Priming nonlinear searches for pathway identification

BACKGROUND: Dense time series of metabolite concentrations or of the expression patterns of proteins may be available in the near future as a result of the rapid development of novel, high-throughput experimental techniques. Such time series implicitly contain valuable information about the connectivity and regulatory structure of the underlying metabolic or proteomic networks. The extraction of this information is a challenging task because it usually requires nonlinear estimation methods that involve iterative search algorithms. Priming these algorithms with high-quality initial guesses can greatly accelerate the search process. In this article, we propose to obtain such guesses by preprocessing the temporal profile data and fitting them preliminarily by multivariate linear regression. RESULTS: The results of a small-scale analysis indicate that the regression coefficients reflect the connectivity of the network quite well. Using the mathematical modeling framework of Biochemical Systems Theory (BST), we also show that the regression coefficients may be translated into constraints on the parameter values of the nonlinear BST model, thereby reducing the parameter search space considerably. CONCLUSION: The proposed method provides a good approach for obtaining a preliminary network structure from dense time series. This will be more valuable as the systems become larger, because preprocessing and effective priming can significantly limit the search space of parameters defining the network connectivity, thereby facilitating the nonlinear estimation task

The genotype-phenotype relationship in multicellular pattern-generating models - the neglected role of pattern descriptors

Background: A deep understanding of what causes the phenotypic variation arising from biological patterning processes, cannot be claimed before we are able to recreate this variation by mathematical models capable of generating genotype-phenotype maps in a causally cohesive way. However, the concept of pattern in a multicellular context implies that what matters is not the state of every single cell, but certain emergent qualities of the total cell aggregate. Thus, in order to set up a genotype-phenotype map in such a spatiotemporal pattern setting one is actually forced to establish new pattern descriptors and derive their relations to parameters of the original model. A pattern descriptor is a variable that describes and quantifies a certain qualitative feature of the pattern, for example the degree to which certain macroscopic structures are present. There is today no general procedure for how to relate a set of patterns and their characteristic features to the functional relationships, parameter values and initial values of an original pattern-generating model. Here we present a new, generic approach for explorative analysis of complex patterning models which focuses on the essential pattern features and their relations to the model parameters. The approach is illustrated on an existing model for Delta-Notch lateral inhibition over a two-dimensional lattice. Results: By combining computer simulations according to a succession of statistical experimental designs, computer graphics, automatic image analysis, human sensory descriptive analysis and multivariate data modelling, we derive a pattern descriptor model of those macroscopic, emergent aspects of the patterns that we consider of interest. The pattern descriptor model relates the values of the new, dedicated pattern descriptors to the parameter values of the original model, for example by predicting the parameter values leading to particular patterns, and provides insights that would have been hard to obtain by traditional methods. Conclusion: The results suggest that our approach may qualify as a general procedure for how to discover and relate relevant features and characteristics of emergent patterns to the functional relationships, parameter values and initial values of an underlying pattern-generating mathematical model

Emerging design principles in the Arabidopsis circadian clock

Recent experimental advances have enabled the identification of direct regulatory targets for transcription factors. Application of these techniques to the circadian regulatory network in Arabidopsis has uncovered a number of discrepancies within established models as well as novel regulatory interactions. This review integrates these new findings and discusses the functional implications of the revised transcriptional network for the oscillatory mechanism of the clock

A sensory scientific approach to visual pattern recognition of complex biological systems

A sensory scientific approach for exploring and interpreting image patterns is presented. It is used for analysis of the behaviour of a complex mathematical model - in this case representing two-dimensional pattern-generating protein signalling during cell differentiation. The approach consists of several consecutive research steps, each including statistical planning, image production, image profiling and multivariate data analysis. Initially, a high number of images were produced and profiled by automatic but non-selective computerised image analysis profiling. Then the most interesting images were analysed by descriptive sensory profiling, in two consecutive, increasingly focused experiments. Partial Least Squares Regression models were applied, on one hand, to predict the sensory profile from automatic image analysis, and, on the other hand, to relate the sensory profile to the mathematical model parameters. Previously unknown pattern types for this biological system were thus revealed. Finally, a preliminary sensory morphological wheel was proposed. (C) 2010 Elsevier Ltd. All rights reserved