Hyperdigraph-theoretic analysis of the EGFR signaling network: initial steps leading to GTP:Ras complex formation.

We construct an algebraic-combinatorial model of the SOS compartment of the EGFR biochemical network. A Petri net is used to construct an initial representation of the biochemical decision making network, which in turn defines a hyperdigraph. We observe that the linear algebraic structure of each hyperdigraph admits a canonical set of algebraic-combinatorial invariants that correspond to the information flow conservation laws governing a molecular kinetic reaction network. The linear algebraic structure of the hyperdigraph and its sets of invariants can be generalized to define a discrete algebraic-geometric structure, which is referred to as an oriented matroid. Oriented matroids define a polyhedral optimization geometry that is used to determine optimal subpaths that span the nullspace of a set of kinetic chemical reaction equations. Sets of constrained submodular path optimizations on the hyperdigraph are objectively obtained as a spanning tree of minimum cycle paths. This complete set of subcircuits is used to identify the network pinch points and invariant flow subpaths. We demonstrate that this family of minimal circuits also characteristically identifies additional significant biochemical reaction pattern features. We use the SOS Compartment A of the EGFR biochemical pathway to develop and demonstrate the application of our algebraic-combinatorial mathematical modeling methodology.     

MCAM: multiple clustering analysis methodology for deriving hypotheses and insights from high-throughput proteomic datasets

Advances in proteomic technologies continue to substantially accelerate capability for generating experimental data on protein levels, states, and activities in biological samples. For example, studies on receptor tyrosine kinase signaling networks can now capture the phosphorylation state of hundreds to thousands of proteins across multiple conditions. However, little is known about the function of many of these protein modifications, or the enzymes responsible for modifying them. To address this challenge, we have developed an approach that enhances the power of clustering techniques to infer functional and regulatory meaning of protein states in cell signaling networks. We have created a new computational framework for applying clustering to biological data in order to overcome the typical dependence on specific a priori assumptions and expert knowledge concerning the technical aspects of clustering. Multiple clustering analysis methodology ('MCAM') employs an array of diverse data transformations, distance metrics, set sizes, and clustering algorithms, in a combinatorial fashion, to create a suite of clustering sets. These sets are then evaluated based on their ability to produce biological insights through statistical enrichment of metadata relating to knowledge concerning protein functions, kinase substrates, and sequence motifs. We applied MCAM to a set of dynamic phosphorylation measurements of the ERRB network to explore the relationships between algorithmic parameters and the biological meaning that could be inferred and report on interesting biological predictions. Further, we applied MCAM to multiple phosphoproteomic datasets for the ERBB network, which allowed us to compare independent and incomplete overlapping measurements of phosphorylation sites in the network. We report specific and global differences of the ERBB network stimulated with different ligands and with changes in HER2 expression. Overall, we offer MCAM as a broadly-applicable approach for analysis of proteomic data which may help increase the current understanding of molecular networks in a variety of biological problems.     

A new method for assembling metabolic networks, with application to the Krebs citric acid cycle

To understand why a molecular network has a particular connectivity one can generate an ensemble of alternative networks, all of which meet the same performance criteria as the real network. We have generated alternatives to the Krebs cycle, allowing group transfers and B(12)-mediated shifts that were excluded in previous work. Our algorithm does not use a reaction list, but determines the reactants and products in generic reactions. It generates networks in order of increasing number of reaction steps. We find that alternatives to the Krebs cycle are very likely to be cycles. Many of the alternatives produce toxic or unstable compounds and use group transfer reactions, which have unfavorable consequences. Although alternatives are better than the Krebs cycle in some respects, the Krebs cycle has the most favorable combination of traits.     

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.     

Thermodynamic-based computational profiling of cellular regulatory control in hepatocyte metabolism

Thermodynamic-based constraints on biochemical fluxes and concentrations are applied in concert with mass balance of fluxes in glycogenesis and glycogenolysis in a model of hepatic cell metabolism. Constraint-based modeling methods that facilitate predictions of reactant concentrations, reaction potentials, and enzyme activities are introduced to identify putative regulatory and control sites in biological networks by computing the minimal control scheme necessary to switch between metabolic modes. Computational predictions of control sites in glycogenic and glycogenolytic operational modes in the hepatocyte network compare favorably with known regulatory mechanisms. The developed hepatic metabolic model is used to computationally analyze the impairment of glucose production in von Gierke's and Hers' diseases, two metabolic diseases impacting glycogen metabolism. The computational methodology introduced here can be generalized to identify downstream targets of agonists, to systematically probe possible drug targets, and to predict the effects of specific inhibitors (or activators) on integrated network function.     

A Robust Structural PGN Model for Control of Cell-Cycle Progression Stabilized by Negative Feedbacks

The cell division cycle comprises a sequence of phenomena controlled by a stable and robust genetic network. We applied a probabilistic genetic network (PGN) to construct a hypothetical model with a dynamical behavior displaying the degree of robustness typical of the biological cell cycle. The structure of our PGN model was inspired in well-established biological facts such as the existence of integrator subsystems, negative and positive feedback loops, and redundant signaling pathways. Our model represents genes interactions as stochastic processes and presents strong robustness in the presence of moderate noise and parameters fluctuations. A recently published deterministic yeast cell-cycle model does not perform as well as our PGN model, even upon moderate noise conditions. In addition, self stimulatory mechanisms can give our PGN model the possibility of having a pacemaker activity similar to the observed in the oscillatory embryonic cell cycle.     

An old paper revisited: "a mathematical model of carbohydrate energy metabolism. Interaction between glycolysis, the Krebs cycle and the H-transporting shuttles at varying ATPases load" by V.V. Dynnik, R. Heinrich and E.E. Sel'kov

We revisit an old Russian paper by V.V. Dynnik, R. Heinrich and E.E. Sel’kov (1980a, b) describing: “A mathematical model of carbohydrate energy metabolism. Interaction between glycolysis, the Krebs cycle and the H-transporting shuttles at varying ATPases load”. We analyse the model mathematically and calculate the control coefficients as a function of ATPase loads. We also evaluate the structure of the metabolic network in terms of elementary flux modes.We show how this model can respond to an ATPase load as well as to the glucose supply. We also show how this simple model can help in understanding the articulation between the major blocks of energetic metabolism, i.e. glycolysis, the Krebs cycle and the H-transporting shuttles.     

In vivo robustness analysis of cell division cycle genes in Saccharomyces cerevisiae

Intracellular biochemical parameters, such as the expression level of gene products, are considered to be optimized so that a biological system, including the parameters, works effectively. Those parameters should have some permissible range so that the systems have robustness against perturbations, such as noise in gene expression. However, little is known about the permissible range in real cells because there has been no experimental technique to test it. In this study, we developed a genetic screening method, named “genetic tug-of-war” (gTOW) that evaluates upper limit copy numbers of genes in a model eukaryote Saccharomyces cerevisiae, and we applied it for 30 cell-cycle related genes (CDC genes). The experiment provided unique quantitative data that could be used to argue the system-level properties of the cell cycle such as robustness and fragility. The data were used to evaluate the current computational model, and refinements to the model were suggested.     

Training signaling pathway maps to biochemical data with constrained fuzzy logic: quantitative analysis of liver cell responses to inflammatory stimuli

Predictive understanding of cell signaling network operation based on general prior knowledge but consistent with empirical data in a specific environmental context is a current challenge in computational biology. Recent work has demonstrated that Boolean logic can be used to create context-specific network models by training proteomic pathway maps to dedicated biochemical data; however, the Boolean formalism is restricted to characterizing protein species as either fully active or inactive. To advance beyond this limitation, we propose a novel form of fuzzy logic sufficiently flexible to model quantitative data but also sufficiently simple to efficiently construct models by training pathway maps on dedicated experimental measurements. Our new approach, termed constrained fuzzy logic (cFL), converts a prior knowledge network (obtained from literature or interactome databases) into a computable model that describes graded values of protein activation across multiple pathways. We train a cFL-converted network to experimental data describing hepatocytic protein activation by inflammatory cytokines and demonstrate the application of the resultant trained models for three important purposes: (a) generating experimentally testable biological hypotheses concerning pathway crosstalk, (b) establishing capability for quantitative prediction of protein activity, and (c) prediction and understanding of the cytokine release phenotypic response. Our methodology systematically and quantitatively trains a protein pathway map summarizing curated literature to context-specific biochemical data. This process generates a computable model yielding successful prediction of new test data and offering biological insight into complex datasets that are difficult to fully analyze by intuition alone.     

Kinetic models of odor transduction implemented as artificial neural networks

We present a formal model of olfactory transduction corresponding to the biochemical reaction cascade found in chemosensory neurons. It assumes that odorants bind to receptor proteins which, in turn, activate transducer mechanisms corresponding to second messenger-mediated processes. The model is reformulated as a mathematically equivalent artificial neural network (ANN). To enable comparison of the computational power of our model, previously suggested models of chemosensory transduction are also presented in ANN versions. In ANNs, certain biological parameters, such as rate constants and affinities, are transformed into weights that can be fitted by training with a given experimental data set. After training, these weights do not necessarily equal the real biological parameters, but represent a set of values that is sufficient to simulate an experimental set of data. We used ANNs to simulate data recorded from bee subplacodes and compare the capacity of our model with ANN versions of other models. Receptor neurons of the nonpheromonal, general odor-processing subsystem of the honeybee are broadly tuned, have overlapping response spectra, and show highly nonlinear concentration dependencies and mixture interactions, i.e., synergistic and inhibitory effects. Our full model alone has the necessary complexity to simulate these complex response characteristics. To account for the complex response characteristics of honeybee receptor neurons, we suggest that several different receptor protein types and at least two second messenger systems are necessary that may interact at various levels of the transduction cascade and may eventually have opposing effects on receptor neuron excitability.     

Exploring the diversity of complex metabolic networks

MOTIVATION: Metabolism, the network of chemical reactions that make life possible, is one of the most complex processes in nature. We describe here the development of a computational approach for the identification of every possible biochemical reaction from a given set of enzyme reaction rules that allows the de novo synthesis of metabolic pathways composed of these reactions, and the evaluation of these novel pathways with respect to their thermodynamic properties. RESULTS: We applied this framework to the analysis of the aromatic amino acid pathways and discovered almost 75,000 novel biochemical routes from chorismate to phenylalanine, more than 350,000 from chorismate to tyrosine, but only 13 from chorismate to tryptophan. Thermodynamic analysis of these pathways suggests that the native pathways are thermodynamically more favorable than the alternative possible pathways. The pathways generated involve compounds that exist in biological databases, as well as compounds that exist in chemical databases and novel compounds, suggesting novel biochemical routes for these compounds and the existence of biochemical compounds that remain to be discovered or synthesized through enzyme and pathway engineering. AVAILABILITY: Framework will be available via web interface at http://systemsbiology.northwestern.edu/BNICE (site under construction). CONTACT: vassily@northwestern.edu or broadbelt@northwestern.edu SUPPLEMENTARY INFORMATION: http://systemsbiology.northwestern.edu/BNICE/publications.     

Algorithmic specification as a technique for computing with informal biological models

Conceptual biological models can sometimes be usefully expressed in algorithmic form. Models expressed in this way are often capable of capturing more aspects of the complete system than could be captured by other modeling approaches, though in general each aspect is captured in a highly simplified way. Two examples are given. The first involves algorithmic specification of the theory of evolution. The second involves a recently implemented computational model of the brain. Work with such models has, to some extent, the style of experimental work. It often suggests interesting problems or exposes subtle features of the system whose importance has been overlooked.     

Carbon sequestration in Synechococcus Sp.: from molecular machines to hierarchical modeling

The U.S. Department of Energy recently announced the first five grants for the Genomes to Life (GTL) Program. The goal of this program is to "achieve the most far-reaching of all biological goals: a fundamental, comprehensive, and systematic understanding of life." While more information about the program can be found at the GTL website (www.doegenomestolife.org), this paper provides an overview of one of the five GTL projects funded, "Carbon Sequestration in Synechococcus Sp.: From Molecular Machines to Hierarchical Modeling." This project is a combined experimental and computational effort emphasizing developing, prototyping, and applying new computational tools and methods to elucidate the biochemical mechanisms of the carbon sequestration of Synechococcus Sp., an abundant marine cyanobacteria known to play an important role in the global carbon cycle. Understanding, predicting, and perhaps manipulating carbon fixation in the oceans has long been a major focus of biological oceanography and has more recently been of interest to a broader audience of scientists and policy makers. It is clear that the oceanic sinks and sources of CO(2) are important terms in the global environmental response to anthropogenic atmospheric inputs of CO(2) and that oceanic microorganisms play a key role in this response. However, the relationship between this global phenomenon and the biochemical mechanisms of carbon fixation in these microorganisms is poorly understood. The project includes five subprojects: an experimental investigation, three computational biology efforts, and a fifth which deals with addressing computational infrastructure challenges of relevance to this project and the Genomes to Life program as a whole. Our experimental effort is designed to provide biology and data to drive the computational efforts and includes significant investment in developing new experimental methods for uncovering protein partners, characterizing protein complexes, identifying new binding domains. We will also develop and apply new data measurement and statistical methods for analyzing microarray experiments. Our computational efforts include coupling molecular simulation methods with knowledge discovery from diverse biological data sets for high-throughput discovery and characterization of protein-protein complexes and developing a set of novel capabilities for inference of regulatory pathways in microbial genomes across multiple sources of information through the integration of computational and experimental technologies. These capabilities will be applied to Synechococcus regulatory pathways to characterize their interaction map and identify component proteins in these pathways. We will also investigate methods for combining experimental and computational results with visualization and natural language tools to accelerate discovery of regulatory pathways. Furthermore, given that the ultimate goal of this effort is to develop a systems-level of understanding of how the Synechococcus genome affects carbon fixation at the global scale, we will develop and apply a set of tools for capturing the carbon fixation behavior of complex of Synechococcus at different levels of resolution. Finally, because the explosion of data being produced by high-throughput experiments requires data analysis and models which are more computationally complex, more heterogeneous, and require coupling to ever increasing amounts of experimentally obtained data in varying formats, we have also established a companion computational infrastructure to support this effort as well as the Genomes to Life program as a whole.     

Ingeneue: a versatile tool for reconstituting genetic networks,with examples from the segment polarity network

Here we describe a software tool for synthesizing molecular genetic data into models of genetic networks. Our software program Ingeneue, written in Java, lets the user quickly turn a map of a genetic network into a dynamical model consisting of a set of ordinary differential equations. We developed Ingeneue as part of an ongoing effort to explore the design and evolvability of genetic networks. Ingeneue has three principal advantages over other available mathematical software: it automates instantiation of the same network model in each cell in a 2-D sheet of cells; it constructs model equations from pre-made building blocks corresponding to common biochemical processes; and it automates searches through parameter space, sensitivity analyses, and other common tasks. Here we discuss the structure of the software and some of the issues we have dealt with. We conclude with some examples of results we have achieved with Ingeneue for the Drosophila segment polarity network.     

Inferring horizontal transfers in the presence of rearrangements by the minimum evolution criterion

MOTIVATION: The evolution of viruses is very rapid and in addition to local point mutations (insertion, deletion, substitution) it also includes frequent recombinations, genome rearrangements and horizontal transfer of genetic materials (HGTS). Evolutionary analysis of viral sequences is therefore a complicated matter for two main reasons: First, due to HGTs and recombinations, the right model of evolution is a network and not a tree. Second, due to genome rearrangements, an alignment of the input sequences is not guaranteed. These facts encourage developing methods for inferring phylogenetic networks that do not require aligned sequences as input. RESULTS: In this work, we present the first computational approach which deals with both genome rearrangements and horizontal gene transfers and does not require a multiple alignment as input. We formalize a new set of computational problems which involve analyzing such complex models of evolution. We investigate their computational complexity, and devise algorithms for solving them. Moreover, we demonstrate the viability of our methods on several synthetic datasets as well as four biological datasets. AVAILABILITY: The code is available from the authors upon request.     

Haplotype inference by maximum parsimony

MOTIVATION: Haplotypes have been attracting increasing attention because of their importance in analysis of many fine-scale molecular-genetics data. Since direct sequencing of haplotype via experimental methods is both time-consuming and expensive, haplotype inference methods that infer haplotypes based on genotype samples become attractive alternatives. RESULTS: (1) We design and implement an algorithm for an important computational model of haplotype inference that has been suggested before in several places. The model finds a set of minimum number of haplotypes that explains the genotype samples. (2) Strong supports of this computational model are given based on the computational results on both real data and simulation data. (3) We also did some comparative study to show the strength and weakness of this computational model using our program. AVAILABILITY: The software HAPAR is free for non-commercial uses. Available upon request (lwang@cs.cityu.edu.hk).