In nature, microorganisms must often cope with hostile environmental conditions. To do so they ha... more In nature, microorganisms must often cope with hostile environmental conditions. To do so they have developed sophisticated cooperative behavior and intricate communication capabilities, such as: direct cellcell physical interactions via extra-membrane polymers, collective production of extracellular "wetting" fluid for movement on hard surfaces, long range chemical signaling such as quorum sensing and chemotactic (bias of movement according to gradient of chemical agent) signaling, collective activation and deactivation of genes and even exchange of genetic material. Utilizing these capabilities, the colonies develop complex spatio-temporal patterns in response to adverse growth conditions. We present a wealth of branching and chiral patterns formed during colonial development of lubricating bacteria (bacteria which produce a wetting layer of fluid for their movement). Invoking ideas from pattern formation in non-living systems and using "generic" modeling we ar...
Various bacterial strains exhibit colonial branching patterns during growth on poor substrates. T... more Various bacterial strains exhibit colonial branching patterns during growth on poor substrates. These patterns reflect bacterial cooperative self-organization and cybernetic processes of communication, regulation and control employed during colonial development. One method of modeling is the continuous, or coupled reaction-diffusion approach, in which continuous time evolution equations describe the bacterial density and the concentration of the relevant chemical fields. In the context of branching growth, this idea has been pursued by a number of groups. We present an additional model which includes a lubrication fluid excreted by the bacteria. We also add fields of chemotactic agents to the other models. We then present a critique of this whole enterprise with focus on the models' potential for revealing new biological features.
We present a new reaction-diffusion model for chiral branching growth of colonies of the bacteria... more We present a new reaction-diffusion model for chiral branching growth of colonies of the bacteria Paenibacillus dendritiformis. In our model the bacteria are represented by a density field with non-linear diffusion and a complex scalar field which represents bacterial orientation. The orientation field introduces anisotropy into the flux of bacteria, representing self-propulsion along their long axes. The model can also reproduce tip-splitting growth of other strains (shorter bacteria) of the same species. The model can capture changes of small number of bacteria, thus it can be used to study the open question of transitions between tip-splitting and chiral dendritic growth.
1Department of Geophysical, Atmospheric and Planetary Sciences, Tel Aviv University, Tel Aviv, Is... more 1Department of Geophysical, Atmospheric and Planetary Sciences, Tel Aviv University, Tel Aviv, Israel 2Department of Respiratory Medicine, NHLI, Imperial College, London, United Kingdom 3School of Medicine, University of Liverpool, Liverpool, United Kingdom 4Pulmonary and Critical Care Medicine Unit, Department of Medicine, Massachusetts General Hospital, Harvard Medical School, Boston, MA, United States 5Department of Medicine, University of Chicago, Chicago, IL, United States 6Harvard School of Public Health, Harvard University, Boston, MA, United States 7PulmOne Advanced Medical Devices, Ltd, Ra’anana, Israel
We report here a new method to determine TLC that requires neither body plethysmography (PLETH), ... more We report here a new method to determine TLC that requires neither body plethysmography (PLETH), gas dilution, nor thoracic imaging. With cheeks supported, the subject breathes through a flow interruption valve downstream of a parallel chamber of known gas volume, comprising a so-called MiniBox (Fig.1 inset). The subject also performs standard spirometry. Pressure and flow metrics were derived from both these maneuvers in a training population, as well as TLC PLETH measured on the same day (Platinum Elite, MGC, and ZAN 500, nSpire). Data mining methods were used to generate a formula from which we calculated TLC of any individual subject. Our population comprised 59 healthy adult women (31.5+15.5y, 23.3+4.9 BMI), 83 healthy adults men, (31.0+14.9y, 24.1+3.3 BMI), 25 patients with restrictive disease (48.8+16.4y, 29.4+6.8 BMI), and 101 patients with obstructive disease (62.9+11.9y, 27.7+4.9 BMI). Across this heterogeneous population we found TLC MiniBox =1.01TLC PLETH , r=0.91 (Pears...
ABSTRACTBackgroundAmong the most basic measures of respiratory function is the total lung capacit... more ABSTRACTBackgroundAmong the most basic measures of respiratory function is the total lung capacity (TLC). TLC is the pulmonary gas volume at maximal lung inflation, which is the sum of the volume of gas that can be exhaled –the vital capacity (VC)– and the volume of gas that cannot –the residual volume (RV). Determination of VC requires only spirometry whereas determination of RV or TLC requires body plethysmography, gas dilution or washout, or thoracic imaging, each of which is more complex than spirometry, and none of which is suited to routine office practice, population screening, or community medicine. To fill this gap, we describe here a new approach to determine TLC without plethysmography.MethodsIn a heterogeneous population of 434 volunteers (265 male, 169 female; 201 healthy, 170 with airflow obstruction, and 63 with ventilatory restriction), we determined TLC in the standard fashion using conventional body plethysmography (TLCpleth). In the same individuals, we also deter...
Page 1. MATHEMATICAL METHODS IN THE APPLIED SCIENCES Math. Meth. Appl. Sci. 2001; 24:14291468 (D... more Page 1. MATHEMATICAL METHODS IN THE APPLIED SCIENCES Math. Meth. Appl. Sci. 2001; 24:14291468 (DOI: 10.1002/mma.190) MOS subject classification: 76 Z 99 Bio uiddynamics of lubricating bacteria I. Cohen1, I. Golding1, IG Ron1;2 and E. Ben-Jacob1;∗ ...
We study the formation of spot patterns seen in a variety of bacterial species when the bacteria ... more We study the formation of spot patterns seen in a variety of bacterial species when the bacteria are subjected to oxidative stress due to hazardous byproducts of respiration. Our approach consists of coupling the cell density field to a chemoattractant concentration as well as to nutrient and waste fields. The latter serves as a triggering field for emission of chemoattractant. Important elements in the proposed model include the propagation of a front of motile bacteria radially outward form an initial site, a Turing instability of the uniformly dense state and a reduction of motility for cells sufficiently far behind the front. The wide variety of patterns seen in the experiments is explained as being due the variation of the details of the initiation of the chemoattractant emission as well as the transition to a non-motile phase.
We study the formation of spot patterns seen in a variety of bacterial species when the bacteria ... more We study the formation of spot patterns seen in a variety of bacterial species when the bacteria are subjected to oxidative stress due to hazardous byproducts of respiration. Our approach consists of coupling the cell density field to a chemoattractant concentration as well as to nutrient and waste fields. The latter serves as a triggering field for emission of chemoattractant. Important elements in the proposed model include the propagation of a front of motile bacteria radially outward form an initial site, a Turing instability of the uniformly dense state and a reduction of motility for cells sufficiently far behind the front. The wide variety of patterns seen in the experiments is explained as being due the variation of the details of the initiation of the chemoattractant emission as well as the transition to a non-motile phase.
Complex bacterial patterns. E Ben-Jacob, I Cohen, O Shochet, I Aranson, H Levine, L Tsimring Natu... more Complex bacterial patterns. E Ben-Jacob, I Cohen, O Shochet, I Aranson, H Levine, L Tsimring Nature 373:65156515, 566-567, 1995. Budrene and Berg have studied patterns of spots, stripes and rings formed by motile cells ...
We investigate a discrete model consisting of self-propelled particles that obey simple interacti... more We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension, the self-organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges.In two-dimensions, we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions, even in the absence of a confining boundary. Furthermore, we develop a continuum version of our discrete model and demonstrate that the agreement between the discrete and the continuum model is excellent.
In nature, microorganisms must often cope with hostile environmental conditions. To do so they ha... more In nature, microorganisms must often cope with hostile environmental conditions. To do so they have developed sophisticated cooperative behavior and intricate communication capabilities, such as: direct cellcell physical interactions via extra-membrane polymers, collective production of extracellular "wetting" uid for movement on hard surfaces, long range chemical signaling such as quorum sensing and chemotactic (bias of movement according to gradient of chemical agent) signaling, collective activation and deactivation of genes and even exchange of genetic material. Utilizing these 1 capabilities, the colonies develop complex spatio-temporal patterns in response to adverse growth conditions. We present a wealth of branching and chiral patterns formed during colonial development of lubricating bacteria (bacteria which produce a wetting layer of uid for their movement). Invoking ideas from pattern formation in non-living systems and using \generic" modeling we are able to reveal novel survival strategies which account for the salient features of the evolved patterns. Using the models, we demonstrate how communication leads to self-organization via cooperative behavior of the cells. 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). We mainly review known results, but include a new model of chiral growth, which enables us to study the e ect of chemotactic signaling on the chiral growth. We also introduce a measure for weak chirality and use this measure to compare the results of model simulations with experimental observations. 7
ABSTRACT Introduction During the course of evolution, bacteria have developed sophisticated coope... more ABSTRACT Introduction During the course of evolution, bacteria have developed sophisticated cooperative behavior and intricate communication capabilities [1--3]. Utilizing these capabilities, bacterial colonies develop complex spatio-temporal patterns in response to adverse growth conditions. It is now understood that the study of cooperative self-organization of bacterial colonies is an exciting new multidisciplinary field of research, necessitating the merger of biological information with the physics of non-equilibrium processes and the mathematics of non-linear dynamics. At this stage, several experimental systems have been identified, and preliminary modeling efforts are making significant progress in providing a framework for the understanding of experimental observations [4--12]. This endevour is not limited to bacteria alone. Studies have been performed of other types of microorganisms as well, such as amoeba [13] and yeast [14]. Fujikawa and Matsushita [5] reported for the fi
Physical Review E Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics, 1999
Various bacterial strains (e.g., strains belonging to the genera Bacillus, Paenibacillus, Serrati... more 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.
We study the effect of discreteness on various models for patterning in bacterial colonies. In a ... more We study the effect of discreteness on various models for patterning in bacterial colonies. In a bacterial colony with branching pattern, there are discrete entities - bacteria - which are only two orders of magnitude smaller than the elements of the macroscopic pattern. We present two types of models. The first is the Communicating Walkers model, a hybrid model composed of both continuous fields and discrete entities - walkers, which are coarse-graining of the bacteria. Models of the second type are systems of reaction diffusion equations, where the branching of the pattern is due to non-constant diffusion coefficient of the bacterial field. The diffusion coefficient represents the effect of self-generated lubrication fluid on the bacterial movement. We implement the discreteness of the biological system by introducing a cutoff in the growth term at low bacterial densities. We demonstrate that the cutoff does not improve the models in any way. Its only effect is to decrease the effective surface tension of the front, making it more sensitive to anisotropy. We compare the models by introducing food chemotaxis and repulsive chemotactic signaling into the models. We find that the growth dynamics of the Communication Walkers model and the growth dynamics of the Non-Linear diffusion model are affected in the same manner. From such similarities and from the insensitivity of the Communication Walkers model to implicit anisotropy we conclude that the increased discreteness, introduced be the coarse-graining of the walkers, is small enough to be neglected.
In nature, microorganisms must often cope with hostile environmental conditions. To do so they ha... more In nature, microorganisms must often cope with hostile environmental conditions. To do so they have developed sophisticated cooperative behavior and intricate communication capabilities, such as: direct cellcell physical interactions via extra-membrane polymers, collective production of extracellular "wetting" fluid for movement on hard surfaces, long range chemical signaling such as quorum sensing and chemotactic (bias of movement according to gradient of chemical agent) signaling, collective activation and deactivation of genes and even exchange of genetic material. Utilizing these capabilities, the colonies develop complex spatio-temporal patterns in response to adverse growth conditions. We present a wealth of branching and chiral patterns formed during colonial development of lubricating bacteria (bacteria which produce a wetting layer of fluid for their movement). Invoking ideas from pattern formation in non-living systems and using "generic" modeling we ar...
Various bacterial strains exhibit colonial branching patterns during growth on poor substrates. T... more Various bacterial strains exhibit colonial branching patterns during growth on poor substrates. These patterns reflect bacterial cooperative self-organization and cybernetic processes of communication, regulation and control employed during colonial development. One method of modeling is the continuous, or coupled reaction-diffusion approach, in which continuous time evolution equations describe the bacterial density and the concentration of the relevant chemical fields. In the context of branching growth, this idea has been pursued by a number of groups. We present an additional model which includes a lubrication fluid excreted by the bacteria. We also add fields of chemotactic agents to the other models. We then present a critique of this whole enterprise with focus on the models' potential for revealing new biological features.
We present a new reaction-diffusion model for chiral branching growth of colonies of the bacteria... more We present a new reaction-diffusion model for chiral branching growth of colonies of the bacteria Paenibacillus dendritiformis. In our model the bacteria are represented by a density field with non-linear diffusion and a complex scalar field which represents bacterial orientation. The orientation field introduces anisotropy into the flux of bacteria, representing self-propulsion along their long axes. The model can also reproduce tip-splitting growth of other strains (shorter bacteria) of the same species. The model can capture changes of small number of bacteria, thus it can be used to study the open question of transitions between tip-splitting and chiral dendritic growth.
1Department of Geophysical, Atmospheric and Planetary Sciences, Tel Aviv University, Tel Aviv, Is... more 1Department of Geophysical, Atmospheric and Planetary Sciences, Tel Aviv University, Tel Aviv, Israel 2Department of Respiratory Medicine, NHLI, Imperial College, London, United Kingdom 3School of Medicine, University of Liverpool, Liverpool, United Kingdom 4Pulmonary and Critical Care Medicine Unit, Department of Medicine, Massachusetts General Hospital, Harvard Medical School, Boston, MA, United States 5Department of Medicine, University of Chicago, Chicago, IL, United States 6Harvard School of Public Health, Harvard University, Boston, MA, United States 7PulmOne Advanced Medical Devices, Ltd, Ra’anana, Israel
We report here a new method to determine TLC that requires neither body plethysmography (PLETH), ... more We report here a new method to determine TLC that requires neither body plethysmography (PLETH), gas dilution, nor thoracic imaging. With cheeks supported, the subject breathes through a flow interruption valve downstream of a parallel chamber of known gas volume, comprising a so-called MiniBox (Fig.1 inset). The subject also performs standard spirometry. Pressure and flow metrics were derived from both these maneuvers in a training population, as well as TLC PLETH measured on the same day (Platinum Elite, MGC, and ZAN 500, nSpire). Data mining methods were used to generate a formula from which we calculated TLC of any individual subject. Our population comprised 59 healthy adult women (31.5+15.5y, 23.3+4.9 BMI), 83 healthy adults men, (31.0+14.9y, 24.1+3.3 BMI), 25 patients with restrictive disease (48.8+16.4y, 29.4+6.8 BMI), and 101 patients with obstructive disease (62.9+11.9y, 27.7+4.9 BMI). Across this heterogeneous population we found TLC MiniBox =1.01TLC PLETH , r=0.91 (Pears...
ABSTRACTBackgroundAmong the most basic measures of respiratory function is the total lung capacit... more ABSTRACTBackgroundAmong the most basic measures of respiratory function is the total lung capacity (TLC). TLC is the pulmonary gas volume at maximal lung inflation, which is the sum of the volume of gas that can be exhaled –the vital capacity (VC)– and the volume of gas that cannot –the residual volume (RV). Determination of VC requires only spirometry whereas determination of RV or TLC requires body plethysmography, gas dilution or washout, or thoracic imaging, each of which is more complex than spirometry, and none of which is suited to routine office practice, population screening, or community medicine. To fill this gap, we describe here a new approach to determine TLC without plethysmography.MethodsIn a heterogeneous population of 434 volunteers (265 male, 169 female; 201 healthy, 170 with airflow obstruction, and 63 with ventilatory restriction), we determined TLC in the standard fashion using conventional body plethysmography (TLCpleth). In the same individuals, we also deter...
Page 1. MATHEMATICAL METHODS IN THE APPLIED SCIENCES Math. Meth. Appl. Sci. 2001; 24:14291468 (D... more Page 1. MATHEMATICAL METHODS IN THE APPLIED SCIENCES Math. Meth. Appl. Sci. 2001; 24:14291468 (DOI: 10.1002/mma.190) MOS subject classification: 76 Z 99 Bio uiddynamics of lubricating bacteria I. Cohen1, I. Golding1, IG Ron1;2 and E. Ben-Jacob1;∗ ...
We study the formation of spot patterns seen in a variety of bacterial species when the bacteria ... more We study the formation of spot patterns seen in a variety of bacterial species when the bacteria are subjected to oxidative stress due to hazardous byproducts of respiration. Our approach consists of coupling the cell density field to a chemoattractant concentration as well as to nutrient and waste fields. The latter serves as a triggering field for emission of chemoattractant. Important elements in the proposed model include the propagation of a front of motile bacteria radially outward form an initial site, a Turing instability of the uniformly dense state and a reduction of motility for cells sufficiently far behind the front. The wide variety of patterns seen in the experiments is explained as being due the variation of the details of the initiation of the chemoattractant emission as well as the transition to a non-motile phase.
We study the formation of spot patterns seen in a variety of bacterial species when the bacteria ... more We study the formation of spot patterns seen in a variety of bacterial species when the bacteria are subjected to oxidative stress due to hazardous byproducts of respiration. Our approach consists of coupling the cell density field to a chemoattractant concentration as well as to nutrient and waste fields. The latter serves as a triggering field for emission of chemoattractant. Important elements in the proposed model include the propagation of a front of motile bacteria radially outward form an initial site, a Turing instability of the uniformly dense state and a reduction of motility for cells sufficiently far behind the front. The wide variety of patterns seen in the experiments is explained as being due the variation of the details of the initiation of the chemoattractant emission as well as the transition to a non-motile phase.
Complex bacterial patterns. E Ben-Jacob, I Cohen, O Shochet, I Aranson, H Levine, L Tsimring Natu... more Complex bacterial patterns. E Ben-Jacob, I Cohen, O Shochet, I Aranson, H Levine, L Tsimring Nature 373:65156515, 566-567, 1995. Budrene and Berg have studied patterns of spots, stripes and rings formed by motile cells ...
We investigate a discrete model consisting of self-propelled particles that obey simple interacti... more We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension, the self-organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges.In two-dimensions, we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions, even in the absence of a confining boundary. Furthermore, we develop a continuum version of our discrete model and demonstrate that the agreement between the discrete and the continuum model is excellent.
In nature, microorganisms must often cope with hostile environmental conditions. To do so they ha... more In nature, microorganisms must often cope with hostile environmental conditions. To do so they have developed sophisticated cooperative behavior and intricate communication capabilities, such as: direct cellcell physical interactions via extra-membrane polymers, collective production of extracellular "wetting" uid for movement on hard surfaces, long range chemical signaling such as quorum sensing and chemotactic (bias of movement according to gradient of chemical agent) signaling, collective activation and deactivation of genes and even exchange of genetic material. Utilizing these 1 capabilities, the colonies develop complex spatio-temporal patterns in response to adverse growth conditions. We present a wealth of branching and chiral patterns formed during colonial development of lubricating bacteria (bacteria which produce a wetting layer of uid for their movement). Invoking ideas from pattern formation in non-living systems and using \generic" modeling we are able to reveal novel survival strategies which account for the salient features of the evolved patterns. Using the models, we demonstrate how communication leads to self-organization via cooperative behavior of the cells. 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). We mainly review known results, but include a new model of chiral growth, which enables us to study the e ect of chemotactic signaling on the chiral growth. We also introduce a measure for weak chirality and use this measure to compare the results of model simulations with experimental observations. 7
ABSTRACT Introduction During the course of evolution, bacteria have developed sophisticated coope... more ABSTRACT Introduction During the course of evolution, bacteria have developed sophisticated cooperative behavior and intricate communication capabilities [1--3]. Utilizing these capabilities, bacterial colonies develop complex spatio-temporal patterns in response to adverse growth conditions. It is now understood that the study of cooperative self-organization of bacterial colonies is an exciting new multidisciplinary field of research, necessitating the merger of biological information with the physics of non-equilibrium processes and the mathematics of non-linear dynamics. At this stage, several experimental systems have been identified, and preliminary modeling efforts are making significant progress in providing a framework for the understanding of experimental observations [4--12]. This endevour is not limited to bacteria alone. Studies have been performed of other types of microorganisms as well, such as amoeba [13] and yeast [14]. Fujikawa and Matsushita [5] reported for the fi
Physical Review E Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics, 1999
Various bacterial strains (e.g., strains belonging to the genera Bacillus, Paenibacillus, Serrati... more 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.
We study the effect of discreteness on various models for patterning in bacterial colonies. In a ... more We study the effect of discreteness on various models for patterning in bacterial colonies. In a bacterial colony with branching pattern, there are discrete entities - bacteria - which are only two orders of magnitude smaller than the elements of the macroscopic pattern. We present two types of models. The first is the Communicating Walkers model, a hybrid model composed of both continuous fields and discrete entities - walkers, which are coarse-graining of the bacteria. Models of the second type are systems of reaction diffusion equations, where the branching of the pattern is due to non-constant diffusion coefficient of the bacterial field. The diffusion coefficient represents the effect of self-generated lubrication fluid on the bacterial movement. We implement the discreteness of the biological system by introducing a cutoff in the growth term at low bacterial densities. We demonstrate that the cutoff does not improve the models in any way. Its only effect is to decrease the effective surface tension of the front, making it more sensitive to anisotropy. We compare the models by introducing food chemotaxis and repulsive chemotactic signaling into the models. We find that the growth dynamics of the Communication Walkers model and the growth dynamics of the Non-Linear diffusion model are affected in the same manner. From such similarities and from the insensitivity of the Communication Walkers model to implicit anisotropy we conclude that the increased discreteness, introduced be the coarse-graining of the walkers, is small enough to be neglected.
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