Galvanotaxis is believed to be driven by the redistribution of transmembrane proteins and other molecules, referred to as "sensors", through electrophoresis and electroosmosis. Here, we update our previous model of the limits of galvanotaxis due to stochasticity of sensor movements to account for cell shape and orientation. Computing the Fisher information, we find that cells in principle possess more information about the electric field direction when their long axis is parallel to the field, but that for weak fields maximum-likelihood estimators of the field direction may actually have lower variability when the cell's long axis is perpendicular to the field. In an alternate possibility, we find that if cells instead estimate the field direction by taking the average of all the sensor locations as its directional cue ("vector sum"), this introduces a bias towards the short axis, an effect not present for isotropic cells. We also explore the possibility that cell elongation arises downstream of sensor redistribution. We argue that if sensors migrate to the cell's rear, the cell will expand perpendicular the field - as is more commonly observed - but if sensors migrate to the front, the cell will elongate parallel to the field.
{"title":"Physical limits on galvanotaxis depends on cell morphology and orientation","authors":"Ifunanya Nwogbaga, Brian A. Camley","doi":"arxiv-2407.17420","DOIUrl":"https://doi.org/arxiv-2407.17420","url":null,"abstract":"Galvanotaxis is believed to be driven by the redistribution of transmembrane\u0000proteins and other molecules, referred to as \"sensors\", through electrophoresis\u0000and electroosmosis. Here, we update our previous model of the limits of\u0000galvanotaxis due to stochasticity of sensor movements to account for cell shape\u0000and orientation. Computing the Fisher information, we find that cells in\u0000principle possess more information about the electric field direction when\u0000their long axis is parallel to the field, but that for weak fields\u0000maximum-likelihood estimators of the field direction may actually have lower\u0000variability when the cell's long axis is perpendicular to the field. In an\u0000alternate possibility, we find that if cells instead estimate the field\u0000direction by taking the average of all the sensor locations as its directional\u0000cue (\"vector sum\"), this introduces a bias towards the short axis, an effect\u0000not present for isotropic cells. We also explore the possibility that cell\u0000elongation arises downstream of sensor redistribution. We argue that if sensors\u0000migrate to the cell's rear, the cell will expand perpendicular the field - as\u0000is more commonly observed - but if sensors migrate to the front, the cell will\u0000elongate parallel to the field.","PeriodicalId":501321,"journal":{"name":"arXiv - QuanBio - Cell Behavior","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Collective migration is a phenomenon observed in various biological systems, where the cooperation of multiple cells leads to complex functions beyond individual capabilities, such as in immunity and development. A distinctive example is cell populations that not only ascend attractant gradient originating from targets, such as damaged tissue, but also actively modify the gradient, through their own production and degradation. While the optimality of single-cell information processing has been extensively studied, the optimality of the collective information processing that includes gradient sensing and gradient generation, remains underexplored. In this study, we formulated a cell population that produces and degrades an attractant while exploring the environment as an agent population performing distributed reinforcement learning. We demonstrated the existence of optimal couplings between gradient sensing and gradient generation, showing that the optimal gradient generation qualitatively differs depending on whether the gradient sensing is logarithmic or linear. The derived dynamics have a structure homogeneous to the Keller-Segel model, suggesting that cell populations might be learning. Additionally, we showed that the distributed information processing structure of the agent population enables a proportion of the population to robustly accumulate at the target. Our results provide a quantitative foundation for understanding the collective information processing mediated by attractants in extracellular environments.
{"title":"Understanding cell populations sharing information through the environment, as reinforcement learning","authors":"Masaki Kato, Tetsuya J. Kobayashi","doi":"arxiv-2407.15298","DOIUrl":"https://doi.org/arxiv-2407.15298","url":null,"abstract":"Collective migration is a phenomenon observed in various biological systems,\u0000where the cooperation of multiple cells leads to complex functions beyond\u0000individual capabilities, such as in immunity and development. A distinctive\u0000example is cell populations that not only ascend attractant gradient\u0000originating from targets, such as damaged tissue, but also actively modify the\u0000gradient, through their own production and degradation. While the optimality of\u0000single-cell information processing has been extensively studied, the optimality\u0000of the collective information processing that includes gradient sensing and\u0000gradient generation, remains underexplored. In this study, we formulated a cell\u0000population that produces and degrades an attractant while exploring the\u0000environment as an agent population performing distributed reinforcement\u0000learning. We demonstrated the existence of optimal couplings between gradient\u0000sensing and gradient generation, showing that the optimal gradient generation\u0000qualitatively differs depending on whether the gradient sensing is logarithmic\u0000or linear. The derived dynamics have a structure homogeneous to the\u0000Keller-Segel model, suggesting that cell populations might be learning.\u0000Additionally, we showed that the distributed information processing structure\u0000of the agent population enables a proportion of the population to robustly\u0000accumulate at the target. Our results provide a quantitative foundation for\u0000understanding the collective information processing mediated by attractants in\u0000extracellular environments.","PeriodicalId":501321,"journal":{"name":"arXiv - QuanBio - Cell Behavior","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The fractional Brownian motion (fBm) is a paradigmatic strongly non-Markovian process with broad applications in various fields. Despite their importance, the properties of the territory covered by a $d$-dimensional fBm have remained elusive so far. Here, we study the visitation dynamics of the fBm by considering the time $tau_n$ required to visit a site, defined as a unit cell of a $d$-dimensional lattice, when $n$ sites have been visited. Relying on scaling arguments, we determine all temporal regimes of the probability distribution function of $tau_n$. These results are confirmed by extensive numerical simulations that employ large-deviation Monte Carlo algorithms. Besides these theoretical aspects, our results account for the tracking data of telomeres in the nucleus of mammalian cells, microspheres in an agorose gel, and vacuoles in the amoeba, which are experimental realizations of fBm.
{"title":"Visitation Dynamics of $d$-Dimensional Fractional Brownian Motion","authors":"L. Régnier, M. Dolgushev, O. Bénichou","doi":"arxiv-2407.11655","DOIUrl":"https://doi.org/arxiv-2407.11655","url":null,"abstract":"The fractional Brownian motion (fBm) is a paradigmatic strongly non-Markovian\u0000process with broad applications in various fields. Despite their importance,\u0000the properties of the territory covered by a $d$-dimensional fBm have remained\u0000elusive so far. Here, we study the visitation dynamics of the fBm by\u0000considering the time $tau_n$ required to visit a site, defined as a unit cell\u0000of a $d$-dimensional lattice, when $n$ sites have been visited. Relying on\u0000scaling arguments, we determine all temporal regimes of the probability\u0000distribution function of $tau_n$. These results are confirmed by extensive\u0000numerical simulations that employ large-deviation Monte Carlo algorithms.\u0000Besides these theoretical aspects, our results account for the tracking data of\u0000telomeres in the nucleus of mammalian cells, microspheres in an agorose gel,\u0000and vacuoles in the amoeba, which are experimental realizations of fBm.","PeriodicalId":501321,"journal":{"name":"arXiv - QuanBio - Cell Behavior","volume":"2013 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141721322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vivaan Patel, Joshua D. Priosoetanto, Aashutosh Mistry, John Newman, Nitash P. Balsara
Classical models for predicting current flow in excitable cells such as axons, originally proposed by Hodgkin and Huxley, rely on empirical voltage-gating parameters that quantify ion transport across sodium and potassium ion channels. We propose a primitive model for predicting these currents based entirely on well-established ion diffusion coefficients. Changes inside the excitable cell due to the opening of a central sodium channel are confined to a growing hemisphere with a radius that is governed by the sodium ion diffusion coefficient. The sodium channel, which is open throughout the calculation, activates and deactivates naturally due to coupled electrodiffusion processes. The characteristic time of current pulses, which are in the picoampere range, increases from 10$^{-5}$ to 10$^{-1}$ s as channel density is decreased from 10,000 to 1 channel per micrometer squared. Model predictions are compared with data obtained from giant squid axons without invoking any gating parameters.
{"title":"A Primitive Model for Predicting Membrane Currents in Excitable Cells Based Only on Ion Diffusion Coefficients","authors":"Vivaan Patel, Joshua D. Priosoetanto, Aashutosh Mistry, John Newman, Nitash P. Balsara","doi":"arxiv-2407.09474","DOIUrl":"https://doi.org/arxiv-2407.09474","url":null,"abstract":"Classical models for predicting current flow in excitable cells such as\u0000axons, originally proposed by Hodgkin and Huxley, rely on empirical\u0000voltage-gating parameters that quantify ion transport across sodium and\u0000potassium ion channels. We propose a primitive model for predicting these\u0000currents based entirely on well-established ion diffusion coefficients. Changes\u0000inside the excitable cell due to the opening of a central sodium channel are\u0000confined to a growing hemisphere with a radius that is governed by the sodium\u0000ion diffusion coefficient. The sodium channel, which is open throughout the\u0000calculation, activates and deactivates naturally due to coupled\u0000electrodiffusion processes. The characteristic time of current pulses, which\u0000are in the picoampere range, increases from 10$^{-5}$ to 10$^{-1}$ s as channel\u0000density is decreased from 10,000 to 1 channel per micrometer squared. Model\u0000predictions are compared with data obtained from giant squid axons without\u0000invoking any gating parameters.","PeriodicalId":501321,"journal":{"name":"arXiv - QuanBio - Cell Behavior","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141721323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Henry H. Mattingly, Keita Kamino, Jude Ong, Rafaela Kottou, Thierry Emonet, Benjamin B. Machta
Organisms must perform sensory-motor behaviors to survive. What bounds or constraints limit behavioral performance? Previously, we found that the gradient-climbing speed of a chemotaxing Escherichia coli is near a bound set by the limited information they acquire from their chemical environments. Here we ask what limits their sensory accuracy. Past theoretical analyses have shown that the stochasticity of single molecule arrivals sets a fundamental limit on the precision of chemical sensing. Although it has been argued that bacteria approach this limit, direct evidence is lacking. Here, using information theory and quantitative experiments, we find that E. coli's chemosensing is not limited by the physics of particle counting. First, we derive the physical limit on the behaviorally-relevant information that any sensor can get about a changing chemical concentration, assuming that every molecule arriving at the sensor is recorded. Then, we derive and measure how much information E. coli's signaling pathway encodes during chemotaxis. We find that E. coli encode two orders of magnitude less information than an ideal sensor limited only by shot noise in particle arrivals. These results strongly suggest that constraints other than particle arrival noise limit E. coli's sensory fidelity.
{"title":"E. coli do not count single molecules","authors":"Henry H. Mattingly, Keita Kamino, Jude Ong, Rafaela Kottou, Thierry Emonet, Benjamin B. Machta","doi":"arxiv-2407.07264","DOIUrl":"https://doi.org/arxiv-2407.07264","url":null,"abstract":"Organisms must perform sensory-motor behaviors to survive. What bounds or\u0000constraints limit behavioral performance? Previously, we found that the\u0000gradient-climbing speed of a chemotaxing Escherichia coli is near a bound set\u0000by the limited information they acquire from their chemical environments. Here\u0000we ask what limits their sensory accuracy. Past theoretical analyses have shown\u0000that the stochasticity of single molecule arrivals sets a fundamental limit on\u0000the precision of chemical sensing. Although it has been argued that bacteria\u0000approach this limit, direct evidence is lacking. Here, using information theory\u0000and quantitative experiments, we find that E. coli's chemosensing is not\u0000limited by the physics of particle counting. First, we derive the physical\u0000limit on the behaviorally-relevant information that any sensor can get about a\u0000changing chemical concentration, assuming that every molecule arriving at the\u0000sensor is recorded. Then, we derive and measure how much information E. coli's\u0000signaling pathway encodes during chemotaxis. We find that E. coli encode two\u0000orders of magnitude less information than an ideal sensor limited only by shot\u0000noise in particle arrivals. These results strongly suggest that constraints\u0000other than particle arrival noise limit E. coli's sensory fidelity.","PeriodicalId":501321,"journal":{"name":"arXiv - QuanBio - Cell Behavior","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141587944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ramya Deshpande, Francesco Mottes, Ariana-Dalia Vlad, Michael P. Brenner, Alma dal Co
Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how these individual actions coordinate over a macroscopic number of cells to grow complex structures with exquisite functionality is unknown. Here we use recent advances in automatic differentiation to discover local interaction rules and genetic networks that yield emergent, systems-level characteristics in a model of development. We consider a growing tissue with cellular interactions are mediated by morphogen diffusion, differential cell adhesion and mechanical stress. Each cell has an internal genetic network that it uses to make decisions based on its local environment. We show that one can simultaneously learn parameters governing the cell interactions and the genetic network for complex developmental scenarios, including the symmetry breaking of an embryo from an initial cell, the creation of emergent chemical gradients,homogenization of growth via mechanical stress, programmed growth into a prespecified shape, and the ability to repair from damage. When combined with recent experimental advances measuring spatio-temporal dynamics and gene expression of cells in a growing tissue, the methodology outlined here offers a promising path to unravelling the cellular basis of development.
{"title":"Engineering morphogenesis of cell clusters with differentiable programming","authors":"Ramya Deshpande, Francesco Mottes, Ariana-Dalia Vlad, Michael P. Brenner, Alma dal Co","doi":"arxiv-2407.06295","DOIUrl":"https://doi.org/arxiv-2407.06295","url":null,"abstract":"Understanding the rules underlying organismal development is a major unsolved\u0000problem in biology. Each cell in a developing organism responds to signals in\u0000its local environment by dividing, excreting, consuming, or reorganizing, yet\u0000how these individual actions coordinate over a macroscopic number of cells to\u0000grow complex structures with exquisite functionality is unknown. Here we use\u0000recent advances in automatic differentiation to discover local interaction\u0000rules and genetic networks that yield emergent, systems-level characteristics\u0000in a model of development. We consider a growing tissue with cellular\u0000interactions are mediated by morphogen diffusion, differential cell adhesion\u0000and mechanical stress. Each cell has an internal genetic network that it uses\u0000to make decisions based on its local environment. We show that one can\u0000simultaneously learn parameters governing the cell interactions and the genetic\u0000network for complex developmental scenarios, including the symmetry breaking of\u0000an embryo from an initial cell, the creation of emergent chemical\u0000gradients,homogenization of growth via mechanical stress, programmed growth\u0000into a prespecified shape, and the ability to repair from damage. When combined\u0000with recent experimental advances measuring spatio-temporal dynamics and gene\u0000expression of cells in a growing tissue, the methodology outlined here offers a\u0000promising path to unravelling the cellular basis of development.","PeriodicalId":501321,"journal":{"name":"arXiv - QuanBio - Cell Behavior","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Within biological fluid dynamics, it is conventional to distinguish between "puller" and "pusher" microswimmers on the basis of the forward or aft location of the flagella relative to the cell body: typically, bacteria are pushers and algae are pullers. Here we note that since many pullers have "outboard" cilia or flagella displaced laterally from the cell centerline on both sides of the organism, there are two important subclasses whose far-field is that of a stresslet, but whose near field is qualitatively more complex. The ciliary beat creates not only a propulsive force but also swirling flows that can be represented by paired rotlets with two possible senses of rotation, either "feeders" that sweep fluid toward the cell apex, or "expellers" that push fluid away. Experimental studies of the rotifer $Brachionus~plicatilis$ in combination with earlier work on the green algae $Chlamydomonas~reinhardtii$ show that the two classes have markedly different interactions with surfaces. When swimming near a surface, expellers such as $C.~reinhardtii$ scatter from the wall, whereas a feeder like $B.~plicatilis$ stably attaches. This results in a stochastic "run-and-stick" locomotion, with periods of ballistic motion parallel to the surface interrupted by trapping at the surface.
{"title":"Feeders and Expellers, Two Types of Animalcules With Outboard Cilia, Have Distinct Surface Interactions","authors":"Praneet Prakash, Marco Vona, Raymond E. Goldstein","doi":"arxiv-2407.00439","DOIUrl":"https://doi.org/arxiv-2407.00439","url":null,"abstract":"Within biological fluid dynamics, it is conventional to distinguish between\u0000\"puller\" and \"pusher\" microswimmers on the basis of the forward or aft location\u0000of the flagella relative to the cell body: typically, bacteria are pushers and\u0000algae are pullers. Here we note that since many pullers have \"outboard\" cilia\u0000or flagella displaced laterally from the cell centerline on both sides of the\u0000organism, there are two important subclasses whose far-field is that of a\u0000stresslet, but whose near field is qualitatively more complex. The ciliary beat\u0000creates not only a propulsive force but also swirling flows that can be\u0000represented by paired rotlets with two possible senses of rotation, either\u0000\"feeders\" that sweep fluid toward the cell apex, or \"expellers\" that push fluid\u0000away. Experimental studies of the rotifer $Brachionus~plicatilis$ in\u0000combination with earlier work on the green algae $Chlamydomonas~reinhardtii$\u0000show that the two classes have markedly different interactions with surfaces.\u0000When swimming near a surface, expellers such as $C.~reinhardtii$ scatter from\u0000the wall, whereas a feeder like $B.~plicatilis$ stably attaches. This results\u0000in a stochastic \"run-and-stick\" locomotion, with periods of ballistic motion\u0000parallel to the surface interrupted by trapping at the surface.","PeriodicalId":501321,"journal":{"name":"arXiv - QuanBio - Cell Behavior","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The current global food system produces substantial waste and carbon emissions while exacerbating the effects of global hunger and protein deficiency. This study aims to address these challenges by exploring the use of lignocellulosic agricultural residues as feedstocks for microbial protein fermentation, focusing on Fusarium venenatum A3/5, a mycelial strain known for its high protein yield and quality. We propose a high throughput microlitre batch fermentation system paired with analytical chemistry to generate time-series data of microbial growth and substrate utilisation. An unstructured biokinetic model was developed using a bootstrap sampling approach to quantify uncertainty in the parameter estimates. The model was validated against an independent dataset of a different glucose-xylose composition to assess the predictive performance. Our results indicate a robust model fit with high coefficients of determination and low root mean squared errors for biomass, glucose, and xylose concentrations. Estimated parameter values provided insights into the resource utilisation strategies of Fusarium venenatum A3/5 in mixed substrate cultures, aligning well with previous research findings. Significant correlations between estimated parameters were observed, highlighting challenges in parameter identifiability. This work provides a foundational model for optimising the production of microbial protein from lignocellulosic waste, contributing to a more sustainable global food system.
{"title":"High Throughput Parameter Estimation and Uncertainty Analysis Applied to the Production of Mycoprotein from Synthetic Lignocellulosic Hydrolysates","authors":"Mason Banks, Mark Taylor, Miao Guo","doi":"arxiv-2407.00209","DOIUrl":"https://doi.org/arxiv-2407.00209","url":null,"abstract":"The current global food system produces substantial waste and carbon\u0000emissions while exacerbating the effects of global hunger and protein\u0000deficiency. This study aims to address these challenges by exploring the use of\u0000lignocellulosic agricultural residues as feedstocks for microbial protein\u0000fermentation, focusing on Fusarium venenatum A3/5, a mycelial strain known for\u0000its high protein yield and quality. We propose a high throughput microlitre\u0000batch fermentation system paired with analytical chemistry to generate\u0000time-series data of microbial growth and substrate utilisation. An unstructured\u0000biokinetic model was developed using a bootstrap sampling approach to quantify\u0000uncertainty in the parameter estimates. The model was validated against an\u0000independent dataset of a different glucose-xylose composition to assess the\u0000predictive performance. Our results indicate a robust model fit with high\u0000coefficients of determination and low root mean squared errors for biomass,\u0000glucose, and xylose concentrations. Estimated parameter values provided\u0000insights into the resource utilisation strategies of Fusarium venenatum A3/5 in\u0000mixed substrate cultures, aligning well with previous research findings.\u0000Significant correlations between estimated parameters were observed,\u0000highlighting challenges in parameter identifiability. This work provides a\u0000foundational model for optimising the production of microbial protein from\u0000lignocellulosic waste, contributing to a more sustainable global food system.","PeriodicalId":501321,"journal":{"name":"arXiv - QuanBio - Cell Behavior","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141524256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Synchronization of mobile oscillators occurs in numerous contexts, including physical, chemical, biological and engineered systems. In vertebrate embryonic development, a segmental body structure is generated by a population of mobile oscillators. Cells in this population produce autonomous gene expression rhythms, and interact with their neighbors through local signaling. These cells form an extended tissue where frequency and cell mobility gradients coexist. Gene expression kinematic waves travel through this tissue and pattern the segment boundaries. It has been shown that oscillator mobility promotes global synchronization. However, in vertebrate segment formation, mobility may also introduce local fluctuations in kinematic waves and impair segment boundaries. Here we derive a general framework for mobile oscillators that relates local mobility fluctuations to synchronization dynamics and pattern robustness. We formulate a statistical description of mobile phase oscillators in terms of a probability density. We obtain and solve diffusion equations for the average phase and variance, revealing the relationship between local fluctuations and global synchronization in a homogeneous population of oscillators. Analysis of the probability density for large mobility identifies a mean-field transition, where locally coupled oscillators start behaving as if each oscillator was coupled with all the others. We extend the statistical description to inhomogeneous systems to address the gradients present in the vertebrate segmenting tissue. The theory relates pattern stability to mobility, coupling and pattern wavelength. The general approach of the statistical description may be applied to mobile oscillators in other contexts, as well as to other patterning systems where mobility is present.
{"title":"Statistical description of mobile oscillators in embryonic pattern formation","authors":"Koichiro Uriu, Luis G. Morelli","doi":"arxiv-2406.10936","DOIUrl":"https://doi.org/arxiv-2406.10936","url":null,"abstract":"Synchronization of mobile oscillators occurs in numerous contexts, including\u0000physical, chemical, biological and engineered systems. In vertebrate embryonic\u0000development, a segmental body structure is generated by a population of mobile\u0000oscillators. Cells in this population produce autonomous gene expression\u0000rhythms, and interact with their neighbors through local signaling. These cells\u0000form an extended tissue where frequency and cell mobility gradients coexist.\u0000Gene expression kinematic waves travel through this tissue and pattern the\u0000segment boundaries. It has been shown that oscillator mobility promotes global\u0000synchronization. However, in vertebrate segment formation, mobility may also\u0000introduce local fluctuations in kinematic waves and impair segment boundaries.\u0000Here we derive a general framework for mobile oscillators that relates local\u0000mobility fluctuations to synchronization dynamics and pattern robustness. We\u0000formulate a statistical description of mobile phase oscillators in terms of a\u0000probability density. We obtain and solve diffusion equations for the average\u0000phase and variance, revealing the relationship between local fluctuations and\u0000global synchronization in a homogeneous population of oscillators. Analysis of\u0000the probability density for large mobility identifies a mean-field transition,\u0000where locally coupled oscillators start behaving as if each oscillator was\u0000coupled with all the others. We extend the statistical description to\u0000inhomogeneous systems to address the gradients present in the vertebrate\u0000segmenting tissue. The theory relates pattern stability to mobility, coupling\u0000and pattern wavelength. The general approach of the statistical description may\u0000be applied to mobile oscillators in other contexts, as well as to other\u0000patterning systems where mobility is present.","PeriodicalId":501321,"journal":{"name":"arXiv - QuanBio - Cell Behavior","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Joseph J. Pollacco, Ruth E. Baker, Philip K. Maini
Real-world cellular invasion processes often take place in curved geometries. Such problems are frequently simplified in models to neglect the curved geometry in favour of computational simplicity, yet doing so risks inaccuracy in any model-based predictions. To quantify the conditions under which neglecting a curved geometry are justifiable, we examined solutions to the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) model, a paradigm nonlinear reaction-diffusion equation typically used to model spatial invasion, on an annular geometry. Defining $epsilon$ as the ratio of the annulus thickness $delta$ and radius $r_0$ we derive, through an asymptotic expansion, the conditions under which it is appropriate to ignore the domain curvature, a result that generalises to other reaction-diffusion equations with constant diffusion coefficient. We further characterise the nature of the solutions through numerical simulation for different $r_0$ and $delta$. Thus, we quantify the size of the deviation from an analogous simulation on the rectangle, and how this deviation changes across the width of the annulus. Our results grant insight into when it is appropriate to neglect the domain curvature in studying travelling wave behaviour in reaction-diffusion equations.
{"title":"Collective Invasion: When does domain curvature matter?","authors":"Joseph J. Pollacco, Ruth E. Baker, Philip K. Maini","doi":"arxiv-2406.08291","DOIUrl":"https://doi.org/arxiv-2406.08291","url":null,"abstract":"Real-world cellular invasion processes often take place in curved geometries.\u0000Such problems are frequently simplified in models to neglect the curved\u0000geometry in favour of computational simplicity, yet doing so risks inaccuracy\u0000in any model-based predictions. To quantify the conditions under which\u0000neglecting a curved geometry are justifiable, we examined solutions to the\u0000Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) model, a paradigm nonlinear\u0000reaction-diffusion equation typically used to model spatial invasion, on an\u0000annular geometry. Defining $epsilon$ as the ratio of the annulus thickness\u0000$delta$ and radius $r_0$ we derive, through an asymptotic expansion, the\u0000conditions under which it is appropriate to ignore the domain curvature, a\u0000result that generalises to other reaction-diffusion equations with constant\u0000diffusion coefficient. We further characterise the nature of the solutions\u0000through numerical simulation for different $r_0$ and $delta$. Thus, we\u0000quantify the size of the deviation from an analogous simulation on the\u0000rectangle, and how this deviation changes across the width of the annulus. Our\u0000results grant insight into when it is appropriate to neglect the domain\u0000curvature in studying travelling wave behaviour in reaction-diffusion\u0000equations.","PeriodicalId":501321,"journal":{"name":"arXiv - QuanBio - Cell Behavior","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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