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Journal articleChen L, Pruessner G, Hoai NH, 2024,
Correlation, crossover and broken scaling in the Abelian Manna Model, Physical Review Research, ISSN: 2643-1564
Journal articleZhang Z, Fehértói-Nagy L, Polackova M, et al., 2024,
The active Brownian particle (ABP) model exemplifies a wide class of active matter particles. In this work, we demonstrate how this model can be cast into a field theory in both two and three dimensions. Our aim is manifold: we wish both to extract useful features of the system, as well as to build a framework which can be used to study more complex systems involving ABPs, such as those involving interaction. Using the two-dimensional model as a template, we calculate the mean squared displacement exactly, and the one-point density in an external potential perturbatively. We show how the effective diffusion constant appears in the barometric density formula to leading order, and determine the corrections to it. We repeat the calculation in three dimensions, clearly a more challenging setup. Comparing different ways to capture the self-propulsion, we find that its perturbative treatment results in more tractable derivations without loss of exactness, where this is accessible.
Journal articleCocconi L, Knight J, Roberts C, 2023,
We identify generic protocols achieving optimal power extraction from a single active particle subject to continuous feedback control under the assumption that its spatial trajectory, but not its instantaneous self-propulsion force, is accessible to direct observation. Our Bayesian approach draws on the Onsager-Machlup path integral formalism and is exemplified in the cases of free run-and-tumble and active Ornstein-Uhlenbeck dynamics in one dimension. Such optimal protocols extract positive work even in models characterized by time-symmetric positional trajectories and thus vanishing informational entropy production rates. We argue that the theoretical bounds derived in this work are those against which the performance of realistic active matter engines should be compared.
Journal articleRoberts C, Zhen Z, 2023,
Run-and-tumble motion in a linear ratchet potential: Analytic solution, power extraction, and first-passage properties., Phys Rev E, Vol: 108
We explore the properties of run-and-tumble particles moving in a piecewise-linear "ratchet" potential by deriving analytic results for the system's steady-state probability density, current, entropy production rate, extractable power, and thermodynamic efficiency. The ratchet's broken spatial symmetry rectifies the particles' self-propelled motion, resulting in a positive current that peaks at finite values of the diffusion strength, ratchet height, and particle self-propulsion speed. Similar nonmonotonic behavior is also observed for the extractable power and efficiency. We find the optimal apex position for generating maximum current varies with diffusion and that entropy production can have nonmonotonic dependence on diffusion. In particular, for vanishing diffusion, entropy production remains finite when particle self-propulsion is weaker than the ratchet force. Furthermore, power extraction with near-perfect efficiency is achievable in certain parameter regimes due to the simplifications afforded by modeling "dry" active particles. In the final part, we derive mean first-passage times and splitting probabilities for different boundary and initial conditions. This work connects the study of work extraction from active matter with exactly solvable active particle models and will therefore facilitate the design of active engines through these analytic results.
Journal articleBothe M, Cocconi L, Zhen Z, et al., 2023,
We introduce a procedure to test a theory for point particle entity, that is, whether said theory takes into account the discrete nature of the constituents of the system. We then identify the mechanism whereby particle entity is enforced in the context of two field-theoretic frameworks designed to incorporate the particle nature of the degrees of freedom, namely the Doi-Peliti field theory and the response field theory that derives from Dean's equation. While the Doi-Peliti field theory encodes the particle nature at a very fundamental level that is easily revealed, demonstrating the same for Dean's equation is more involved and results in a number of surprising diagrammatic identities. We derive those and discuss their implications. These results are particularly pertinent in the context of active matter, whose surprising and often counterintuitive phenomenology rests wholly on the particle nature of the agents and their degrees of freedom as particles.
Journal articleWalter B, Pruessner G, Salbreux G, 2022,
Field theory of survival probabilities, extreme values, first-passage times, and mean span of non-Markovian stochastic processes, Physical Review Research, Vol: 4, Pages: 1-21, ISSN: 2643-1564
We provide a perturbative framework to calculate extreme events ofnon-Markovian processes, by mapping the stochastic process to a two-speciesreaction diffusion process in a Doi-Peliti field theory combined with theMartin-Siggia-Rose formalism. This field theory treats interactions and theeffect of external, possibly self-correlated noise in a perturbation about aMarkovian process, thereby providing a systematic, diagrammatic approach toextreme events. We apply the formalism to Brownian Motion and calculate itssurvival probability distribution subject to self-correlated noise.
Working paperCocconi L, Knight J, Roberts C, 2022,
Optimal power extraction from active particles with hidden states, Publisher: arXiv
We identify generic protocols achieving optimal power extraction from asingle active particle subject to continuous feedback control under theassumption that the instantaneous velocity, but not the fluctuatingself-propulsion velocity, is accessible to direct observation. Our Bayesianapproach draws on the Onsager-Machlup path integral formalism and isexemplified in the cases of free run-and-tumble and active Ornstein-Uhlenbeckdynamics in one dimension. Such optimal protocols extract positive work even inmodels characterised by time-symmetric positional trajectories and thusvanishing informational entropy production rates. We argue that the theoreticalbounds derived in this work are those against which the performance ofrealistic active matter engines should be compared.
Journal articleGuo Y, Al-Jibury E, Garcia-Millan R, et al., 2022,
Complex genomes show intricate organization in three-dimensional (3D) nuclear space. Current models posit that cohesin extrudes loops to form self-interacting domains delimited by the DNA binding protein CTCF. Here, we describe and quantitatively characterize cohesin-propelled, jet-like chromatin contacts as landmarks of loop extrusion in quiescent mammalian lymphocytes. Experimental observations and polymer simulations indicate that narrow origins of loop extrusion favor jet formation. Unless constrained by CTCF, jets propagate symmetrically for 1-2 Mb, providing an estimate for the range of in vivo loop extrusion. Asymmetric CTCF binding deflects the angle of jet propagation as experimental evidence that cohesin-mediated loop extrusion can switch from bi- to unidirectional and is controlled independently in both directions. These data offer new insights into the physiological behavior of in vivo cohesin-mediated loop extrusion and further our understanding of the principles that underlie genome organization.
Journal articleRoberts C, Pruessner G, 2022,
We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by exploiting an elegant underlying structure of the perturbationtheory. We calculate the particle densities, currents and variance as well as characteristics of the boundary tumbling. The analytical findings, in agreement with Monte-Carlo simulations, show how the particle densities are linked to the scale of diffusive fluctuations at the boundaries. The generality of our approach suggests it could be readily applied to similar problems described by Fokker-Planck equations containing localised reaction terms.
Journal articleCocconi L, Salbreux G, Pruessner G, 2022,
Entropy production plays a fundamental role in the study of non-equilibriumsystems by offering a quantitative handle on the degree of time-reversalsymmetry breaking. It depends crucially on the degree of freedom considered aswell as on the scale of description. It was hitherto unknown how the entropyproduction at one resolution of the degrees of freedom is related to theentropy production at another resolution. This relationship is of particularrelevance to coarse grained and continuum descriptions of a given phenomenon.In this work, we derive the scaling of the entropy production under iterativecoarse graining on the basis of the correlations of the underlying microscopictransition rates. Our approach unveils a natural criterion to distinguishequilibrium-like and genuinely non-equilibrium macroscopic phenomena based onthe sign of the scaling exponent of the entropy production per mesostate.
Journal articleZhang Z, Pruessner G, 2022,
In this work, Doi–Peliti field theory is used to describe the motion of free run and tumble particles in arbitrary dimensions. After deriving action and propagators, the mean squared displacement and the corresponding entropy production at stationarity are calculated in this framework. We further derive the field theory of free active Brownian particles in two dimensions for comparison.
Journal articleGarcia-Millan R, Pruessner G, 2021,
Run-and-tumble (RnT) motion is an example of active motility where particles move at constant speed and change direction at random times. In this work we study RnT motion with diffusion in a harmonic potential in one dimension via a path integral approach. We derive a Doi-Peliti field theory and use it to calculate the entropy production and other observables in closed form. All our results are exact.
Journal articleBothe M, Pruessner G, 2021,
We derive a Doi-Peliti field theory for free active Ornstein-Uhlenbeck particles, or, equivalently, free inertial Brownian particles, and present a way to diagonalize the quadratic part of the action and calculate the propagator. Unlike previous coarse-grained approaches this formulation correctly tracks particle identity and yet can easily be expanded to include potentials and arbitrary reactions.
Journal articleNesbitt D, Pruessner G, Lee CF, 2021,
Uncovering novel phase transitions in dense dry polar active fluids using a lattice Boltzmann method, New Journal of Physics, Vol: 23, ISSN: 1367-2630
The dynamics of dry active matter have implications for a diverse collection of biological phenomena spanning a range of length and time scales, such as animal flocking, cell tissue dynamics, and swarming of inserts and bacteria. Uniting these systems are a common set of symmetries and conservation laws, defining dry active fluids as a class of physical system. Many interesting behaviours have been observed at high densities, which remain difficult to simulate due to the computational demand. Here, we show how two-dimensional dry active fluids in a dense regime can be studied using a simple modification of the lattice Boltzmann method. We apply our method on a model that exhibits motility-induced phase separation, and an active model with contact inhibition of locomotion, which has relevance to collective cell migration. For the latter, we uncover multiple novel phase transitions: two first-order and one potentially critical. We further support our simulation results with an analytical treatment of the hydrodynamic equations obtained via the Chapman-Enskog coarse-graining procedure.
Journal articleAmarteifio S, Fallesen T, Pruessner G, et al., 2021,
BackgroundParticle-tracking in 3D is an indispensable computational tool to extract critical information on dynamical processes from raw time-lapse imaging. This is particularly true with in vivo time-lapse fluorescence imaging in cell and developmental biology, where complex dynamics are observed at high temporal resolution. Common tracking algorithms used with time-lapse data in fluorescence microscopy typically assume a continuous signal where background, recognisable keypoints and independently moving objects of interest are permanently visible. Under these conditions, simple registration and identity management algorithms can track the objects of interest over time. In contrast, here we consider the case of transient signals and objects whose movements are constrained within a tissue, where standard algorithms fail to provide robust tracking.ResultsTo optimize 3D tracking in these conditions, we propose the merging of registration and tracking tasks into a registration algorithm that uses random sampling to solve the identity management problem. We describe the design and application of such an algorithm, illustrated in the domain of plant biology, and make it available as an open-source software implementation. The algorithm is tested on mitotic events in 4D data-sets obtained with light-sheet fluorescence microscopy on growing Arabidopsis thaliana roots expressing CYCB::GFP. We validate the method by comparing the algorithm performance against both surrogate data and manual tracking.ConclusionThis method fills a gap in existing tracking techniques, following mitotic events in challenging data-sets using transient fluorescent markers in unregistered images.
Journal articleWalter B, Pruessner G, Salbreux G, 2021,
We introduce a perturbative method to calculate all moments of thefirst-passage time distribution in stochastic one-dimensional processes whichare subject to both white and coloured noise. This class of non-Markovianprocesses is at the centre of the study of thermal active matter, that isself-propelled particles subject to diffusion. The perturbation theory aboutthe Markov process considers the effect of self-propulsion to be small comparedto that of thermal fluctuations. To illustrate our method, we apply it to thecase of active thermal particles (i) in a harmonic trap (ii) on a ring. Forboth we calculate the first-order correction of the moment-generating functionof first-passage times, and thus to all its moments. Our analytical results arecompared to numerics.
Journal articleCocconi L, Garcia Millan R, Zhen Z, et al., 2020,
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which global detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms.
Journal articleBordeu Weldt I, Garcin C, Habib SJ, et al., 2020,
Cell signalling is essential for cell fate determination and tissue patterning. As signalling ligandsare presented to the receiving cell, they are recruited and recognised by the cell membrane as to elicita biological response and to pattern multicellular tissues. Cells can accumulate and transport theseligands, which results in an emergent organisation of the ligands' spatial distribution. To study thisorganisation, we make use of a simpli ed experimental setup, in which single mouse embryonic stemcells (mESCs) can interact with immobilized ligands. We introduce a two species age-dependentcorrelation function that allows the description and quanti cation of the spatio-temporal dynamicsof single cell-ligand interactions. Through the analysis of mESC data and numerical simulations weshow that cells act as e ective force- eld generators, perturbing and organising their environment.This organisation, captured in the form of an ageing e ective potential, is an emergent property ofthe population of single cells interacting with randomly distributed localized ligands.
Journal articlePausch J, Garcia-Millan R, Pruessner G, 2020,
Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existenceof a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinarycontinuous-time branching processes with constant extinction and branching rates are commonly used as models of neuronalactivity, yet they lack any such time-dependence. In the present work, we extend a basic branching process by allowing theextinction rate to oscillate in time as a new model to describe cortical dynamics. By means of a perturbative field theory, wederive relevant observables in closed form. We support our findings by quantitative comparison to numerics and qualitativecomparison to available experimental results.
Journal articleHiratsuka T, Bordeu I, Pruessner G, et al., 2020,
Regulation of ERK basal and pulsatile activity control proliferation and exit from the stem cell compartment in mammalian epidermis., Proceedings of the National Academy of Sciences of USA, Vol: 117, Pages: 17796-17807, ISSN: 0027-8424
Fluctuation in signal transduction pathways is frequently observed during mammalian development. However, its role in regulating stem cells has not been explored. Here we tracked spatiotemporal ERK MAPK dynamics in human epidermal stem cells. While stem cells and differentiated cells were distinguished by high and low stable basal ERK activity, respectively, we also found cells with pulsatile ERK activity. Transitions from Basalhi-Pulselo (stem) to Basalhi-Pulsehi, Basalmid-Pulsehi, and Basallo-Pulselo (differentiated) cells occurred in expanding keratinocyte colonies and in response to differentiation stimuli. Pharmacological inhibition of ERK induced differentiation only when cells were in the Basalmid-Pulsehi state. Basal ERK activity and pulses were differentially regulated by DUSP10 and DUSP6, leading us to speculate that DUSP6-mediated ERK pulse down-regulation promotes initiation of differentiation, whereas DUSP10-mediated down-regulation of mean ERK activity promotes and stabilizes postcommitment differentiation. Levels of MAPK1/MAPK3 transcripts correlated with DUSP6 and DUSP10 transcripts in individual cells, suggesting that ERK activity is negatively regulated by transcriptional and posttranslational mechanisms. When cells were cultured on a topography that mimics the epidermal-dermal interface, spatial segregation of mean ERK activity and pulses was observed. In vivo imaging of mouse epidermis revealed a patterned distribution of basal cells with pulsatile ERK activity, and down-regulation was linked to the onset of differentiation. Our findings demonstrate that ERK MAPK signal fluctuations link kinase activity to stem cell dynamics.
Journal articleGcina M, Luca C, Pruessner G, et al., 2020,
Among observables characterizing the random exploration of a graph or lattice, the cover time, namely, the time to visit every site, continues to attract widespread interest. Much insight about cover times is gained by mapping to the (spaceless) coupon collector problem, which amounts to ignoring spatiotemporal correlations, and an early conjecture that the limiting cover time distribution of regular random walks on large lattices converges to the Gumbel distribution in d≥3 was recently proved rigorously. Furthermore, a number of mathematical and numerical studies point to the robustness of the Gumbel universality to modifications of the spatial features of the random search processes (e.g., introducing persistence and/or intermittence, or changing the graph topology). Here we investigate the robustness of the Gumbel universality to dynamical modification of the temporal features of the search, specifically by allowing the random walker to “accelerate” or “decelerate” upon visiting a previously unexplored site. We generalize the mapping mentioned above by relating the statistics of cover times to the roughness of 1/fα Gaussian signals, leading to the conjecture that the Gumbel distribution is but one of a family of cover time distributions, ranging from Gaussian for highly accelerated cover, to exponential for highly decelerated cover. While our conjecture is confirmed by systematic Monte Carlo simulations in dimensions d>3, our results for acceleration in d=3 challenge the current understanding of the role of correlations in the cover time problem.
Working paperAmarteifio S, Fallesen T, Pruessner G, et al., 2020,
Journal articleBordeu Weldt I, Amarteifio S, Garcia Millan R, et al., 2019,
Branching processes are used to model diverse social and physical scenarios, from extinction of family names to nuclear fission. However, for a better description of natural phenomena, such as viral epidemics in cellular tissues, animal populations and social networks, a spatial embedding---the branching random walk (BRW)---is required. Despite its wide range of applications, the properties of the volume explored by the BRW so far remained elusive, with exact results limited to one dimension. Here we present analytical results, supported by numerical simulations, on the scaling of the volume explored by a BRW in the critical regime, the onset of epidemics, in general environments. Our results characterise the spreading dynamics on regular lattices and general graphs, such as fractals, random trees and scale-free networks, revealing the direct relation between the graphs' dimensionality and the rate of propagation of the viral process. Furthermore, we use the BRW to determine the spectral properties of real social and metabolic networks, where we observe that a lack of information of the network structure can lead to differences in the observed behaviour of the spreading process. Our results provide observables of broad interest for the characterisation of real world lattices, tissues, and networks.
Journal articleWei N, Pruessner G, 2019,
A multitype branching process is introduced to mimic the evolution of the avalanche activity and determine the critical density of the Abelian Manna model. This branching process incorporates partially the spatiotemporal correlations of the activity, which are essential for the dynamics, in particular in low dimensions. An analytical expression for the critical density in arbitrary dimensions is derived, which significantly improves the results over mean-field theories, as confirmed by comparison to the literature on numerical estimates from simulations. The method can easily be extended to lattices and dynamics other than those studied in the present work.
Journal articlePausch J, Pruessner G, 2019,
Inside cells of living organisms, actin filaments and microtubules selfassemble 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 article, 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 bulkdensity 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.
Journal articleDuarte D, Amarteifio S, Ang H, et al., 2019,
The majority of acute myeloid leukemia (AML) patients have a poor response to conventional chemotherapy. The survival of chemoresistant cells is thought to depend on leukemia-bone marrow (BM) microenvironment interactions, which are not well understood. The CXCL12/CXCR4 axis has been proposed to support AML growth but was not studied at the single AML cell level. We recently showed that T-cell acute lymphoblastic leukemia (T-ALL) cells are highly motile in the BM; however, the characteristics of AML cell migration within the BM remain undefined. Here, we characterize the in vivo migratory behavior of AML cells and their response to chemotherapy and CXCR4 antagonism, using high-resolution 2-photon and confocal intravital microscopy of mouse calvarium BM and the well-established MLL-AF9-driven AML mouse model. We used the Notch1-driven T-ALL model as a benchmark comparison and AMD3100 for CXCR4 antagonism experiments. We show that AML cells are migratory, and in contrast with T-ALL, chemoresistant AML cells become less motile. Moreover, and in contrast with T-ALL, the in vivo exploratory behavior of expanding and chemoresistant AML cells is unaffected by AMD3100. These results expand our understanding of AML cells-BM microenvironment interactions, highlighting unique traits of leukemia of different lineages.
Journal articleReijne A-M, Bordeu I, Pruessner G, et al., 2018,
One of the key characteristics of multicellular organisms is the ability to establish and maintain shapes, or morphologies, under a variety of physical and chemical perturbations. A quantitative description of the underlying morphological dynamics is a critical step to fully understand the self-organising properties of multicellular systems. Although many powerful mathematical tools have been developed to analyse stochastic dynamics, rarely these are applied to experimental developmental biology.Here, we take root tip regeneration in the plant model system Arabidopsis thaliana as an example of robust morphogenesis in living tissue, and present a novel approach to quantify and model the relaxation of the system to its unperturbed morphology. By generating and analysing time-lapse series of regenerating root tips captured with confocal microscopy, we are able to extract and model the dynamics of key morphological traits at cellular resolution. We present a linear stability analysis of its Markovian dynamics, with the stationary state representing the intact root in the space of morphological traits. This analysis suggests the intriguing co-existence of two distinct temporal scales during the process of root regeneration in Arabidopsis.We discuss the possible biological implications of our specific results, and suggest future experiments to further probe the self-organising properties of living tissue.
Journal articleGarcia Millan R, Pausch J, Walter B, et al., 2018,
Branching processes are widely used to model phenomena from networks to neuronal avalanching. In a large class of continuous-time branching processes, we study the temporal scaling of the moments of the instant population size, the survival probability, expected avalanche duration, the so-called avalanche shape, the n-point correlation function, and the probability density function of the total avalanche size. Previous studies have shown universality in certain observables of branching processes using probabilistic arguments; however, a comprehensive description is lacking. We derive the field theory that describes the process and demonstrate how to use it to calculate the relevant observables and their scaling to leading order in time, revealing the universality of the moments of the population size. Our results explain why the first and second moment of the offspring distribution are sufficient to fully characterize the process in the vicinity of criticality, regardless of the underlying offspring distribution. This finding implies that branching processes are universal. We illustrate our analytical results with computer simulations.
Journal articleJensen HJ, Pazuki RH, Pruessner G, et al., 2018,
The volume of phase space may grow super-exponentially ('explosively') with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create new emergent states. Standard ensemble theory can break down as we demonstrate in a simple model reminiscent of complex systems where new collective states emerge. We present an axiomatically defined entropy and argue that it is extensive in the micro-canonical, equal probability, and canonical (max-entropy) ensemble for super-exponentially growing phase spaces. This entropy may be useful in determining probability measures in analogy with how statistical mechanics establishes statistical ensembles by maximising entropy.
Journal articleGarcia Millan R, Pruessner G, Pickering L, et al., 2018,
Certain random processes display anticorrelations resulting in local Poisson-like disorder and global order, where correlations suppress fluctuations. Such processes are called hyperuniform. Using a map to an interface picture we show via analytic calculations that a sequence of avalanche sizes of the Oslo model is hyperuniform in the temporal domain with the minimal exponent $\lambda=0$ . We identify the conserved quantity in the interface picture that gives rise to the hyperuniformity in the avalanche size. We further discuss the fluctuations of the avalanche size in two variants of the Oslo model. We support our findings with numerical results.
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