Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ``phantom traffic jams'' even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ``freeze by heating''? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.

Traffic and related self-driven many-particle systems

We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior Our aim is to provide a balanced discussion of the various facets of this highly multidisciplinary field, including experiments, mathematical methods and models for simulations, so that readers with a variety of background could get both the basics and a broader, more detailed picture of the field The observations we report on include systems consisting of units ranging from macromolecules through metallic rods and robots to groups of animals and people Some emphasis is put on models that are simple and realistic enough to reproduce the numerous related observations and are useful for developing concepts for a better understanding of the complexity of systems consisting of many simultaneously moving entities As such, these models allow the establishing of a few fundamental principles of flocking In particular, it is demonstrated, that in spite of considerable differences, a number of deep analogies exist between equilibrium statistical physics systems and those made of self-propelled (in most cases living) units In both cases only a few well defined macroscopic/collective states occur and the transitions between these states follow a similar scenario, involving discontinuity and algebraic divergences

Collective Motion

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.

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A synthetic multicellular system for programmed pattern formation

Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics

It has been a decade since multicellularity was proposed as a general bacterial trait. Intercellular communication and multicellular coordination are now known to be widespread among prokaryotes and to affect multiple phenotypes. Many different classes of signaling molecules have been identified in both Gram-positive and Gram-negative species. Bacteria have sophisticated signal transduction networks for integrating intercellular signals with other information to make decisions about gene expression and cellular differentiation. Coordinated multicellular behavior can be observed in a variety of situations, including development of E. coli and B. subtilis colonies, swarming by Proteus and Serratia, and spatially organized interspecific metabolic cooperation in anaerobic bioreactor granules. Bacteria benefit from multicellular cooperation by using cellular division of labor, accessing resources that cannot effectively be utilized by single cells, collectively defending against antagonists, and optimizing population survival by differentiating into distinct cell types.

Thinking about bacterial populations as multicellular organisms

Bacterial colonies must often cope with unfavourable environmental conditions. To do so, they have developed sophisticated modes of cooperative behaviour. It has been found that such behaviour can cause bacterial colonies to exhibit complex growth patterns similar to those observed during non-equilibrium growth processes in non-living systems; some of the qualitative features of the latter may be invoked to account for the complex patterns of bacterial growth. Here we show that a simple model of bacterial growth can reproduce the salient features of the observed growth patterns. The model incorporates random walkers, representing aggregates of bacteria, which move in response to gradients in nutrient concentration and communicate with each other by means of chemotactic 'feedback'. These simple features allow the colony to respond efficiently to adverse growth conditions, and generate self-organization over a wide range of length scales.

Generic modelling of cooperative growth patterns in bacterial colonies

We present a study of interfacial pattern formation during diffusion-limited growth of Bacillus subtilis It is demonstrated that bacterial colonies can develop patterns similar to morphologies observed during diffusion-limited growth in non-living (azoic) systems such as solidification and electro-chemical deposition The various growth morphologies, that is the global structure of the colony, are observed as we vary the growth conditions These include fractal growth, dense-branching growth, compact growth, dendritic growth and chiral growth The results demonstrate the action of a singular interplay between the micro-level (individual bacterium) and macro-level (the colony) in selecting the observed morphologies as is understood for non-living systems Furthermore, the observed morphologies can be organized within a morphology diagram indicating the existence of a morphology selection principle similar to the one proposed for azoic systems We propose a phase-field-like model (the phase being the bacterial concentration and the field being the nutrient concentration) to describe the growth The bacteria-bacteria interaction is manifested as a phase dependent diffusion constant Growth of a bacterial colony presents an inherent additional level of complexity compared to azoic systems, since the building blocks themselves are living systems Thus, our studies also focus on the transition between morphologies We have observed extended morphology transitions due to phenotypic changes of the bacteria, as well as bursts of new morphologies resulting from genotypic changes In addition, we have observed extended and heritable transitions (mainly between dense branching growth and chiral growth) as well as phenotypic transitions that turn genotypic over time We discuss the implications of our results in the context of the evolving picture of genome cybernetics Diffusion limited growth of bacterial colonies combined with new understanding of pattern formation in azoic systems provide new tools for the study of adaptive self-organization and mutation in the presence of selective pressures We include brief reviews of both the recent developments in the study of interfacial pattern formation in non-living systems and the current trends in the view of mutation dynamics

Adaptive self-organization during growth of bacterial colonies

Bacterial colonies can develop chiral morphology in which the colony consists of twisted branches, all with the same handedness. Microscopic observations of the chiral growth are presented. We propose that the observed (macroscopic) chirality results from the microscopic chirality of the flagella (via handedness in tumbling) together with orientation interaction between the bacteria. The above assumptions are tested using a generalized version of the communicating walkers model.

Cooperative formation of chiral patterns during growth of bacterial colonies.

We present a study of colony transformations during growth of Bacillus subtilis under adverse environmental conditions. It is a continuation of our pilot study of “Adaptive self-organization during growth of bacterial colonies” (Physica A 187 (1992) 378). First we identify and describe the transformations pathway, i.e. the excitation of the branching modes from Bacillus subtilis 168 (grown under diffusion limited conditions) and the phase transformations between the tip-splitting phase (phase T) and the chiral phase (phase C) which belong to the same mode. This pathway shows the evolution of complexity as the bacteria are exposed to adverse growth conditions. We present the morphology diagram of phases T and C as a function of agar concentration and pepton level. As expected, the growth of phase T is ramified (fractal-like or DLA-like) at low pepton level (about 1 g/1) and turns compact at high pepton level (about 10 g/1). The growth of phase C is also ramified at low pepton level and turns denser and finally compact as the pepton level increases. Generally speaking, the colonies develop more complex patterns and higher micro-level organization for more adverse environments. We use the growth velocity as a response function to describe the growth. At low agar concentration (and low pepton level) phase C grows faster than phase T, and for a high agar concentration (about 2%) phase T grows faster. We observe colony transformations between the two phases (phase transformations). They are found to be consistent with the “fastest growing morphology” selection principle adopted from azoic systems. The transformations are always from the slower phase to the faster one. Hence, we observe T→C transformations at low agar concentrations and C→T transformations at high agar concentrations. We have observed both localized and extended transformations. Usually, the transformations are localized for more adverse growth conditions, and extended for growth conditions close to the boundaries between morphologies. We have observed also transformations between different branching modes, as well as transformations via virtual states.

Motivated by the contemporary knowledge about phages and plasmids, we postulate a theoretical framework to comply with our experimental findings. We explain our observations using these assumptions as well as our proposal of co-mutations and auto-catalytic mutations as presented in the above mentioned pilot paper. This theoretical framework is a part of the new evolving picture of genome cybernetics. We also discuss the concept of adaptive genome changes which are based on pre-existing knowledge as well as the concept of genetic learning. i.e. changes (in response to a new problem) which develop the potential for adaptive genome changes. These concepts follow naturally if the picture of genome cybernetics is accepted. We conclude with a discussion of the implications and with further predictions (to be tested experimentally) derived from our assumptions.

Holotransformations of bacterial colonies and genome cybernetics

We present a study of interfacial pattern formation during growth of bacterial colonies. Growth of bacterial colony bears similarities to but presents an inherent additional level of complexity compared to non-living systems. In the former case, the building blocks themselves are living systems each with its own autonomous self-interest and internal degrees of freedom. At the same time, efficient adaptation of the colony to adverse growth conditions requires self-organization on all levels — which can be achieved only via cooperative behavior of the bacteria. To do so, the bacteria have developed sophisticated communication channels on all levels. Here we present a non-local communicating walkers model to study the effect of local bacterium-bacterium interaction and communication via chemotaxis signaling. We demonstrate how communication enables the colony to develop complex patterns in response to adverse growth conditions. Efficient response of the colony requires self-organization on all levels, which can be achieved only via cooperative behavior of the bacteria. It can be viewed as the action of an interplay between the micro-level (the individual bacterium) and the macro-level (the colony) in the determination of the emerging pattern. Some qualitative features of the complex morphologies can be accounted for by invoking ideas from pattern formation in non-living systems together with a simplified model of chemotactic "feedback."

Adam Tenenbaum

Papers

Generic modelling of cooperative growth patterns in bacterial colonies

Adaptive self-organization during growth of bacterial colonies

Cooperative formation of chiral patterns during growth of bacterial colonies.

Holotransformations of bacterial colonies and genome cybernetics

Communication, regulation and control during complex patterning of bacterial colonies