Characterization of p97 mutations causing multisystem proteinopathy support a gain-of-function model for pathology

Valosin‐containing protein (VCP, or p97) is an ATPase essential in numerous protein quality control (PQC) pathways, such as ER‐associated degradation. p97 functions as a segregase, extracting ubiquitylated proteins from membranes or complexes so they can be degraded by the proteasome. However, the complexity of native p97 PQC substrates has stymied the detailed biochemical study of this function. Previously, to address this problem, we developed an in vitro p97 substrate based on an ubiquitin fusion degradation (UFD) pathway substrate, Ub‐GFP, and showed that the unfolding of this substrate by p97 is dependent upon extensive substrate ubiquitylation, the p97 adaptors NPLOC4‐UFD1L, and ATP hydrolysis. Here, we make use of this system, employing an updated version of this substrate, to explore how mutations in p97 that cause multisystem proteinopathy (MSP) affect substrate processing. Previous studies have shown that MSP mutants have higher basal ATP rates than wild type yet cause deficiencies in many p97‐dependent pathways, creating controversy as to whether these dominantly inherited mutations cause disease through a gain‐of‐function or a loss‐of‐function. We have now analyzed seven distinct MSP mutants, all of which showed modestly improved unfolding of our model substrate over wild type p97, providing evidence that the increased ATPase activity leads to a gain‐of‐function. Furthermore, we showed evidence that p97 inhibitors may restore proper p97 function to MSP mutants, suggesting a potential treatment strategy for p97 diseases

Inter-particle ratchet effect determines global current of heterogeneous particles diffusing in confinement

In a model of $N$ volume-excluding spheres in a $d$-dimensional tube, we consider how differences between particles in their drift velocities, diffusivities, and sizes influence the steady state distribution and axial particle current. We show that the model is exactly solvable when the geometrical constraints prevent any particle from overtaking every other -- a notion we term quasi-one-dimensionality. Then, due to a ratchet effect, the current is biased towards the velocities of the least diffusive particles. We consider special cases of this model in one dimension, and derive the exact joint gap distribution for driven tracers in a passive bath. We describe the relationship between phase space structure and irreversible drift that makes the quasi-one-dimensional supposition key to the model's solvability.Comment: 26 pages, 7 figure

A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension

We compare the fluctuations in the velocity and in the fraction of time spent at a given position for minimal models of a passive and an active particle: an asymmetric random walker and a run-and-tumble particle in continuous time and on a 1D lattice. We compute rate functions and effective dynamics conditioned on large deviations for these observables. While generally different, for a unique and non-trivial choice of rates (up to a rescaling of time) the velocity rate functions for the two models become identical, whereas the effective processes generating the fluctuations remain distinct. This equivalence coincides with a remarkable parity of the spectra of the processes' generators. For the occupation-time problem, we show that both the passive and active particles undergo a prototypical dynamical phase transition when the average velocity is non-vanishing in the long-time limit.Comment: 27 pages, 10 figure

Exact spectral solution of two interacting run-and-tumble particles on a ring lattice

Exact solutions of interacting random walk models, such as 1D lattice gases, offer precise insight into the origin of nonequilibrium phenomena. Here, we study a model of run-and-tumble particles on a ring lattice interacting via hardcore exclusion. We present the exact solution for one and two particles using a generating function technique. For two particles, the eigenvectors and eigenvalues are explicitly expressed using two parameters reminiscent of Bethe roots, whose numerical values are determined by polynomial equations which we derive. The spectrum depends in a complicated way on the ratio of direction reversal rate to lattice jump rate, $\omega$. For both one and two particles, the spectrum consists of separate real bands for large $\omega$, which mix and become complex-valued for small $\omega$. At exceptional values of $\omega$, two or more eigenvalues coalesce such that the Markov matrix is non-diagonalizable. A consequence of this intricate parameter dependence is the appearance of dynamical transitions: non-analytic minima in the longest relaxation times as functions of $\omega$ (for a given lattice size). Exceptional points are theoretically and experimentally relevant in, e.g., open quantum systems and multichannel scattering. We propose that the phenomenon should be a ubiquitous feature of classical nonequilibrium models as well, and of relevance to physical observables in this context.Comment: 29 pages, 7 figures, revised submission to J. Stat. Mec

Exact joint density-current probability function for the asymmetric exclusion process

We study the asymmetric exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach, and by the introduction of new operators satisfying a modified version of the original algebra.Comment: 4 pages, 3 figure

From a microscopic solution to a continuum description of active particles with a recoil interaction in one dimension

We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we find that the stationary inter-particle distribution functions are governed by an inhomogeneous fourth-order differential equation. Our main focus is on determining the boundary conditions that these distribution functions should satisfy. We find that these do not arise naturally from physical considerations, but need to be carefully matched to functional forms that arise from the analysis of an underlying discrete process. The inter-particle distribution functions, or their first derivatives, are generically found to be discontinuous at the boundaries.Comment: 16 pages; 5 figures; published in PR

Combinatorial mappings of exclusion processes

We review various combinatorial interpretations and mappings of stationary-state probabilities of the totally asymmetric, partially asymmetric and symmetric simple exclusion processes (TASEP, PASEP, SSEP respectively). In these steady states, the statistical weight of a configuration is determined from a matrix product, which can be written explicitly in terms of generalised ladder operators. This lends a natural association to the enumeration of random walks with certain properties. Specifically, there is a one-to-many mapping of steady-state configurations to a larger state space of discrete paths, which themselves map to an even larger state space of number permutations. It is often the case that the configuration weights in the extended space are of a relatively simple form (e.g., a Boltzmann-like distribution). Meanwhile, various physical properties of the nonequilibrium steady state - such as the entropy - can be interpreted in terms of how this larger state space has been partitioned. These mappings sometimes allow physical results to be derived very simply, and conversely the physical approach allows some new combinatorial problems to be solved. This work brings together results and observations scattered in the combinatorics and statistical physics literature, and also presents new results. The review is pitched at statistical physicists who, though not professional combinatorialists, are competent and enthusiastic amateurs.Comment: 56 pages, 21 figure

Exact probability function for bulk density and current in the asymmetric exclusion process

We examine the asymmetric simple exclusion process with open boundaries, a paradigm of driven diffusive systems, having a nonequilibrium steady state transition. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Depken and R. Stinchcombe, Phys. Rev. Lett. {\bf 93}, 040602, (2004). In particular we derive an exact form for the joint probability function for the bulk density and current, both for finite systems, and also in the thermodynamic limit. The resulting distribution is non-Gaussian, and while the fluctuations in the current are continuous at the continuous phase transitions, the density fluctuations are discontinuous. The derivations are done by using the standard operator algebraic techniques, and by introducing a modified version of the original operator algebra. As a byproduct of these considerations we also arrive at a novel and very simple way of calculating the normalization constant appearing in the standard treatment with the operator algebra. Like the partition function in equilibrium systems, this normalization constant is shown to completely characterize the fluctuations, albeit in a very different manner.Comment: 10 pages, 4 figure

The cost of stochastic resetting

Resetting a stochastic process has been shown to expedite the completion time of some complex task, such as finding a target for the first time. Here we consider the cost of resetting by associating a cost to each reset, which is a function of the distance travelled during the reset event. We compute the Laplace transform of the joint probability of first passage time $t_f$, number of resets $N$ and resetting cost $C$, and use this to study the statistics of the total cost. We show that in the limit of zero resetting rate the mean cost is finite for a linear cost function, vanishes for a sub-linear cost function and diverges for a super-linear cost function. This result contrasts with the case of no resetting where the cost is always zero. For the case of an exponentially increasing cost function we show that the mean cost diverges at a finite resetting rate. We explain this by showing that the distribution of the cost has a power-law tail with continuously varying exponent that depends on the resetting rate.Comment: 22 pages, 7 figure