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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 Poincar\'e 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 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

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.

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

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 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.