Combined in silico/in vivo analysis of mechanisms providing for root apical meristem self-organization and maintenance.

BACKGROUND AND AIMS: The root apical meristem (RAM) is the plant stem cell niche which provides for the formation and continuous development of the root. Auxin is the main regulator of RAM functioning, and auxin maxima coincide with the sites of RAM initiation and maintenance. Auxin gradients are formed due to local auxin biosynthesis and polar auxin transport. The PIN family of auxin transporters plays a critical role in polar auxin transport, and two mechanisms of auxin maximum formation in the RAM based on PIN-mediated auxin transport have been proposed to date: the reverse fountain and the reflected flow mechanisms. METHODS: The two mechanisms are combined here in in silico studies of auxin distribution in intact roots and roots cut into two pieces in the proximal meristem region. In parallel, corresponding experiments were performed in vivo using DR5::GFP Arabidopsis plants. KEY RESULTS: The reverse fountain and the reflected flow mechanism naturally cooperate for RAM patterning and maintenance in intact root. Regeneration of the RAM in decapitated roots is provided by the reflected flow mechanism. In the excised root tips local auxin biosynthesis either alone or in cooperation with the reverse fountain enables RAM maintenance. CONCLUSIONS: The efficiency of a dual-mechanism model in guiding biological experiments on RAM regeneration and maintenance is demonstrated. The model also allows estimation of the concentrations of auxin and PINs in root cells during development and under various treatments. The dual-mechanism model proposed here can be a powerful tool for the study of several different aspects of auxin function in root.

A 'random steady-state' model for the pyruvate dehydrogenase and alpha-ketoglutarate dehydrogenase enzyme complexes.

The multienzyme complexes, pyruvate dehydrogenase and alpha-ketoglutarate dehydrogenase, involved in the central metabolism of Escherichia coli consist of multiple copies of three different enzymes, E1, E2 and E3, that cooperate to channel substrate intermediates between their active sites. The E2 components form the core of the complex, while a mixture of E1 and E3 components binds to the core. We present a random steady-state model to describe catalysis by such multienzyme complexes. At a fast time scale, the model describes the enzyme catalytic mechanisms of substrate channeling at a steady state, by polynomially approximating the analytic solution of a biochemical master equation. At a slower time scale, the structural organization of the different enzymes in the complex and their random binding/unbinding to the core is modeled using methods from equilibrium statistical mechanics. Biologically, the model describes the optimization of catalytic activity by substrate sharing over the entire enzyme complex. The resulting enzymatic models illustrate the random steady state (RSS) for modeling multienzyme complexes in metabolic pathways.

The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models.

MOTIVATION: Molecular biotechnology now makes it possible to build elaborate systems models, but the systems biology community needs information standards if models are to be shared, evaluated and developed cooperatively. RESULTS: We summarize the Systems Biology Markup Language (SBML) Level 1, a free, open, XML-based format for representing biochemical reaction networks. SBML is a software-independent language for describing models common to research in many areas of computational biology, including cell signaling pathways, metabolic pathways, gene regulation, and others. AVAILABILITY: The specification of SBML Level 1 is freely available from http://www.sbml.org/

Machine learning for science: state of the art and future prospects.

Recent advances in machine learning methods, along with successful applications across a wide variety of fields such as planetary science and bioinformatics, promise powerful new tools for practicing scientists. This viewpoint highlights some useful characteristics of modern machine learning methods and their relevance to scientific applications. We conclude with some speculations on near-term progress and promising directions.

Delta-Notch lateral inhibitory patterning in the emergence of ciliated cells in Xenopus: experimental observations and a gene network model.

In diverse vertebrate and invertebrate systems, lateral inhibition through the Delta-Notch signaling pathway can lead to cells in initially uniform epithelial tissues differentiating in "salt-and-pepper", regular spacing patterns. In this paper we examine lateral inhibition during the emergence of ciliated cells in Xenopus embryonic skin, using experimental manipulations of the Delta-Notch pathway and a connectionist gene-network model of the process. The results of our model are in agreement with previous models of regular patterning through lateral inhibition and reproduce the observations of our experimental assays. Moreover, the model provides an account for the variability of embryonic responses to the experimental assays, points to a component of lateral inhibition that may be the chief source of this variability, and suggests ways to control it. Our model could thus serve as a tool to generate predictions about this and other regular patterning systems governed by lateral inhibition.

Convergence properties of the softassign quadratic assignment algorithm.

The softassign quadratic assignment algorithm is a discrete-time, continuous-state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching, and graph partitioning in thousands of simulations, its convergence properties have not been studied. Here, we construct discrete-time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction, which show convergence to a fixed point. The combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization.

A gene network approach to modeling early neurogenesis in Drosophila.

We have produced a model of genetic regulation to simulate how neuroblasts and sensory organ precursor (SOP) cells differentiate from proneural clusters of equivalent cells. Parameters of the model (mainly gene interaction strengths) are optimized in order to fit schematic patterns of expression, drawn from the literature, of genes that are involved in this process of cell fate specification. The model provides suggestions about the role of lateral signalling in neurogenesis and yields specific and testable predictions about the timing and position of appearance of neuroblasts and SOPs within proneural clusters, and about the dynamics of gene expression in individual cells. Experimental testing of these predictions and fits to more accurate quantitative data will help determine which set of model parameters can best describe early neurogenesis.

A robust point-matching algorithm for autoradiograph alignment.

We present a novel method for the geometric alignment of autoradiographs of the brain. The method is based on finding the spatial mapping and the one-to-one correspondences (or homologies) between point features extracted from the images and rejecting non-homologies as outliers. In this way, we attempt to account for the local, natural and artifactual differences between the autoradiograph slices. We have used the resulting automated algorithm on a set of left prefrontal cortex autoradiograph slices, specifically demonstrated its ability to perform point outlier rejection, validated its robustness property using synthetically generated spatial mappings and provided an anecdotal visual comparison with the well-known iterated closest-point (ICP) algorithm. Visualization of a stack of aligned left prefrontal cortex autoradiograph slices is also provided.

A Lagrangian relaxation network for graph matching.

A Lagrangian relaxation network for graph matching is presented. The problem is formulated as follows: given graphs G and g, find a permutation matrix M that brings the two sets of vertices into correspondence. Permutation matrix constraints are formulated in the framework of deterministic annealing. Our approach is in the same spirit as a Lagrangian decomposition approach in that the row and column constraints are satisfied separately with a Lagrange multiplier used to equate the two "solutions". Due to the unavoidable symmetries in graph isomorphism (resulting in multiple global minima), we add a symmetry-breaking self-amplification term in order to obtain a permutation matrix. With the application of a fixpoint preserving algebraic transformation to both the distance measure and self-amplification terms, we obtain a Lagrangian relaxation network. The network performs minimization with respect to the Lagrange parameters and maximization with respect to the permutation matrix variables. Simulation results are shown on 100 node random graphs and for a wide range of connectivities.

Model for cooperative control of positional information in Drosophila by bicoid and maternal hunchback.

The blastoderm of the fruit fly Drosophila melanogaster is unusually well suited for analysis of fundamental questions in animal development. One such question is how genes specify the positional information which determines the developmental pathways (fate) of cells at appropriate spatial locations. In this paper we propose a dynamical model of gene regulation which explicitly describes how positional information is used in the blastoderm. The model is applied to analyze important experimental findings on the dependence of cell fate on the concentration of the Bicoid morphogen. The model shows that positional information in the presumptive middle body is cooperatively determined by maternal products of the bicoid and hunchback genes.

Optimization dynamics for partitioned neural networks.

Given a relaxation-based neural network and a desired partition of the neurons in the network into modules with relatively slow communication between modules, we investigate relaxation dynamics for the resulting partitioned neural network. In particular, we show how the slow inter-module communication channels can be modeled by means of certain transformations of the original objective function which introduce new state variables for the inter-module communication links. We report on a parallel implementation of the resulting relaxation dynamics, for a two-dimensional image segmentation network, using a network of workstations. Experiments demonstrate a functional and efficient parallelization of this neural network algorithm. We also discuss implications for analog hardware implementations of relaxation networks.

A center-of-mass computation describes the precision of random dot displacement discrimination.

We test three specific models of how the human visual system computes a just-noticeable-difference (jnd) in spatial separation. The strategies employed by these three models range from strictly local to global, and use a new discrimination task that measures the precision with which displacements of random dots in random dot arrays can be detected. Fits of these models to the data convincingly exclude the two most local models where the displacement discrimination is based on either point-to-point or bin-to-bin measurements of local dot positions. However, the data are consistent with a model where displacement discrimination is based on a globally computed center-of-mass parameter. This finding enlarges current views of what determines the precision of spatial discrimination to include the effects of stimulus complexity (number of dots) and multiplicity (number of dots displaced).

A connectionist model of development.

We present a phenomenological modeling framework for development. Our purpose is to provide a systematic method for discovering and expressing correlations in experimental data on gene expression and other developmental processes. The modeling framework is based on a connectionist or "neural net" dynamics for biochemical regulators, coupled to "grammatical rules" which describe certain features of the birth, growth, and death of cells, synapses and other biological entities. We outline how spatial geometry can be included, although this part of the model is not complete. As an example of the application of our results to a specific biological system, we show in detail how to derive a rigorously testable model of the network of segmentation genes operating in the blastoderm of Drosophila. To further illustrate our methods, we sketch how they could be applied to two other important developmental processes: cell cycle control and cell-cell induction. We also present a simple biochemical model leading to our assumed connectionist dynamics which shows that the dynamics used is at least compatible with known chemical mechanisms.

Multiscale optimization in neural nets.

One way to speed up convergence in a large optimization problem is to introduce a smaller, approximate version of the problem at a coarser scale and to alternate between relaxation steps for the fine-scale and coarse-scale problems. Such an optimization method for neural networks governed by quite general objective functions is presented. At the coarse scale, there is a smaller approximating neural net which, like the original net, is nonlinear and has a nonquadratic objective function. The transitions and information flow from fine to coarse scale and back do not disrupt the optimization, and the user need only specify a partition of the original fine-scale variables. Thus, the method can be applied easily to many problems and networks. There is generally about a fivefold improvement in estimated cost under the multiscale method. In the networks to which it was applied, a nontrivial speedup by a constant factor of between two and five was observed, independent of problem size. Further improvements in computational cost are very likely to be available, especially for problem-specific multiscale neural net methods.