Detecting functional interactions in a gene and signaling network by time-resolved somatic complementation analysis

Somatic complementation by fusion of two mutant cells and mixing of their cytoplasms occurs when the genetic defect of one fusion partner is cured by the functional gene product provided by the other. We have found that complementation of mutational defects in the network mediating stimulus-induced commitment and sporulation of Physarum polycephalum may reflect time-dependent changes in the signaling state of its molecular building blocks. Network perturbation by fusion of mutant plasmodial cells in different states of activation, and the time-resolved analysis of somatic complementation effects can be used to systematically probe network structure and dynamics. Time-resolved somatic complementation quantitatively detects regulatory interactions between the functional modules of a network, independent of their biochemical composition or subcellular localization, and without being limited to direct physical interactions.     

Reconstructing the regulatory network controlling commitment and sporulation in Physarum polycephalum based on hierarchical Petri Net modelling and simulation

We reconstruct the regulatory network controlling commitment and sporulation of Physarum polycephalum from experimental results using a hierarchical Petri Net-based modelling and simulation framework. The stochastic Petri Net consistently describes the structure and simulates the dynamics of the molecular network as analysed by genetic, biochemical and physiological experiments within a single coherent model. The Petri Net then is extended to simulate time-resolved somatic complementation experiments performed by mixing the cytoplasms of mutants altered in the sporulation response, to systematically explore the network structure and to probe its dynamics. This reverse engineering approach presumably can be employed to explore other molecular or genetic signalling systems where the activity of genes or their products can be experimentally controlled in a time-resolved manner.     

From intracellular signaling to population oscillations: bridging size- and time-scales in collective behavior

Collective behavior in cellular populations is coordinated by biochemical signaling networks within individual cells. Connecting the dynamics of these intracellular networks to the population phenomena they control poses a considerable challenge because of network complexity and our limited knowledge of kinetic parameters. However, from physical systems, we know that behavioral changes in the individual constituents of a collectively behaving system occur in a limited number of well-defined classes, and these can be described using simple models. Here, we apply such an approach to the emergence of collective oscillations in cellular populations of the social amoeba Dictyostelium discoideum. Through direct tests of our model with quantitative in vivo measurements of single-cell and population signaling dynamics, we show how a simple model can effectively describe a complex molecular signaling network at multiple size and temporal scales. The model predicts novel noise-driven single-cell and population-level signaling phenomena that we then experimentally observe. Our results suggest that like physical systems, collective behavior in biology may be universal and described using simple mathematical models.     

Effect of regulatory mechanism on hyperbolic reaction network properties

The notion that the regulated and flux-controlling enzyme in a metabolic network need not correspond suggests that the purpose of regulation may not be flux homeostasis under all physiological circumstances. Additionally, the fact that diversity in the function of intact metabolic networks exists suggests that in addition to time constant separation, other kinetic structure/regulatory mechanism patterns exist. In order to compliment and expand prior work on identifying kinetic structure-property relationships in networks, the present work explores in a general way how the control, dynamic, and energetic properties of metabolic networks depend on operating point, kinetic structure, and regulatory mechanism. The basic feature of trade-offs between properties is illustrated and used as a basis for indicating how particular subsets of structure, regulatory mechanism, and operating point emphasize certain properties that can be associated with a physiological function. Examples of scavenging trace metabolites and amphibolite coordination are proposed. Microstructure logic in terms of turnover number distributions as well as a potential mixed polynomial network analysis approach are also discussed.     

Towards building the silicon cell: a modular approach

Systems Biology aims to understand quantitatively how properties of biological systems can be understood as functions of the characteristics of, and interactions between their macromolecular components. Whereas, traditional biochemistry focused on isolation and characterization of cellular components, the challenge for Systems Biology lies in integration of this knowledge and the knowledge about molecular interactions. Computer models play an important role in this integration. We here discuss an approach with which we aim to link kinetic models on small parts of metabolism together, so as to form detailed kinetic models of larger chunks of metabolism, and ultimately of the entire living cell. Specifically, we will discuss techniques that can be used to model a sub-network in isolation of a larger network of which it is a part, while still maintaining the dynamics of the larger complete network. We will start by outlining the JWS online system, the silicon cell project, and the type of models we propose. JWS online is a model repository, which can be used for the storage, simulation and analysis of kinetic models. We advocate to integrate a top-down approach, where measurements on the complete system are used to derive fluxes in a detailed structural model, with a bottom-up approach, consisting of the integration of molecular mechanism-based detailed kinetic models into the structural model.     

Regulation of somatic firing dynamics by backpropagating dendritic spikes

Pyramidal cells of the apteronotid ELL have been shown to display a characteristic mechanism of burst discharge, which has been shown to play an important role in sensory coding. This form of bursting depends on a reciprocal dendro-somatic interaction, in which discharge of a somatic spike causes a dendritic spike, which in turn contributes a dendro-somatic current flow to create a depolarizing afterpotential (DAP) in the soma. We review here our recent work showing how the timing of this DAP influences the somatic firing dynamics, and how the degree of inactivation of dendritic Na⁺ currents can cause an increased delay between somatic and dendritic spikes. This ultimately allows the DAP to become more effective at increasing the excitability of the somatic spike generating mechanism. Further, this delay between dendritic and somatic spiking can be regulated by strongly hyperpolarizing GABA_B mediated dendritic inhibition, allowing the burst dynamics to fall under synaptic regulation. In contrast, a weaker, shunting inhibition due to GABA_A mediated dendritic inhibition can regulate the dendritic spike waveform to decrease the dendro-somatic current flow and the resulting DAP. We therefore show that the qualitative behaviour of an individual cell can depend on the degree of synaptic input, and the exact timing of events across the spatial extent of the neuron. Thus, our results serve to illustrate the complex dynamics that can be observed in cells with significant dendritic arborisation, a nearly ubiquitous adaptation amongst principal neurons.     

Body mass dynamics of Daphnia in the context of life history theory: an approach based on contribution analysis

In this paper, we elaborate on the method of contribution analysis in relation to body mass dynamics which has been proposed recently (Polishchuk, Vijverberg, 2005. Oecologia. V. 144. P. 268-277). We suggest that contribution analysis as applied to body mass dynamics makes a bridge between production-energetic approach and life history theory. Production is conventionally divided into somatic and reproductive components, and our approach shows how to estimate the role (i.e. contributions) of these components in body mass dynamics. The pattern of contributions is further interpreted in terms of life history. The approach is applied to study body mass dynamics of the cladoceran Daphnia galeata in response to improving trophic conditions. The performance of the method is found to depend on the resolution of food concentrations, that is, on how many food concentrations are examined and how far they are spaced on the food concentration axis. When resolution is fine, a shift in resource allocation priorities is detected - from somatic component attracting more resources under harsh food conditions to reproduction attracting more resources under favorable conditions. However, when resolution is poor this pattern remains hidden. In that case, we observe roughly equal contributions of somatic and reproductive components to body mass dynamics.     

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.     

Structural Analysis to Determine the Core of Hypoxia Response Network

The advent of sophisticated molecular biology techniques allows to deduce the structure of complex biological networks. However, networks tend to be huge and impose computational challenges on traditional mathematical analysis due to their high dimension and lack of reliable kinetic data. To overcome this problem, complex biological networks are decomposed into modules that are assumed to capture essential aspects of the full network''s dynamics. The question that begs for an answer is how to identify the core that is representative of a network''s dynamics, its function and robustness. One of the powerful methods to probe into the structure of a network is Petri net analysis. Petri nets support network visualization and execution. They are also equipped with sound mathematical and formal reasoning based on which a network can be decomposed into modules. The structural analysis provides insight into the robustness and facilitates the identification of fragile nodes. The application of these techniques to a previously proposed hypoxia control network reveals three functional modules responsible for degrading the hypoxia-inducible factor (HIF). Interestingly, the structural analysis identifies superfluous network parts and suggests that the reversibility of the reactions are not important for the essential functionality. The core network is determined to be the union of the three reduced individual modules. The structural analysis results are confirmed by numerical integration of the differential equations induced by the individual modules as well as their composition. The structural analysis leads also to a coarse network structure highlighting the structural principles inherent in the three functional modules. Importantly, our analysis identifies the fragile node in this robust network without which the switch-like behavior is shown to be completely absent.     

dsg, a gene required for cell-cell interaction early in Myxococcus development.

dsg mutants of Myxococcus xanthus are conditionally defective in fruiting body development, including sporulation. Unable to develop on their own, these mutants can assemble fruiting bodies with spores if they are mixed with wild-type cells. To elucidate the developmental defect in dsg mutants by close comparison with wild type, such mutants have been backcrossed by transduction, using a closely linked insertion of transposon Tn5 for selection. Backcrossed dsg mutants form aggregates that are larger, less compact, and less symmetrical than dsg+ fruiting bodies. Also, the starvation-induced sporulation in dsg aggregates is delayed and reduced. However, dsg mutants can be induced by glycerol or dimethyl sulfoxide to sporulate at levels approaching those of wild type. dsg mutants may thus have a primary defect early in development which diminishes their capacity to aggregate and which indirectly decreases the number of fruiting body spores. The linked insertion of Tn5 also facilitated cloning the dsg gene. The cloned dsg+ allele was shown to be dominant to both the dsg-429 and dsg-439 alleles, and both mutant alleles were shown to belong to the same genetic complementation group. Subcloning of restriction fragments, deletions, and insertions of transposon Tn5 agree in locating the dsg gene to an 850-base-pair segment of the cloned region.     

Network dynamics in nociceptive pathways assessed by the neuronal avalanche model

ABSTRACT: BACKGROUND: Traditional electroencephalography provides a critical assessment of pain responses. The perception of pain, however, may involve a series of signal transmission pathways in higher cortical function. Recent studies have shown that a mathematical method, the neuronal avalanche model, may be applied to evaluate higher-order network dynamics. The neuronal avalanche is a cascade of neuronal activity, the size distribution of which can be approximated by a power law relationship manifested by the slope of a straight line (i.e., the alpha value). We investigated whether the neuronal avalanche could be a useful index for nociceptive assessment. FINDINGS: Neuronal activities were recorded with 4 X 8 multichannel electrode arrays in the primary somatosensory cortex (S1) and anterior cingulate cortex (ACC). Under light anesthesia, peripheral pinch stimulation increased the slope of the alpha value in both the ACC and S1, whereas brush stimulation increased the alpha value only in the S1. The increase in alpha values was blocked in both regions under deep anesthesia. The increase in alpha values in the ACC induced by peripheral pinch stimulation was blocked by medial thalamic lesion, but the increase in alpha values in the S1 induced by brush and pinch stimulation was not affected. CONCLUSIONS: The neuronal avalanche model shows a critical state in the cortical network for noxious-related signal processing. The alpha value may provide an index of brain network activity that distinguishes the responses to somatic stimuli from the control state. These network dynamics may be valuable for the evaluation of acute nociceptive processes and may be applied to chronic pathological pain conditions.     

Qualitative simulation of the initiation of sporulation in <Emphasis Type="Italic">Bacillus subtilis</Emphasis>

Under conditions of nutrient deprivation, the Gram positive soil bacterium Bacillus subtilis can abandon vegetative growth and form a dormant, environmentally-resistant spore instead. The decision to either divide or sporulate is controlled by a large and complex genetic regulatory network integrating various environmental, cell-cycle, and metabolic signals. Although sporulation in B. subtilis is one of the best-understood model systems for prokaryotic development, very little quantitative data on kinetic parameters and molecular concentrations are available. A qualitative simulation method is used to model the sporulation network and simulate the response of the cell to nutrient deprivation. Using this method, we have been able to reproduce essential features of the choice between vegetative growth and sporulation, in particular the role played by competing positive and negative feedback loops.     

Protein dynamics and the diversity of an antibody response

The immune system is remarkable in its ability to produce antibodies (Abs) with virtually any specificity from a limited repertoire of germ line precursors. Although the contribution of sequence diversity to this molecular recognition has been studied for decades, recent models suggest that protein dynamics may also broaden the range of targets recognized. To characterize the contribution of protein dynamics to immunological molecular recognition, we report the sequence, thermodynamic, and time-resolved spectroscopic characterization of a panel of eight Abs elicited to the chromophoric antigen 8-methoxypyrene-1,3,6-trisulfonate (MPTS). Based on the sequence data, three of the Abs arose from unique germ line Abs, whereas the remaining five comprise two sets of siblings that arose by somatic mutation of a common precursor. The thermodynamic data indicate that the Abs recognize MPTS via a variety of mechanisms. Although the spectroscopic data reveal small differences in protein dynamics, the anti-MPTS Abs generally show similar levels of flexibility and conformational heterogeneity, possibly representing the convergent evolution of the dynamics necessary for function. However, one Ab is significantly more rigid and conformationally homogeneous than the others, including a sibling Ab from which it differs by only five somatic mutations. This example of divergent evolution demonstrates that point mutations are capable of fixing significant differences in protein dynamics. The results provide unique insight into how high affinity Abs may be produced that bind virtually any target and possibly, from a more general perspective, how new protein functions are evolved.     

Failure of Delayed Feedback Deep Brain Stimulation for Intermittent Pathological Synchronization in Parkinson’s Disease

Suppression of excessively synchronous beta-band oscillatory activity in the brain is believed to suppress hypokinetic motor symptoms of Parkinson’s disease. Recently, a lot of interest has been devoted to desynchronizing delayed feedback deep brain stimulation (DBS). This type of synchrony control was shown to destabilize the synchronized state in networks of simple model oscillators as well as in networks of coupled model neurons. However, the dynamics of the neural activity in Parkinson’s disease exhibits complex intermittent synchronous patterns, far from the idealized synchronous dynamics used to study the delayed feedback stimulation. This study explores the action of delayed feedback stimulation on partially synchronized oscillatory dynamics, similar to what one observes experimentally in parkinsonian patients. We employ a computational model of the basal ganglia networks which reproduces experimentally observed fine temporal structure of the synchronous dynamics. When the parameters of our model are such that the synchrony is unphysiologically strong, the feedback exerts a desynchronizing action. However, when the network is tuned to reproduce the highly variable temporal patterns observed experimentally, the same kind of delayed feedback may actually increase the synchrony. As network parameters are changed from the range which produces complete synchrony to those favoring less synchronous dynamics, desynchronizing delayed feedback may gradually turn into synchronizing stimulation. This suggests that delayed feedback DBS in Parkinson’s disease may boost rather than suppress synchronization and is unlikely to be clinically successful. The study also indicates that delayed feedback stimulation may not necessarily exhibit a desynchronization effect when acting on a physiologically realistic partially synchronous dynamics, and provides an example of how to estimate the stimulation effect.     

Modeling DNA sequence-based cis-regulatory gene networks

Gene network analysis requires computationally based models which represent the functional architecture of regulatory interactions, and which provide directly testable predictions. The type of model that is useful is constrained by the particular features of developmentally active cis-regulatory systems. These systems function by processing diverse regulatory inputs, generating novel regulatory outputs. A computational model which explicitly accommodates this basic concept was developed earlier for the cis-regulatory system of the endo16 gene of the sea urchin. This model represents the genetically mandated logic functions that the system executes, but also shows how time-varying kinetic inputs are processed in different circumstances into particular kinetic outputs. The same basic design features can be utilized to construct models that connect the large number of cis-regulatory elements constituting developmental gene networks. The ultimate aim of the network models discussed here is to represent the regulatory relationships among the genomic control systems of the genes in the network, and to state their functional meaning. The target site sequences of the cis-regulatory elements of these genes constitute the physical basis of the network architecture. Useful models for developmental regulatory networks must represent the genetic logic by which the system operates, but must also be capable of explaining the real time dynamics of cis-regulatory response as kinetic input and output data become available. Most importantly, however, such models must display in a direct and transparent manner fundamental network design features such as intra- and intercellular feedback circuitry; the sources of parallel inputs into each cis-regulatory element; gene battery organization; and use of repressive spatial inputs in specification and boundary formation. Successful network models lead to direct tests of key architectural features by targeted cis-regulatory analysis.     

Kinetic modeling of sporulation and product formation in stationary phase by Bacillus coagulans RK-02 vis-à-vis other Bacilli

A logistic kinetic model was derived and validated to characterize the dynamics of a sporogenous bacterium in stationary phase with respect to sporulation and product formation. The kinetic constants as determined using this model are particularly important for describing intrinsic properties of a sporogenous bacterial culture in stationary phase. Non-linear curve fitting of the experimental data into the mathematical model showed very good correlation with the predicted values for sporulation and lipase production by Bacillus coagulans RK-02 culture in minimal media. Model fitting of literature data of sporulation and product (protease and amylase) formation in the stationary phase by some other Bacilli and comparison of the results of model fitting with those of Bacillus coagulans helped validate the significance and robustness of the developed kinetic model.