Genomics. Molecular prodigality

Generalizing Gillespie's Direct Method to Enable Network-Free Simulations

Gillespie's direct method for stochastic simulation of chemical kinetics is a staple of computational systems biology research. However, the algorithm requires explicit enumeration of all reactions and all chemical species that may arise in the system. In many cases, this is not feasible due to the combinatorial explosion of reactions and species in biological networks. Rule-based modeling frameworks provide a way to exactly represent networks containing such combinatorial complexity, and generalizations of Gillespie's direct method have been developed as simulation engines for rule-based modeling languages. Here, we provide both a high-level description of the algorithms underlying the simulation engines, termed network-free simulation algorithms, and how they have been applied in systems biology research. We also define a generic rule-based modeling framework and describe a number of technical details required for adapting Gillespie's direct method for network-free simulation. Finally, we briefly discuss potential avenues for advancing network-free simulation and the role they continue to play in modeling dynamical systems in biology.

How prokaryotes 'encode' their environment: Systemic tools for organizing the information flow

An important issue related to code biology concerns the cell's informational relationships with the environment. As an open self-producing system, a great variety of inputs and outputs are necessary for the living cell, not only consisting of matter and energy but also involving information flows. The analysis here of the simplest cells will involve two basic aspects. On the one side, the molecular apparatuses of the prokaryotic signaling system, with all its variety of environmental signals and component pathways (which have been called 1-2-3 Component Systems), including the role of a few second messengers which have been pointed out in bacteria too. And in the other side, the gene transcription system as depending not only on signaling inputs but also on a diversity of factors. Amidst the continuum of energy, matter, and information flows, there seems to be evidence for signaling codes, mostly established around the arrangement of life-cycle stages, in large metabolic changes, or in the relationships with conspecifics (quorum sensing) and within microbial ecosystems. Additionally, and considering the complexity growth of signaling systems from prokaryotes to eukaryotes, four avenues or "roots" for the advancement of such complexity would come out. A comparative will be established in between the signaling strategies and organization of both kinds of cellular systems. Finally, a new characterization of "informational architectures" will be proposed in order to explain the coding spectrum of both prokaryotic and eukaryotic signaling systems. Among other evolutionary aspects, cellular strategies for the construction of novel functional codes via the intermixing of informational architectures could be related to the persistence of retro-elements with obvious viral ancestry.

MESOSCOPIC MODELING OF STOCHASTIC REACTION-DIFFUSION KINETICS IN THE SUBDIFFUSIVE REGIME

Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model of subdiffusion into an accurate and consistent reaction-subdiffusion computational framework. Two different possible models of chemical reaction are revealed and some basic dynamic properties are derived. In certain cases those mesoscopic models have a direct interpretation at the macroscopic level as fractional partial differential equations in a bounded time interval. Through analysis and numerical experiments we estimate the macroscopic effects of reactions under subdiffusive mixing. The models display properties observed also in experiments: for a short time interval the behavior of the diffusion and the reaction is ordinary, in an intermediate interval the behavior is anomalous, and at long times the behavior is ordinary again.

Multi-state modeling of biomolecules

Multi-state modeling of biomolecules refers to a series of techniques used to represent and compute the behavior of biological molecules or complexes that can adopt a large number of possible functional states. Biological signaling systems often rely on complexes of biological macromolecules that can undergo several functionally significant modifications that are mutually compatible. Thus, they can exist in a very large number of functionally different states. Modeling such multi-state systems poses two problems: the problem of how to describe and specify a multi-state system (the “specification problem”) and the problem of how to use a computer to simulate the progress of the system over time (the “computation problem”). To address the specification problem, modelers have in recent years moved away from explicit specification of all possible states and towards rule-based formalisms that allow for implicit model specification, including the κ-calculus [1], BioNetGen [2]–[5], the Allosteric Network Compiler [6], and others [7], [8]. To tackle the computation problem, they have turned to particle-based methods that have in many cases proved more computationally efficient than population-based methods based on ordinary differential equations, partial differential equations, or the Gillespie stochastic simulation algorithm[9], [10]. Given current computing technology, particle-based methods are sometimes the only possible option. Particle-based simulators fall into two further categories: nonspatial simulators, such as StochSim [11], DYNSTOC [12], RuleMonkey [9], [13], and the Network-Free Stochastic Simulator (NFSim) [14], and spatial simulators, including Meredys [15], SRSim [16], [17], and MCell [18]–[20]. Modelers can thus choose from a variety of tools, the best choice depending on the particular problem. Development of faster and more powerful methods is ongoing, promising the ability to simulate ever more complex signaling processes in the future.

Meredys, a multi-compartment reaction-diffusion simulator using multistate realistic molecular complexes

Background

Most cellular signal transduction mechanisms depend on a few molecular partners whose roles depend on their position and movement in relation to the input signal. This movement can follow various rules and take place in different compartments. Additionally, the molecules can form transient complexes. Complexation and signal transduction depend on the specific states partners and complexes adopt. Several spatial simulator have been developed to date, but none are able to model reaction-diffusion of realistic multi-state transient complexes.

Results

Meredys allows for the simulation of multi-component, multi-feature state molecular species in two and three dimensions. Several compartments can be defined with different diffusion and boundary properties. The software employs a Brownian dynamics engine to simulate reaction-diffusion systems at the reactive particle level, based on compartment properties, complex structure, and hydro-dynamic radii. Zeroth-, first-, and second order reactions are supported. The molecular complexes have realistic geometries. Reactive species can contain user-defined feature states which can modify reaction rates and outcome. Models are defined in a versatile NeuroML input file. The simulation volume can be split in subvolumes to speed up run-time.

Conclusions

Meredys provides a powerful and versatile way to run accurate simulations of molecular and sub-cellular systems, that complement existing multi-agent simulation systems. Meredys is a Free Software and the source code is available at http://meredys.sourceforge.net/.

On prokaryotic intelligence: strategies for sensing the environment

The adaptive relationship with the environment is a sine qua non condition for any intelligent system. Discussions on the nature of cellular intelligence, however, have not systematically pursued yet the question of whether there is a fundamental way of sensing the environment, which may characterize prokaryotic cells, or not. The molecular systems found in bacterial signaling are extremely diverse, ranging from very simple transcription regulators (single proteins comprising just two domains) to the multi-component, multi-pathway signaling cascades that regulate crucial stages of the cell cycle, such as sporulation, biofilm formation, dormancy, pathogenesis or flagellar biosynthesis. The combined complexity of the environment and of the cellular way of life is reflected as a whole in the aggregate of signaling elements: an interesting power-law relationship emerges in that regard. In a basic taxonomy of bacterial signaling systems, the first level of complexity corresponds to the simplest regulators, the "one-component systems" (OCSs), which are defined as proteins that contain known or predicted input and output domains but lack histidine kinase and receiver domains. They are evolutionary precursors of the "two-component systems" (TCSs), which include histidine protein-kinase receptors and an independent response regulator, and are considered as the central signaling paradigm within prokaryotic organisms. The addition of independent receptors begets further functional complexity: thus, "three-component systems" (ThCSs) should be applied to those two-component systems that incorporate an extra non-kinase receptor to activate the protein-kinase. Further, the combined information processing functions (cross-talk) and integrative dynamics that OCS, TCS and ThCS may achieve together in the prokaryotic cell have to be depicted, as well as the relationship of these informational functions with the life cycle organization and its checkpoints. Finally, the extent to which formal models would capture the ongoing relationship of the living cell with its medium has to be gauged, in the light of both the complexity of molecular recognition events and the impredicative nature of living systems.

Kinetic Monte Carlo method for rule-based modeling of biochemical networks

We present a kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes. A rule identifies the molecular components involved in a transformation, how these components change, conditions that affect whether a transformation occurs, and a rate law. The computational cost of the method, unlike conventional simulation approaches, is independent of the number of possible reactions, which need not be specified in advance or explicitly generated in a simulation. To demonstrate the method, we apply it to study the kinetics of multivalent ligand-receptor interactions. We expect the method will be useful for studying cellular signaling systems and other physical systems involving aggregation phenomena.

XML Encoding of Features Describing Rule-Based Modeling of Reaction Networks with Multi-Component Molecular Complexes

Multi-state molecules and multi-component complexes are commonly involved in cellular signaling. Accounting for molecules that have multiple potential states, such as a protein that may be phosphorylated on multiple residues, and molecules that combine to form heterogeneous complexes located among multiple compartments, generates an effect of combinatorial complexity. Models involving relatively few signaling molecules can include thousands of distinct chemical species. Several software tools (StochSim, BioNetGen) are already available to deal with combinatorial complexity. Such tools need information standards if models are to be shared, jointly evaluated and developed. Here we discuss XML conventions that can be adopted for modeling biochemical reaction networks described by user-specified reaction rules. These could form a basis for possible future extensions of the Systems Biology Markup Language (SBML).

Combinatorial complexity and dynamical restriction of network flows in signal transduction

The activities and interactions of proteins that govern the cellular response to a signal generate a multitude of protein phosphorylation states and heterogeneous protein complexes. Here, using a computational model that accounts for 307 molecular species implied by specified interactions of four proteins involved in signalling by the immunoreceptor FcepsilonRI, we determine the relative importance of molecular species that can be generated during signalling, chemical transitions among these species, and reaction paths that lead to activation of the protein tyrosine kinase (PTK) Syk. By all of these measures and over two- and ten-fold ranges of model parameters--rate constants and initial concentrations--only a small portion of the biochemical network is active. The spectrum of active complexes, however, can be shifted dramatically, even by a change in the concentration of a single protein, which suggests that the network can produce qualitatively different responses under different cellular conditions and in response to different inputs. Reduced models that reproduce predictions of the full model for a particular set of parameters lose their predictive capacity when parameters are varied over two-fold ranges.

Rules for modeling signal-transduction systems

Formalized rules for protein-protein interactions have recently been introduced to represent the binding and enzymatic activities of proteins in cellular signaling. Rules encode an understanding of how a system works in terms of the biomolecules in the system and their possible states and interactions. A set of rules can be as easy to read as a diagrammatic interaction map, but unlike most such maps, rules have precise interpretations. Rules can be processed to automatically generate a mathematical or computational model for a system, which enables explanatory and predictive insights into the system's behavior. Rules are independent units of a model specification that facilitate model revision. Instead of changing a large number of equations or lines of code, as may be required in the case of a conventional mathematical model, a protein interaction can be introduced or modified simply by adding or changing a single rule that represents the interaction of interest. Rules can be defined and visualized by using graphs, so no specialized training in mathematics or computer science is necessary to create models or to take advantage of the representational precision of rules. Rules can be encoded in a machine-readable format to enable electronic storage and exchange of models, as well as basic knowledge about protein-protein interactions. Here, we review the motivation for rule-based modeling; applications of the approach; and issues that arise in model specification, simulation, and testing. We also discuss rule visualization and exchange and the software available for rule-based modeling.

Adaptational assistance in clusters of bacterial chemoreceptors

Sensory adaptation of low-abundance chemoreceptors in Escherichia coli requires assistance from high-abundance receptors, because only high-abundance receptors carry the carboxyl-terminal pentapeptide sequence NWETF that enhances adaptational covalent modification. Using membrane vesicles containing both high-abundance receptor Tar and low-abundance receptor Trg, we observed effective assistance in vitro for all three adaptational modifications: methylation, demethylation and deamidation. These results demonstrated that adaptational assistance involves not only the previously documented assistance for methylation but also assistance for the two CheB-catalysed reactions. We determined rates of assisted methylation and demethylation at many ratios of assisting to assisted receptor. Analysis by a model of assistance indicated one Tar dimer could assist seven Trg dimers in methylation or five in demethylation, defining assistance neighbourhoods. These neighbourhoods were larger than a trimer of homodimers, required only receptors and were minimally affected by formation of signalling complexes. Time courses of assisted Trg methylation in membranes with low amounts of Tar showed that assisting receptors did not diffuse beyond initial neighbourhoods for at least two hours. Taken together, these observations indicate that chemoreceptors can form stable neighbourhoods larger than trimers in the absence of other chemotaxis proteins. Such interactions are likely to occur in natural receptor clusters in vivo.

Epigenetic Inheritance and the Intergenerational Transfer of Experience

Currently, behavioral development is thought to result from the interplay among genetic inheritance, congenital characteristics, cultural contexts, and parental practices as they directly impact the individual. Evolutionary ecology points to another contributor, epigenetic inheritance, the transmission to offspring of parental phenotypic responses to environmental challenges-even when the young do not experience the challenges themselves. Genetic inheritance is not altered, gene expression is. Organismic pathways for such transmission exist. Maternal stress during the latter half of a daughter's gestation may affect not only the daughter's but also grand-offspring's physical growth. The author argues that temperamental variation may be influenced in the same way. Implications for theory and research design are presented along with testable predictions.

Making sense of it all: bacterial chemotaxis

Bacteria must be able to respond to a changing environment, and one way to respond is to move. The transduction of sensory signals alters the concentration of small phosphorylated response regulators that bind to the rotary flagellar motor and cause switching. This simple pathway has provided a paradigm for sensory systems in general. However, the increasing number of sequenced bacterial genomes shows that although the central sensory mechanism seems to be common to all bacteria, there is added complexity in a wide range of species.

The complexity of complexes in signal transduction

Many activities of cells are controlled by cell-surface receptors, which in response to ligands, trigger intracellular signaling reactions that elicit cellular responses. A hallmark of these signaling reactions is the reversible nucleation of multicomponent complexes, which typically begin to assemble when ligand-receptor binding allows an enzyme, often a kinase, to create docking sites for signaling molecules through chemical modifications, such as tyrosine phosphorylation. One function of such docking sites is the co-localization of enzymes with their substrates, which can enhance both enzyme activity and specificity. The directed assembly of complexes can also influence the sensitivity of cellular responses to ligand-receptor binding kinetics and determine whether a cellular response is up- or downregulated in response to a ligand stimulus. The full functional implications of ligand-stimulated complex formation are difficult to discern intuitively. Complex formation is governed by conditional interactions among multivalent signaling molecules and influenced by quantitative properties of both the components in a system and the system itself. Even a simple list of the complexes that can potentially form in response to a ligand stimulus is problematic because of the number of ways signaling molecules can be modified and combined. Here, we review the role of multicomponent complexes in signal transduction and advocate the use of mathematical models that incorporate detail at the level of molecular domains to study this important aspect of cellular signaling.

After the genome--the phenome?

What next? The Human Genome Project signifies complexity rather than simplification in the relationship between genotype and phenotype. Genotypes are embedded in genomes. Individuality in phenotypes is embedded in components of the phenome (transcriptome, metabolome, proteome, etc.). The phenome, its layers, and its nodes, links and networks, require elucidation; there is a need for a Human Phenome Project (Freimer and Sabatti 2003). Biology has largely been a reductive science in the recent past; integrative biology lies ahead. Clinician-scientists (including human biochemical geneticists) will be recognized as key participants in the 'medical' Phenome Project as it reveals components of individuality, and their contributions, in simple or combinatorial fashion, to Mendelian and complex traits; better ways to treat 'genetic disease' will be by-products of the project. Although the Word is common to all, most men live as if each had a private wisdom of his own.Herakleitos

Application of comparative genomics in the identification and analysis of novel families of membrane-associated receptors in bacteria

BACKGROUND

A great diversity of multi-pass membrane receptors, typically with 7 transmembrane (TM) helices, is observed in the eukaryote crown group. So far, they are relatively rare in the prokaryotes, and are restricted to the well-characterized sensory rhodopsins of various phototropic prokaryotes.

RESULTS

Utilizing the currently available wealth of prokaryotic genomic sequences, we set up a computational screen to identify putative 7 (TM) and other multi-pass membrane receptors in prokaryotes. As a result of this procedure we were able to recover two widespread families of 7 TM receptors in bacteria that are distantly related to the eukaryotic 7 TM receptors and prokaryotic rhodopsins. Using sequence profile analysis, we were able to establish that the first members of these receptor families contain one of two distinct N-terminal extracellular globular domains, which are predicted to bind ligands such as carbohydrates. In their intracellular portions they contain fusions to a variety of signaling domains, which suggest that they are likely to transduce signals via cyclic AMP, cyclic diguanylate, histidine phosphorylation, dephosphorylation, and through direct interactions with DNA. The second family of bacterial 7 TM receptors possesses an alpha-helical extracellular domain, and is predicted to transduce a signal via an intracellular HD hydrolase domain. Based on comparative analysis of gene neighborhoods, this receptor is predicted to function as a regulator of the diacylglycerol-kinase-dependent glycerolipid pathway. Additionally, our procedure also recovered other types of putative prokaryotic multi-pass membrane associated receptor domains. Of these, we characterized two widespread, evolutionarily mobile multi-TM domains that are fused to a variety of C-terminal intracellular signaling domains. One of these typified by the Gram-positive LytS protein is predicted to be a potential sensor of murein derivatives, whereas the other one typified by the Escherichia coli UhpB protein is predicted to function as sensor of conformational changes occurring in associated membrane proteins

CONCLUSIONS

We present evidence for considerable variety in the types of uncharacterized surface receptors in bacteria, and reconstruct the evolutionary processes that model their diversity. The identification of novel receptor families in prokaryotes is likely to aid in the experimental analysis of signal transduction and environmental responses of several bacteria, including pathogens such as Leptospira, Treponema, Corynebacterium, Coxiella, Bacillus anthracis and Cytophaga.