Fractal morphogenesis by a bacterial cell population

Cognitive and Neural Representations of Fractals in Vision, Music, and Action

The concept of fractal was popularized by Mandelbrot as a tool to tame the geometrical structure of objects with infinite hierarchical depth. The key aspect of fractals is the use of simple parsimonious rules and initial conditions, which when applied recursively can generate unbounded complexity. Fractals are structures ubiquitous in nature, being present in coast lines, bacteria colonies, trees, and physiological time series. However, within the field of cognitive science, the core question is not which phenomena can generate fractal structures, but whether human or animal minds can represent recursive processes, and if so in which domains. In this chapter, we will explore the cognitive and neural mechanisms underlying the representation of recursive hierarchical embedding. Language is the domain in which this capacity is best studied. Humans can generate an infinite array of hierarchically structured sentences, and this capacity distinguishes us from other species. However, recent research suggests that humans can represent similar structures in the domains of music, vision, and action and has provided additional cues as to how these capacities are cognitively implemented. Using a comparative approach, we will map the commonalities and differences across domains and offer a roadmap to understand the neurobiological implementation of fractal cognition.

Geometrical control of interface patterning underlies active matter invasion

Interaction between active materials and the boundaries of geometrical confinement is key to many emergent phenomena in active systems. For living active matter consisting of animal cells or motile bacteria, the confinement boundary is often a deformable interface, and it has been unclear how activity-induced interface dynamics might lead to morphogenesis and pattern formation. Here, we studied the evolution of bacterial active matter confined by a deformable boundary. We found that an ordered morphological pattern emerged at the interface characterized by periodically spaced interfacial protrusions; behind the interfacial protrusions, bacterial swimmers self-organized into multicellular clusters displaying +1/2 nematic defects. Subsequently, a hierarchical sequence of transitions from interfacial protrusions to creeping branches allowed the bacterial active drop to rapidly invade surrounding space with a striking self-similar branch pattern. We found that this interface patterning is geometrically controlled by the local curvature of the interface, a phenomenon we denote as collective curvature sensing. Using a continuum active model, we revealed that the collective curvature sensing arises from enhanced active stresses near high-curvature regions, with the active length scale setting the characteristic distance between the interfacial protrusions. Our findings reveal a protrusion-to-branch transition as a unique mode of active matter invasion and suggest a strategy to engineer pattern formation of active materials.

C. elegans episodic swimming is driven by multifractal kinetics

Fractal scaling is a common property of temporal change in various modes of animal behavior. The molecular mechanisms of fractal scaling in animal behaviors remain largely unexplored. The nematode C. elegans alternates between swimming and resting states in a liquid solution. Here, we report that C. elegans episodic swimming is characterized by scale-free kinetics with long-range temporal correlation and local temporal clusterization, namely consistent with multifractal kinetics. Residence times in actively-moving and inactive states were distributed in a power law-based scale-free manner. Multifractal analysis showed that temporal correlation and temporal clusterization were distinct between the actively-moving state and the inactive state. These results indicate that C. elegans episodic swimming is driven by transition between two behavioral states, in which each of two transition kinetics follows distinct multifractal kinetics. We found that a conserved behavioral modulator, cyclic GMP dependent kinase (PKG) may regulate the multifractal kinetics underlying an animal behavior. Our combinatorial analysis approach involving molecular genetics and kinetics provides a platform for the molecular dissection of the fractal nature of physiological and behavioral phenomena.

Random Spacing between Metal Tree Electrodeposits in Linear DLA Arrays

When we examine the random growth of trees along a linear alley in a rural area, we wonder what governs the location of those trees, and hence the distance between adjacent ones. The same question arises when we observe the growth of metal electro-deposition trees along a linear cathode in a rectangular film of solution. We carry out different sets of experiments wherein zinc trees are grown by electrolysis from a linear graphite cathode in a 2D film of zinc sulfate solution toward a thick zinc metal anode. We measure the distance between adjacent trees, calculate the average for each set, and correlate the latter with probability and entropy. We also obtain a computational image of the grown trees as a function of parameters such as the cell size, number of particles, and sticking probability. The dependence of average distance on concentration is studied and assessed.

From plants to nematodes: Serratia grimesii BXF1 genome reveals an adaptation to the modulation of multi-species interactions

Serratia grimesii BXF1 is a bacterium with the ability to modulate the development of several eukaryotic hosts. Strain BXF1 was isolated from the pinewood nematode, Bursaphelenchus xylophilus, the causative agent of pine wilt disease affecting pine forests worldwide. This bacterium potentiates Bursaphelenchus xylophilus reproduction, acts as a beneficial pine endophyte, and possesses fungal and bacterial antagonistic activities, further indicating a complex role in a wide range of trophic relationships. In this work, we describe and analyse the genome sequence of strain BXF1, and discuss several important aspects of its ecological role. Genome analysis indicates the presence of several genes related to the observed production of antagonistic traits, plant growth regulation and the modulation of nematode development. Moreover, most of the BXF1 genes are involved in environmental and genetic information processing, which is consistent with its ability to sense and colonize several niches. The results obtained in this study provide the basis to a better understanding of the role and evolution of strain BXF1 as a mediator of interactions between organisms involved in a complex disease system. These results may also bring new insights into general Serratia and Enterobacteriaceae evolution towards multitrophic interactions.

Ag fractal structures in electroless metal deposition systems with and without magnetic field

Metal electrodeposition systems display tree-like structures with extensive ramification and a fractal character. Electrolysis is not a necessary route for the growth of such dendritic metal deposits. We can grow beautiful ramification patterns via a simple redox reaction. We present here a study of silver (Ag) deposits from the reduction of Ag⁺ in (AgNO₃) solution by metallic copper. The experiments are carried out in discotic geometry, in a Petri dish hosting a thin AgNO₃ solution film. A variety of deposited structures and patterns is obtained at different Ag⁺ concentrations, yet with essentially the same fractal dimension averaged at 1.64, typical of diffusion-limited aggregation (DLA). A linear magnetic field of low induction (0.50-1.0 T) applied across the medium causes a notable transformation in the morphology of the deposits. In both the field off and the field on cases, the effect of vertical (hence 3D) heaving seems to be dominant, perhaps explaining the nearly constant fractal dimension.

My encounters with bacteria--learning about communication, cooperation and choice

My journey into the physics of living systems began with the most fundamental organisms on Earth, bacteria, that three decades ago were perceived as solitary, primitive creatures of limited capabilities. A decade later this notion had faded away and bacteria came to be recognized as the smart beasts they are, engaging in intricate social life through a sophisticated chemical language. Acting jointly, these tiny organisms can sense the environment, process information, solve problems and make decisions so as to thrive in harsh environments. The bacterial power of cooperation manifests in their ability to develop large colonies of astonishing complexity. The number of bacteria in a colony can amount to many billions, yet they exchange 'chemical tweets' that reach each and every one of them so they all know what they're all doing, each cell being both actor and spectator in the bacterial Game of Life. I share my encounters with bacteria, what I learned about the secrets of their social life and wisdom of the crowd, and why and how, starting as a theoretical physicist, I found myself studying social intelligence of bacteria. The story ends with a bacteria guide to cyber-war on cancer.

Serratia marcescensGene Required for Surfactant Serrawettin W1 Production Encodes Putative Aminolipid Synthetase Belonging to Nonribosomal Peptide Synthetase Family

Serrawettin W1 produced by Serratia marcescens is a surface active exolipid having various functions supporting behaviors of bacteria on surface environments. Through the genetic analyses of serrawettin-less mutants of S. marcescens 274, the swrW gene encoding putative serrawettin W1 synthetase was identified. Homology analysis of the putative SwrW demonstrated the presence of condensation, adenylation, thiolation, and thioesterase domains which are characteristic for nonribosomal peptide synthetase (NRPS). NRPSs have been known as multi-modular enzymes. Linear alignment of these modules specifying respective amino acids will enable peptide bond formation resulting in a specific amino acid sequence. Putative SwrW was uni-modular NRPS specifying only L-serine. Possible steps in this simple unimodular NRPS for biosynthesis of serrawettin W1 [ cyclo-(D-3-hydroxydecanoyl-L-seryl) (2) ] were predicted by referring to the ingenious enzymatic activity of gramicidin S synthetase (multi-modular NRPS) of Brevibacillus brevis.

Transcriptional Downregulator HexS Controlling Prodigiosin and Serrawettin W1 Biosynthesis inSerratia marcescens

Serratia marcescens has been known as a temperature-dependent producer of two chemically different exolipids (red pigment prodigiosin and biosurfactant serrawettin W1) in parallel. During genetic investigation of such control mechanisms, mini-Tn 5 insertional mutant Tan1 overproducing these exolipids was isolated. The gene concerning such disregulation was identified as hexS by DNA cloning followed by sequencing and homology analysis of the presumed product with 314 amino-acids. The product HexS was the homologue of HexA of Erwinia carotovora ssp. carotovora and classified as a transcriptional regulator belonging to LysR family. By RT-PCR analysis, the hexS mutant was shown to over-transcribe the pigA gene (the first gene of the pig cluster involved in prodigiosin synthesis) and the swrW gene encoding serrawettin W1 synthetase belonging to the nonribosomal peptide synthetase family. In contrast, transcription of the pswP gene encoding phosphopantetheinyl transferase in Tan1 was in the level of parent strain 274. Purified protein encoded in his(6)-hexS demonstrated binding activity to DNA fragments of the upstream region of pigA and swrW genes and not to that of the pswP gene. S. marcescens strain 274 transformed with a low-copy plasmid carrying hexS demonstrated reduced production of prodigiosin and serrawettin W1, and reduced activity of exoenzymes (protease, chitinase, and DNase) except phospholipase C. Possible generation of virulent S. marcescens by derepression or mutation of the hexS gene in infected tissues or ex vivo environments was suggested.

Identification and Characterization of thepswPGene Required for the Parallel Production of Prodigiosin and Serrawettin W1 inSerratia marcescens

Serratia marcescens mutants defective in production of the red pigment prodigiosin and the biosurfactant serrawettin W1 in parallel were isolated by transposon mutagenesis of strain 274. Cloning of the DNA fragment required for production of these secondary metabolites with different chemical structures pointed out a novel open reading frame (ORF) named pswP. The putative product PswP (230 aa) has the distinct signature sequence consensus among members of phosphopantetheinyl transferase (PPTase) which phosphopantetheinylates peptidyl carrier protein (PCP) mostly integrated in the nonribosomal peptide synthetases (NRPSs) system. Since serrawettin W1 belongs to the cyclodepsipeptides, which are biosynthesized through the NRPSs system, and one pyrrole ring in prodigiosin has been reported as a derivative of L -proline tethered to phosphopantetheinylated PCP, the mutation in the single gene pswP seems responsible for parallel failure in production of prodigiosin and serrawettin W1.

Identification and characterization of a highly motile and antibiotic refractory subpopulation involved in the expansion of swarming colonies of Paenibacillus vortex

Bacteria often use sophisticated cooperative behaviours, such as the development of complex colonies, elaborate biofilms and advanced dispersal strategies, to cope with the harsh and variable conditions of natural habitats, including the presence of antibiotics. Paenibacillus vortex uses swarming motility and cell-to-cell communication to form complex, structured colonies. The modular organization of P. vortex colony has been found to facilitate its dispersal on agar surfaces. The current study reveals that the complex structure of the colony is generated by the coexistence and transition between two morphotypes – ‘builders’ and ‘explorers’ – with distinct functions in colony formation. Here, we focused on the explorers, which are highly motile and spearhead colonial expansion. Explorers are characterized by high expression levels of flagellar genes, such as flagellin (hag), motA, fliI, flgK and sigD, hyperflagellation, decrease in ATP (adenosine-5′-triphosphate) levels, and increased resistance to antibiotics. Their tolerance to many antibiotics gives them the advantage of translocation through antibiotics-containing areas. This work gives new insights on the importance of cell differentiation and task distribution in colony morphogenesis and adaptation to antibiotics.

Mathematics make microbes beautiful, beneficial, and bountiful

Microbiology is a rich area for visualizing the importance of mathematics in terms of designing experiments, data mining, testing hypotheses, and visualizing relationships. Historically, Nobel Prizes have acknowledged the close interplay between mathematics and microbiology in such examples as the fluctuation test and mutation rates using Poisson statistics by Luria and Delbrück and the use of graph theory of polyhedra by Caspar and Klug. More and more contemporary microbiology journals feature mathematical models, computational algorithms and heuristics, and multidimensional visualizations. While revolutions in research have driven these initiatives, a commensurate effort needs to be made to incorporate much more mathematics into the professional preparation of microbiologists. In order not to be daunting to many educators, a Bloom-like "Taxonomy of Quantitative Reasoning" is shared with explicit examples of microbiological activities for engaging students in (a) counting, measuring, calculating using image analysis of bacterial colonies and viral infections on variegated leaves, measurement of fractal dimensions of beautiful colony morphologies, and counting vertices, edges, and faces on viral capsids and using graph theory to understand self assembly; (b) graphing, mapping, ordering by applying linear, exponential, and logistic growth models of public health and sanitation problems, revisiting Snow's epidemiological map of cholera with computational geometry, and using interval graphs to do complementation mapping, deletion mapping, food webs, and microarray heatmaps; (c) problem solving by doing gene mapping and experimental design, and applying Boolean algebra to gene regulation of operons; (d) analysis of the "Bacterial Bonanza" of microbial sequence and genomic data using bioinformatics and phylogenetics; (e) hypothesis testing-again with phylogenetic trees and use of Poisson statistics and the Luria-Delbrück fluctuation test; and (f) modeling of biodiversity by using game theory, of epidemics with algebraic models, bacterial motion by using motion picture analysis and fluid mechanics of motility in multiple dimensions through the physics of "Life at Low Reynolds Numbers," and pattern formation of quorum sensing bacterial populations. Through a developmental model for preprofessional education that emphasizes the beauty, utility, and diversity of microbiological systems, we hope to foster creativity as well as mathematically rigorous reasoning.

Surface hardness impairment of quorum sensing and swarming for Pseudomonas aeruginosa

The importance of rhamnolipid to swarming of the bacterium Pseudomonas aeruginosa is well established. It is frequently, but not exclusively, observed that P. aeruginosa swarms in tendril patterns—formation of these tendrils requires rhamnolipid. We were interested to explain the impact of surface changes on P. aeruginosa swarm tendril development. Here we report that P. aeruginosa quorum sensing and rhamnolipid production is impaired when growing on harder semi-solid surfaces. P. aeruginosa wild-type swarms showed huge variation in tendril formation with small deviations to the “standard” swarm agar concentration of 0.5%. These macroscopic differences correlated with microscopic investigation of cells close to the advancing swarm edge using fluorescent gene reporters. Tendril swarms showed significant rhlA-gfp reporter expression right up to the advancing edge of swarming cells while swarms without tendrils (grown on harder agar) showed no rhlA-gfp reporter expression near the advancing edge. This difference in rhamnolipid gene expression can be explained by the necessity of quorum sensing for rhamnolipid production. We provide evidence that harder surfaces seem to limit induction of quorum sensing genes near the advancing swarm edge and these localized effects were sufficient to explain the lack of tendril formation on hard agar. We were unable to artificially stimulate rhamnolipid tendril formation with added acyl-homoserine lactone signals or increasing the carbon nutrients. This suggests that quorum sensing on surfaces is controlled in a manner that is not solely population dependent.

Glucose induced fractal colony pattern of Bacillus thuringiensis

Growing colonies of bacteria on the surface of thin agar plates exhibit fractal patterns as a result of nonlinear response to environmental conditions, such as nutrients, solidity of the agar medium and temperature. Here, we examine the effect of glucose on pattern formation by growing colonies of Bacillus thuringiensis isolate KPWP1. We also present the theoretical modeling of the colony growth of KPWP1 and the associated spatio-temporal patterns. Our experimental results are in excellent agreement with simulations based on a reaction-diffusion model that describes diffusion-limited aggregation and branching, in which individual cells move actively in the periphery, but become immotile in the inner regions of the growing colony. We obtain the Hausdorff fractal dimension of the colony patterns: D(H.Expt)=1.1969 and D(H, R.D.=)1.1965, for experiment and reaction-diffusion model, respectively. Results of our experiments and modeling clearly show how glucose at higher concentration can prove to be inhibitory for motility of growing colonies of B. thuringiensis cells on semisolid support and be responsible for changes in the growth pattern.

Bacterial Swarming: A Model System for Studying Dynamic Self-assembly

Bacterial swarming is an example of dynamic self-assembly in microbiology in which the collective interaction of a population of bacterial cells leads to emergent behavior. Swarming occurs when cells interact with surfaces, reprogram their physiology and behavior, and adapt to changes in their environment by coordinating their growth and motility with other cells in the colony. This review summarizes the salient biological and biophysical features of this system and describes our current understanding of swarming motility. We have organized this review into four sections: 1) The biophysics and mechanisms of bacterial motility in fluids and its relevance to swarming. 2) The role of cell/molecule, cell/surface, and cell/cell interactions during swarming. 3) The changes in physiology and behavior that accompany swarming motility. 4) A concluding discussion of several interesting, unanswered questions that is particularly relevant to soft matter scientists.

Living on a surface: swarming and biofilm formation

Swarming is the fastest known bacterial mode of surface translocation and enables the rapid colonization of a nutrient-rich environment and host tissues. This complex multicellular behavior requires the integration of chemical and physical signals, which leads to the physiological and morphological differentiation of the bacteria into swarmer cells. Here, we provide a review of recent advances in the study of the regulatory pathways that lead to swarming behavior of different model bacteria. It has now become clear that many of these pathways also affect the formation of biofilms, surface-attached bacterial colonies. Decision-making between rapidly colonizing a surface and biofilm formation is central to bacterial survival among competitors. In the second part of this article, we review recent developments in the understanding of the transition between motile and sessile lifestyles of bacteria.

Swarming of Pseudomonas aeruginosa PAO1 without differentiation into elongated hyperflagellates on hard agar minimal medium

Polar flagellated Pseudomonas aeruginosa PAO1 demonstrated extensive spreading growth in 2 days on 1.5% agar medium. Such spreading growth of P. aeruginosa PAO1 strains was absent on Luria-Bertani 1.5% agar medium, but remarkable on Davis minimal synthetic agar medium (especially that containing 0.8% sodium citrate and 1.5% Eiken agar) under aerobic 37 degrees C conditions. Analyses using isogenic mutants and complementation transformants showed that bacterial flagella and rhamnolipid contributed to the surface-spreading behavior. On the other hand, a type IV pilus-deficient pilA mutant did not lose the spreading growth activity. Flagella staining of PAO1 T cells from the frontal edge of a spreading colony showed unipolar and normal-sized rods with one or two flagella. Thus, the polar flagellate P. aeruginosa PAO1 T appears to swarm on high-agar medium by producing biosurfactant rhamnolipid and without differentiation into an elongated peritrichous hyperflagellate.

Rhamnolipid-dependent spreading growth of Pseudomonas aeruginosa on a high-agar medium: marked enhancement under CO2-rich anaerobic conditions

Anaerobiosis of Pseudomonas aeruginosa in infected organs is now gaining attention as a unique physiological feature. After anaerobic cultivation of P. aeruginosa wild type strain PAO1 T, we noticed an unexpectedly expanding colony on a 1.5% agar medium. The basic factors involved in this spreading growth were investigated by growing the PAO1 T strain and its isogenic mutants on a Davis high-agar minimal synthetic medium under various experimental conditions. The most promotive environment for this spreading growth was an O(2)-depleted 8% CO(2) condition. From mutational analysis of this spreading growth, flagella and type IV pili were shown to be ancillary factors for this bacterial activity. On the other hand, a rhamnolipid-deficient rhlA mutant TR failed to exhibit spreading growth on a high-agar medium. Complementation of the gene defect of the mutant TR with a plasmid carrying the rhlAB operon resulted in the restoration of the spreading growth. In addition, an external supply of rhamnolipid or other surfactants (surfactin from Bacillus subtilis or artificial product Tween 80) also restored the spreading growth of the mutant TR. Such activity of surfactants on bacterial spreading on a hard-agar medium was unique to P. aeruginosa under CO(2)-rich anaerobic conditions.

A mechanical role for the chemotaxis system in swarming motility

The chemotaxis system, but not chemotaxis, is essential for swarming motility in Salmonella enterica serovar Typhimurium. Mutants in the chemotaxis pathway exhibit fewer and shorter flagella, downregulate class 3 or 'late' motility genes, and appear to be less hydrated when propagated on a surface. We show here that the output of the chemotaxis system, CheY approximately P, modulates motor bias during swarming as it does during chemotaxis, but for a distinctly different end. A constitutively active form of CheY was found to promote swarming in the absence of several upstream chemotaxis components. Two point mutations that suppressed the swarming defect of a cheY null mutation mapped to FliM, a protein in the motor switch complex with which CheY approximately P interacts. A common property of these suppressors was their increased frequency of motor reversal. These and other data suggest that the ability to switch motor direction is important for promoting optimal surface wetness. If the surface is sufficiently wet, exclusively clockwise or counterclockwise directions of motor rotation will support swarming, suggesting also that the bacteria can move on a surface with flagellar bundles of either handedness.

Measurements of the three-dimensional shape of ice crystals in supercooled water

Experimentally grown ice crystals from ultrapure supercooled water are imaged by means of Mach-Zehnder interferometry. By analyzing the fringe patterns the phase information and thus the three-dimensional shape of the ice crystals is recovered quantitatively. The integral parameters height of the basal plane, volume, and surface of the crystals are measured as a function of time and supercooling. It is found that all measured parameters follow a power law as a function of time and the exponents are found to be independent of the supercooling. The shape transition from the prismatic to the basal face along the main growth direction of the ice dendrites as a function of the distance from the tip is found to be a power law as well. Our findings support the validity of universal growth laws in pattern forming systems.

Lubricating bacteria model for the growth of bacterial colonies exposed to ultraviolet radiation

In this paper, we study the morphological transition of bacterial colonies exposed to ultraviolet radiation by modifying the bacteria model proposed by Delprato Our model considers four factors: the lubricant fluid generated by bacterial colonies, a chemotaxis initiated by the ultraviolet radiation, the intensity of the ultraviolet radiation, and the bacteria's two-stage destruction rate with given radiation intensities. Using this modified model, we simulate the ringlike pattern formation of the bacterial colony exposed to uniform ultraviolet radiation. The following is shown. (1) Without the UV radiation the colony forms a disklike pattern and reaches a constant front velocity. (2) After the radiation is switched on, the bacterial population migrates to the edge of the colony and forms a ringlike pattern. As the intensity of the UV radiation is increased the ring forms faster and the outer velocity of the colony decreases. (3) For higher radiation intensities the total population decreases, while for lower intensities the total population increases initially at a small rate and then decreases. (4) After the UV radiation is switched off, the bacterial population grows both outward as well as into the inner region, and the colony's outer front velocity recovers to a constant value. All these results agree well with the experimental observations [Phys. Rev. Lett. 87, 158102 (2001)]. Along with the chemotaxis, we find that lubricant fluid and the two-stage destruction rate are critical to the dynamics of the growth of the bacterial colony when exposed to UV radiation, and these were not previously considered.

Double dendrite growth in solidification

We present experiments on the doublon growth morphology in directional solidification. Samples used are succinonitrile with small amounts of poly(ethylene oxide), acetone, or camphor as the solute. Doublons, or symmetry-broken dendrites, are generic diffusion-limited growth structures expected at large undercooling and low anisotropy. Low anisotropy growth is achieved by selecting a grain near the {111} plane leading to either seaweed (dense branching morphology) or doublon growth depending on experimental parameters. We find selection of doublons to be strongly dependent on solute concentration and sample orientation. Doublons are selected at low concentrations (low solutal undercooling) in contrast to the prediction of doublons at large thermal undercooling in pure materials. Doublons also exhibit preferred growth directions and changing the orientation of a specific doublonic grain changes the character and stability of the doublons. We observe transitions between seaweed and doublon growth with changes in concentration and sample orientation.

Hydrodynamics of bacterial colonies: phase diagrams

We present numerical simulations of a recent hydrodynamic model describing the growth of bacterial colonies on agar plates. We show that this model is able to qualitatively reproduce experimentally observed phase diagrams, which relate a colony shape to the initial quantity of nutrients on the plate and the initial wetness of the agar. We also discuss the principal features resulting from the interplay between hydrodynamic motions and colony growth, as described by our model.

Bacterial motility on a surface: many ways to a common goal

When free-living bacteria colonize biotic or abiotic surfaces, the resultant changes in physiology and morphology have important consequences on their growth, development, and survival. Surface motility, biofilm formation, fruiting body development, and host invasion are some of the manifestations of functional responses to surface colonization. Bacteria may sense the growth surface either directly through physical contact or indirectly by sensing the proximity of fellow bacteria. Extracellular signals that elicit new gene expression include autoinducers, amino acids, peptides, proteins, and carbohydrates. This review focuses mainly on surface motility and makes comparisons to features shared by other surface phenomenon.

Hydrodynamics of bacterial colonies: a model

We propose a hydrodynamic model for the evolution of bacterial colonies growing on soft agar plates. This model consists of reaction-diffusion equations for the concentrations of nutrients, water, and bacteria, coupled to a single hydrodynamic equation for the velocity field of the bacteria-water mixture. It captures the dynamics inside the colony as well as on its boundary and allows us to identify a mechanism for collective motion towards fresh nutrients, which, in its modeling aspects, is similar to classical chemotaxis. As shown in numerical simulations, our model reproduces both usual colony shapes and typical hydrodynamic motions, such as the whirls and jets recently observed in wet colonies of Bacillus subtilis. The approach presented here could be extended to different experimental situations and provides a general framework for the use of advection-reaction-diffusion equations in modeling bacterial colonies.

Dynamics of low anisotropy morphologies in directional solidification

We report experimental results on quasi-two-dimensional diffusion limited growth in directionally solidified succinonitrile with small amounts of poly(ethylene oxide), acetone, or camphor as a solute. Seaweed growth, or dense branching morphology, is selected by growing grains close to the [111] plane, where the in-plane surface tension is nearly isotropic. The observed growth morphologies are very sensitive to small anisotropies in surface tension caused by misorientations from the [111] plane. Different seaweed morphologies are found, including the degenerate, the stabilized, and the strongly tilted seaweeds. The degenerate seaweeds show a limited fractal scaling range and, with increased undercooling, suggests a transition from "fractal" to "compact" seaweed. Strongly tilted seaweeds demonstrate a significant twofold anisotropy. In addition, seaweed-dendrite transitions are observed in low anisotropy growth.

Flagellum-independent surface migration of Vibrio cholerae and Escherichia coli

Surface translocation has been described in a large variety of microorganisms, including some gram-negative enteric bacteria. Here, we describe the novel observation of the flagellum-independent migration of Vibrio cholerae and Escherichia coli on semisolid surfaces with remarkable speeds. Important aspects of this motility are the form of inoculation, the medium composition, and the use of agarose rather than agar. Mutations in several known regulatory or surface structure proteins, such as ToxR, ToxT, TCP, and PilA, did not affect migration, whereas a defect in lipopolysaccharide biosynthesis prevented translocation. We propose that the observed surface migration is an active process, since heat, protease, or chloramphenicol treatments of the cells have strong negative effects on this phenotype. Furthermore, several V. cholerae strains strongly expressing the hemagglutinin/protease but not their isogenic hap-negative mutants, lacked the ability of surface motility, and the treatment of migrating strains with culture supernatants from hap strains but not hap-null strains prevented surface translocation.

Alternating tip splitting in directional solidification

We report experimental results on the tip splitting dynamics of seaweed growth in directional solidification of succinonitrile alloys. Despite the random appearance of the growth, a tip splitting morphology was observed in which the tip alternately splits to the left and to the right. The tip splitting frequency f was found to be related to the growth velocity V as a power law f~V1.5. This finding is consistent with the predictions of a tip splitting model that is also presented. Small anisotropies are shown to lead to different kinds of seaweed morphologies.

The role of RsmA in the regulation of swarming motility in Serratia marcescens

Swarming motility is a multicellular phenomenon comprising population migration across surfaces by specially differentiated cells. In Serratia marcescens, a network exists in which the flhDC flagellar regulatory master operon, temperature, nutrient status, and quorum sensing all contribute to the regulation of swarming motility. In this study, the rsmA (repressor of secondary metabolites) gene (hereafter rsmA(Sm)) was cloned from S. marcescens. The presence of multicopy, plasmid-encoded rsmA(Sm) expressed from its native promoter in S. marcescens inhibits swarming. Synthesis of N-acylhomoserine lactones, presumably by the product of smaI (a luxI homolog isolated from S. marcescens), was also inhibited. Knockout of rsmA(Sm) on the S. marcescens chromosome shortens the time before swarming motility begins after inoculation to an agar surface. A single copy of the chromosomal PrsmA(Sm)::luxAB reporter of rsmA(Sm) transcription was constructed. Using this reporter, the roles of the flhDC flagellar regulatory master operon, temperature and autoregulation in the control of rsmA(Sm) expression were determined. Our findings indicate that RsmA(Sm) is a component of the complex regulatory network that controls swarming.

Dynamic aspects of the structured cell population in a swarming colony of Proteus mirabilis

Proteus mirabilis forms a concentric-ring colony by undergoing periodic swarming. A colony in the process of such synchronized expansion was examined for its internal population structure. In alternating phases, i.e., swarming (active migration) and consolidation (growth without colony perimeter expansion), phase-specific distribution of cells differing in length, in situ mobility, and migration ability on an agar medium were recognized. In the consolidation phase, the distribution of mobile cells was restricted to the inner part of a new ring and a previous terrace. Cells composing the outer part of the ring were immobile in spite of their ordinary swimming ability in a viscous solution. A sectorial cell population having such an internal structure was replica printed on fresh agar medium. After printing, a transplant which was in the swarming phase continued its ongoing swarming while a transplanted consolidation front continued its scheduled consolidation. This shows that cessation of migration during the consolidation phase was not due to substances present in the underlying agar medium. The ongoing swarming schedule was modifiable by separative cutting of the swarming front or disruption of the ring pattern by random mixing of the pattern-forming cell population. The structured cell population seemed to play a role in characteristic colony growth. However, separation of a narrow consolidation front from a backward area did not induce disturbance in the ongoing swarming schedule. Thus, cells at the frontal part of consolidation area were independent of the internal cell population and destined to exert consolidation and swarming with the ongoing ordinary schedule.

Pattern formation by competition: a biological example

We present a simple model based on a reaction-diffusion equation to explain pattern formation in a multicellular bacterium (Streptomyces). We assume competition for resources as the basic mechanism that leads to pattern formation; in particular we are able to reproduce the spatial pattern formed by bacterial aerial mycelium in the case of growth in minimal (low resources) and maximal (large resources) culture media.

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).

Fractal characterization of chromatin appearance for diagnosis in breast cytology

This study explores the use of fractal analysis in the numerical description of chromatin appearance in breast cytology. Images of nuclei from fine-needle aspiration biopsies of the breast are characterized in terms of their Minkowski and spectral fractal dimensions, for 19 patients with benign epithelial cell lesions and 22 with invasive ductal carcinomas. Chromatin appearance in breast epithelial cell nuclear images is demonstrated to be fractal, suggesting that the three-dimensional chromatin structure in these cells also has fractal properties. A statistically significant difference between the mean spectral dimensions of the benign and malignant cases is demonstrated. The two fractal dimensions are very weakly correlated. A statistically significant difference between the benign and malignant cases in lacunarity, a fractal property characterizing the size of holes or gaps in a texture, is found over a wide range of scales. These differences are particularly pronounced at the smallest and largest scales, corresponding respectively to fine-scale texture, indicating whether chromatin is clumped or fine, and to large-scale structures like nucleoli. Logistic regression and artificial neural network classification models are developed to classify unknown cases on the basis of fractal measures of chromatin texture. Using leave-one-out cross-validation, the best logistic regression classifier correctly diagnoses 95.1 per cent of the cases. The best neural network model can correctly classify all of the cases, but it is unclear whether this is due to overtraining. Fractal dimensions and lacunarity are useful tools for the quantitative characterization of chromatin appearance, and can potentially be incorporated into image analysis devices to assure the quality and reproducibility of diagnosis by breast fine-needle aspiration biopsy.

Classification and genetic characterization of pattern-forming Bacilli

One of the more natural but less commonly studied forms of colonial bacterial growth is pattern formation. This type of growth is characterized by bacterial populations behaving in an organized manner to generate readily identifiable geometric and predictable morphologies on solid and semi-solid surfaces. In our first attempt to study the molecular basis of pattern formation in Bacillus subtilis, we stumbled upon an enigma: some strains used to describe pattern formation in B. subtilis did not have the phenotypic or genotypic characteristics of B. subtilis. In this report, we show that these strains are actually not B. subtilis, but belong to a different class of Bacilli, group I. We show further that commonly used laboratory strains of B. subtilis can co-exist as mixed cultures with group I Bacilli, and that the latter go unnoticed when grown on frequently used laboratory substrates. However, when B. subtilis is grown under more stringent semiarid conditions, members of group I emerge in the form of complex patterns. When B. subtilis is grown under less stringent and more motile conditions, B. subtilis forms its own pattern, and members of group I remain unnoticed. These findings have led us to revise some of the mechanistic and evolutionary hypotheses that have been proposed to explain pattern growth in Bacilli.

Patterns of reporter gene expression in the phase diagram of Bacillus subtilis colony forms

Factors governing the morphogenesis of Bacillus subtilis colonies as well as the spatial-temporal pattern of expression of a reporter gene during colony development were examined by systematically varying the initial nutrient levels and agar concentrations (wetness), the relative humidity throughout incubation, and the genotype of the inoculum. A relationship between colony form and reporter gene expression pattern was found, indicating that cells respond to local signals during colony development as well as global conditions. The most complex colony forms were produced by motile strains grown under specific conditions such that cells could swim within the colony but not swarm outward uniformly from the colony periphery. The wetness of the growth environment was found to be a critical factor. Complex colonies consisted of structures produced by growth of finger-like projections that expanded outward a finite distance before giving rise to a successive round of fingers that behaved in a similar fashion. Finger tip expansion occurred when groups of cells penetrated the peripheral boundary. Although surfactin production was found to influence similar colony forms in other B. subtilis strains, the strains used here to study reporter gene expression do not produce it. The temporal expression of a reporter gene during morphogenesis of complex colonies by motile strains such as M18 was investigated. Expression arose first in cells located at the tips of fingers that were no longer expanding. The final expression pattern obtained reflects the developmental history of the colony.

Mutational analysis of flagellum-independent surface spreading of Serratia marcescens 274 on a low-agar medium

In a previous study (J. O'Rear, L. Alberti, and R. M. Harshey, J. Bacteriol. 174:6125-6137, 1992) we reported the isolation of several transposon mutants of Serratia marcescens 274 that were defective either in swarming alone or in both swimming and swarming motility. All the nonflagellate (Fla-) mutants, while defective in both types of motility, were able to spread rapidly on the surface of low-agar (0.35%) media. We show here that some of the swarming-defective mutants are defective in the production of serrawettin W1, an extracellular cyclic lipopeptide produced by S. marcescens 274. When combined with a Fla defect, the serrawettin (Swt) mutants are deficient in spreading on low-agar media. The spreading deficiency can be overcome by serrawettin supplied extracellularly. Introduction of Fla defects into chemotaxis mutants does not affect this mode of surface translocation. These results suggest that spreading may be a passive form of translocation. We also report that swarming defects in all mutants showing a Dps phenotype (able to swarm within the inoculated area but unable to move outward) in the earlier study can be overcome by changing the commercial source of agar.

Dimorphic transition in Escherichia coli and Salmonella typhimurium: surface-induced differentiation into hyperflagellate swarmer cells

We describe a new behavioral response in Escherichia coli and Salmonella typhimurium in which the bacteria differentiate into filamentous, multinucleate, hyperflagellate cells that navigate the surface of solid media by means of coordinated swarming motility. The cue for differentiation into swarmer cells is provided by the concentration and composition of the agar. Examination of the behavior of various mutants shows that the flagellar apparatus used for swimming motility and the chemotaxis system are indispensable for swarming motility.

Dynamics of Bacillus colony growth

A growing bacterial colony is not an amorphous mass but is a dynamic and differentiated system. It may appear chaotic in the details of its structure but it can be accurately described by simple models for fractal geometry. As Benoit Mandelbrot said: 'Surprise, simple rules can generate rich structures'.