메뉴 건너뛰기




Volumn 260, Issue 3-4, 1998, Pages 510-554

Studies of bacterial branching growth using reaction-diffusion models for colonial development

Author keywords

Bacillus subtilis; Model; Morphology transition; Organization; Reaction diffusion

Indexed keywords

CYBERNETICS; DIFFUSION; MATHEMATICAL MODELS;

EID: 0032207792     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(98)00345-8     Document Type: Article
Times cited : (183)

References (94)
  • 2
    • 0002748956 scopus 로고
    • Bacteria as multicellular organisms
    • J.A. Shapiro, Bacteria as multicellular organisms, Scientific American 258 (6) (1988) 62-69.
    • (1988) Scientific American , vol.258 , Issue.6 , pp. 62-69
    • Shapiro, J.A.1
  • 3
    • 0040007234 scopus 로고    scopus 로고
    • From snowflake formation to the growth of bacterial colonies. Part II: Cooperative formation of complex colonial patterns
    • E. Ben-Jacob, From snowflake formation to the growth of bacterial colonies. Part II: Cooperative formation of complex colonial patterns, Contemp. Phys. 38 (1997) 205-241.
    • (1997) Contemp. Phys. , vol.38 , pp. 205-241
    • Ben-Jacob, E.1
  • 4
    • 0041710824 scopus 로고    scopus 로고
    • Cooperative self-organization of microorganisms
    • in press
    • E. Ben-Jacob, I. Cohen, H. Levine, Cooperative self-organization of microorganisms, Adv. Phys. (1998), in press.
    • (1998) Adv. Phys.
    • Ben-Jacob, E.1    Cohen, I.2    Levine, H.3
  • 6
    • 0001478135 scopus 로고
    • Helical Bacillus subtilis macrofibers: Morphogenesis of a bacterial multicellular macroorganism
    • N.H. Mendelson, Helical Bacillus subtilis macrofibers: morphogenesis of a bacterial multicellular macroorganism, Proc. Natl. Acad. Sci. USA 75 (5) (1978) 2478-2482.
    • (1978) Proc. Natl. Acad. Sci. USA , vol.75 , Issue.5 , pp. 2478-2482
    • Mendelson, N.H.1
  • 7
    • 0024423023 scopus 로고
    • Dictyostelium discoideum: A model system for cell-cell interactions in development
    • P. Devreotes, Dictyostelium discoideum: a model system for cell-cell interactions in development, Science 245 (1989) 1054-1058.
    • (1989) Science , vol.245 , pp. 1054-1058
    • Devreotes, P.1
  • 8
    • 0026519880 scopus 로고
    • A novel extracellular cyclic lipopeptide which promotes flagellum-dependent and - Independent spreading growth of serratia marcescens
    • T. Matsuyama, K. Kaneda, Y. Nakagawa, K. Isa, H. Hara-Hotta, I. Yano, A novel extracellular cyclic lipopeptide which promotes flagellum-dependent and - independent spreading growth of serratia marcescens, J. Bacteriol. 174 (1992) 1769-1776.
    • (1992) J. Bacteriol. , vol.174 , pp. 1769-1776
    • Matsuyama, T.1    Kaneda, K.2    Nakagawa, Y.3    Isa, K.4    Hara-Hotta, H.5    Yano, I.6
  • 9
    • 0028147156 scopus 로고
    • Bees aren't the only ones: Swarming in gram-negative bacteria
    • R.M. Harshey, Bees aren't the only ones: swarming in gram-negative bacteria, Mol. Microbiol. 13 (1994) 389-394.
    • (1994) Mol. Microbiol. , vol.13 , pp. 389-394
    • Harshey, R.M.1
  • 10
    • 0027957161 scopus 로고
    • Quorum sensing in bacteria: The LuxR-LuxI family of cell density-responsive transcriptional regulators
    • W.C. Fuqua, S.C. Winans, E.P. Greenberg, Quorum sensing in bacteria: the LuxR-LuxI family of cell density-responsive transcriptional regulators, J. Bacteriol. 176 (1994) 269-275.
    • (1994) J. Bacteriol. , vol.176 , pp. 269-275
    • Fuqua, W.C.1    Winans, S.C.2    Greenberg, E.P.3
  • 11
    • 0029145808 scopus 로고
    • Multiple homologues of luxr and luxi control expression of virulence determinants and secondary metabolites through quorum sensing in pseudomonas aeruginosa paol
    • A. Latifi, M.K. Winson, M. Foglino, B.W. Bycroft, G.S. Stewart, A. Lazdunski, P. Williams, Multiple homologues of luxr and luxi control expression of virulence determinants and secondary metabolites through quorum sensing in pseudomonas aeruginosa paol, Mol. Microbiol. 17 (1995) 333-343
    • (1995) Mol. Microbiol. , vol.17 , pp. 333-343
    • Latifi, A.1    Winson, M.K.2    Foglino, M.3    Bycroft, B.W.4    Stewart, G.S.5    Lazdunski, A.6    Williams, P.7
  • 12
    • 0029818809 scopus 로고    scopus 로고
    • Census and consensus in bacterial ecosystems: The LuxR-LuxI family of quorum-sensing transcriptional regulators
    • C. Fuqua, S.C. Winans, E.P. Greenberg, Census and consensus in bacterial ecosystems: the LuxR-LuxI family of quorum-sensing transcriptional regulators, Annu. Rev. Microbiol. 50 (1996) 727-751.
    • (1996) Annu. Rev. Microbiol. , vol.50 , pp. 727-751
    • Fuqua, C.1    Winans, S.C.2    Greenberg, E.P.3
  • 13
    • 0026023209 scopus 로고
    • Complex patterns formed by motile cells of esherichia coli
    • E.O. Budrene, H.C. Berg, Complex patterns formed by motile cells of esherichia coli, Nature 349 (1991) 630-633.
    • (1991) Nature , vol.349 , pp. 630-633
    • Budrene, E.O.1    Berg, H.C.2
  • 14
    • 0028940607 scopus 로고
    • Tar-dependent and -independent pattern formation by Salmonella typhimurium
    • Y. Blat, M. Eisenbach, Tar-dependent and -independent pattern formation by Salmonella typhimurium, J. Bacteriol. 177 (7) (1995) 1683-1691.
    • (1995) J. Bacteriol. , vol.177 , Issue.7 , pp. 1683-1691
    • Blat, Y.1    Eisenbach, M.2
  • 15
    • 0029023398 scopus 로고
    • Dynamics of formation of symmetrical patterns by chemotactic bacteria
    • E.O. Budrene, H.C. Berg, Dynamics of formation of symmetrical patterns by chemotactic bacteria, Nature 376 (1995) 49-53.
    • (1995) Nature , vol.376 , pp. 49-53
    • Budrene, E.O.1    Berg, H.C.2
  • 16
    • 0002146045 scopus 로고
    • Sequential events in bacterial colony morphogenesis
    • J.A. Shapiro, D. Trubatch, Sequential events in bacterial colony morphogenesis, Physica D 49 (1991) 214-223.
    • (1991) Physica D , vol.49 , pp. 214-223
    • Shapiro, J.A.1    Trubatch, D.2
  • 17
    • 0027219811 scopus 로고
    • Patterns of gene expression in Bacillus subtilis colonies
    • B. Salhi, N.H. Mendelson, Patterns of gene expression in Bacillus subtilis colonies, J. Bacteriol. 175 (1993) 5000-5008.
    • (1993) J. Bacteriol. , vol.175 , pp. 5000-5008
    • Salhi, B.1    Mendelson, N.H.2
  • 18
    • 0029972434 scopus 로고    scopus 로고
    • Patterns of reporter gene expression in the phase diagram of Bacillus subtilis colony forms
    • N.H. Mendelson, B. Salhi, Patterns of reporter gene expression in the phase diagram of Bacillus subtilis colony forms, J. Bacteriol. 178 (1996) 1980-1989.
    • (1996) J. Bacteriol. , vol.178 , pp. 1980-1989
    • Mendelson, N.H.1    Salhi, B.2
  • 19
    • 0029003985 scopus 로고
    • Evidence that F plasmid transfer replication underlies apparent adaptive mutation
    • T. Galitski, J.R. Roth, Evidence that F plasmid transfer replication underlies apparent adaptive mutation, Science 268 (1995) 421-423.
    • (1995) Science , vol.268 , pp. 421-423
    • Galitski, T.1    Roth, J.R.2
  • 20
    • 0029052121 scopus 로고
    • Adaptive mutation in Escherichia coli: A role for conjugation
    • J.P. Rasicella, P.U. Park, M.S. Fox, Adaptive mutation in Escherichia coli: a role for conjugation, Science 268 (1995) 418-420.
    • (1995) Science , vol.268 , pp. 418-420
    • Rasicella, J.P.1    Park, P.U.2    Fox, M.S.3
  • 21
    • 0031614083 scopus 로고    scopus 로고
    • Bacterial gene swapping in nature
    • January
    • R.V. Miller, Bacterial gene swapping in nature, Scientific American (January 1998).
    • (1998) Scientific American
    • Miller, R.V.1
  • 22
    • 0001522934 scopus 로고
    • Co-operative and concentrative phenomena of swimming micro-organisms
    • J.O. Kessler, Co-operative and concentrative phenomena of swimming micro-organisms, Contemp. Phys. 26 (1985) 147-166.
    • (1985) Contemp. Phys. , vol.26 , pp. 147-166
    • Kessler, J.O.1
  • 23
    • 0000510478 scopus 로고
    • Fractal growth of Bacillus subtilis on agar plates
    • H. Fujikawa, M. Matsushita, Fractal growth of Bacillus subtilis on agar plates, J. Phys. Soc. Japan 58 (1989) 3875-3878.
    • (1989) J. Phys. Soc. Japan , vol.58 , pp. 3875-3878
    • Fujikawa, H.1    Matsushita, M.2
  • 25
    • 25544479059 scopus 로고
    • Adaptive self-organization during growth of bacterial colonies
    • E. Ben-Jacob, H. Shmueli, O. Shochet, A. Tenenbaum, Adaptive self-organization during growth of bacterial colonies, Physica A 187 (1992) 378-424.
    • (1992) Physica A , vol.187 , pp. 378-424
    • Ben-Jacob, E.1    Shmueli, H.2    Shochet, O.3    Tenenbaum, A.4
  • 26
    • 0001661265 scopus 로고
    • Self-similar colony morphogenesis by bacteria as the experimental model of fractal growth by a cell population
    • T. Matsuyama, R.M. Harshey, M. Matsushita, Self-similar colony morphogenesis by bacteria as the experimental model of fractal growth by a cell population, Fractals 1 (3) (1993) 302-311.
    • (1993) Fractals , vol.1 , Issue.3 , pp. 302-311
    • Matsuyama, T.1    Harshey, R.M.2    Matsushita, M.3
  • 30
    • 0031118285 scopus 로고    scopus 로고
    • Chemomodulation of cellular movement and collective formation of vortices by swarming bacteria and colonial development
    • E. Ben-Jacob, I. Cohen, A. Czirók, T. Vicsek, D.L. Gutnick, Chemomodulation of cellular movement and collective formation of vortices by swarming bacteria and colonial development, Physica A 238 (1997) 181-197.
    • (1997) Physica A , vol.238 , pp. 181-197
    • Ben-Jacob, E.1    Cohen, I.2    Czirók, A.3    Vicsek, T.4    Gutnick, D.L.5
  • 31
    • 0000041357 scopus 로고    scopus 로고
    • Collective behavior and dynamics of swimming bacteria
    • J.A. Shapiro, M. Dworkin (Eds.), Oxford University Press, New York
    • J.O. Kessler, M.F. Wojciechowski, Collective behavior and dynamics of swimming bacteria, in: J.A. Shapiro, M. Dworkin (Eds.), Bacteria as Multicellular Organisms, Oxford University Press, New York, 1997, pp. 417-450.
    • (1997) Bacteria as Multicellular Organisms , pp. 417-450
    • Kessler, J.O.1    Wojciechowski, M.F.2
  • 32
    • 0000183119 scopus 로고    scopus 로고
    • Kinetic model of proteus mirabilis swarm colony development
    • S.E. Esipov, J.A. Shapiro, Kinetic model of proteus mirabilis swarm colony development, J. Math. Biol. 36 (1998) 249-268.
    • (1998) J. Math. Biol. , vol.36 , pp. 249-268
    • Esipov, S.E.1    Shapiro, J.A.2
  • 33
    • 44949291022 scopus 로고
    • Diffusion-limited growth in bacterial colony formation
    • M. Matsushita, H. Fujikawa, Diffusion-limited growth in bacterial colony formation, Physica A 168 (1990) 498-506.
    • (1990) Physica A , vol.168 , pp. 498-506
    • Matsushita, M.1    Fujikawa, H.2
  • 34
    • 0002210190 scopus 로고
    • Bacterial fractal growth in the concentration field of nutrient
    • H. Fujikawa, M. Matsushita, Bacterial fractal growth in the concentration field of nutrient, J. Phys. Soc. Japan 60 (1991) 88-94.
    • (1991) J. Phys. Soc. Japan , vol.60 , pp. 88-94
    • Fujikawa, H.1    Matsushita, M.2
  • 35
    • 0002350768 scopus 로고
    • Motile colonies of bacillus alvei and other bacteria
    • R.N. Smith, F.E. Clarck, Motile colonies of bacillus alvei and other bacteria, J. Bacteriol. 35 (1938) 59-60.
    • (1938) J. Bacteriol. , vol.35 , pp. 59-60
    • Smith, R.N.1    Clarck, F.E.2
  • 37
    • 4243632346 scopus 로고
    • Diffusion-limited aggregation, a kinetic critical phenomenon
    • T.A. Witten, L.M. Sander, Diffusion-limited aggregation, a kinetic critical phenomenon, Phys. Rev. Lett. 47 (1981) 1400.
    • (1981) Phys. Rev. Lett. , vol.47 , pp. 1400
    • Witten, T.A.1    Sander, L.M.2
  • 38
    • 0000080147 scopus 로고
    • Fractal growth processes
    • L.M. Sander, Fractal growth processes, Nature 322 (1986) 789-793.
    • (1986) Nature , vol.322 , pp. 789-793
    • Sander, L.M.1
  • 41
    • 6144272856 scopus 로고
    • Holotransformations of bacterial colonies and genome cybernetics
    • E. Ben-Jacob, A. Tenenbaum, O. Shochet, O. Avidan, Holotransformations of bacterial colonies and genome cybernetics, Physica A 202 (1994) 1-47.
    • (1994) Physica A , vol.202 , pp. 1-47
    • Ben-Jacob, E.1    Tenenbaum, A.2    Shochet, O.3    Avidan, O.4
  • 42
    • 0043213488 scopus 로고    scopus 로고
    • Identification of two pattern-forming strains and their localization in a phylogenetic cluster
    • in press
    • M. Tcherpikov, E. Ben-Jacob, D. Gutnick, Identification of two pattern-forming strains and their localization in a phylogenetic cluster, Int. J. Syst. Bacteriol. (1998), in press.
    • (1998) Int. J. Syst. Bacteriol.
    • Tcherpikov, M.1    Ben-Jacob, E.2    Gutnick, D.3
  • 43
    • 0031726425 scopus 로고    scopus 로고
    • Cooperative organization of bacterial colonies: From genotype to morphotype
    • in press
    • E. Ben-Jacob, I. Cohen, D. Gutnick, Cooperative organization of bacterial colonies: From genotype to morphotype, Annu. Rev. Microbiol. (1998), in press.
    • (1998) Annu. Rev. Microbiol.
    • Ben-Jacob, E.1    Cohen, I.2    Gutnick, D.3
  • 44
    • 0027235453 scopus 로고
    • Fractal morphogenesis by a bacterial cell population
    • T. Matsuyama, M. Matsushita, Fractal morphogenesis by a bacterial cell population, Crit. Rev. Microbiol. 19 (1993) 117-135.
    • (1993) Crit. Rev. Microbiol. , vol.19 , pp. 117-135
    • Matsuyama, T.1    Matsushita, M.2
  • 45
    • 0024000989 scopus 로고
    • Pattern selection in fingered growth phenomena
    • D.A. Kessler, J. Koplik, H. Levine, Pattern selection in fingered growth phenomena, Adv. Phys. 37 (1988) 255.
    • (1988) Adv. Phys. , vol.37 , pp. 255
    • Kessler, D.A.1    Koplik, J.2    Levine, H.3
  • 46
    • 5544302094 scopus 로고
    • Dendrites, viscous fingering, and the theory of pattern formation
    • J.S. Langer, Dendrites, viscous fingering, and the theory of pattern formation, Science 243 (1989) 1150-1154.
    • (1989) Science , vol.243 , pp. 1150-1154
    • Langer, J.S.1
  • 47
    • 0001698566 scopus 로고
    • The formation of patterns in non-equilibrium growth
    • E. Ben-Jacob, P. Garik, The formation of patterns in non-equilibrium growth, Nature 343 (1990) 523-530.
    • (1990) Nature , vol.343 , pp. 523-530
    • Ben-Jacob, E.1    Garik, P.2
  • 48
    • 0008160556 scopus 로고
    • From snowflake formation to the growth of bacterial colonies. Part I: Diffusive patterning in non-living systems
    • E. Ben-Jacob, From snowflake formation to the growth of bacterial colonies. Part I: Diffusive patterning in non-living systems, Contemp. Phys. 34 (1993) 247-273.
    • (1993) Contemp. Phys. , vol.34 , pp. 247-273
    • Ben-Jacob, E.1
  • 49
    • 0000639607 scopus 로고
    • From complexity to perplexity
    • J. Horgan, From complexity to perplexity, Scientific American 95 (1995) 74-79.
    • (1995) Scientific American , vol.95 , pp. 74-79
    • Horgan, J.1
  • 50
    • 4243679719 scopus 로고
    • Pattern formation in dictyostelium via the dynamics of cooperative biological entities
    • D.A. Kessler, H. Levine, Pattern formation in dictyostelium via the dynamics of cooperative biological entities, Phys. Rev. E 48 (1993) 4801-4804.
    • (1993) Phys. Rev. E , vol.48 , pp. 4801-4804
    • Kessler, D.A.1    Levine, H.2
  • 51
    • 84956064474 scopus 로고
    • Survival-extinction transition in bacteria growth
    • M.Y. Azbel, Survival-extinction transition in bacteria growth, Europhys. Lett. 22 (4) (1993) 311-316.
    • (1993) Europhys. Lett. , vol.22 , Issue.4 , pp. 311-316
    • Azbel, M.Y.1
  • 52
    • 11644306695 scopus 로고
    • Cooperative formation of chiral patterns during growth of bacterial colonies
    • E. Ben-Jacob, I. Cohen, O. Shochet, A. Czirók, T. Vicsek, Cooperative formation of chiral patterns during growth of bacterial colonies, Phys. Rev. Lett. 75 (15) (1995) 2899-2902.
    • (1995) Phys. Rev. Lett. , vol.75 , Issue.15 , pp. 2899-2902
    • Ben-Jacob, E.1    Cohen, I.2    Shochet, O.3    Czirók, A.4    Vicsek, T.5
  • 53
    • 22244448709 scopus 로고    scopus 로고
    • Computational modeling of mound development in dictyostelium
    • D.A. Kessler, H. Levine, L. Tsimring, Computational modeling of mound development in dictyostelium, Physica D 106 (3-4) (1997) 375-388.
    • (1997) Physica D , vol.106 , Issue.3-4 , pp. 375-388
    • Kessler, D.A.1    Levine, H.2    Tsimring, L.3
  • 54
    • 0017855620 scopus 로고
    • A computer simulation of pulsatile aggregation in Dictyostelium discoideum
    • H. Parnas, L. Segel, A computer simulation of pulsatile aggregation in Dictyostelium discoideum, J. Theor. Biol. 71 (1978) 185-207.
    • (1978) J. Theor. Biol. , vol.71 , pp. 185-207
    • Parnas, H.1    Segel, L.2
  • 55
    • 0018196228 scopus 로고
    • Computer simulation of aggregation in dictyostelium discoideum
    • S.A. Mackay, Computer simulation of aggregation in dictyostelium discoideum, J. Cell. Sci. 33 (1978) 1-16.
    • (1978) J. Cell. Sci. , vol.33 , pp. 1-16
    • Mackay, S.A.1
  • 59
    • 0031501713 scopus 로고    scopus 로고
    • Interface dynamics for bacterial colony formation
    • S. Kitsunezaki, Interface dynamics for bacterial colony formation, J. Phys. Soc. Japan 66 (5) (1997) 1544-1550.
    • (1997) J. Phys. Soc. Japan , vol.66 , Issue.5 , pp. 1544-1550
    • Kitsunezaki, S.1
  • 61
    • 0032491002 scopus 로고    scopus 로고
    • Fluctuation-induced diffusive instabilities
    • D.A. Kessler, H. Levine, Fluctuation-induced diffusive instabilities, Nature 394 (1998) 556-558.
    • (1998) Nature , vol.394 , pp. 556-558
    • Kessler, D.A.1    Levine, H.2
  • 62
    • 0002552501 scopus 로고
    • Communication, regulation and control during complex patterning of bacterial colonies
    • E. Ben-Jacob, O. Shochet, A. Tenenbaum, I. Cohen, A. Czirók, T. Vicsek, Communication, regulation and control during complex patterning of bacterial colonies, Fractals 2 (1) (1994) 15-44.
    • (1994) Fractals , vol.2 , Issue.1 , pp. 15-44
    • Ben-Jacob, E.1    Shochet, O.2    Tenenbaum, A.3    Cohen, I.4    Czirók, A.5    Vicsek, T.6
  • 63
    • 33646950662 scopus 로고
    • Characterization of morphology transitions in diffusion-controlled systems
    • E. Ben-Jacob, P. Garik, T. Muller, D. Grier, Characterization of morphology transitions in diffusion-controlled systems, Phys. Rev. A 38 (1988) 1370.
    • (1988) Phys. Rev. A , vol.38 , pp. 1370
    • Ben-Jacob, E.1    Garik, P.2    Muller, T.3    Grier, D.4
  • 64
    • 0025056597 scopus 로고
    • Functions of the flagellar modes of rotation in bacterial motility and chemotaxis
    • M. Eisenbach, Functions of the flagellar modes of rotation in bacterial motility and chemotaxis, Mol. Microbiol. 4 (2) (1990) 161-167.
    • (1990) Mol. Microbiol. , vol.4 , Issue.2 , pp. 161-167
    • Eisenbach, M.1
  • 65
    • 0015444704 scopus 로고
    • Bacterial surface translocation: A survey and a classification
    • J. Henrichsen, Bacterial surface translocation: a survey and a classification, Bac. Rev. 36 (1972) 478-503.
    • (1972) Bac. Rev. , vol.36 , pp. 478-503
    • Henrichsen, J.1
  • 66
    • 0004232671 scopus 로고
    • Princeton University Press, Princeton, NJ
    • H.C. Berg, Random Walks in Biology, Princeton University Press, Princeton, NJ, 1993.
    • (1993) Random Walks in Biology
    • Berg, H.C.1
  • 67
    • 0014692237 scopus 로고
    • Chemoreceptors in bacteria
    • J. Adler, Chemoreceptors in bacteria, Science 166 (1969) 1588-1597.
    • (1969) Science , vol.166 , pp. 1588-1597
    • Adler, J.1
  • 68
    • 0017664223 scopus 로고
    • Physics of chemoreception
    • H.C. Berg, E.M. Purcell, Physics of chemoreception, Biophys. J. 20 (1977) 193-219.
    • (1977) Biophys. J. , vol.20 , pp. 193-219
    • Berg, H.C.1    Purcell, E.M.2
  • 70
    • 0031968908 scopus 로고    scopus 로고
    • Spatial sensing of stimulus gradients can be superior to temporal sensing for free-swimming bacteria
    • D.B. Dusenbery, Spatial sensing of stimulus gradients can be superior to temporal sensing for free-swimming bacteria, Biophys. J. 74 (1998) 2272-2277.
    • (1998) Biophys. J. , vol.74 , pp. 2272-2277
    • Dusenbery, D.B.1
  • 71
    • 0014013196 scopus 로고
    • Chemotaxis in bacteria
    • J. Adler, Chemotaxis in bacteria, Science 153 (1966) 708-716.
    • (1966) Science , vol.153 , pp. 708-716
    • Adler, J.1
  • 72
    • 0015526205 scopus 로고
    • Chemotaxis in Escherichia coli analyzed by three-dimensional tracking
    • H.C. Berg, D.A. Brown, Chemotaxis in Escherichia coli analyzed by three-dimensional tracking, Nature 239 (1972) 500-504.
    • (1972) Nature , vol.239 , pp. 500-504
    • Berg, H.C.1    Brown, D.A.2
  • 74
    • 0007809063 scopus 로고
    • Migration of bacteria in semisolid agar
    • A.J. Wolfe, H.C. Berg, Migration of bacteria in semisolid agar, Proc. Natl. Acad. Sci. USA 86 (1989) 6973-6977.
    • (1989) Proc. Natl. Acad. Sci. USA , vol.86 , pp. 6973-6977
    • Wolfe, A.J.1    Berg, H.C.2
  • 75
    • 0030395297 scopus 로고    scopus 로고
    • Chemotactic-based adaptive self organization during colonial development
    • I. Cohen, A. Czirók, E. Ben-Jacob, Chemotactic-based adaptive self organization during colonial development, Physica A 233 (1996) 678-698.
    • (1996) Physica A , vol.233 , pp. 678-698
    • Cohen, I.1    Czirók, A.2    Ben-Jacob, E.3
  • 76
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • R.A. Fisher, The wave of advance of advantageous genes, Annu. Eugenics 7 (1937) 255-369.
    • (1937) Annu. Eugenics , vol.7 , pp. 255-369
    • Fisher, R.A.1
  • 77
    • 0002722044 scopus 로고
    • Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique
    • A.I. Kolmogorov, I. Petrovsky, N. Piscounov, Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Moscow Univ. Bull. Math. 1 (1937) 1-25.
    • (1937) Moscow Univ. Bull. Math. , vol.1 , pp. 1-25
    • Kolmogorov, A.I.1    Petrovsky, I.2    Piscounov, N.3
  • 80
    • 3743079140 scopus 로고
    • Front propagation into unstable states: Marginal stability as a dynamical mechanism for velocity selection
    • W. van Saarloos, Front propagation into unstable states: marginal stability as a dynamical mechanism for velocity selection, Phys. Rev. A 37 (1988) 211-229.
    • (1988) Phys. Rev. A , vol.37 , pp. 211-229
    • Van Saarloos, W.1
  • 81
    • 6444221633 scopus 로고
    • Front propagation into unstable states: II. Linear versus non-linear marginal stability and rate of convergence
    • W. van Saarloos, Front propagation into unstable states: II. Linear versus non-linear marginal stability and rate of convergence, Phys. Rev. A 39 (1989) 6367-6389.
    • (1989) Phys. Rev. A , vol.39 , pp. 6367-6389
    • Van Saarloos, W.1
  • 84
    • 36849120852 scopus 로고
    • Stability of a planar interface during solidification of a dilute binary alloy
    • W.W. Mullins, R.F. Sekerka, Stability of a planar interface during solidification of a dilute binary alloy, J. Appl. Phys. 35 (1964) 444.
    • (1964) J. Appl. Phys. , vol.35 , pp. 444
    • Mullins, W.W.1    Sekerka, R.F.2
  • 87
    • 21344478362 scopus 로고
    • Experimental investigation on the validity of population dynamics approach to bacterial colony formation
    • J. Wakita, K. Komatsu, A. Nakahara, T. Matsuyama et al., Experimental investigation on the validity of population dynamics approach to bacterial colony formation, J. Phys. Soc. Japan 63 (1994) 1205-1211.
    • (1994) J. Phys. Soc. Japan , vol.63 , pp. 1205-1211
    • Wakita, J.1    Komatsu, K.2    Nakahara, A.3    Matsuyama, T.4
  • 88
    • 0001221440 scopus 로고
    • Numerical study of morphology diagram in the large undercooling limit using a phase-field model
    • R. Kupferman, O. Shochet, E. Ben-Jacob, Numerical study of morphology diagram in the large undercooling limit using a phase-field model, Phys. Rev. E 50 (1994) 1005.
    • (1994) Phys. Rev. E , vol.50 , pp. 1005
    • Kupferman, R.1    Shochet, O.2    Ben-Jacob, E.3
  • 91
    • 0042211254 scopus 로고    scopus 로고
    • Cooperative self-organization of microorganisms
    • to appear
    • E. Ben-Jacob, H. Levine, I. Cohen, Cooperative self-organization of microorganisms, Adv. Phys., to appear.
    • Adv. Phys.
    • Ben-Jacob, E.1    Levine, H.2    Cohen, I.3
  • 92
    • 0000293263 scopus 로고
    • The long-time behavior of the solution to a non-linear diffusion problem in population genetics and combustion
    • W.I. Newman, The long-time behavior of the solution to a non-linear diffusion problem in population genetics and combustion, J. Theor. Biol. 104 (1983) 473-484.
    • (1983) J. Theor. Biol. , vol.104 , pp. 473-484
    • Newman, W.I.1
  • 93
    • 4243189993 scopus 로고
    • Morphology transition in a mean-field model of diffusion-limited growth
    • Y. Tu, H. Levine, D. Ridgway, Morphology transition in a mean-field model of diffusion-limited growth, Phys. Rev. Lett. 71 (23) (1993) 3838-3841.
    • (1993) Phys. Rev. Lett. , vol.71 , Issue.23 , pp. 3838-3841
    • Tu, Y.1    Levine, H.2    Ridgway, D.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.