Is Actin Filament and Microtubule Growth Reaction- or Diffusion-Limited?

Inside cells of living organisms, actin filaments and microtubules self-assemble and dissemble dynamically by incorporating actin or tubulin from the cell plasma or releasing it into their tips' surroundings. Such reaction-diffusion systems can show diffusion- or reaction-limited behaviour. However, neither limit explains the experimental data: while the offset of the linear relation between growth speed and bulk tubulin density contradicts the diffusion limit, the surprisingly large variance of the growth speed rejects a pure reaction limit. In this Letter, we accommodate both limits and use a Doi-Peliti field-theory model to estimate how diffusive transport is perturbing the chemical reactions at the filament tip. Furthermore, a crossover bulk density is predicted at which the limiting process changes from chemical reactions to diffusive transport. In addition, we explain and estimate larger variances of the growth speed

Theory of Hyperuniformity at the Absorbing State Transition

Hyperuniformity, whereby the static structure factor (or density correlator) obeys $S(q)\sim q^{\varsigma}$ with $\varsigma> 0$, emerges at criticality in systems having multiple absorbing states, such as periodically sheared suspensions. These lie in the conserved directed percolation (C-DP) universality class, for which analytic results for $\varsigma$ are lacking. Specifically, $\varsigma$ appears inaccessible within an exact `interfacial mapping' that yields other C-DP exponents via functional renormalization group (FRG). Here, using Doi-Peliti field theory for interacting particles and perturbative RG about a Gaussian model, we find $\varsigma = 0^+$ and $\varsigma= 2\epsilon/9 + O(\epsilon^2)$ in dimension $d>4$ and $d=4-\epsilon$ respectively. The latter disproves a previously conjectured scaling relation for $\varsigma$. We show how hyperuniformity emerges from anticorrelation of strongly fluctuating active and passive densities. Our calculations also yield the remaining C-DP exponents without recourse to functional RG methods

Active Ising Models of Flocking: A Field-Theoretic Approach

Using an approach based on Doi-Peliti field theory, we study several different Active Ising Models (AIMs), in each of which collective motion (flocking) of self-propelled particles arises from the spontaneous breaking of a discrete symmetry. We test the predictive power of our field theories by deriving the hydrodynamic equations for the different microscopic choices of aligning processes that define our various models. At deterministic level, the resulting equations largely confirm known results, but our approach has the advantage of allowing systematic generalization to include noise terms. Study of the resulting hydrodynamics allows us to confirm that the various AIMs share the same phenomenology of a first order transition from isotropic to flocked states whenever the self propulsion speed is nonzero, with an important exception for the case where particles align only pairwise locally. Remarkably, this variant fails entirely to give flocking -- an outcome that was foreseen in previous work, but is confirmed here and explained in terms of the scalings of various terms in the hydrodynamic limit. Finally, we discuss our AIMs in the limit of zero self-propulsion where the ordering transition is continuous. In this limit, each model is still out of equilibrium because the dynamical rules continue to break detailed balance, yet it has been argued that an equilibrium universality class (Model C) prevails. We study field-theoretically the connection between our AIMs and Model C, arguing that these particular models (though not AIMs in general) lie outside the Model C class. We link this to the fact that in our AIMs without self propulsion, detailed balance is not merely still broken, but replaced by a different dynamical symmetry in which the dynamics of the particle density is independent of the spin state.Comment: 16+8 page

Time-dependent branching processes: a model of oscillating neuronal avalanches

Funder: Engineering and Physical Sciences Research Council; doi: http://dx.doi.org/10.13039/501100000266Abstract: Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary continuous-time branching processes with constant extinction and branching rates are commonly used as models of neuronal activity, yet they lack any such time-dependence. In the present work, we extend a basic branching process by allowing the extinction rate to oscillate in time as a new model to describe cortical dynamics. By means of a perturbative field theory, we derive relevant observables in closed form. We support our findings by quantitative comparison to numerics and qualitative comparison to available experimental results

Range assessment in particle therapy based on prompt gamma-ray timing measurements

Proton and ion beams open up new vistas for the curative treatment of tumors, but adequate technologies for monitoring the compliance of dose delivery with treatment plans in real time are still missing. Range assessment, meaning the monitoring of therapy-particle ranges in tissue during dose delivery (treatment), is a continuous challenge considered a key for tapping the full potential of particle therapies. In this context the paper introduces an unconventional concept of range assessment by prompt-gamma timing (PGT), which is based on an elementary physical effect not considered so far: therapy particles penetrating tissue move very fast, but still need a finite transit time-about 1-2 ns in case of protons with a 5-20 cm range-from entering the patient's body until stopping in the target volume. The transit time increases with the particle range. This causes measurable effects in PGT spectra, usable for range verification. The concept was verified by proton irradiation experiments at the AGOR cyclotron, KVI-CART, University of Groningen. Based on the presented kinematical relations, we describe model calculations that very precisely reproduce the experimental results. As the clinical treatment conditions entail measurement constraints (e.g. limited treatment time), we propose a setup, based on clinical irradiation conditions, capable of determining proton range deviations within a few seconds of irradiation, thus allowing for a fast safety survey. Range variations of 2 mm are expected to be clearly detectable

Structural variation and introgression from wild populations in East Asian cattle genomes confer adaptation to local environment

BACKGROUND: Structural variations (SVs) in individual genomes are major determinants of complex traits, including adaptability to environmental variables. The Mongolian and Hainan cattle breeds in East Asia are of taurine and indicine origins that have evolved to adapt to cold and hot environments, respectively. However, few studies have investigated SVs in East Asian cattle genomes and their roles in environmental adaptation, and little is known about adaptively introgressed SVs in East Asian cattle. RESULTS: In this study, we examine the roles of SVs in the climate adaptation of these two cattle lineages by generating highly contiguous chromosome-scale genome assemblies. Comparison of the two assemblies along with 18 Mongolian and Hainan cattle genomes obtained by long-read sequencing data provides a catalog of 123,898 nonredundant SVs. Several SVs detected from long reads are in exons of genes associated with epidermal differentiation, skin barrier, and bovine tuberculosis resistance. Functional investigations show that a 108-bp exonic insertion in SPN may affect the uptake of Mycobacterium tuberculosis by macrophages, which might contribute to the low susceptibility of Hainan cattle to bovine tuberculosis. Genotyping of 373 whole genomes from 39 breeds identifies 2610 SVs that are differentiated along a "north-south" gradient in China and overlap with 862 related genes that are enriched in pathways related to environmental adaptation. We identify 1457 Chinese indicine-stratified SVs that possibly originate from banteng and are frequent in Chinese indicine cattle. CONCLUSIONS: Our findings highlight the unique contribution of SVs in East Asian cattle to environmental adaptation and disease resistance

Topics in statistical mechanics

This thesis aims to showcase the versatility of statistical mechanics. It splits into two parts: firstly, applications of Doi-Peliti field theory to filament growth and branching processes, and secondly, wetting phenomena on structured surfaces. In Chapter 1, I derive the Doi-Peliti field theory; the derivation starts with stochastic processes that obey the Markov property and goes on to link them to the master equation. It is then recast as a partial differential equation of the probability generating function, the solution of which is found perturbatively with the Doi-Peliti path integral. This path integral formulation is used in Chapter 2 to model continuous-time branching processes. The critical behaviour of these processes is studied analytically and corroborated with simulations. The results were also published in [51] and show a natural link between the mathematics of stochastic processes and Doi-Peliti field theory. The field theory is then applied to the reaction-diffusion process of filament growth in Chapter 3. The filaments are polymers found in cells of living organisms, which assemble by incorporating their building blocks from the environment. However, if the environment does not contain enough building blocks, the filaments disassemble. The stochastic switching between disassembly and assembly leads to intriguing dynamics. Some of the results are part of a published article [118]. Statistical mechanics is also concerned with equilibrium phenomena. A class of these phenomena is studied in Chapter 4 in the context of wetting. Wetting occurs when a fluid forms a liquid film on a solid surface. If the surface is structured, i.e. has edges or corners, the occurrence of phase transitions of the liquid film depends on its specific structure. The structured surfaces studied in this thesis are the wedge and the apex; the results for them were also published in [133].Open Acces

From neuronal spikes to avalanches: Effects and circumvention of time binning

Branching with immigration is one of the most common models for the stochastic processes observed in neuronal circuits. However, it is not observed directly and, in order to create branching-like processes, the observed spike time series is processed by attaching time bins to spikes. It has been shown that results such as criticality and size distributions depend on the chosen time bin. A different methodology whose results do not depend on the choice of time bin might therefore be useful and is proposed in this article. This methodology circumvents using time bins altogether by replacing the previously used discrete-time models by continuous-time models. First, the article introduces and characterizes a continuous-time version of the branching process with immigration, which will be called the pumped branching process, and second, it presents an analytical derivation of the corresponding spike statistics, which can be directly compared to observed spike time series. The presented approach allows determining the degree of criticality, the average number of overlapping avalanches, and other observables without using a time bin. Furthermore, the effects caused by using time bins are analyzed and the influence of temporal and spatial subsampling discussed, all of which is compared to experimental data and supported by Monte Carlo simulations

Time-dependent branching processes: a model of oscillating neuronal avalanches

Funder: Engineering and Physical Sciences Research Council; doi: http://dx.doi.org/10.13039/501100000266Abstract: Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary continuous-time branching processes with constant extinction and branching rates are commonly used as models of neuronal activity, yet they lack any such time-dependence. In the present work, we extend a basic branching process by allowing the extinction rate to oscillate in time as a new model to describe cortical dynamics. By means of a perturbative field theory, we derive relevant observables in closed form. We support our findings by quantitative comparison to numerics and qualitative comparison to available experimental results