Approximate simulation of cortical microtubule models using dynamical graph grammars.

Dynamical graph grammars (DGGs) are capable of modeling and simulating the dynamics of the cortical microtubule array (CMA) in plant cells by using an exact simulation algorithm derived from a master equation; however, the exact method is slow for large systems. We present preliminary work on an approximate simulation algorithm that is compatible with the DGG formalism. The approximate simulation algorithm uses a spatial decomposition of the domain at the level of the system's time-evolution operator, to gain efficiency at the cost of some reactions firing out of order, which may introduce errors.

Explicit Calculation of Structural Commutation Relations for Stochastic and Dynamical Graph Grammar Rule Operators in Biological Morphodynamics.

Many emergent, non-fundamental models of complex systems can be described naturally by the temporal evolution of spatial structures with some nontrivial discretized topology, such as a graph with suitable parameter vectors labeling its vertices. For example, the cytoskeleton of a single cell, such as the cortical microtubule network in a plant cell or the actin filaments in a synapse, comprises many interconnected polymers whose topology is naturally graph-like and dynamic. The same can be said for cells connected dynamically in a developing tissue.

Graph metric learning quantifies morphological differences between two genotypes of shoot apical meristem cells in .

We present a method for learning 'spectrally descriptive' edge weights for graphs. We generalize a previously known distance measure on graphs (graph diffusion distance [GDD]), thereby allowing it to be tuned to minimize an arbitrary loss function. Because all steps involved in calculating this modified GDD are differentiable, we demonstrate that it is possible for a small neural network model to learn edge weights which minimize loss.

Graph diffusion distance: Properties and efficient computation.

We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which attempts find a map minimizing the discrepancy between two graph Laplacian exponential matrices, under norm-preserving and sparsity constraints. Variants of the distance metric are introduced to consider such optimized maps under sparsity constraints as well as fixed time-scaling between the two Laplacians.

SBML Level 3: an extensible format for the exchange and reuse of biological models.

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose.