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.

Transcriptional diversity and bioenergetic shift in human breast cancer metastasis revealed by single-cell RNA sequencing.

Although metastasis remains the cause of most cancer-related mortality, mechanisms governing seeding in distal tissues are poorly understood. Here, we establish a robust method for the identification of global transcriptomic changes in rare metastatic cells during seeding using single-cell RNA sequencing and patient-derived-xenograft models of breast cancer. We find that both primary tumours and micrometastases display transcriptional heterogeneity but micrometastases harbour a distinct transcriptome program conserved across patient-derived-xenograft models that is highly predictive of poor survival of patients.

Learning moment closure in reaction-diffusion systems with spatial dynamic Boltzmann distributions.

Many physical systems are described by probability distributions that evolve in both time and space. Modeling these systems is often challenging due to their large state space and analytically intractable or computationally expensive dynamics. To address these problems, we study a machine-learning approach to model reduction based on the Boltzmann machine.

Prospects for Declarative Mathematical Modeling of Complex Biological Systems.

Declarative modeling uses symbolic expressions to represent models. With such expressions, one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation program, in a general-purpose programming language. Examples of such computations on models include model analysis, relatively general-purpose model reduction maps, and the initial phases of model implementation, all of which should preserve or approximate the mathematical semantics of a complex biological model.

Are microtubules tension sensors?

Mechanical signals play many roles in cell and developmental biology. Several mechanotransduction pathways have been uncovered, but the mechanisms identified so far only address the perception of stress intensity. Mechanical stresses are tensorial in nature, and thus provide dual mechanical information: stress magnitude and direction.

A Pycellerator Tutorial.

We present a tutorial on using Pycellerator for biomolecular simulations. Models are described in human readable (and editable) text files (UTF8 or ASCII) containing collections of reactions, assignments, initial conditions, function definitions, and rate constants. These models are then converted into a Python program that can optionally solve the system, e.

Learning dynamic Boltzmann distributions as reduced models of spatial chemical kinetics.

Finding reduced models of spatially distributed chemical reaction networks requires an estimation of which effective dynamics are relevant. We propose a machine learning approach to this coarse graining problem, where a maximum entropy approximation is constructed that evolves slowly in time. The dynamical model governing the approximation is expressed as a functional, allowing a general treatment of spatial interactions.

Pycellerator: an arrow-based reaction-like modelling language for biological simulations.

Motivation: We introduce Pycellerator, a Python library for reading Cellerator arrow notation from standard text files, conversion to differential equations, generating stand-alone Python solvers, and optionally running and plotting the solutions. All of the original Cellerator arrows, which represent reactions ranging from mass action, Michales-Menten-Henri (MMH) and Gene-Regulation (GRN) to Monod-Wyman-Changeaux (MWC), user defined reactions and enzymatic expansions (KMech), were previously represented with the Mathematica extended character set. These are now typed as reaction-like commands in ASCII text files that are read by Pycellerator, which includes a Python command line interface (CLI), a Python application programming interface (API) and an iPython notebook interface.

Model reduction for stochastic CaMKII reaction kinetics in synapses by graph-constrained correlation dynamics.

A stochastic reaction network model of Ca(2+) dynamics in synapses (Pepke et al PLoS Comput. Biol. 6 e1000675) is expressed and simulated using rule-based reaction modeling notation in dynamical grammars and in MCell.

Analysis of cell division patterns in the Arabidopsis shoot apical meristem.

The stereotypic pattern of cell shapes in the Arabidopsis shoot apical meristem (SAM) suggests that strict rules govern the placement of new walls during cell division. When a cell in the SAM divides, a new wall is built that connects existing walls and divides the cytoplasm of the daughter cells. Because features that are determined by the placement of new walls such as cell size, shape, and number of neighbors are highly regular, rules must exist for maintaining such order.

Using cellzilla for plant growth simulations at the cellular level.

Cellzilla is a two-dimensional tissue simulation platform for plant modeling utilizing Cellerator arrows. Cellerator describes biochemical interactions with a simplified arrow-based notation; all interactions are input as reactions and are automatically translated to the appropriate differential equations using a computer algebra system. Cells are represented by a polygonal mesh of well-mixed compartments.

Time-ordered product expansions for computational stochastic system biology.

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions.

Mathematics of small stochastic reaction networks: a boundary layer theory for eigenstate analysis.

We study and analyze the stochastic dynamics of a reversible bimolecular reaction A + B ↔ C called the "trivalent reaction." This reaction is of a fundamental nature and is part of many biochemical reaction networks. The stochastic dynamics is given by the stochastic master equation, which is difficult to solve except when the equilibrium state solution is desired.

A hierarchical exact accelerated stochastic simulation algorithm.

A new algorithm, "HiER-leap" (hierarchical exact reaction-leaping), is derived which improves on the computational properties of the ER-leap algorithm for exact accelerated simulation of stochastic chemical kinetics. Unlike ER-leap, HiER-leap utilizes a hierarchical or divide-and-conquer organization of reaction channels into tightly coupled "blocks" and is thereby able to speed up systems with many reaction channels. Like ER-leap, HiER-leap is based on the use of upper and lower bounds on the reaction propensities to define a rejection sampling algorithm with inexpensive early rejection and acceptance steps.

Computational analysis of live cell images of the Arabidopsis thaliana plant.

Quantitative studies in plant developmental biology require monitoring and measuring the changes in cells and tissues as growth gives rise to intricate patterns. The success of these studies has been amplified by the combined strengths of two complementary techniques, namely live imaging and computational image analysis. Live imaging records time-lapse images showing the spatial-temporal progress of tissue growth with cells dividing and changing shape under controlled laboratory experiments.

Measuring single-cell gene expression dynamics in bacteria using fluorescence time-lapse microscopy.

Quantitative single-cell time-lapse microscopy is a powerful method for analyzing gene circuit dynamics and heterogeneous cell behavior. We describe the application of this method to imaging bacteria by using an automated microscopy system. This protocol has been used to analyze sporulation and competence differentiation in Bacillus subtilis, and to quantify gene regulation and its fluctuations in individual Escherichia coli cells.

Towards Measurable Types for Dynamical Process Modeling Languages.

Process modeling languages such as "Dynamical Grammars" are highly expressive in the processes they model using stochastic and deterministic dynamical systems, and can be given formal semantics in terms of an operator algebra. However such process languages may be more limited in the types of objects whose dynamics is easily expressible. For many applications in biology, the dynamics of spatial objects in particular (including combinations of discrete and continuous spatial structures) should be formalizable at a high level of abstraction.

A scalable and integrative system for pathway bioinformatics and systems biology.

Motivation: Progress in systems biology depends on developing scalable informatics tools to predictively model, visualize, and flexibly store information about complex biological systems. Scalability of these tools, as well as their ability to integrate within larger frameworks of evolving tools, is critical to address the multi-scale and size complexity of biological systems.

Results: Using current software technology, such as self-generation of database and object code from UML schemas, facilitates rapid updating of a scalable expert assistance system for modeling biological pathways.

Parameter inference for discretely observed stochastic kinetic models using stochastic gradient descent.

Background: Stochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms.

A plausible mechanism for auxin patterning along the developing root.

Background: In plant roots, auxin is critical for patterning and morphogenesis. It regulates cell elongation and division, the development and maintenance of root apical meristems, and other processes. In Arabidopsis, auxin distribution along the central root axis has several maxima: in the root tip, in the basal meristem and at the shoot/root junction.