Sequential Establishment of Stripe Patterns in an Expanding Cell Population

Liu, Chenli; Fu, Xiaofeng; Liu, Lizhong; Ren, Xiaojing; Chau, Carlos Kwan‐Long; Li, Sihong; Xiang, Lei; Zeng, Hualing; Chen, Guanhua; Tang, Lei-Han; Lenz, Peter; Cui, Xiaodong; Huang, Wei; Hwa, Terence; Huang, Jian

doi:10.1126/science.1209042

Cited by 405 publications

(417 citation statements)

References 56 publications

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“…), violating the FDT [39,40]. To be specific, let us consider a run-and-tumble motion of a swimming bacterium, which locomotes with a velocity V b in search of a food.…”

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confidence: 99%

Quantifying the Heat Dissipation from Molecular Motor’s Transport Properties in Nonequilibrium Steady States

Hwang

Hyeon

2016

Preprint

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Theoretical analysis, which maps single molecule time trajectories of a molecular motor onto unicyclic Markov processes, allows us to evaluate the heat dissipated from the motor and to elucidate its dependence on the mean velocity and diffusivity. Unlike passive Brownian particles in equilibrium, the velocity and diffusion constant of molecular motors are closely inter-related to each other. In particular, our study makes it clear that the increase of diffusivity with the heat production is a natural outcome of active particles, which is reminiscent of the recent experimental premise that the diffusion of an exothermic enzyme is enhanced by the heat released from its own catalytic turnover. Compared with freely diffusing exothermic enzymes, kinesin-1 whose dynamics is confined on one-dimensional tracks is highly efficient in transforming conformational fluctuations into a locally directed motion, thus displaying a significantly higher enhancement in diffusivity with its turnover rate. Putting molecular motors and freely diffusing enzymes on an equal footing, our study offers thermodynamic basis to understand the heat enhanced self-diffusion of exothermic enzymes.Together with recent studies [1][2][3][4], Riedel et al. [5] have demonstrated a rather surprising result, from a perspective of equilibrium statistical mechanics: Diffusion constants (D) of exothermic enzymes, measured from fluorescence correlation spectroscopy (FCS), increase linearly with their catalytic turnover rates V cat , so that the enhancement of diffusivity at maximal activity (maximum V cat ) is as large aswhere D 0 and D max are the diffusion constants measured by FCS at V cat = 0 and maximal V cat , respectively. Their enigmatic observation [5] has called much attention of biophysics community to the physical origin of the activity-dependent diffusivity of a single enzyme. Golestanian [6] considered four distinct scenarios (self-thermophoresis, boost in kinetic energy, stochastic swimming, collective heating) to account for this observation quantitatively; however, the extent of enhancement observed in the experiment was still orders of magnitude greater than the theoretical estimates from the suggested mechanisms. Bai et al.[7] also drew a similar conclusion by considering hydrodynamic coupling between the conformational change of enzyme and surrounding media. The experimental demonstration of enzymes' enhanced diffusion with multiple control experiments in Ref.[5] is straightforward; however, physical insight of the observed phenomena is currently missing [5,6,8,9].While seemingly entirely different from freely diffusing enzymes, kinesin-1 [10-15] is also a substrate-catalyzing enzyme. Conformational dynamics of kinesin-1, induced by ATP hydrolysis and thermal fluctuations, is rectified into a unidirectional movement with a high fidelity [16,17]; hydrolysis of a single ATP almost always leads to 8 nm step [18]. Every step of kinesin-1 along 1D tracks, an outcome of cyclic chemical reaction, can be mapped (2)µ, ..., (N )µ denote distinc...

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“…), violating the FDT [39,40]. To be specific, let us consider a run-and-tumble motion of a swimming bacterium, which locomotes with a velocity V b in search of a food.…”

mentioning

confidence: 99%

Quantifying the Heat Dissipation from Molecular Motor’s Transport Properties in Nonequilibrium Steady States

Hwang

Hyeon

2016

Preprint

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“…Extracellular polymeric substances (EPSs) play an important role in determining the structural and mechanical architecture of a biofilm (7)(8)(9)(10)(11)(12). Generally, the collective dynamics of bacterial colony involves a complex interplay of various physical, chemical, and biological mechanisms, such as growth and differentiation of cells, production of EPSs, the collective movement of cells determined by interacting physical forces and chemical cues, e.g., chemotaxis, motility, cellcell signaling, adhesion, and gene regulation (13)(14)(15)(16)(17)(18)(19). At low density, communication among cells occurs mainly through chemical signals (20).…”

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confidence: 99%

Mechanically-driven phase separation in a growing bacterial colony

Ghosh

Mondal

Ben‐Jacob

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

110

163

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Secretion of extracellular polymeric substances (EPSs) by growing bacteria is an integral part of forming biofilm-like structures. In such dense systems, mechanical interactions among the structural components can be expected to significantly contribute to morphological properties. Here, we use a particle-based modeling approach to study the self-organization of nonmotile rod-shaped bacterial cells growing on a solid substrate in the presence of selfproduced EPSs. In our simulation, all of the components interact mechanically via repulsive forces, occurring as the bacterial cells grow and divide (via consuming diffusing nutrient) and produce EPSs. Based on our simulation, we show that mechanical interactions control the collective behavior of the system. In particular, we find that the presence of nonadsorbing EPSs can lead to spontaneous aggregation of bacterial cells by a depletion attraction and thereby generates phase separated patterns in the nonequilibrium growing colony. Both repulsive interactions between cell and EPSs and the overall concentration of EPSs are important factors in the self-organization in a nonequilibrium growing colony. Furthermore, we investigate the interplay of mechanics with the nutrient diffusion and consumption by bacterial cells and observe that suppression of branch formation occurs due to EPSs compared with the case where no EPS is produced.A common underlying theme of biophysics of living matter is the quest to understand how local interactions of individual components lead to collective behavior and formation of highly self-organized systems (1-6). In this regard, bacterial systems are an especially interesting example. Bacteria are known to selforganize into multicellular communities, commonly known as biofilms, in which microbial cells live in close association with a solid surface or liquid-air interface and are embedded in a self-produced extracellular matrix. Extracellular polymeric substances (EPSs) play an important role in determining the structural and mechanical architecture of a biofilm (7-12). Generally, the collective dynamics of bacterial colony involves a complex interplay of various physical, chemical, and biological mechanisms, such as growth and differentiation of cells, production of EPSs, the collective movement of cells determined by interacting physical forces and chemical cues, e.g., chemotaxis, motility, cellcell signaling, adhesion, and gene regulation (13)(14)(15)(16)(17)(18)(19). At low density, communication among cells occurs mainly through chemical signals (20). However, at a higher density, as bacteria aggregate and form dense communities, direct mechanical interaction becomes increasingly relevant in the self-organization (21-23). In this regard, microfluidics-based experiments coupled with continuum modeling of cellular dynamics by Volfson et al.(24) was a pioneering study emphasizing the role of cell-cell mechanical interaction in the growth of a highly organized bacterial colony. As a significant extension, Farrell and coworkers (25, 26) hav...

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“…PACS numbers: 87.18.Gh, 05.65.+b, 87.18.Hf Bacterial suspensions self-organize into a variety of intriguing patterns visible under the microscope. For instance, Escherichia coli and Salmonella typhimurium colonies growing on soft agar form crystalline or amorphous arrangements of high-density bacterial clumps [1][2][3], as well as stripe patterns [4]. Biofilms exhibit even more elaborate patterns of high density immobile regions and low-density spots or voids [5].…”

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confidence: 99%

“…A large amount of theoretical work has been devoted to understanding the role of external chemical cues in driving such pattern formation by modeling the system via coupled nonlinear diffusionreaction equations [1,6]. It was recently demonstrated [7][8][9] that effective models of reproducing organisms that do not explicitly include chemotaxis can also yield stable patterns, as a result of the interplay between bacterial reproduction and death and the suppression of cell motility, which may arise from local crowding or biochemical signaling such as quorum sensing [4,10]. Motility suppression has been further explored theoretically in models of self-propelled particles with density conservation [10][11][12][13][14].…”

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confidence: 99%

Spiral and never-settling patterns in active systems

2014

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We present a combined numerical and analytical study of pattern formation in an active system where particles align, possess a density-dependent motility, and are subject to a logistic reaction. This is a model for suspensions of reproducing bacteria, but it can also represent, in the ordered phase, actomyosin gels in vitro or in vivo. In the disordered phase, we find that motility suppression and growth compete to yield stable or blinking patterns, which, when dense enough, acquire internal orientational ordering, to yield asters or spirals. In the ordered phase, the reaction term leads to previously unobserved never-settling patterns which can provide a simple framework to understand the formation of motile and spiral patterns in actin. PACS numbers: 87.18.Gh, 05.65.+b, 87.18.Hf Bacterial suspensions self-organize into a variety of intriguing patterns visible under the microscope. For instance, Escherichia coli and Salmonella typhimurium colonies growing on soft agar form crystalline or amorphous arrangements of high-density bacterial clumps [1][2][3], as well as stripe patterns [4]. Biofilms exhibit even more elaborate patterns of high density immobile regions and low-density spots or voids [5]. A large amount of theoretical work has been devoted to understanding the role of external chemical cues in driving such pattern formation by modeling the system via coupled nonlinear diffusionreaction equations [1,6]. It was recently demonstrated [7][8][9] that effective models of reproducing organisms that do not explicitly include chemotaxis can also yield stable patterns, as a result of the interplay between bacterial reproduction and death and the suppression of cell motility, which may arise from local crowding or biochemical signaling such as quorum sensing [4,10]. Motility suppression has been further explored theoretically in models of self-propelled particles with density conservation [10][11][12][13][14]. With only steric repulsion and no alignment, motility suppression yields macroscopic phase separation, with large pretransitional density fluctuations [11,12]. In Vicsektype models with aligning interactions [13], the interplay of self-trapping and alignment yields a rich collection of traveling patterns, including bands, clumps and lanes [13].In this paper we consider a continuum model of active matter where activity couples to a reactive logistic term, hence density is not conserved. This provides a model for bacterial suspensions that incorporates cell reproduction and death [15], motility suppression, as well as cell alignment as it may be induced by medium-mediated hydrodynamic interaction, quorum sensing, or anisotropic cell shape. In the context of actin gels and solutions, a reactive term may arise due to e.g. polymerization (limited by crowding) [16].Our model is formulated in terms of two continuum fields, the cell density, ρ(r, t), and the cell polarization density, w(r, t). The vector field w plays the dual role of orientational order parameter describing the local polar alignment of cells tr...

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Sequential Establishment of Stripe Patterns in an Expanding Cell Population

Cited by 405 publications

References 56 publications

Quantifying the Heat Dissipation from Molecular Motor’s Transport Properties in Nonequilibrium Steady States

Quantifying the Heat Dissipation from Molecular Motor’s Transport Properties in Nonequilibrium Steady States

Mechanically-driven phase separation in a growing bacterial colony

Spiral and never-settling patterns in active systems

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