This paper illustrates an informatic technique for inferring and quantifying the dynamic role of ... more This paper illustrates an informatic technique for inferring and quantifying the dynamic role of a single intrinsic current in a mechanism of neural bursting activity. We analyze the patterns of the most dominant currents in a model of half-center oscillation in the leech heartbeat central pattern generator. We find that the patterns of dominance change substantially over a cycle, allowing different local reductions to be applied to the model. The result is a hybrid dynamical systems model, which is a piecewise representation of the mechanism combining multiple vector fields and discrete state changes. The simulation of such a model tests explicit hypotheses about the mechanism and is a novel way to retain both mathematical clarity and scientific detail in answering mechanistic questions about a complex model. Several insights into the central mechanism of "escape-release" in the model are elucidated by this analysis and compared with previous studies. The broader application and extension of this technique is also discussed.
Near an orbit of interest in a dynamical system, it is typical to ask which variables dominate it... more Near an orbit of interest in a dynamical system, it is typical to ask which variables dominate its structure at what times. What are its principal local degrees of freedom? What local bifurcation structure is most appropriate? We introduce a combined numerical and analytical technique that aids the identification of structure in a class of systems of nonlinear ordinary differential equations (ODEs) that are commonly applied in dynamical models of physical processes. This "dominant scale" technique prioritizes consideration of the influence that distinguished "inputs" to an ODE have on its dynamics. On this basis a sequence of reduced models is derived, where each model is valid for a duration that is determined self-consistently as the system's state variables evolve. The characteristic time scales of all sufficiently dominant variables are also taken into account to further reduce the model. The result is a hybrid dynamical system of reduced differential-algebraic models that are switched at discrete event times. The technique does not rely on explicit small parameters in the ODEs and automatically detects changing scale separation both in time and in "dominance strength" (a quantity we derive to measure an input's influence). Reduced regimes describing the full system have quantified domains of validity in time and with respect to variation in state variables. This enables the qualitative analysis of the system near known orbits (e.g., to study bifurcations) without sole reliance on numerical shooting methods. These methods have been incorporated into a new software tool named Dssrt, which we demonstrate on a limit cycle of a synaptically driven Hodgkin-Huxley neuron model.
Journal of Computational Neuroscience, Jul 2, 2008
The large number of variables involved in many biophysical models can conceal potentially simple ... more The large number of variables involved in many biophysical models can conceal potentially simple dynamical mechanisms governing the properties of its solutions and the transitions between them as parameters are varied. To address this issue, we extend a novel model reduction method, based on "scales of dominance," to multi-compartment models. We use this method to systematically reduce the dimension of a two-compartment conductance-based model of a crustacean pyloric dilator (PD) neuron that exhibits distinct modes of oscillation-tonic spiking, intermediate bursting and strong bursting. A cursory analysis of the scales of dominance in a trajectory of this sixteen-variable model leads to a globally-reduced, nine-variable model. In a finer analysis we divide the trajectory into intervals dominated by a smaller number of variables, resulting in a locally-reduced hybrid model whose dimension varies between two and six in different temporal regimes. Both reduced models exhibit the same modes of oscillation as the sixteen-dimensional model over a comparable parameter range. The reduced models highlight low-dimensional organizing structure in the dynamics of the PD neuron, and the dependence of its oscillations on parameters such as the maximal conductances of calcium currents. Our technique could be used to build hybrid low-dimensional models from any large multi-compartment conductance-based model in order to analyze the interactions between different modes of activity.
The PyDSTool software environment is designed to develop, simulate, and analyze dynamical systems... more The PyDSTool software environment is designed to develop, simulate, and analyze dynamical systems models, particularly for biological applications. Unlike the engineering application focus and graphical specification environments of most general purpose simulation tools, PyDSTool provides a programmatic environment well suited to exploratory data-and hypothesis-driven biological modeling problems. In this work, we show how the environment facilitates the application of hybrid dynamical modeling to the reverse engineering of complex biophysical dynamics; in this case, of an excitable membrane. The example demonstrates how the software provides novel tools that support the inference and validation of mechanistic hypotheses and the inclusion of data constraints in both quantitative and qualitative ways. The biophysical application is broadly relevant to models in the biosciences. The open source and platform-independent PyDSTool package is freely available under the BSD license from http://sourceforge.net/projects/pydstool/. The hosting service provides links to documentation and online forums for user support.
Studies of the degrees of freedom or "synergies" in musculoskeletal systems rely critically on al... more Studies of the degrees of freedom or "synergies" in musculoskeletal systems rely critically on algorithms to estimate the "dimension" of kinematic or neural data. Linear algorithms such as principal component analysis (PCA) are used almost exclusively for this purpose. However, biological systems tend to possess nonlinearities and operate at multiple spatial and temporal scales so that the set of reachable system states typically does not lie close to a single linear subspace. We compare the performance of PCA to two alternative nonlinear algorithms (Isomap and our novel pointwise dimension estimation (PD-E)) using synthetic and motion capture data from a robotic arm with known kinematic dimensions, as well as motion capture data from human hands. We find that consideration of the spectral properties of the singular value decomposition in PCA can lead to more accurate dimension estimates than the dominant practice of using a fixed variance capture threshold. We investigate methods for identifying a single integer dimension using PCA and Isomap. In contrast, PD-E provides a range of estimates of fractal dimension. This helps to identify heterogeneous geometric structure of data sets such as unions of manifolds of differing dimensions, to which Isomap is less sensitive. Contrary to common opinion regarding fractal dimension methods, PD-E yielded reasonable results with reasonable amounts of data. We conclude that it is necessary and feasible to complement PCA with other methods that take into consideration the nonlinear properties of biological systems for a more robust estimation of their degrees of freedom.
Journal of Computational Neuroscience, Jun 25, 2014
The Hodgkin-Huxley (HH) model is the basis for numerous neural models. There are two negative fee... more The Hodgkin-Huxley (HH) model is the basis for numerous neural models. There are two negative feedback processes in the HH model that regulate rhythmic spiking. The first is an outward current with an activation variable n that has an opposite influence to the excitatory inward current and therefore provides subtractive negative feedback. The other is the inactivation of an inward current with an inactivation variable h that reduces the amount of positive feedback and therefore provides divisive feedback. Rhythmic spiking can be obtained with either negative feedback process, so we ask what is gained by having two feedback processes. We also ask how the different negative feedback processes contribute to spiking. We show that having two negative feedback processes makes the HH model more robust to changes in applied currents and conductance densities than models that possess only one negative feedback variable. We also show that the contributions made by the subtractive and divisive feedback variables are not static, but depend on time scales and conductance values. In particular, they contribute differently to the dynamics in Type I versus Type II neurons.
SIGLEAvailable from British Library Document Supply Centre- DSC:DXN060383 / BLDSC - British Libra... more SIGLEAvailable from British Library Document Supply Centre- DSC:DXN060383 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
Centrosome amplification (CA) and resultant chromosomal instability have long been associated wit... more Centrosome amplification (CA) and resultant chromosomal instability have long been associated with tumorigenesis. However, exacerbation of CA and relentless centrosome declustering engender robust spindle multipolarity (SM) during mitosis and may induce cell death. Recently, we demonstrated that a noscapinoid member, reduced bromonoscapine, (S)-3-(R)-9-bromo-5-(4,5dimethoxy-1,3-dihydroisobenzofuran-1-yl)-4-methoxy-6-methyl-5,6,7,8-tetrahydro-[1,3]dioxolo-[4,5-g]isoquinoline (Red-Br-nos), induces reactive oxygen species (ROS)-mediated autophagy and caspase-independent death in prostate cancer PC-3 cells. Herein, we show that Red-Br-nos induces ROS-dependent DNA damage that resulted in high-grade CA and SM in PC-3 cells. Unlike doxorubicin, which causes double-stranded DNA breaks and chronic G2 arrest accompanied by 'templated' CA, Red-Brnos-mediated DNA damage elicits de novo CA during a transient S/G2 stall, followed by checkpoint abrogation and mitotic entry to form aberrant mitotic figures with supernumerary spindle poles. Attenuation of multipolar phenotype in the presence of tiron, a ROS inhibitor, indicated that ROS-mediated DNA damage was partly responsible for driving CA and SM. Although a few cells (B5%) yielded to aberrant cytokinesis following an 'anaphase catastrophe', most mitotically arrested cells (B70%) succumbed to 'metaphase catastrophe,' which was caspase-independent. This report is the first documentation of rapid de novo centrosome formation in the presence of parent centrosome by a noscapinoid family member, which triggers death-inducing SM via a unique mechanism that distinguishes it from other ROS-inducers, conventional DNA-damaging agents, as well as other microtubule-binding drugs.
Unlike normal cells, cancer cells contain amplified centrosomes and rely on centrosome clustering... more Unlike normal cells, cancer cells contain amplified centrosomes and rely on centrosome clustering mechanisms to form a pseudobipolar spindle that circumvents potentially fatal spindle multipolarity (MP). Centrosome clustering also promotes lowgrade chromosome missegregation, which can drive malignant transformation and tumor progression. Putative 'centrosome declustering drugs' represent a cancer cell-specific class of chemotherapeutics that produces a common phenotype of centrosome declustering and spindle MP. However, differences between individual agents in terms of efficacy and phenotypic nuances remain unexplored. Herein, we have developed a conceptual framework for the quantitative evaluation of centrosome declustering drugs by investigating their impact on centrosomes, clustering, spindle polarity, cell cycle arrest, and death in various cancer cell lines at multiple drug concentrations over time. Surprisingly, all centrosome declustering drugs evaluated in our study were also centrosome-amplifying drugs to varying extents. Notably, all declustering drugs induced spindle MP, and the peak extent of MP positively correlated with the induction of hypodiploid DNA-containing cells. Our data suggest acentriolar spindle pole amplification as a hitherto undescribed activity of some declustering drugs, resulting in spindle MP in cells that may not have amplified centrosomes. In general, declustering drugs were more toxic to cancer cell lines than non-transformed ones, with some exceptions. Through a comprehensive description and quantitative analysis of numerous phenotypes induced by declustering drugs, we propose a novel framework for the assessment of putative centrosome declustering drugs and describe cellular characteristics that may enhance susceptibility to them.
IEEE Transactions on Biomedical Engineering, Feb 1, 2008
Studies of the degrees of freedom and "synergies" in musculoskeletal systems rely critically on a... more Studies of the degrees of freedom and "synergies" in musculoskeletal systems rely critically on algorithms to estimate the "dimension" of kinematic or neural data. Linear algorithms such as principal component analysis (PCA) are the most popular. However, many biological data (or realistic experimental data) may be better represented by nonlinear sets than linear subspaces. We evaluate the performance of PCA and compare it to two nonlinear algorithms [Isomap and our novel pointwise dimension estimation (PD-E)] using synthetic and motion capture data from a robotic arm with known kinematic dimensions, as well as motion capture data from human hands. We find that PCA can lead to more accurate dimension estimates when considering additional properties of the PCA residuals, instead of the dominant method of using a threshold of variance captured. In contrast to the single integer dimension estimates of PCA and Isomap, PD-E provides a distribution and range of estimates of fractal dimension that identify the heterogeneous geometric structure in the experimental data. A strength of the PD-E method is that it associates a distribution of dimensions to the data. Since there is no a priori reason to assume that the sets of interest have a single dimension, these distributions incorporate more information than a single summary statistic. Our preliminary findings suggest that fewer than ten DOFs are involved in some hand motion tasks. Contrary to common opinion regarding fractal dimension methods, PD-E yielded reasonable results with reasonable amounts of data. Given the complex nature of experimental and biological data, we conclude that it is necessary and feasible to complement PCA with methods that take into consideration the nonlinear properties of biological systems for a more robust estimation of their DOFs.
We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of ... more We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multi-functional central pattern generator (CPG). Such CPGs are neural microcircuits of cells whose synergetic interactions produce multiple states with distinct phase-locked patterns of bursting activity. To study biologically plausible CPG models, we develop a suite of computational tools that reduce the problem of stability and existence of rhythmic patterns in networks to the bifurcation analysis of fixed points and invariant curves of a Poincare ́ return maps for phase lags between cells. We explore different functional possibilities for motifs involving symmetry breaking and heterogeneity. This is achieved by varying coupling properties of the synapses between the cells and studying the quali-tative changes in the structure of the corresponding return maps. Our findings provide a systematic basis for understanding plausible biophysical mechanisms for the regulation of rhythmic pa...
We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of ... more We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multi-functional central pattern generator (CPG). Such CPGs are neural microcircuits of cells whose synergetic interactions produce multiple states with distinct phase-locked patterns of bursting activity. To study biologically plausible CPG models, we develop a suite of computational tools that reduce the problem of stability and existence of rhythmic patterns in networks to the bifurcation analysis of fixed points and invariant curves of a Poincare ́ return maps for phase lags between cells. We explore different functional possibilities for motifs involving symmetry breaking and heterogeneity. This is achieved by varying coupling properties of the synapses between the cells and studying the quali-tative changes in the structure of the corresponding return maps. Our findings provide a systematic basis for understanding plausible biophysical mechanisms for the regulation of rhythmic pa...
This paper illustrates an informatic technique for inferring and quantifying the dynamic role of ... more This paper illustrates an informatic technique for inferring and quantifying the dynamic role of a single intrinsic current in a mechanism of neural bursting activity. We analyze the patterns of the most dominant currents in a model of half-center oscillation in the leech heartbeat central pattern generator. We find that the patterns of dominance change substantially over a cycle, allowing different local reductions to be applied to the model. The result is a hybrid dynamical systems model, which is a piecewise representation of the mechanism combining multiple vector fields and discrete state changes. The simulation of such a model tests explicit hypotheses about the mechanism and is a novel way to retain both mathematical clarity and scientific detail in answering mechanistic questions about a complex model. Several insights into the central mechanism of "escape-release" in the model are elucidated by this analysis and compared with previous studies. The broader application and extension of this technique is also discussed.
Near an orbit of interest in a dynamical system, it is typical to ask which variables dominate it... more Near an orbit of interest in a dynamical system, it is typical to ask which variables dominate its structure at what times. What are its principal local degrees of freedom? What local bifurcation structure is most appropriate? We introduce a combined numerical and analytical technique that aids the identification of structure in a class of systems of nonlinear ordinary differential equations (ODEs) that are commonly applied in dynamical models of physical processes. This "dominant scale" technique prioritizes consideration of the influence that distinguished "inputs" to an ODE have on its dynamics. On this basis a sequence of reduced models is derived, where each model is valid for a duration that is determined self-consistently as the system's state variables evolve. The characteristic time scales of all sufficiently dominant variables are also taken into account to further reduce the model. The result is a hybrid dynamical system of reduced differential-algebraic models that are switched at discrete event times. The technique does not rely on explicit small parameters in the ODEs and automatically detects changing scale separation both in time and in "dominance strength" (a quantity we derive to measure an input's influence). Reduced regimes describing the full system have quantified domains of validity in time and with respect to variation in state variables. This enables the qualitative analysis of the system near known orbits (e.g., to study bifurcations) without sole reliance on numerical shooting methods. These methods have been incorporated into a new software tool named Dssrt, which we demonstrate on a limit cycle of a synaptically driven Hodgkin-Huxley neuron model.
Journal of Computational Neuroscience, Jul 2, 2008
The large number of variables involved in many biophysical models can conceal potentially simple ... more The large number of variables involved in many biophysical models can conceal potentially simple dynamical mechanisms governing the properties of its solutions and the transitions between them as parameters are varied. To address this issue, we extend a novel model reduction method, based on "scales of dominance," to multi-compartment models. We use this method to systematically reduce the dimension of a two-compartment conductance-based model of a crustacean pyloric dilator (PD) neuron that exhibits distinct modes of oscillation-tonic spiking, intermediate bursting and strong bursting. A cursory analysis of the scales of dominance in a trajectory of this sixteen-variable model leads to a globally-reduced, nine-variable model. In a finer analysis we divide the trajectory into intervals dominated by a smaller number of variables, resulting in a locally-reduced hybrid model whose dimension varies between two and six in different temporal regimes. Both reduced models exhibit the same modes of oscillation as the sixteen-dimensional model over a comparable parameter range. The reduced models highlight low-dimensional organizing structure in the dynamics of the PD neuron, and the dependence of its oscillations on parameters such as the maximal conductances of calcium currents. Our technique could be used to build hybrid low-dimensional models from any large multi-compartment conductance-based model in order to analyze the interactions between different modes of activity.
The PyDSTool software environment is designed to develop, simulate, and analyze dynamical systems... more The PyDSTool software environment is designed to develop, simulate, and analyze dynamical systems models, particularly for biological applications. Unlike the engineering application focus and graphical specification environments of most general purpose simulation tools, PyDSTool provides a programmatic environment well suited to exploratory data-and hypothesis-driven biological modeling problems. In this work, we show how the environment facilitates the application of hybrid dynamical modeling to the reverse engineering of complex biophysical dynamics; in this case, of an excitable membrane. The example demonstrates how the software provides novel tools that support the inference and validation of mechanistic hypotheses and the inclusion of data constraints in both quantitative and qualitative ways. The biophysical application is broadly relevant to models in the biosciences. The open source and platform-independent PyDSTool package is freely available under the BSD license from http://sourceforge.net/projects/pydstool/. The hosting service provides links to documentation and online forums for user support.
Studies of the degrees of freedom or "synergies" in musculoskeletal systems rely critically on al... more Studies of the degrees of freedom or "synergies" in musculoskeletal systems rely critically on algorithms to estimate the "dimension" of kinematic or neural data. Linear algorithms such as principal component analysis (PCA) are used almost exclusively for this purpose. However, biological systems tend to possess nonlinearities and operate at multiple spatial and temporal scales so that the set of reachable system states typically does not lie close to a single linear subspace. We compare the performance of PCA to two alternative nonlinear algorithms (Isomap and our novel pointwise dimension estimation (PD-E)) using synthetic and motion capture data from a robotic arm with known kinematic dimensions, as well as motion capture data from human hands. We find that consideration of the spectral properties of the singular value decomposition in PCA can lead to more accurate dimension estimates than the dominant practice of using a fixed variance capture threshold. We investigate methods for identifying a single integer dimension using PCA and Isomap. In contrast, PD-E provides a range of estimates of fractal dimension. This helps to identify heterogeneous geometric structure of data sets such as unions of manifolds of differing dimensions, to which Isomap is less sensitive. Contrary to common opinion regarding fractal dimension methods, PD-E yielded reasonable results with reasonable amounts of data. We conclude that it is necessary and feasible to complement PCA with other methods that take into consideration the nonlinear properties of biological systems for a more robust estimation of their degrees of freedom.
Journal of Computational Neuroscience, Jun 25, 2014
The Hodgkin-Huxley (HH) model is the basis for numerous neural models. There are two negative fee... more The Hodgkin-Huxley (HH) model is the basis for numerous neural models. There are two negative feedback processes in the HH model that regulate rhythmic spiking. The first is an outward current with an activation variable n that has an opposite influence to the excitatory inward current and therefore provides subtractive negative feedback. The other is the inactivation of an inward current with an inactivation variable h that reduces the amount of positive feedback and therefore provides divisive feedback. Rhythmic spiking can be obtained with either negative feedback process, so we ask what is gained by having two feedback processes. We also ask how the different negative feedback processes contribute to spiking. We show that having two negative feedback processes makes the HH model more robust to changes in applied currents and conductance densities than models that possess only one negative feedback variable. We also show that the contributions made by the subtractive and divisive feedback variables are not static, but depend on time scales and conductance values. In particular, they contribute differently to the dynamics in Type I versus Type II neurons.
SIGLEAvailable from British Library Document Supply Centre- DSC:DXN060383 / BLDSC - British Libra... more SIGLEAvailable from British Library Document Supply Centre- DSC:DXN060383 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
Centrosome amplification (CA) and resultant chromosomal instability have long been associated wit... more Centrosome amplification (CA) and resultant chromosomal instability have long been associated with tumorigenesis. However, exacerbation of CA and relentless centrosome declustering engender robust spindle multipolarity (SM) during mitosis and may induce cell death. Recently, we demonstrated that a noscapinoid member, reduced bromonoscapine, (S)-3-(R)-9-bromo-5-(4,5dimethoxy-1,3-dihydroisobenzofuran-1-yl)-4-methoxy-6-methyl-5,6,7,8-tetrahydro-[1,3]dioxolo-[4,5-g]isoquinoline (Red-Br-nos), induces reactive oxygen species (ROS)-mediated autophagy and caspase-independent death in prostate cancer PC-3 cells. Herein, we show that Red-Br-nos induces ROS-dependent DNA damage that resulted in high-grade CA and SM in PC-3 cells. Unlike doxorubicin, which causes double-stranded DNA breaks and chronic G2 arrest accompanied by 'templated' CA, Red-Brnos-mediated DNA damage elicits de novo CA during a transient S/G2 stall, followed by checkpoint abrogation and mitotic entry to form aberrant mitotic figures with supernumerary spindle poles. Attenuation of multipolar phenotype in the presence of tiron, a ROS inhibitor, indicated that ROS-mediated DNA damage was partly responsible for driving CA and SM. Although a few cells (B5%) yielded to aberrant cytokinesis following an 'anaphase catastrophe', most mitotically arrested cells (B70%) succumbed to 'metaphase catastrophe,' which was caspase-independent. This report is the first documentation of rapid de novo centrosome formation in the presence of parent centrosome by a noscapinoid family member, which triggers death-inducing SM via a unique mechanism that distinguishes it from other ROS-inducers, conventional DNA-damaging agents, as well as other microtubule-binding drugs.
Unlike normal cells, cancer cells contain amplified centrosomes and rely on centrosome clustering... more Unlike normal cells, cancer cells contain amplified centrosomes and rely on centrosome clustering mechanisms to form a pseudobipolar spindle that circumvents potentially fatal spindle multipolarity (MP). Centrosome clustering also promotes lowgrade chromosome missegregation, which can drive malignant transformation and tumor progression. Putative 'centrosome declustering drugs' represent a cancer cell-specific class of chemotherapeutics that produces a common phenotype of centrosome declustering and spindle MP. However, differences between individual agents in terms of efficacy and phenotypic nuances remain unexplored. Herein, we have developed a conceptual framework for the quantitative evaluation of centrosome declustering drugs by investigating their impact on centrosomes, clustering, spindle polarity, cell cycle arrest, and death in various cancer cell lines at multiple drug concentrations over time. Surprisingly, all centrosome declustering drugs evaluated in our study were also centrosome-amplifying drugs to varying extents. Notably, all declustering drugs induced spindle MP, and the peak extent of MP positively correlated with the induction of hypodiploid DNA-containing cells. Our data suggest acentriolar spindle pole amplification as a hitherto undescribed activity of some declustering drugs, resulting in spindle MP in cells that may not have amplified centrosomes. In general, declustering drugs were more toxic to cancer cell lines than non-transformed ones, with some exceptions. Through a comprehensive description and quantitative analysis of numerous phenotypes induced by declustering drugs, we propose a novel framework for the assessment of putative centrosome declustering drugs and describe cellular characteristics that may enhance susceptibility to them.
IEEE Transactions on Biomedical Engineering, Feb 1, 2008
Studies of the degrees of freedom and "synergies" in musculoskeletal systems rely critically on a... more Studies of the degrees of freedom and "synergies" in musculoskeletal systems rely critically on algorithms to estimate the "dimension" of kinematic or neural data. Linear algorithms such as principal component analysis (PCA) are the most popular. However, many biological data (or realistic experimental data) may be better represented by nonlinear sets than linear subspaces. We evaluate the performance of PCA and compare it to two nonlinear algorithms [Isomap and our novel pointwise dimension estimation (PD-E)] using synthetic and motion capture data from a robotic arm with known kinematic dimensions, as well as motion capture data from human hands. We find that PCA can lead to more accurate dimension estimates when considering additional properties of the PCA residuals, instead of the dominant method of using a threshold of variance captured. In contrast to the single integer dimension estimates of PCA and Isomap, PD-E provides a distribution and range of estimates of fractal dimension that identify the heterogeneous geometric structure in the experimental data. A strength of the PD-E method is that it associates a distribution of dimensions to the data. Since there is no a priori reason to assume that the sets of interest have a single dimension, these distributions incorporate more information than a single summary statistic. Our preliminary findings suggest that fewer than ten DOFs are involved in some hand motion tasks. Contrary to common opinion regarding fractal dimension methods, PD-E yielded reasonable results with reasonable amounts of data. Given the complex nature of experimental and biological data, we conclude that it is necessary and feasible to complement PCA with methods that take into consideration the nonlinear properties of biological systems for a more robust estimation of their DOFs.
We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of ... more We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multi-functional central pattern generator (CPG). Such CPGs are neural microcircuits of cells whose synergetic interactions produce multiple states with distinct phase-locked patterns of bursting activity. To study biologically plausible CPG models, we develop a suite of computational tools that reduce the problem of stability and existence of rhythmic patterns in networks to the bifurcation analysis of fixed points and invariant curves of a Poincare ́ return maps for phase lags between cells. We explore different functional possibilities for motifs involving symmetry breaking and heterogeneity. This is achieved by varying coupling properties of the synapses between the cells and studying the quali-tative changes in the structure of the corresponding return maps. Our findings provide a systematic basis for understanding plausible biophysical mechanisms for the regulation of rhythmic pa...
We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of ... more We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multi-functional central pattern generator (CPG). Such CPGs are neural microcircuits of cells whose synergetic interactions produce multiple states with distinct phase-locked patterns of bursting activity. To study biologically plausible CPG models, we develop a suite of computational tools that reduce the problem of stability and existence of rhythmic patterns in networks to the bifurcation analysis of fixed points and invariant curves of a Poincare ́ return maps for phase lags between cells. We explore different functional possibilities for motifs involving symmetry breaking and heterogeneity. This is achieved by varying coupling properties of the synapses between the cells and studying the quali-tative changes in the structure of the corresponding return maps. Our findings provide a systematic basis for understanding plausible biophysical mechanisms for the regulation of rhythmic pa...
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Papers by Robert Clewley