Biofluiddynamics of lubricating bacteria. (English) Zbl 1097.76618
Summary: Various bacterial strains exhibit colonial branching patterns during growth on thin poor substrates. The growth can be either diffusion-limited or kinetic-limited, according to the imposed growth conditions. We present experimental observations of patterns exhibited by the bacterial strains Paenibacillus dendritiformis and Paenibacillus vortex. All manners of branching patterns are observed, the three main being: (1) basic branching; (2) chiral branching; (3) vortex branching. We show that the following biological features can explain the spectrum of observed patterns: (1) Formation of a lubricating fluid. (2) Food chemotactic. (3) Attractive and repulsive chemotactic signaling. (4) Flagella handedness. (5) Transition into pre-spore state. In the theoretical studies we employ knowledge drawn from branching patterning in non-living systems and the mathematical properties of reaction-diffusion models and atomistic models. The above can be used not just to describe existing biological understanding, but also to derive new understanding. For example, reaction-diffusion models that include bacterial density and nutrient concentration, can exhibit branching dynamics if the growth term is a meta-stable fixed point or if the diffusion is state dependent. We show that biologically the growth term has to be an unstable fixed point, but that state-dependent diffusion can represent the lubrication fluid excreted by the bacteria.
MSC:
| 76Z99 | Biological fluid mechanics |
Keywords:
Biofluid dynamicsReferences:
| [1] | Ben-Jacob, Contemporary Physics 34 pp 247– (1993) |
| [2] | Ben-Jacob, Contemporary Physics 38 pp 205– (1997) |
| [3] | Ben-Jacob, Nature 343 pp 523– (1990) |
| [4] | Kessler, Advances in Physics 37 pp 255– (1988) |
| [5] | Langer, Science 243 pp 1150– (1989) |
| [6] | Fractals. Plenum: New York, 1988. · doi:10.1007/978-1-4899-2124-6 |
| [7] | The Fractal Geometry of Nature. Freeman: San Francisco, 1977. |
| [8] | Fractals: Form, Chance and Dimension. Freeman: San Francisco, 1977. · Zbl 0376.28020 |
| [9] | Sander, Nature 322 pp 789– (1986) |
| [10] | Fractal Growth Phenomena. World Scientific: New York, 1989. · doi:10.1142/0511 |
| [11] | Ben-Jacob, Physica A 187 pp 378– (1992) |
| [12] | Bakterien schließen sich zu bizarren formationen zusammen. In Muster des Ledendigen: Faszination inher Entstehung und Simulation, (ed.). Verlag Vieweg: Braunschweig, 1994. |
| [13] | Evolution of complexity during growth of bacterial colonies. In Spatio-Temporal Patterns in Nonequilibrium Complex Systems, Santa-Fe Institute Studies in the Sciences of Complexity, (eds). Addison-Wesley Publishing Company: Reading, MA, 1995. |
| [14] | Ben-Jacob, Physica A 202 pp 1– (1994) |
| [15] | Fujikawa, Journal of the Physical Society of Japan 58 pp 3875– (1989) |
| [16] | Fujikawa, Journal of the Physical Society of Japan 60 pp 88– (1991) |
| [17] | Matsushita, Physica A 168 pp 498– (1990) |
| [18] | Growth and morphological changes of bacteria colonies. In Spatio-Temporal Patterns in Nonequilibrium Complex Systems, Santa-Fe Institute Studies in the Sciences of Complexity, (eds). Addison-Wesley Publishing Company: Reading, MA, 1995; 609-618. |
| [19] | Matsuyama, Fractals 1 pp 302– (1993) |
| [20] | Matsuyama, Critical Reviews in Microbiology 19 pp 117– (1993) |
| [21] | Ben-Jacob, Physica A 238 pp 181– (1997) |
| [22] | Ben-Jacob, Nature 373 pp 566– (1995) |
| [23] | Ben-Jacob, Physical Review Letters 75 pp 2899– (1995) |
| [24] | Ben-Jacob, Fractals 2 pp 15– (1994) |
| [25] | Ben-Jacob, Nature 368 pp 46– (1994) |
| [26] | Levine, Physical Review E 63 pp 017101– (2001) |
| [27] | Kessler, Physical Reviews E 48 pp 4801– (1993) |
| [28] | Kessler, Physica D 106 pp 375– (1997) |
| [29] | Mackay, Journal of Cell Science 33 pp 1– (1978) |
| [30] | Parnas, Journal of Theoretical Biology 71 pp 185– (1978) |
| [31] | Matsushita, Physica A 249 pp 517– (1998) |
| [32] | A reaction-diffusion approach to bacterial colony formation. Preprint, 1997. |
| [33] | Kawasaki, Journal of Theoretical Biology 188 pp 177– (1997) |
| [34] | Kitsunezaki, Journal of the Physical Society of Japan 66 pp 1544– (1997) · Zbl 0897.76040 |
| [35] | Kozlovsky, Physical Reviews E 59 pp 7025– (1999) |
| [36] | Formation of concentric rings in bacterial colonies. M.Sc. Thesis, Chuo University, Japan, 1998. |
| [37] | Golding, Physica A 260 pp 510– (1998) |
| [38] | Tcherpakov, International Journal of Systematic Bacteriology 49 pp 239– (1999) |
| [39] | Tcherpakov, International Journal of Systematic Bacteriology |
| [40] | Ben-Jacob, Annual Reviews in Microbiology 52 pp 779– (1998) |
| [41] | Modelling branching and chiral colonial patterning of lubricating bacteria. In Mathematical Models for Biological Pattern Formation, IMA volumes, Frontiers in Applied Mathematics Series. (eds). Springer-Verlag: New-York, 2000; 211-254. |
| [42] | Isolation and characterization of bacteria growing in patterns on the surface of solid agar. Senior Project under the supervision of D. Gutnick., Tel-Aviv University, 1993. |
| [43] | Ben-Jacob, Physica A 282 pp 247– (2000) |
| [44] | van Sinderen, Molecular Microbiology 15 pp 213– (1995) |
| [45] | Shih, Canadian Journal of Microbiology 42 pp 628– (1996) |
| [46] | Deak, Microbiology 144 pp 2169– (1998) |
| [47] | Cohen, Physica A 233 pp 678– (1996) |
| [48] | Henrichsen, Bacteriological Reviews 36 pp 478– (1972) |
| [49] | Alberti, Journal of Bacteriology 172 pp 4322– (1990) |
| [50] | Harshey, Proceedings of the National Academy of Science USA 91 pp 8631– (1994) |
| [51] | Hoiczyk, Current Biology 8 pp 1161– (1998) |
| [52] | Rauprich, Journal of Bacteriology 178 pp 6525– (1998) |
| [53] | Spormann, Microbiology and Molecular Biology Review 63 pp 621– (1999) |
| [54] | Young, Journal of Bacteriology 181 pp 2823– (1999) |
| [55] | Mendelson, Journal of Bacteriology 181 pp 600– (1999) |
| [56] | DeRosier, Cell 93 pp 17– (1998) |
| [57] | Eisenbach, Molecular Microbiology 4 pp 161– (1990) |
| [58] | Random walks in biology. Princeton, N.J.: Princeton University Press, 1993. |
| [59] | Matsuyama, Journal of Bacteriology 174 pp 1769– (1992) |
| [60] | Peypoux, Applied Microbiology and Biotechnology 51 pp 553– (1999) |
| [61] | Desai, Microbiology and Molecular Biology Review 61 pp 47– (1997) |
| [62] | Matsuyama, Colloids Surface B: Biointerfaces 7 pp 207– (1996) |
| [63] | Stahl, Journal of Bacteriology 154 pp 930– (1983) |
| [64] | Mathematical modelling and analysis of pattern formation and colonial organization in bacterial colonies. M.Sc. Thesis, Tel-Aviv University, Israel, 1997. |
| [65] | Lacasta, Physical Review E 59 pp 7036– (1999) |
| [66] | Kessler, Nature 394 pp 556– (1998) |
| [67] | Cohen, Fractals 7 pp 235– (1999) |
| [68] | Sánchez-Garduño, Journal of Mathematical Biology 33 pp 163– (1994) |
| [69] | Sánchez-Garduño, Forma 11 pp 45– (1996) |
| [70] | Gurtin, Mathematical Biosciences 33 pp 35– (1977) |
| [71] | Density-dependent interaction-diffusion systems. In: Dynamics and Modelling of Reactive Systems. New York: Academic Press, 1980; 161-176. · doi:10.1016/B978-0-12-669550-2.50010-5 |
| [72] | Newman, Journal of Theoretical Biology 85 pp 325– (1980) |
| [73] | Newman, Journal of Theoretical Biology 104 pp 473– (1983) |
| [74] | Hegstrom, Scientific American 262 pp 108– (1990) |
| [75] | Avetisov, Physics Today 44 pp 33– (1991) |
| [76] | Mendelson, Proceedings of the National Academy of Sciences USA 75 pp 2478– (1978) |
| [77] | Mendelson, Journal of Bacteriology 151 pp 455– (1982) |
| [78] | Mendelson, Journal of Bacteriology 171 pp 1055– (1989) |
| [79] | Mendelson, Science in Progress 74 pp 425– (1990) |
| [80] | Stock, Nature 344 pp 395– (1990) |
| [81] | Shaw, BioEssays 13 pp 25– (1991) |
| [82] | Shochet, Physica A 181 pp 136– (1992) |
| [83] | Shochet, Physica A 187 pp 87– (1992) |
| [84] | Study of late-stage growth and morphology selection during diffusive patterning. Ph.D. Thesis, Tel-Aviv University, 1995. |
| [85] | Orientation field model for chiral branching growth of bacterial colonies, arXiv:cond-mat/0008446.2000. |
| [86] | Adler, Science 166 pp 1588– (1969) |
| [87] | Berg, Biophysical Journal 20 pp 193– (1977) |
| [88] | (ed.). Biology of the Chemotactic Response. Cambridge University Press: Cambridge, 1986. |
| [89] | Eisenbach, Molecular Microbiology 20 pp 903– (1996) |
| [90] | Spiro, Proceedings of the National Academy of Science USA 94 pp 7263– (1997) |
| [91] | Mathematical Biology. Springer: Berlin, 1989. · Zbl 0682.92001 · doi:10.1007/978-3-662-08539-4 |
| [92] | Smart bacterial colonies. In Physics of Biological Systems: From Molecules to Species, Lecture Notes in Physics. Springer: Berlin, 1997; 307-324. · doi:10.1007/978-3-540-49733-2_14 |
| [93] | Cooperative formation of bacterial patterns. In Bacteria as Multicellular Organisms, (eds). Oxford University Press: New-York, 1997. |
| [94] | Budrene, Nature 349 pp 630– (1991) |
| [95] | Tsimring, Physical Review Letters 75 pp 1859– (1995) |
| [96] | Budrene, Nature 376 pp 49– (1995) |
| [97] | Segall, Proceedings of the National Academy of Science USA 83 pp 8987– (1986) |
| [98] | Hemmingsson, Journal of Physics A 28 pp 4245– (1995) · Zbl 0860.65090 |
| [99] | Duparcmeur, Journal de Physique I 5 pp 1119– (1995) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
