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 low-grade 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.

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.

We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multifunctional 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 Poincaré 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 qualitative 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 patterns generated by various CPGs in the context of motor control such as gait-switching in locomotion. Our analysis does not require knowledge of the equations modeling the system and provides a powerful qualitative approach to studying detailed models of rhythmic behavior. Thus, our approach is applicable to a wide range of biological phenomena beyond motor control.

We describe a novel computational approach to reduce detailed models of central pattern generation to an equationless mapping that can be studied geometrically. Changes in model parameters, coupling properties, or external inputs produce qualitative changes in the mapping. These changes uncover possible biophysical mechanisms for control and modulation of rhythmic activity. Our analysis does not require knowledge of the equations that model the system, and so provides a powerful new approach to studying detailed models, applicable to a variety of biological phenomena beyond motor control. We demonstrate our technique on a motif of three reciprocally inhibitory cells that is able to produce multiple patterns of bursting rhythms. In particular, we examine the qualitative geometric structure of two-dimensional maps for phase lag between the cells.

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.

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.

We describe and expand on a novel computational approach to reduce detailed models of central pattern generation to equationless return mapping for the phase lags between the constituting bursting interneurons [1]. Such mappings are then studied geometrically as the model parameters, including coupling properties of inhibitory and excitatory synapses, or external inputs are varied. Bifurcations of the fixed points and invariant circles of the mappings corresponding to various types of rhythmic activity are examined. These changes uncover possible biophysical mechanisms for control and modulation of motor-pattern generation. Our analysis does not require knowledge of the equations that model the system, and so provides a powerful new approach to studying detailed models, applicable to a variety of biological phenomena beyond motor control. Motifs of three coupled cells are a common network configuration including models of biological central pattern generators. We demonstrate our technique on a motif of three reciprocally coupled, inhibitory and excitatory, cells that is able to produce multiple patterns of bursting rhythms. In particular, we examine the qualitative geometric structure of two-dimensional maps for phase lag between the cells. This reveals the organizing centers of emergent polyrhythmic patterns and their bifurcations, as the asymmetry of the synaptic coupling is varied. The presence of multistability and the types of attractors in the network are shown to be determined by the duty cycle of bursting, as well as coupling interactions. Figure 1 (A). We defined phase-lags for a 3 cell CPG model on a 2D torus. (B) A “flattened” phase-lag mapping showing convergence to 5 distinct attractors. Each stable fixed point represents a rhythmic output of the CPG

Recent mathematical and computational work on the space-clamped Hodgkin-Huxley (H-H) model of neural excitability identifies major dynamic features of the changing nullclines in 2D phase plane projections during action potential (AP) initiation [1,2]. Such analysis provides novel mechanistic and geometric understanding (in terms of interplay between variables and currents) of the “soft threshold” dynamics. We perform visualization of the nullcline dynamics around threshold, and characterize important geometric properties via “dominant scale analysis” [3], which avoids the need to make asymptotic approximations. In particular, we analyze the transient dynamics during the passage through the ghost of a saddle-node bifurcation in the (V, m) phase-plane projection of a local 3D approximation to the 4D H-H equations (where sodium inactivation h is held constant). Linear analysis of the moving V-nullcline in these projections indicates that a necessary condition for AP initiation is the eventual holding of the following inequalities in the neighborhood of the ghost of the saddle node:

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-(4,5-dimethoxy-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-Br-nos-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 (∼5%) yielded to aberrant cytokinesis following an 'anaphase catastrophe', most mitotically arrested cells (∼70%) 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.

This work presents a neuroinformatic method for deriving mechanistic descriptions of fine-structured neural activity. This is a new development in the computer-assisted analysis of dynamics in conductance-based models, which is illustrated using single compartment models of an action potential. A sequence of abstract, qualitative motifs is inferred from this analysis, forming a template that is independent of the specific equations from which they were abstracted. The template encodes the assumptions behind the model reduction steps used to derive the motifs, and so specifies quantitative information about their domains of validity. The template representation of a mechanism is converted to a hybrid dynamical system, which is simulated as a sequence of low-dimensional reduced models (in this example, phase plane models) with appropriate switching conditions taken from the motifs. We demonstrate the validity of the template on a detailed single neuron model of spiking taken from the literature, and show that the corresponding hybrid system simulation closely mimics the spiking dynamics of the full model.

The growing number of large-scale neuronal network models has created a need for standards and guidelines to ease model sharing and facilitate the replication of results across different simulators. To foster community efforts towards such standards, the International Neuroinformatics Coordinating Facility (INCF) has formed its Multiscale Modeling program, and has assembled a task force of simulator developers to propose a declarative computer language for descriptions of large-scale neuronal networks. The name of the proposed language is Network Interchange for Neuroscience Modeling Language (NineML) and its initial focus is restricted to point neuron models. The INCF Multiscale Modeling task force has identified the key concepts of network modeling to be 1) spiking neurons 2) synapses 3) populations of neurons and 4) connectivity patterns across populations of neurons. Accordingly, the definition of NineML includes a set of mathematical abstractions to represent these concepts. NineML aims to provide tool support for explicit declarative definition of spiking neuronal network models both conceptually and mathematically in a simulator independent manner. In addition, NineML is designed to be self-consistent and highly flexible, allowing addition of new models and mathematical descriptions without modification of the previous structure and organization of the language. To achieve these goals, the language is being iteratively designed using several representative models with various levels of complexity as test cases. The design of NineML is divided in two semantic layers: the Abstraction Layer, which consists of core mathematical concepts necessary to express neuronal and synaptic dynamics and network connectivity patterns, and the User Layer, which provides constructs to specify the instantiation of a network model in terms that are familiar to computational neuroscience modelers. As part of the Abstraction Layer, NineML includes a flexible block diagram notation for describing spiking dynamics. The notation represents continuous and discrete variables, their evolution according to a set of rules such as a system of ordinary differential equations, and the conditions that induce a regime change, such as the transition from subthreshold mode to spiking and refractory modes. The User Layer provides syntax for specifying the structure of the elements of a spiking neuronal network. This includes parameters for each of the individual elements (cells, synapses, inputs) and the grouping of these entities into networks. In addition, the user layer defines the syntax for supplying parameter values to abstract connectivity patterns. The NineML specification is defined as an implementation-neutral object model representing all the concepts in the User and Abstraction Layers. Libraries for creating, manipulating, querying and serializing the NineML object model to a standard XML representation will be delivered for a variety of languages. The first priority of the task force is to deliver a publicly available Python implementation to support the wide range of simulators which provide a Python user interface (NEURON, NEST, Brian, MOOSE, GENESIS-3, PCSIM, PyNN, etc.). These libraries will allow simulator developers to quickly add support for NineML, and will thus catalyze the emergence of a broad software ecosystem supporting model definition interoperability around NineML.

We examine multistability of several coexisting bursting patterns in a central pattern generator network composed of three Hodgkin-Huxley type cells coupled reciprocally by inhibitory synapses. We establish that the control of switching between bursting polyrhythms and their bifurcations are determined by the temporal characteristics, such as the duty cycle, of networked interneurons and the coupling strength asymmetry. A computationally effective approach to the reduction of dynamics of the nine-dimensional network to two-dimensional Poincaré return mappings for phase lags between the interneurons is presented.

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.

We present a novel computational technique that enables more efficient optimization of qualitative features in biophysical neural models. We extend the idea of multiple objective optimization for a single comparison modality (such as comparison of individual voltage traces) [1] into multiple modalities. For instance, features may be defined in terms of measurements from different experimental scenarios, and might include not only action potential spike shape characteristics (Cf. [1,2]) but also complex features such as the frequency response curve, and phase response curve (PRC). Multiple fuzzy feature modalities provide additional ways to distinguish solutions that might otherwise appear similarly fit in the restrictive view of a single modality and with crisp measures of fitness. An ill-posed optimization problem with many local minima typically arises from relative insensitivities of some parameters to features in a single modality, or parameter co-variation/modulation [2]. We use an implementation in the PyDSTool software [3] to demonstrate how the multi-modal approach can be prepared and embedded in conventional gradient-based or global optimization algorithms. Among other applications, we discuss the transformation over 25 model parameters of a Hodgkin-Huxley neuron model with a Type I PRC [4] to a Type II PRC, using a goal PRC shape and other periodic trajectory statistics as fuzzy objective modalities.

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.

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. We divide trajectories 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. The reduced model exhibits the same modes of oscillation as the 16 dimensional model over a comparable parameter range, and requires fewer ad hoc simplifications than a more traditional reduction to a single, globally valid model. The hybrid model highlights 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.

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.