for sampling thermal fluctuations of a systems size and shape proceed through a series of homogeneous de
formations, whose magnitudes can be severely restricted by its stiffest parts. Here we present a Monte Carlo algorithm designed to circumvent this difficulty, which can be prohibitive in many systems of modern interest. By deforming randomly selected subvolumes alone, it naturally distributes the amplitude of spontaneous elastic fluctuations according to intrinsic heterogeneity. We describe in detail implementations of such slice moves that are consistent with detailed balance. Their practical application is illustrated for a random network of cross-linked polymers.
Models of protein energetics which neglect interactions between amino acids that are not adjacent in the native state, such as the Go model, encode or underlie many influential ideas on protein folding. Implicit in this simplification is a crucial as
sumption that has never been critically evaluated in a broad context: Detailed mechanisms of protein folding are not biased by non-native contacts, typically imagined as a consequence of sequence design and/or topology. Here we present, using computer simulations of a well-studied lattice heteropolymer model, the first systematic test of this oft-assumed correspondence over the statistically significant range of hundreds of thousands of amino acid sequences, and a concomitantly diverse set of folding pathways. Enabled by a novel means of fingerprinting folding trajectories, our study reveals a profound insensitivity of the order in which native contacts accumulate to the omission of non-native interactions. Contrary to conventional thinking, this robustness does not arise from topological restrictions and does not depend on folding rate. We find instead that the crucial factor in discriminating among topological pathways is the heterogeneity of native contact energies. Our results challenge conventional thinking on the relationship between sequence design and free energy landscapes for protein folding, and help justify the widespread use of Go-like models to scrutinize detailed folding mechanisms of real proteins.
Double-stranded DNA `overstretches at a pulling force of about 65 pN, increasing in length by a factor of 1.7. The nature of the overstretched state is unknown, despite its considerable importance for DNAs biological function and technological applic
ation. Overstretching is thought by some to be a force-induced denaturation, and by others to consist of a transition to an elongated, hybridized state called S-DNA. Within a statistical mechanical model we consider the effect upon overstretching of extreme sequence heterogeneity. `Chimeric sequences possessing halves of markedly different AT composition elongate under fixed external conditions via distinct, spatially segregated transitions. The corresponding force-extension data display two plateaux at forces whose difference varies with pulling rate in a manner that depends qualitatively upon whether the hybridized S-form is accessible. This observation implies a test for S-DNA that could be performed in experiment. Our results suggest that qualitatively different, spatially segregated conformational transitions can occur at a single thermodynamic state within single molecules of DNA.
Filopodia are long, finger-like membrane tubes supported by cytoskeletal filaments. Their shape is determined by the stiffness of the actin filament bundles found inside them and by the interplay between the surface tension and bending rigidity of th
e membrane. Although one might expect the Euler buckling instability to limit the length of filopodia, we show through simple energetic considerations that this is in general not the case. By further analyzing the statics of filaments inside membrane tubes, and through computer simulations that capture membrane and filament fluctuations, we show under which conditions filopodia of arbitrary lengths are stable. We discuss several in vitro experiments where this kind of stability has already been observed. Furthermore, we predict that the filaments in long, stable filopodia adopt a helical shape.
