Protein turnover dynamics suggest a diffusion-to-capture mechanism for peri-basal body recruitment and retention of intraflagellar transport proteins.

Intraflagellar transport (IFT) is essential for construction and maintenance of cilia. IFT proteins concentrate at the basal body where they are thought to assemble into trains and bind cargoes for transport. To study the mechanisms of IFT recruitment to this peri-basal body pool, we quantified protein dynamics of eight IFT proteins, as well as five other basal body localizing proteins using fluorescence recovery after photobleaching in vertebrate multiciliated cells. We found that members of the IFT-A and IFT-B protein complexes show distinct turnover kinetics from other basal body components. Additionally, known IFT subcomplexes displayed shared dynamics, suggesting shared basal body recruitment and/or retention mechanisms. Finally, we evaluated the mechanisms of basal body recruitment by depolymerizing cytosolic MTs, which suggested that IFT proteins are recruited to basal bodies through a diffusion-to-capture mechanism. Our survey of IFT protein dynamics provides new insights into IFT recruitment to basal bodies, a crucial step in ciliogenesis and ciliary signaling.

Transition Path Dynamics of a Dielectric Particle in a Bistable Optical Trap.

Many processes in chemistry, physics, and biology involve rare events in which the system escapes from a metastable state by surmounting an activation barrier. Examples range from chemical reactions, protein folding, and nucleation events to the catastrophic failure of bridges. A challenge in understanding the underlying mechanisms is that the most interesting information is contained within the rare transition paths, the exceedingly short periods when the barrier is crossed. To establish a model process that enables access to all relevant timescales, although highly disparate, we probe the dynamics of single dielectric particles in a bistable optical trap in solution. Precise localization by high-speed tracking enables us to resolve the transition paths and relate them to the detailed properties of the 3D potential within which the particle diffuses. By varying the barrier height and shape, the experiments provide a stringent benchmark of current theories of transition path dynamics.

Broad distributions of transition-path times are fingerprints of multidimensionality of the underlying free energy landscapes.

Recent single-molecule experiments have observed transition paths, i.e., brief events where molecules (particularly biomolecules) are caught in the act of surmounting activation barriers. Such measurements offer unprecedented mechanistic insights into the dynamics of biomolecular folding and binding, molecular machines, and biological membrane channels. A key challenge to these studies is to infer the complex details of the multidimensional energy landscape traversed by the transition paths from inherently low-dimensional experimental signals. A common minimalist model attempting to do so is that of one-dimensional diffusion along a reaction coordinate, yet its validity has been called into question. Here, we show that the distribution of the transition path time, which is a common experimental observable, can be used to differentiate between the dynamics described by models of one-dimensional diffusion from the dynamics in which multidimensionality is essential. Specifically, we prove that the coefficient of variation obtained from this distribution cannot possibly exceed 1 for any one-dimensional diffusive model, no matter how rugged its underlying free energy landscape is: In other words, this distribution cannot be broader than the single-exponential one. Thus, a coefficient of variation exceeding 1 is a fingerprint of multidimensional dynamics. Analysis of transition paths in atomistic simulations of proteins shows that this coefficient often exceeds 1, signifying essential multidimensionality of those systems.

Kinetics of Loop Closure in Disordered Proteins: Theory vs Simulations vs Experiments.

We study intrachain dynamics of intrinsically disordered proteins, as manifested by the time scales of loop formation, using atomistic simulations, experiment-parametrized coarse-grained models, and one-dimensional theories assuming Markov or non-Markov dynamics along the reaction coordinate. Despite the generally non-Markov character of monomer dynamics in polymers, we find that the simplest model of one-dimensional diffusion along the reaction coordinate (equated to the distance between the loop-forming monomers) well captures the mean first passage times to loop closure measured in coarse-grained and atomistic simulations, which, in turn, agree with the experimental values. This justifies use of the one-dimensional diffusion model in interpretation of experimental data. At the same time, the transition path times for loop closure in longer polypeptide chains show significant non-Markov effects; at intermediate times, these effects are better captured by the generalized Langevin equation model. At long times, however, atomistic simulations predict long tails in the distributions of transition path times, which are at odds with both the one-dimensional diffusion model and the generalized Langevin equation model.

Generalized Langevin Equation as a Model for Barrier Crossing Dynamics in Biomolecular Folding.

Conformational memory in single-molecule dynamics has attracted recent attention and, in particular, has been invoked as a possible explanation of some of the intriguing properties of transition paths observed in single-molecule force spectroscopy (SMFS) studies. Here we study one candidate for a non-Markovian model that can account for conformational memory, the generalized Langevin equation with a friction force that depends not only on the instantaneous velocity but also on the velocities in the past. The memory in this model is determined by a time-dependent friction memory kernel. We propose a method for extracting this kernel directly from an experimental signal and illustrate its feasibility by applying it to a generalized Rouse model of a SMFS experiment, where the memory kernel is known exactly. Using the same model, we further study how memory affects various statistical properties of transition paths observed in SMFS experiments and evaluate the performance of recent approximate analytical theories of non-Markovian dynamics of barrier crossing. We argue that the same type of analysis can be applied to recent single-molecule observations of transition paths in protein and DNA folding.

Insights into the role of ribonuclease 4 polymorphisms in amyotrophic lateral sclerosis.

Mutations in certain genes of the Ribonuclease (RNASE) superfamily can cause amyotrophic lateral sclerosis (ALS) through altered RNA processing mechanisms. About 30 of these missense mutations in RNASE5/ANG gene have already been reported in ALS patients. In another gene of the ribonuclease superfamily, ribonuclease 4 (RNASE4), missense mutations and single nucleotide polymorphisms have been identified in patients suffering from ALS. However, their plausible molecular mechanisms of association with ALS are not known. Here, we present the molecular mechanisms of RNASE4 polymorphisms with ALS using all-atom molecular dynamics (MD) simulations followed by functional assay experiments. As most ALS causing mutations in RNASE superfamily proteins affect either the ribonucleolytic or nuclear translocation activity, we examined these functional properties of wild-type and known RNASE4 variants, R10W, A98V, E48D and V75I, using MD simulations. Our simulation predicted that these variants would retain nuclear translocation activity and that E48D would exhibit loss of ribonucleolytic activity, which was subsequently validated by ribonucleolytic assay. Our results give a mechanistic insight into the association of RNASE4 polymorphisms with ALS and show that E48D-RNASE4 would probably be deleterious and cause ALS in individuals harbouring this polymorphism.

Transition Path Times in Non-Markovian Activated Rate Processes.

Transition paths are brief excursions taken by molecules when they cross barriers separating stable molecular conformations. When observed in single-molecule experiments, they offer insights into the underlying reaction dynamics and mechanisms. A common model used to analyze transition paths assumes that the dynamics along the reaction coordinate is a memoryless, diffusive process. Recent work, however, suggests that memory effects are often important in the dynamics of the reaction coordinates that can be accessed experimentally. Here we study how memory affects the temporal duration of transition paths using the simple model of dynamics governed by a generalized Langevin equation with an exponential memory kernel. We discuss several approximate theories for the distribution and the mean of the transition path times and test them against numerical simulations. We find that the extreme case of long memory is particularly interesting in that it cannot be described by the existing approximations; yet it can be explained using the view where the non-Markov effects arise as a result of coupling of the reaction coordinate to an auxiliary degree of freedom.

Transition path times reveal memory effects and anomalous diffusion in the dynamics of protein folding.

Recent single-molecule experiments probed transition paths of biomolecular folding and, in particular, measured the time biomolecules spend while crossing their free energy barriers. A surprising finding from these studies is that the transition barriers crossed by transition paths, as inferred from experimentally observed transition path times, are often lower than the independently determined free energy barriers. Here we explore memory effects leading to anomalous diffusion as a possible origin of this discrepancy. Our analysis of several molecular dynamics trajectories shows that the dynamics of common reaction coordinates used to describe protein folding is subdiffusive, at least at sufficiently short times. We capture this effect using a one-dimensional fractional Brownian motion (FBM) model, in which the system undergoes a subdiffusive process in the presence of a potential of mean force, and show that this model yields much broader distributions of transition path times with stretched exponential long-time tails. Without any adjustable parameters, these distributions agree well with the transition path times computed directly from protein trajectories. We further discuss how the FBM model can be tested experimentally.

Design of a Toolbox of RNA Thermometers.

Biomolecular temperature sensors can be used for efficient control of large-volume bioreactors, for spatiotemporal imaging and control of gene expression, and to engineer robustness to temperature in biomolecular circuit design. Although RNA-based sensors, called "thermometers", have been investigated in both natural and synthetic contexts, an important challenge is to design diverse responses to temperature differing in sensitivity and threshold. We address this issue by constructing a library of RNA thermometers based on thermodynamic computations and experimentally measuring their activities in cell-free biomolecular "breadboards". Using free energies of the minimum free energy structures as well as melt profile computations, we estimated that a diverse set of temperature responses were possible. We experimentally found a wide range of responses to temperature in the range 29-37 °C with fold-changes varying over 3-fold around the starting thermometer. The sensitivities of these responses ranged over 10-fold around the starting thermometer. We correlated these measurements with computational expectations, finding that although there was no strong correlation for the individual thermometers, overall trends of diversity, fold-changes, and sensitivities were similar. These results present a toolbox of RNA-based circuit elements with diverse temperature responses.

Theoretical and computational validation of the Kuhn barrier friction mechanism in unfolded proteins.

A long time ago, Kuhn predicted that long polymers should approach a limit where their global motion is controlled by solvent friction alone, with ruggedness of their energy landscapes having no consequences for their dynamics. In contrast, internal friction effects are important for polymers of modest length. Internal friction in proteins, in particular, affects how fast they fold or find their binding targets and, as such, has attracted much recent attention. Here we explore the molecular origins of internal friction in unfolded proteins using atomistic simulations, coarse-grained models and analytic theory. We show that the characteristic internal friction timescale is directly proportional to the timescale of hindered dihedral rotations within the polypeptide chain, with a proportionality coefficient b that is independent of the chain length. Such chain length independence of b provides experimentally testable evidence that internal friction arises from concerted, crankshaft-like dihedral rearrangements. In accord with phenomenological models of internal friction, we find the global reconfiguration timescale of a polypeptide to be the sum of solvent friction and internal friction timescales. At the same time, the time evolution of inter-monomer distances within polypeptides deviates both from the predictions of those models and from a simple, one-dimensional diffusion model.