Cooperative formation of chiral patterns during growth of bacterial colonies

Symbiotic dynamics in living liquid crystals

An amalgam of nematic liquid crystals and active matter, referred to as living liquid crystals, is a promising self-healing material with futuristic applications for targeted delivery of information and microcargo. We provide a phenomenological model to study the symbiotic pattern dynamics in this contemporary system using the Toner-Tu model for active matter (AM), the Landau-de Gennes free energy for liquid crystals (LCs), and an experimentally motivated coupling term that favours coalignment of the active and nematic components. Our extensive theoretical studies unfold two novel steady states, chimeras and solitons, with sharp regions of distinct orientational order that sweep through the coupled system in synchrony. The induced dynamics in the passive nematic is unprecedented. We show that the symbiotic dynamics of the AM and LC components can be exploited to induce and manipulate order in an otherwise disordered system.

Colloidal Active Matter Mimics the Behavior of Biological Microorganisms-An Overview

This article provides a review of the recent development of biomimicking behaviors in active colloids. While the behavior of biological microswimmers is undoubtedly influenced by physics, it is frequently guided and manipulated by active sensing processes. Understanding the respective influences of the surrounding environment can help to engineering the desired response also in artificial swimmers. More often than not, the achievement of biomimicking behavior requires the understanding of both biological and artificial microswimmers swimming mechanisms and the parameters inducing mechanosensory responses. The comparison of both classes of microswimmers provides with analogies in their dependence on fuels, interaction with boundaries and stimuli induced motion, or taxis.

Characterizing the Impact of Communication on Cellular and Collective Behavior Using a Three-Dimensional Multiscale Cellular Model

Communication between cells enables the coordination that drives structural and functional complexity in biological systems. Both single and multicellular organisms have evolved diverse communication systems for a range of purposes, including synchronization of behavior, division of labor, and spatial organization. Synthetic systems are also increasingly being engineered to utilize cell-cell communication. While research has elucidated the form and function of cell-cell communication in many biological systems, our knowledge is still limited by the confounding effects of other biological phenomena at play and the bias of the evolutionary background. In this work, our goal is to push forward the context-free understanding of what impact cell-cell communication can have on cellular and population behavior to more fully understand the extent to which cell-cell communication systems can be utilized, modified, and engineered. We use an in silico model of 3D multiscale cellular populations, with dynamic intracellular networks interacting via diffusible signals. We focus on two key communication parameters: the effective interaction distance at which cells are able to interact and the receptor activation threshold. We found that cell-cell communication can be divided into six different forms along the parameter axes, three asocial and three social. We also show that cellular behavior, tissue composition, and tissue diversity are all highly sensitive to both the general form and specific parameters of communication even when the cellular network has not been biased towards that behavior.

Effective single component description of steady state structures of passive particles in an active bath

We model a binary mixture of passive and active Brownian particles in two dimensions using the effective interaction between passive particles in the active bath. The activity of active particles and the size ratio of two types of particles are the two control parameters in the system. The effective interaction is calculated from the average force on two particles generated by the active particles. The effective interaction can be attractive or repulsive, depending on the system parameters. The passive particles form four distinct structural orders for different system parameters, viz., homogeneous structures, disordered cluster, ordered cluster, and crystalline structure. The change in structure is dictated by the change in nature of the effective interaction. We further confirm the four structures using a full microscopic simulation of active and passive mixture. Our study is useful to understand the different collective behavior in non-equilibrium systems.

Cell Chirality as a Novel Measure for Cytotoxicity

Cytotoxicity assessment has great importance in both research and pharmaceutical development. The mainstream in vitro cytotoxicity assays are mostly biochemical assays that evaluate a specific cellular activity such as proliferation and apoptosis. Few assays assess toxicity by characterizing overall functional outcomes in cellular physiology such as multicellular morphogenesis. The intrinsic cellular chiral bias (also known as cell chirality, left-right asymmetry, or handedness), which determines cellular polarization along the left-right axis, is demonstrated to play important roles in development and disease. This chiral property of cells gives insights not only into functions of individual cells, such as motility and polarity but also into emerging behaviors of cell clusters, such as collective cell migration. Therefore, cell chirality characterization can be potentially used as a biomarker for assessing the overall effects of pharmaceutical drugs and environmental factors on the health of the cell. In this review article, the current in vitro techniques for cell chirality characterization and their applications are discussed and the advantages and limitations of these cell chirality assays as potential tools for detecting cytotoxicity are discussed.

Large-Scale Vortices with Dynamic Rotation Emerged from Monolayer Collective Motion of Gliding Flavobacteria

A collective motion of self-driven particles has been a fascinating subject in physics and biology. Sophisticated macroscopic behavior emerges through a population of thousands or millions of bacterial cells propelling itself by flagellar rotation and chemotactic responses. Here, we found a series of collective motions accompanying successive phase transitions for a nonflagellated rod-shaped soil bacterium, Flavobacterium johnsoniae, which was driven by a surface cell movement known as gliding motility. When we spotted the cells on an agar plate with a low level of nutrients, the bacterial community exhibited vortex patterns that spontaneously appeared as lattice and integrated into a large-scale circular plate. All patterns were exhibited with a monolayer of bacteria, which enabled us to two-dimensionally visualize an individual cell with high resolution within a wide-range pattern. The single cells moved with random orientation, but the cells that were connected with one another showed left-turn-biased trajectories in a starved environment. This feature is possibly due to the collision of cells inducing a nematic alignment of dense cells as self-propelled rods. Subsequently, each vortex oscillated independently and then transformed to the rotating mode as an independent circular plate. Notably, the rotational direction of the circular plate was counterclockwise without exception. The plates developed accompanying rotation with constant angular velocity, suggesting that the mode is an efficient strategy for bacterial survival. IMPORTANCE Self-propelled bacteria propelled by flagellar rotation often display highly organized dynamic patterns at high cell densities. Here, we found a new mode of collective motion in nonflagellated bacteria; vortex patterns spontaneously appeared as lattice and were integrated into a large-scale circular plate, comprising hundreds of thousands of cells, which exhibited unidirectional rotation in a counterclockwise manner and expanded in size on agar. A series of collective motions was driven by gliding motility of the rod-shaped soil bacterium Flavobacterium johnsoniae. In a low-nutrient environment, single cells moved with random orientation, while cells at high density moved together as a unitary cluster. This might be an efficient strategy for cells of this species to find nutrients.

Exploration of possible cell chirality using material techniques of surface patterning

Consistent left-right (LR) asymmetry or chirality is critical for embryonic development and function maintenance. While chirality on either molecular or organism level has been well established, that on the cellular level has remained an open question for a long time. Although it remains unclear whether chirality exists universally on the cellular level, valuable efforts have recently been made to explore this fundamental topic pertinent to both cell biology and biomaterial science. The development of material fabrication techniques, surface patterning, in particular, has afforded a unique platform to study cell-material interactions. By using patterning techniques, chirality on the cellular level has been examined for cell clusters and single cells in vitro in well-designed experiments. In this review, we first introduce typical fabrication techniques of surface patterning suitable for cell studies and then summarize the main aspects of preliminary evidence of cell chirality on patterned surfaces to date. We finally indicate the limitations of the studies conducted thus far and describe the perspectives of future research in this challenging field. STATEMENT OF SIGNIFICANCE: While both biomacromolecules and organisms can exhibit chirality, it is not yet conclusive whether a cell has left-right (LR) asymmetry. It is important yet challenging to study and reveal the possible existence of cell chirality. By using the technique of surface patterning, the recent decade has witnessed progress in the exploration of possible cell chirality within cell clusters and single cells. Herein, some important preliminary evidence of cell chirality is collected and analyzed. The open questions and perspectives are also described to promote further investigations of cell chirality in biomaterials.

Pattern Formation and Defect Ordering in Active Chiral Nematics

Many biological systems display intriguing chiral patterns and dynamics. Here, we present an active nematic theory accounting for individual spin to explore the collective handedness in chiral rod-shaped aggregations. We show that coordinated individual spin and motility can engender a vortex-array pattern with chirality and drive ordering of topological defects. During this chiral process, the stationary trefoil-like defects self-organize into a periodic, hexagon-dominated polygonal network, which segregates persistently rotating cometlike defects in pairs within each polygon, leading to a translation symmetry at the global scale while a broken reflection symmetry at the local scale. Such defect ordering agrees exactly with the Voronoi tiling of two-dimensional space and the emergence of the hexagonal symmetry is deciphered in analogy with topological charge neutralization. We calculate energy barriers to the topological transition of the defect ordering and explain the existing metastable states with nonhexagonal polygons. Our findings shed light on the chiral morphodynamics in life processes and also suggest a potential route towards tuning self-organization in active materials.

Plasmonic nanoparticles assemblies templated by helical bacteria and resulting optical activity

Plasmonic nanoparticles (NPs) adsorbing onto helical bacteria can lead to formation of NP helicoids with micron scale pitch. Associated chiroptical effects can be utilized as bioanalytical tool for bacterial detection and better understanding of the spectral behavior of helical self-assembled structures with different scales. Here, we report that enantiomerically pure helices with micron scale of chirality can be assembled on Campylobacter jejuni, a helical bacterium known for severe stomach infections. These organisms have right-handed helical shapes with a pitch of 1-2 microns and can serve as versatile templates for a variety of NPs. The bacteria itself shows no observable rotatory activity in the visible, red, and near-IR ranges of electromagnetic spectrum. The bacterial dispersion acquires chiroptical activity at 500-750 nm upon plasmonic functionalization with Au NPs. Finite-difference time-domain simulations confirmed the attribution of the chiroptical activity to the helical assembly of gold nanoparticles. The position of the circular dichroism peaks observed for these chiral structures overlaps with those obtained before for Au NPs and their constructs with molecular and nanoscale chirality. This work provides an experimental and computational pathway to utilize chiroplasmonic particles assembled on bacteria for bioanalytical purposes.

Clusterization of self-propelled particles in a two-component system

We consider a mixture of active solute molecules in a suspension of passive solvent particles comprising a thermal bath. The solute molecules are considered to be extended objects with two chemically distinct heads, one head of which having chemical affinity towards the solvent particles. The coupled Langevin equations for the solvent particles along with the equations governing the dynamics of active molecules are numerically simulated to show how the active molecules self-assemble to form clusters which remain in dynamic equilibrium with the free solute molecules. We observe an interesting crossover at an intermediate time in the variation of the order parameter with time when the temperature of the bath is changed signifying the differential behavior of clusterization below and above the crossover time associated with a transition between a thermodynamic and a quasithermodynamic regime. Enthalpy-entropy compensation in the formation of clusters below the crossover is demonstrated.

Engineered Living Materials: Prospects and Challenges for Using Biological Systems to Direct the Assembly of Smart Materials

Vast potential exists for the development of novel, engineered platforms that manipulate biology for the production of programmed advanced materials. Such systems would possess the autonomous, adaptive, and self-healing characteristics of living organisms, but would be engineered with the goal of assembling bulk materials with designer physicochemical or mechanical properties, across multiple length scales. Early efforts toward such engineered living materials (ELMs) are reviewed here, with an emphasis on engineered bacterial systems, living composite materials which integrate inorganic components, successful examples of large-scale implementation, and production methods. In addition, a conceptual exploration of the fundamental criteria of ELM technology and its future challenges is presented. Cradled within the rich intersection of synthetic biology and self-assembling materials, the development of ELM technologies allows the power of biology to be leveraged to grow complex structures and objects using a palette of bio-nanomaterials.

Brownian dynamics of self-regulated particles with additional degrees of freedom: Symmetry breaking and homochirality

We consider the Brownian motion of a collection of particles each with an additional degree of freedom. The degree of freedom of a particle (or, in general, a molecule) can assume distinct values corresponding to certain states or conformations. The time evolution of the additional degree of freedom of a particle is guided by those of its neighbors as well as the temperature of the system. We show that the local averaging over these degrees of freedom results in emergence of a collective order in the dynamics in the form of selection or dominance of one of the isomers leading to a symmetry-broken state. Our statistical model captures the basic features of homochirality, e.g., autocatalysis and chiral inhibition.

Nonequilibrium transition and pattern formation in a linear reaction-diffusion system with self-regulated kinetics

We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.

Cell chirality: emergence of asymmetry from cell culture

Increasing evidence suggests that intrinsic cell chirality significantly contributes to the left-right (LR) asymmetry in embryonic development, which is a well-conserved characteristic of living organisms. With animal embryos, several theories have been established, but there are still controversies regarding mechanisms associated with embryonic LR symmetry breaking and the formation of asymmetric internal organs. Recently, in vitro systems have been developed to determine cell chirality and to recapitulate multicellular chiral morphogenesis on a chip. These studies demonstrate that chirality is indeed a universal property of the cell that can be observed with well-controlled experiments such as micropatterning. In this paper, we discuss the possible benefits of these in vitro systems to research in LR asymmetry, categorize available platforms for single-cell chirality and multicellular chiral morphogenesis, and review mathematical models used for in vitro cell chirality and its applications in in vivo embryonic development. These recent developments enable the interrogation of the intracellular machinery in LR axis establishment and accelerate research in birth defects in laterality.This article is part of the themed issue 'Provocative questions in left-right asymmetry'.

Order-disorder transition in active nematic: A lattice model study

We introduce a lattice model for active nematic composed of self-propelled apolar particles, study its different ordering states in the density-temperature parameter space, and compare with the corresponding equilibrium model. The active particles interact with their neighbours within the framework of the Lebwohl-Lasher model, and move anisotropically along their orientation to an unoccupied nearest neighbour lattice site. An interplay of the activity, thermal fluctuations and density gives rise distinct states in the system. For a fixed temperature, the active nematic shows a disordered isotropic state, a locally ordered inhomogeneous mixed state, and bistability between the inhomogeneous mixed and a homogeneous globally ordered state in different density regime. In the low temperature regime, the isotropic to the inhomogeneous mixed state transition occurs with a jump in the order parameter at a density less than the corresponding equilibrium disorder-order transition density. Our analytical calculations justify the shift in the transition density and the jump in the order parameter. We construct the phase diagram of the active nematic in the density-temperature plane.

Growth of bacteria in 3-d colonies

The dynamics of growth of bacterial populations has been extensively studied for planktonic cells in well-agitated liquid culture, in which all cells have equal access to nutrients. In the real world, bacteria are more likely to live in physically structured habitats as colonies, within which individual cells vary in their access to nutrients. The dynamics of bacterial growth in such conditions is poorly understood, and, unlike that for liquid culture, there is not a standard broadly used mathematical model for bacterial populations growing in colonies in three dimensions (3-d). By extending the classic Monod model of resource-limited population growth to allow for spatial heterogeneity in the bacterial access to nutrients, we develop a 3-d model of colonies, in which bacteria consume diffusing nutrients in their vicinity. By following the changes in density of E. coli in liquid and embedded in glucose-limited soft agar, we evaluate the fit of this model to experimental data. The model accounts for the experimentally observed presence of a sub-exponential, diffusion-limited growth regime in colonies, which is absent in liquid cultures. The model predicts and our experiments confirm that, as a consequence of inter-colony competition for the diffusing nutrients and of cell death, there is a non-monotonic relationship between total number of colonies within the habitat and the total number of individual cells in all of these colonies. This combined theoretical-experimental study reveals that, within 3-d colonies, E. coli cells are loosely packed, and colonies produce about 2.5 times as many cells as the liquid culture from the same amount of nutrients. We verify that this is because cells in liquid culture are larger than in colonies. Our model provides a baseline description of bacterial growth in 3-d, deviations from which can be used to identify phenotypic heterogeneities and inter-cellular interactions that further contribute to the structure of bacterial communities.

The vast majority of theoretical and experimental studies assume that bacteria exist as planktonic cells in well-mixed liquid cultures, all with equal access to nutrients, wastes, toxins, antibiotics, bacterial viruses, and each other. However, in the real world, bacteria are more often found in physically structured, spatially heterogeneous habitats as colonies and micro-colonies. While one can experimentally explore the population and evolutionary dynamics of bacteria in such physically structured habitats, there is dearth of mathematical models to generate hypotheses for and to interpret results of these experiments. As a step towards the construction of a theory of the population dynamics of bacteria in physically structured habitats, we develop and experientially explore the simplest such model of the dynamics of bacterial growth in 3-d structured colonies.

Chirality in microbial biofilms is mediated by close interactions between the cell surface and the substratum

From microbial biofilms to human migrations, spatial competition is central to the evolutionary history of many species. The boundary between expanding populations is the focal point of competition for space and resources and is of particular interest in ecology. For all Escherichia coli strains studied here, these boundaries move in a counterclockwise direction even when the competing strains have the same fitness. We find that chiral growth of bacterial colonies is strongly suppressed by the expression of extracellular features such as adhesive structures and pili. Experiments with other microbial species show that chiral growth is found in other bacteria and exclude cell wall biosynthesis and anisotropic shape as the primary causes of chirality. Instead, intimate contact with the substratum is necessary for chirality. Our results demonstrate that through a handful of surface molecules cells can fundamentally reorganize their migration patterns, which might affect intra- and interspecific competitions through colony morphology or other mechanisms.

Escherichia coli adhesive coating as a chiral stationary phase for open tubular capillary electrochromatography enantioseparation

Bacteria, the microorganism with intrinsic chirality, have numerous fascinating chiral phenomena such as various chirality-triggered biological processes and behaviors. Herein, bacteria were firstly explored as novel chiral stationary phases in open-tubular capillary electrochromatography (OT-CEC) for enantioseparation of fluoroquinolone enantiomers and simultaneous separation of six fluoroquinolone antibiotics. The model strain, i.e. non-pathogenic Escherichia coli (E. coli) DH5α, was adhered onto the inner surface of positively charged polyethyleneimine (PEI) modified capillaries based on the bacterial adhesion characteristics and strong electrostatic interaction. The morphology and thickness of the bacteria adhesive coatings in the capillary were characterized by field emission scanning electron microscopy (FESEM) and atomic force microscopy (AFM). Baseline separation of ofloxacin and partial separation of lomefloxacin enantiomers could be achieved by the E. coli coated columns. The preparation parameters including the coating time and concentration of bacteria that affecting the chiral resolution were intensively investigated. The electrophoretic parameters, including pH, buffer concentration and applied voltage, were also optimized. The developed method was validated (linearity, LOD, LOQ, intra-day, inter-day and column-to-column repeatability and recovery) and successfully utilized for the quantitative analysis of ofloxacin enantiomers in the ofloxacin tablets. Moreover, only a slight decrease in the separation efficiency was observed after 90 consecutive runs on the E. coli@capillary. These results demonstrated that bacteria are promising stationary phases for chiral separation in CEC.

Variations and heredity in bacterial colonies

Spontaneous variation in appearance was studied in bacterial colonies of Serratia marcescens F morphotype¹: (i) A defined array of non-heritable phenotype variations does appear repeatedly; (ii) The presence of colonies of different bacterial species will narrow the variability toward the typical F appearance, as if such an added environmental factor curtailed the capacity of colony morphospace; (iii) Similarly the morphospace becomes reduced by random mutations leading to new, heritable morphotypes—at the same time opening a new array of variations typical for the mutant but not accessible directly from the original F morphospace. Results are discussed in context with biphasic model of early morphogenesis applicable to all multicellular bodies.

Spontaneous chiral symmetry breaking in collective active motion

Chiral symmetry breaking is ubiquitous in biological systems, from DNA to bacterial suspensions. A key unresolved problem is how chiral structures may spontaneously emerge from achiral interactions. We study a simple model of active swimmers in three dimensions that effectively incorporates hydrodynamic interactions. We perform large-scale molecular dynamics simulations (up to 10(6) particles) and find long-lived metastable collective states that exhibit chiral organization although the interactions are achiral. We elucidate under which conditions these chiral states will emerge and grow to large scales. To explore the complex phase space available to the system, we perform nonequilibrium quenches on a one-dimensional Lebwohl-Lasher model with periodic boundary conditions to study the likelihood of formation of chiral structures.

Two-dimensionality of yeast colony expansion accompanied by pattern formation

Yeasts can form multicellular patterns as they expand on agar plates, a phenotype that requires a functional copy of the FLO11 gene. Although the biochemical and molecular requirements for such patterns have been examined, the mechanisms underlying their formation are not entirely clear. Here we develop quantitative methods to accurately characterize the size, shape, and surface patterns of yeast colonies for various combinations of agar and sugar concentrations. We combine these measurements with mathematical and physical models and find that FLO11 gene constrains cells to grow near the agar surface, causing the formation of larger and more irregular colonies that undergo hierarchical wrinkling. Head-to-head competition assays on agar plates indicate that two-dimensional constraint on the expansion of FLO11 wild type (FLO11) cells confers a fitness advantage over FLO11 knockout (flo11Δ) cells on the agar surface.

Microbial biofilms are commonly found in nature and are highly relevant to public health. Biofilms can impose high risks to drinking water distribution by stable adherence to the interior of water pipes, and to food industry by contamination of food processing systems. Biofilm adherence to indwelling medical devices causes high rates of clinical infections that are difficult to eliminate as biofilm microbes resist treatment with antibiotics and biocides. These microbial abilities are related to the spatial composition and overall morphology of the biofilm. While the mechanisms underlying biofilm structure and morphology have been examined for bacteria, much less is known about eukaryotic biofilms. Here we find that the size, shape and patterning of budding yeast colonies can arise from constraining colony expansion to the surface of agar plates. Through computational analysis and mathematical modeling, we find that rapid colony expansion, colony shape irregularity and hierarchical wrinkling of the yeast colony surface can result from two-dimensionality of expansion imposed by the adhesin FLO11. Finally, we find that two-dimensional expansion conveys competitive advantage during head-to-head competition with the mutant cells lacking FLO11.

Development of an integrated optical analyzer for characterization of growth dynamics of bacterial colonies

In order to understand the biophysics behind collective behavior of a bacterial colony, a confocal displacement meter was used to measure the profiles of the bacterial colonies, together with a custom built optical density circuits. The system delivered essential information related to the quantitative growth dynamics (height, diameter, aspect ratio, optical density) of the bacterial colony. For example, the aspect ratio of S. aureus was approximately two times higher than that of E. coli O157 : H7, while the OD of S. aureus was approximately 1/3 higher than that of E. coli O157 : H7.

Menaquinone and iron are essential for complex colony development in Bacillus subtilis

Cells of undomesticated species of Bacillus subtilis frequently form complex colonies during spreading on agar surfaces. Given that menaquinone is involved in another form of coordinated behavior, namely, sporulation, we looked for a possible role for menaquinone in complex colony development (CCD) in the B. subtilis strain NCIB 3610. Here we show that inhibition of menaquinone biosynthesis in B. subtilis indeed abolished its ability to develop complex colonies. Additionally some mutations of B. subtilis which confer defective CCD could be suppressed by menaquinone derivatives. Several such mutants mapped to the dhb operon encoding the genes responsible for the biosynthesis of the iron siderophore, bacillibactin. Our results demonstrate that both menaquinone and iron are essential for CCD in B. subtilis.

Periodic reversals in Paenibacillus dendritiformis swarming

Bacterial swarming is a type of motility characterized by a rapid and collective migration of bacteria on surfaces. Most swarming species form densely packed dynamic clusters in the form of whirls and jets, in which hundreds of rod-shaped rigid cells move in circular and straight patterns, respectively. Recent studies have suggested that short-range steric interactions may dominate hydrodynamic interactions and that geometrical factors, such as a cell's aspect ratio, play an important role in bacterial swarming. Typically, the aspect ratio for most swarming species is only up to 5, and a detailed understanding of the role of much larger aspect ratios remains an open challenge. Here we study the dynamics of Paenibacillus dendritiformis C morphotype, a very long, hyperflagellated, straight (rigid), rod-shaped bacterium with an aspect ratio of ~20. We find that instead of swarming in whirls and jets as observed in most species, including the shorter T morphotype of P. dendritiformis, the C morphotype moves in densely packed straight but thin long lines. Within these lines, all bacteria show periodic reversals, with a typical reversal time of 20 s, which is independent of their neighbors, the initial nutrient level, agar rigidity, surfactant addition, humidity level, temperature, nutrient chemotaxis, oxygen level, illumination intensity or gradient, and cell length. The evolutionary advantage of this unique back-and-forth surface translocation remains unclear.

Micropatterning of cells reveals chiral morphogenesis

Invariant left-right (LR) patterning or chirality is critical for embryonic development. The loss or reversal of LR asymmetry is often associated with malformations and disease. Although several theories have been proposed, the exact mechanism of the initiation of the LR symmetry has not yet been fully elucidated. Recently, chirality has been detected within single cells as well as multicellular structures using several in vitro approaches. These studies demonstrated the universality of cell chirality, its dependence on cell phenotype, and the role of physical boundaries. In this review, we discuss the theories for developmental LR asymmetry, compare various in vitro cell chirality model systems, and highlight possible roles of cell chirality in stem cell differentiation. We emphasize that the in vitro cell chirality systems have great promise for helping unveil the nature of chiral morphogenesis in development.

Collective dynamics of self-propelled particles with variable speed

Understanding the organization of collective motion in biological systems is an ongoing challenge. In this paper we consider a minimal model of self-propelled particles with variable speed. Inspired by experimental data from schooling fish, we introduce a power-law dependency of the speed of each particle on the degree of polarization order in its neighborhood. We derive analytically a coarse-grained continuous approximation for this model and find that, while the specific variable speed rule used does not change the details of the ordering transition leading to collective motion, it induces an inverse power-law correlation between the speed or the local polarization order and the local density. Using numerical simulations, we verify the range of validity of this continuous description and explore regimes beyond it. We discover, in disordered states close to the transition, a phase-segregated regime where most particles cluster into almost static groups surrounded by isolated high-speed particles. We argue that the mechanism responsible for this regime could be present in a wide range of collective motion dynamics.

Communication-induced multistability and multirhythmicity in a synthetic multicellular system

Traditionally, the main role of cell-to-cell communication was thought of as synchronizing a population of cells, thereby coordinating cellular behavior. Here we show that cell density, which quantifies cellular communication, can induce multistability and multirhythmicity in a synthetic multicellular system, where individual oscillators are a combination of repressillator and hysteresis-based oscillators and are coupled through a quorum-sensing mechanism. Specifically, for moderately small cell densities, the coupled system can exhibit multistability including stable homogenous and inhomogeneous steady states. For moderately large cell densities, it has the potential to generate multirhythmicity including multimode oscillations such as an in-phase periodic solution, antiphase periodic solution, asymmetric periodic solution, mixed-mode oscillations, coexistence of periodic orbits of several different modes, and bursting oscillations such as periodic bursting, torus quasiperiodic bursting, and chaotic bursting. Such versatility of cell-to-cell communication would be beneficial for cells or organisms to live in diversely changeable environments.

Fluctuations and pattern formation in self-propelled particles

We consider a coarse-grained description of a collection of self-propelled particles given by hydrodynamic equations for the density and polarization fields. We find that the ordered moving or flocking state of the system is unstable to spatial fluctuations beyond a threshold set by the self-propulsion velocity of the individual units. In this region, the system organizes itself into an inhomogeneous state of well-defined propagating stripes of flocking particles interspersed with low-density disordered regions. Further, we find that even in the regime where the homogeneous flocking state is stable, the system exhibits large fluctuations in both density and orientational order. We study the hydrodynamic equations analytically and numerically to characterize both regimes.

Lethal protein produced in response to competition between sibling bacterial colonies

Sibling Paenibacillus dendritiformis bacterial colonies grown on low-nutrient agar medium mutually inhibit growth through secretion of a lethal factor. Analysis of secretions reveals the presence of subtilisin (a protease) and a 12 kDa protein, termed sibling lethal factor (Slf). Purified subtilisin promotes the growth and expansion of P. dendritiformis colonies, whereas Slf is lethal and lyses P. dendritiformis cells in culture. Slf is encoded by a gene belonging to a large family of bacterial genes of unknown function, and the gene is predicted to encode a protein of approximately 20 kDa, termed dendritiformis sibling bacteriocin. The 20 kDa recombinant protein was produced and found to be inactive, but exposure to subtilisin resulted in cleavage to the active, 12 kDa form. The experimental results, combined with mathematical modeling, show that subtilisin serves to regulate growth of the colony. Below a threshold concentration, subtilisin promotes colony growth and expansion. However, once it exceeds a threshold, as occurs at the interface between competing colonies, Slf is then secreted into the medium to rapidly reduce cell density by lysis of the bacterial cells. The presence of genes encoding homologs of dendritiformis sibling bacteriocin in other bacterial species suggests that this mechanism for self-regulation of colony growth might not be limited to P. dendritiformis.

Paenibacillus dendritiformis bacterial colony growth depends on surfactant but not on bacterial motion

Most research on growing bacterial colonies on agar plates has concerned the effect of genetic or morphotype variation. Some studies have indicated that there is a correlation between microscopic bacterial motion and macroscopic colonial expansion, especially for swarming strains, but no measurements have been obtained for a single strain to relate the microscopic scale to the macroscopic scale. We examined here a single strain (Paenibacillus dendritiformis type T; tip splitting) to determine both the macroscopic growth of colonies and the microscopic bacterial motion within the colonies. Our multiscale measurements for a variety of growth conditions revealed that motion on the microscopic scale and colonial growth are largely independent. Instead, the growth of the colony is strongly affected by the availability of a surfactant that reduces surface tension.

Transitions in a self-propelled-particles model with coupling of accelerations

We consider a three-dimensional, generalized version of the original self-propelled-particles (SPP) model for collective motion. By extending the factors influencing the ordering, we investigate the case when the movement of the SPPs depends on both the velocity and the acceleration of the neighboring particles, instead of being determined solely by the former one. By changing the value of a weight parameter s determining the relative influence of the velocity and the acceleration terms, the system undergoes a kinetic phase transition as a function of a behavioral pattern. Below a critical value of s the system exhibits disordered motion, while above it the dynamics resembles that of the SPP model. We show that the critical value of the strategy variable could correspond to an evolutionary optimum in the sense that the information exchange between the units of the system is maximal in this point.

Self-propelled particle model for cell-sorting phenomena

A self-propelled particle model is introduced to study cell sorting occurring in some living organisms. This allows us to evaluate the influence of intrinsic cell motility separately from differential adhesion with fluctuations, a mechanism previously shown to be sufficient to explain a variety of cell rearrangement processes. We find that the tendency of cells to actively follow their neighbors greatly reduces segregation time scales. A finite-size analysis of the sorting process reveals clear algebraic growth laws as in physical phase-ordering processes, albeit with unusual scaling exponents.

Effective temperature of active matter

We follow the dynamics of an ensemble of interacting self-propelled motorized particles in contact with an equilibrated thermal bath. We find that the fluctuation-dissipation relation allows for the definition of an effective temperature that is compatible with the results obtained using a tracer particle as a thermometer. The effective temperature takes a value which is higher than the temperature of the bath, and it is continuously controlled by the motor intensity.

Stability analysis of a hybrid cellular automaton model of cell colony growth

Cell colonies of bacteria, tumor cells, and fungi, under nutrient limited growth conditions, exhibit complex branched growth patterns. In order to investigate this phenomenon we present a simple hybrid cellular automaton model of cell colony growth. In the model the growth of the colony is limited by a nutrient that is consumed by the cells and which inhibits cell division if it falls below a certain threshold. Using this model we have investigated how the nutrient consumption rate of the cells affects the growth dynamics of the colony. We found that for low consumption rates the colony takes on an Eden-like morphology, while for higher consumption rates the morphology of the colony is branched with a fractal geometry. These findings are in agreement with previous results, but the simplicity of the model presented here allows for a linear stability analysis of the system. By observing that the local growth of the colony is proportional to the flux of the nutrient we derive an approximate dispersion relation for the growth of the colony interface. This dispersion relation shows that the stability of the growth depends on how far the nutrient penetrates into the colony. For low nutrient consumption rates the penetration distance is large, which stabilizes the growth, while for high consumption rates the penetration distance is small, which leads to unstable branched growth. When the penetration distance vanishes the dispersion relation is reduced to the one describing Laplacian growth without ultra-violet regularization. The dispersion relation was verified by measuring how the average branch width depends on the consumption rate of the cells and shows good agreement between theory and simulations.

A synthetic multicellular system for programmed pattern formation

Pattern formation is a hallmark of coordinated cell behaviour in both single and multicellular organisms. It typically involves cell-cell communication and intracellular signal processing. Here we show a synthetic multicellular system in which genetically engineered 'receiver' cells are programmed to form ring-like patterns of differentiation based on chemical gradients of an acyl-homoserine lactone (AHL) signal that is synthesized by 'sender' cells. In receiver cells, 'band-detect' gene networks respond to user-defined ranges of AHL concentrations. By fusing different fluorescent proteins as outputs of network variants, an initially undifferentiated 'lawn' of receivers is engineered to form a bullseye pattern around a sender colony. Other patterns, such as ellipses and clovers, are achieved by placing senders in different configurations. Experimental and theoretical analyses reveal which kinetic parameters most significantly affect ring development over time. Construction and study of such synthetic multicellular systems can improve our quantitative understanding of naturally occurring developmental processes and may foster applications in tissue engineering, biomaterial fabrication and biosensing.

Reaction-diffusion model for pattern formation in E. coli swarming colonies with slime

A new experimental colonial pattern and pattern transition observed in E. coli MG1655 swarming cells grown on semisolid agar are described. We present a reaction-diffusion model that, taking into account the slime generated by these cells and its influence on the bacterial differentiation and motion, reproduces the pattern and successfully predicts the observed changes when the colonial collective motility is limited. In spite of having small nonhyperflagellated swarming cells, under these experimental conditions E. coli MG1655 can very rapidly colonize a surface, with a low branching rate, thanks to a strong fluid production and a locally incremented density of motile, lubricating cells.

Single-cell microbiology: tools, technologies, and applications

The field of microbiology has traditionally been concerned with and focused on studies at the population level. Information on how cells respond to their environment, interact with each other, or undergo complex processes such as cellular differentiation or gene expression has been obtained mostly by inference from population-level data. Individual microorganisms, even those in supposedly "clonal" populations, may differ widely from each other in terms of their genetic composition, physiology, biochemistry, or behavior. This genetic and phenotypic heterogeneity has important practical consequences for a number of human interests, including antibiotic or biocide resistance, the productivity and stability of industrial fermentations, the efficacy of food preservatives, and the potential of pathogens to cause disease. New appreciation of the importance of cellular heterogeneity, coupled with recent advances in technology, has driven the development of new tools and techniques for the study of individual microbial cells. Because observations made at the single-cell level are not subject to the "averaging" effects characteristic of bulk-phase, population-level methods, they offer the unique capacity to observe discrete microbiological phenomena unavailable using traditional approaches. As a result, scientists have been able to characterize microorganisms, their activities, and their interactions at unprecedented levels of detail.

Hierarchical population model with a carrying capacity distribution for bacterial biofilms

In order to describe biological colonies with a conspicuous hierarchical structure, a time- and space-discrete model for the growth of a rapidly saturating local biological population N(x,t) is derived from a hierarchical random deposition process previously studied in statistical physics. Two biologically relevant parameters, the probabilities of birth, B, and of death, D, determine the carrying capacity K. Due to the randomness the population depends strongly on position x and there is a distribution of carrying capacities, Pi(K). This distribution has self-similar character owing to the exponential slowing down of the growth, assumed in this hierarchical model. The most probable carrying capacity and its probability are studied as a function of B and D. The effective growth rate decreases with time, roughly as in a Verhulst process. The model is possibly applicable, for example, to bacteria forming a "towering pillar" biofilm, a structure poorly described by standard Eden or diffusion-limited-aggregation models. The bacteria divide on randomly distributed nutrient-rich regions and are exposed to a random local bactericidal agent (antibiotic spray). A gradual overall temperature or chemical change away from optimal growth conditions reduces bacterial reproduction, while biofilm development degrades antimicrobial susceptibility, causing stagnation into a stationary state.

Bacterial self-organization: co-enhancement of complexification and adaptability in a dynamic environment

During colonial development, bacteria generate a wealth of patterns, some of which are reminiscent of those occurring in abiotic systems. They can exhibit rich behaviour, reflecting informative communication capabilities that include exchange of genetic materials and the fact that the colony's building blocks are biotic. Each has internal degrees of freedom, informatic capabilities and freedom to respond by altering itself and others via emission of signals in a self-regulated manner. To unravel the special secrets of bacterial self-organization, we conducted an integrative (experimental and theoretical) study of abiotic and biotic systems. Guided by the notion of general biotic motives and principles, I propose that the informative communication between individuals makes possible the enhancement of the individuals' regulated freedom, while increasing their cooperation. This process is accomplished via cooperative complexification of the colony through self-organization of hierarchical spatio-temporal patterning. The colonial higher complexity provides the degree of plasticity and flexibility required for better colonial adaptability and endurability in a dynamic environment. The biotic system can modify the environment and obtain environmental information for further self-improvement. I reflect on the potential applications of the new understanding on 'engineered self-organization of systems too complex to design' and other issues.

Macroscopic equations for pattern formation in mixtures of microtubules and molecular motors

Inspired by patterns observed in mixtures of microtubules and molecular motors, we propose continuum equations for the evolution of motor density and microtubule orientation. The chief ingredients are the transport of motors along tubules, and the alignment of tubules in the process. The macroscopic equations lead to aster and vortex patterns in qualitative agreement with experiments. While the early stages of evolution of tubules are similar to coarsening of spins following a quench, the rearrangement of motors leads to arrested coarsening at low densities. Even in one dimension, the equations exhibit a variety of interesting behaviors, such as symmetry breaking, moving fronts, and motor localization.

Statistical mechanics of canonical-dissipative systems and applications to swarm dynamics

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the takeup/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of nonequilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e., for active motion, and (b) interactions between the particles based on global couplings. We derive analytical expressions for the nonequilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.

Buckling instabilities of one-layered growing tissues

Growth and folding in one-layered model tissue sheets are studied in a stochastic, lattice-free single cell model which considers the discrete cellular structure of the tissue, and in a coarse grained analytical approach. The polarity of the one-layered tissue is considered by a bending term. Cell division gives rise to a locally increasing metric. An exponential and a power-law growth regime are identified. In both regimes, folding occurs as soon as the bending contribution becomes too small to compensate the destabilizing effect of the cell proliferation. The potential biological relevance is discussed.

Reaction-diffusion waves of advance in the transition to agricultural economics

In a previous paper [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)], the possible importance of higher-order terms in a human population wave of advance has been studied. However, only a few such terms were considered. Here we develop a theory including all higher-order terms. Results are in good agreement with the experimental evidence involving the expansion of agriculture in Europe.

Lubricating bacteria model for branching growth of bacterial colonies

Various bacterial strains (e.g., strains belonging to the genera Bacillus, Paenibacillus, Serratia, and Salmonella) exhibit colonial branching patterns during growth on poor semisolid substrates. These patterns reflect the bacterial cooperative self-organization. A central part of the cooperation is the collective formation of a lubricant on top of the agar which enables the bacteria to swim. Hence it provides the colony means to advance towards the food. One method of modeling the colonial development is via coupled reaction-diffusion equations which describe the time evolution of the bacterial density and the concentrations of the relevant chemical fields. This idea has been pursued by a number of groups. Here we present an additional model which specifically includes an evolution equation for the lubricant excreted by the bacteria. We show that when the diffusion of the fluid is governed by a nonlinear diffusion coefficient, branching patterns evolve. We study the effect of the rates of emission and decomposition of the lubricant fluid on the observed patterns. The results are compared with experimental observations. We also include fields of chemotactic agents and food chemotaxis and conclude that these features are needed in order to explain the observations.

Cooperative organization of bacterial colonies: from genotype to morphotype

In nature, bacteria must often cope with difficult environmental conditions. To do so they have developed sophisticated cooperative behavior and intricate communication pathways. Utilizing these elements, motile microbial colonies frequently develop complex patterns in response to adverse growth conditions on hard surfaces under conditions of energy limitation. We employ the term morphotype to refer to specific properties of colonial development. The morphologies we discuss include a tip-splitting (T) morphotype, chiral (C) morphotype, and vortex (V) morphotype. A generic modeling approach was developed by combining a detailed study of the cellular behavior and dynamics during colonial development and invoking concepts derived from the study of pattern formation in nonliving systems. Analysis of patterning behavior of the models suggests bacterial processes whereby communication leads to self-organization by using cooperative cellular interactions. New features emerging from the model include various models of cell-cell signaling, such as long-range chemorepulsion, short-range chemoattraction, and, in the case of the V morphotype, rotational chemotaxis. In this regard, pattern formation in microorganisms can be viewed as the result of the exchange of information between the micro-level (the individual cells) and the macro-level (the colony).