Genetic "code": representations and dynamical models of genetic components and networks

Network analysis of the autophagy biochemical network in relation to various autophagy-targeted proteins found among SARS-CoV-2 variants of concern

Autophagy is an important cellular process that triggers a coordinated action involving multiple individual proteins and protein complexes while SARS-CoV-2 (SARS2) was found to both hinder autophagy to evade host defense and utilize autophagy for viral replication. Interestingly, the possible significant stages of the autophagy biochemical network in relation to the corresponding autophagy-targeted SARS2 proteins from the different variants of concern (VOC) were never established. In this study, we performed the following: autophagy biochemical network design and centrality analyses; generated autophagy-targeted SARS2 protein models; and superimposed protein models for structural comparison. We identified 2 significant biochemical pathways (one starts from the ULK complex and the other starts from the PI3P complex) within the autophagy biochemical network. Similarly, we determined that the autophagy-targeted SARS2 proteins (Nsp15, M, ORF7a, ORF3a, and E) are structurally conserved throughout the different SARS2 VOC suggesting that the function of each protein is preserved during SARS2 evolution. Interestingly, among the autophagy-targeted SARS2 proteins, the M protein coincides with the 2 significant biochemical pathways we identified within the autophagy biochemical network. In this regard, we propose that the SARS2 M protein is the main determinant that would influence autophagy outcome in regard to SARS2 infection.

Structural patterns of SARS-CoV-2 variants of concern (alpha, beta, gamma, delta) spike protein are influenced by variant-specific amino acid mutations: A computational study with implications on viral evolution

SARS-CoV-2 (SARS2) regularly mutates resulting to variants of concern (VOC) which have higher virulence and transmissibility rates while concurrently evading available therapeutic strategies. This highlights the importance of amino acid mutations occurring in the SARS2 spike protein structure since it may affect virus biology. However, this was never fully elucidated. Here, network analysis was performed based on the COVID-19 genomic epidemiology network between December 2019-July 2021. Representative SARS2 VOC spike protein models were generated and quality checked, protein model superimposition was done, and common contact based on contact mapping was established. Throughout this study, we found that: (1) certain individual variant-specific amino acid mutations can affect the spike protein structural pattern; (2) certain individual variant-specific amino acid mutations had no affect on the spike protein structural pattern; and (3) certain combination of variant-specific amino acids are putatively epistatic mutations that can potentially influence the VOC spike protein structural pattern. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Thermodynamic Modelling of Transcriptional Control: A Sensitivity Analysis

Modelling is a tool used to decipher the biochemical mechanisms involved in transcriptional control. Experimental evidence in genetics is usually supported by theoretical models in order to evaluate the effects of all the possible interactions that can occur in these complicated processes. Models derived from the thermodynamic method are critical in this labour because they are able to take into account multiple mechanisms operating simultaneously at the molecular micro-scale and relate them to transcriptional initiation at the tissular macro-scale. This work is devoted to adapting computational techniques to this context in order to theoretically evaluate the role played by several biochemical mechanisms. The interest of this theoretical analysis relies on the fact that it can be contrasted against those biological experiments where the response to perturbations in the transcriptional machinery environment is evaluated in terms of genetically activated/repressed regions. The theoretical reproduction of these experiments leads to a sensitivity analysis whose results are expressed in terms of the elasticity of a threshold function determining those activated/repressed regions. The study of this elasticity function in thermodynamic models already proposed in the literature reveals that certain modelling approaches can alter the balance between the biochemical mechanisms considered, and this can cause false/misleading outcomes. The reevaluation of classical thermodynamic models gives us a more accurate and complete picture of the interactions involved in gene regulation and transcriptional control, which enables more specific predictions. This sensitivity approach provides a definite advantage in the interpretation of a wide range of genetic experimental results.

Insights on the Structural Variations of the Furin-Like Cleavage Site Found Among the December 2019-July 2020 SARS-CoV-2 Spike Glycoprotein: A Computational Study Linking Viral Evolution and Infection

The SARS-CoV-2 (SARS2) is the cause of the coronavirus disease 2019 (COVID-19) pandemic. One unique structural feature of the SARS2 spike protein is the presence of a furin-like cleavage site (FLC) which is associated with both viral pathogenesis and host tropism. Specifically, SARS2 spike protein binds to the host ACE-2 receptor which in-turn is cleaved by furin proteases at the FLC site, suggesting that SARS2 FLC structural variations may have an impact on viral infectivity. However, this has not yet been fully elucidated. This study designed and analyzed a COVID-19 genomic epidemiology network for December 2019 to July 2020, and subsequently generated and analyzed representative SARS2 spike protein models from significant node clusters within the network. To distinguish possible structural variations, a model quality assessment was performed before further protein model analyses and superimposition of the protein models, particularly in both the receptor-binding domain (RBD) and FLC. Mutant spike models were generated with the unique ⁶⁸¹PRRA⁶⁸⁴ amino acid sequence found within the deleted FLC. We found 9 SARS2 FLC structural patterns that could potentially correspond to nine node clusters encompassing various countries found within the COVID-19 genomic epidemiology network. Similarly, we associated this with the rapid evolution of the SARS2 genome. Furthermore, we observed that either in the presence or absence of the unique ⁶⁸¹PRRA⁶⁸⁴ amino acid sequence no structural changes occurred within the SARS2 RBD, which we believe would mean that the SARS2 FLC has no structural influence on SARS2 RBD and may explain why host tropism was maintained.

Heat-Killed Fusobacterium nucleatum Triggers Varying Heme-Related Inflammatory and Stress Responses Depending on Primary Human Respiratory Epithelial Cell Type

Fusobacterium nucleatum (Fn) is generally an opportunistic oral pathogen that adheres to mammalian mucosal sites, triggering a host inflammatory response. In general, Fn is normally found within the human oral cavity; however, it was previously reported that Fn is a risk factor for certain respiratory diseases. Surprisingly, this was never fully elucidated. Here, we investigated the virulence potential of heat-killed Fn on primary human tracheal, bronchial, and alveolar epithelial cells. In this study, we measured the secretion of inflammatory- (IL-8 and IL-6), stress- (total heme and hydrogen peroxide), and cell death-related (caspase-1 and caspase-3) signals. We established that the inflammatory response mechanism varies in each epithelial cell type: (1) along tracheal cells, possible Fn adherence would trigger increased heme secretion and regulated inflammatory response; (2) along bronchial cells, potential Fn adherence would simultaneously initiate an increase in secreted H₂O₂ and inflammatory response (ascribable to decreased secreted heme amounts); and (3) along alveolar cells, putative Fn adherence would instigate the increased secretion of inflammatory responses attributable to a decrease in secreted heme levels. Moreover, regardless of the epithelial cell-specific inflammatory mechanism, we believe these are putative, not harmful. Taken together, we propose that any potential Fn-driven inflammation along the respiratory tract would be initiated by differing epithelial cell-specific inflammatory mechanisms that are collectively dependent on secreted heme.

Structural insights into the potential changes in receptor binding site found in the 1998-2018 influenza B/Yamagata hemagglutinin: A putative correlation between receptor binding site structural variability and seasonal infection

Influenza B virus has two distinct lineages (Victoria and Yamagata) and are associated with seasonal influenza epidemics that cause respiratory illness. Influenza B hemagglutinin (HA) is a major surface glycoprotein with the receptor-binding site (RBS) primarily involved in viral pathogenesis. Generally, influenza B exclusively infects the human population which would insinuate that the structural variability of the influenza B HA RBS rarely changes. However, to our knowledge, the potential impact of variations in the influenza B HA RBS structural variability was not fully elucidated. Throughout this study, we generated models from the transitioning (evolving viral lineage) 1998-2018 influenza B/Yamagata HA, verified the quality of each HA model, performed HA RBS structural variability measurements, superimposed varying HA models for comparison, and designed a phylogenetic tree network for further analyses. We found that measurements of the transitioning HA RBS structural variability were generally maintained and, similarly, measurements of the altered (years that differed from the evolving viral lineage, specifically 2003, 2007, 2017) HA RBS structural variability differed from the transitioning HA RBS. Moreover, we observed that the altered HA RBS structural variability favored the formation of a putative Y202-H191 hydrogen bond which we postulate may increase structural stability, thereby, allowing for a winter infection of the virus. Furthermore, we established that changes in HA RBS structural variability does not influence viral evolution, but putatively seasonal infection.

Algorithmic and Stochastic Representations of Gene Regulatory Networks and Protein-Protein Interactions

BACKGROUND

Latest studies reveal the importance of Protein-Protein interactions on physiologic functions and biological structures. Several stochastic and algorithmic methods have been published until now, for the modeling of the complex nature of the biological systems.

OBJECTIVE

Biological Networks computational modeling is still a challenging task. The formulation of the complex cellular interactions is a research field of great interest. In this review paper, several computational methods for the modeling of GRN and PPI are presented analytically.

METHODS

Several well-known GRN and PPI models are presented and discussed in this review study such as: Graphs representation, Boolean Networks, Generalized Logical Networks, Bayesian Networks, Relevance Networks, Graphical Gaussian models, Weight Matrices, Reverse Engineering Approach, Evolutionary Algorithms, Forward Modeling Approach, Deterministic models, Static models, Hybrid models, Stochastic models, Petri Nets, BioAmbients calculus and Differential Equations.

RESULTS

GRN and PPI methods have been already applied in various clinical processes with potential positive results, establishing promising diagnostic tools.

CONCLUSION

In literature many stochastic algorithms are focused in the simulation, analysis and visualization of the various biological networks and their dynamics interactions, which are referred and described in depth in this review paper.

Structural significance of residues 158-160 in the H3N2 hemagglutnin globular head: A computational study with implications in viral evolution and infection

Influenza A H3N2 has been linked to annual outbreaks within the human population attributable to continuous structural changes. H3N2 HA contains well identified antigenic sites and receptor-binding sites (RBS) that are possibly correlated to viral evolution and infection. However, the structural significance of amino acid residues associated with both viral evolution and infection were not fully demonstrated. Throughout this study, we generated and analyzed H3N2 HA models that represented the clade 3C.2 population (comprised of clades 3C.2, 3C.2a, and 3C.21 from the transitioning 2014-2018 H3N2 strains) and 3C.3a (from the 2016 H3N2 strain). Model quality estimation, structural analyses and superimposition, and network analytics of H3N2 HA1 evolution were performed. We found that the structural properties of residues 158-160 could influence the overall HA backbone. More specifically, amino acid substitutions at residues 159-160 affected the amino acid orientation at residue 158, thereby, causing the overall HA backbone structure to vary. Our results were consistent with 1968-2018 HA1 evolution. Taken together, we propose that our results would highlight the structural significance of residues 158-160 in HA1 for both antigenic drift and RBS.

Analysis of the transcriptional logic governing differential spatial expression in Hh target genes

This work provides theoretical tools to analyse the transcriptional effects of certain biochemical mechanisms (i.e. affinity and cooperativity) that have been proposed in previous literature to explain the proper spatial expression of Hedgehog target genes involved in Drosophila development. Specifically we have focused on the expression of decapentaplegic, wingless, stripe and patched. The transcription of these genes is believed to be controlled by enhancer modules able to interpret opposing gradients of the activator and repressor forms of the transcription factor Cubitus interruptus (Ci). This study is based on a thermodynamic approach, which provides expression rates for these genes. These expression rates are controlled by transcription factors which are competing and cooperating for common binding sites. We have made mathematical representations of the different expression rates which depend on multiple factors and variables. The expressions obtained with the model have been refined to produce simpler equivalent formulae which allow for their mathematical analysis. Thanks to this, we can evaluate the correlation between the different interactions involved in transcription and the biological features observed at tissular level. These mathematical models can be applied to other morphogenes to help understand the complex transcriptional logic of opposing activator and repressor gradients.

Gingival Periodontal Disease (PD) Level-Butyric Acid Affects the Systemic Blood and Brain Organ: Insights Into the Systemic Inflammation of Periodontal Disease

Butyric acid (BA) is produced by periodontopathic bacterial pathogens and contributes to periodontal disease (PD) induction. Moreover, PD has been associated with detrimental effects which subsequently may lead to systemic disease (SD) development affecting certain organs. Surprisingly, the potential systemic manifestations and organ-localized effects of BA have never been elucidated. Here, we simulated BA-based oral infection among young (20-week-old) rats and isolated blood cytosol to determine BA effects on stress network-related signals [total heme, hydrogen peroxide (H₂O₂), catalase (CAT), glutathione reductase (GR), free fatty acid (FFA), NADP/NADPH], inflammation-associated signals [caspases (CASP12 and CASP1), IL-1β, TNF-α, metallomatrix proteinase-9 (MMP-9), and toll-like receptor-2 (TLR2)], and neurological blood biomarkers [presenilin (PS1 and PS2) and amyloid precursor protein (APP)]. Similarly, we extracted the brain from both control and BA-treated rats, isolated the major regions (hippocampus, pineal gland, hypothalamus, cerebrum, and cerebellum), and, subsequently, measured stress network-related signals [oxidative stress: total heme, NADPH, H₂O₂, GR, and FFA; ER stress: GADD153, calcium, CASP1, and CASP3] and a brain neurodegenerative biomarker (Tau). In the blood, we found that BA was no longer detectable. Nevertheless, oxidative stress and inflammation were induced. Interestingly, amounts of representative inflammatory signals (CASP12, CASP1, IL-1β, and TNF-α) decreased while MMP-9 levels increased which we believe would suggest that inflammation was MMP-9-modulated and would serve as an alternative inflammatory mechanism. Similarly, TLR2 activity was increased which would insinuate that neurological blood biomarkers (APP, PS1, and PS2) were likewise affected. In the brain, BA was not detected, however, we found that both oxidative and ER stresses were likewise altered in all brain regions. Interestingly, tau protein amounts were significantly affected in the cerebellar and hippocampal regions which coincidentally are the major brain regions affected in several neurological disorders. Taken together, we propose that gingival BA can potentially cause systemic inflammation ascribable to prolonged systemic manifestations in the blood and localized detrimental effects within the brain organ.

Network analytics approach towards identifying potential antivirulence drug targets within the Staphylococcus aureus staphyloxanthin biosynthetic network

Staphylococcus aureus is associated with several clinically significant infections among humans and infections associated with antibiotic-resistant strains are growing in frequency. Antivirulence strategies shift the target of drugs from bacterial growth to the infection process resulting to milder evolutionary pressure for the development of bacterial resistant strains. Staphyloxanthin (STX) is a yellowish-orange carotenoid pigment synthesized by S. aureus and this carotenoid functions as an important virulence factor for the bacteria. In this study, we elucidated whether network analytics can be used as a viable tool to identify significant components in the STX biosynthetic network which in-turn could serve as possible antivirulence drug targets. For confirmation, we correlated our results to known drugs that were able to inhibit STX biosynthesis. Throughout this study, we established that crtN(1) activity and 4,4'-diaponeurosporene amounts are significant components in the STX biosynthetic network and, moreover, network analytics can aid in identifying antivirulence drug targets within the STX biosynthetic network. Similarly, we found that network analytics is capable of identifying multiple potential targets simultaneously. Taken together, we propose that an effective antivirulence drug against S. aureus STX biosynthesis would involve targeting crtN(1) activity, 4,4'-diaponeurosporene levels, or both components.

Various cellular stress components change as the rat ages: An insight into the putative overall age-related cellular stress network

Cellular stress is mainly comprised of oxidative, nitrosative, and endoplasmic reticulum stresses and has long been correlated to the ageing process. Surprisingly, the age-related difference among the various components in each independent stress pathway and the possible significance of these components in relation to the overall cellular stress network remain to be clearly elucidated. In this study, we obtained blood from ageing rats upon reaching 20-, 40-, and 72-wk.-old. Subsequently, we measured representative cellular stress-linked biomolecules (H₂O₂, glutathione reductase, heme, NADPH, NADP, nitric oxide, GADD153) and cell signals [substance P (SP), free fatty acid, calcium, NF-κB] in either or both blood serum and cytosol. Subsequently, network analysis of the overall cellular stress network was performed. Our results show that there are changes affecting stress-linked biomolecules and cell signals as the rat ages. Additionally, based on our network analysis data, we postulate that NADPH, H₂O₂, GADD153, and SP are the key components and the interactions between these components are central to the overall age-related cellular stress network in the rat blood. Thus, we propose that the main pathway affecting the overall age-related cellular stress network in the rat blood would entail NADPH-related oxidative stress (involving H₂O₂) triggering GADD153 activation leading to SP induction which in-turn affects other cell signals.

Stochastic modeling of biochemical systems with multistep reactions using state-dependent time delay

To deal with the growing scale of molecular systems, sophisticated modelling techniques have been designed in recent years to reduce the complexity of mathematical models. Among them, a widely used approach is delayed reaction for simplifying multistep reactions. However, recent research results suggest that a delayed reaction with constant time delay is unable to describe multistep reactions accurately. To address this issue, we propose a novel approach using state-dependent time delay to approximate multistep reactions. We first use stochastic simulations to calculate time delay arising from multistep reactions exactly. Then we design algorithms to calculate time delay based on system dynamics precisely. To demonstrate the power of proposed method, two processes of mRNA degradation are used to investigate the function of time delay in determining system dynamics. In addition, a multistep pathway of metabolic synthesis is used to explore the potential of the proposed method to simplify multistep reactions with nonlinear reaction rates. Simulation results suggest that the state-dependent time delay is a promising and accurate approach to reduce model complexity and decrease the number of unknown parameters in the models.

A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks

Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily large networks by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving the system; (iv) one may obtain the classical rate equations form the corresponding stochastic version by averaging the dynamic random variables (small noise limit). It is important to emphasize that unlike the deterministic case, where coupling two equations is a trivial matter, coupling two RDS is non-trivial, specially in our case, where the coupling is performed between a state variable of one gene and the switching stochastic process of another gene and, hence, it is not a priori true that the resulting coupled system will satisfy the definition of a random dynamical system. We shall provide the necessary arguments that ensure that our coupling prescription does indeed furnish a coupled regulatory network of random dynamical systems. Finally, the fact that classical rate equations are the small noise limit of our stochastic model ensures that any validation or prediction made on the basis of the classical theory is also a validation or prediction of our model. We illustrate our framework with some simple examples of single-gene system and network motifs.

Stochastic simulation of notch signaling reveals novel factors that mediate the differentiation of neural stem cells

Notch signaling controls cell fate decisions and regulates multiple biological processes, such as cell proliferation, differentiation, and apoptosis. Computational modeling of the deterministic simulation of Notch signaling has provided important insight into the possible molecular mechanisms that underlie the switch from the undifferentiated stem cell to the differentiated cell. Here, we constructed a stochastic model of a Notch signaling model containing Hes1, Notch1, RBP-Jk, Mash1, Hes6, and Delta. mRNA and protein were represented as a discrete state, and 334 reactions were employed for each biochemical reaction using a graphics processing unit-accelerated Gillespie scheme. We employed the tuning of 40 molecular mechanisms and revealed several potential mediators capable of enabling the switch from cell stemness to differentiation. These effective mediators encompass different aspects of cellular regulations, including the nuclear transport of Hes1, the degradation of mRNA (Hes1 and Notch1) and protein (Notch1), the association between RBP-Jk and Notch intracellular domain (NICD), and the cleavage efficiency of the NICD. These mechanisms overlap with many modifiers that have only recently been discovered to modulate the Notch signaling output, including microRNA action, ubiquitin-mediated proteolysis, and the competitive binding of the RBP-Jk-DNA complex. Moreover, we identified the degradation of Hes1 mRNA and nuclear transport of Hes1 as the dominant mechanisms that were capable of abolishing the cell state transition induced by other molecular mechanisms.

One Hand Clapping: detection of condition-specific transcription factor interactions from genome-wide gene activity data

We present One Hand Clapping (OHC), a method for the detection of condition-specific interactions between transcription factors (TFs) from genome-wide gene activity measurements. OHC is based on a mapping between transcription factors and their target genes. Given a single case–control experiment, it uses a linear regression model to assess whether the common targets of two arbitrary TFs behave differently than expected from the genes targeted by only one of the TFs. When applied to osmotic stress data in S. cerevisiae, OHC produces consistent results across three types of expression measurements: gene expression microarray data, RNA Polymerase II ChIP-chip binding data and messenger RNA synthesis rates. Among the eight novel, condition-specific TF pairs, we validate the interaction between Gcn4p and Arr1p experimentally. We apply OHC to a large gene activity dataset in S. cerevisiae and provide a compendium of condition-specific TF interactions.

Design principles of the bacterial quorum sensing gene networks

Bacterial quorum sensing (QS) has attracted much interest as the manifestation of collective behavior in prokaryotic organisms once considered strictly solitary. Significant amount of genetic, biochemical, and structural data which, has been accumulated in studies on QS in many species allows us to map properties of specific molecules and their interactions on the observed population-wide bacterial behavior. The present review attempts to give a systems biology perspective on the structure of genetic regulatory networks that control QS and considers functional implications of a variety of design principles that recur in the organization of these networks across species.

Computational models of the Notch network elucidate mechanisms of context-dependent signaling

The Notch signaling pathway controls numerous cell fate decisions during development and adulthood through diverse mechanisms. Thus, whereas it functions as an oscillator during somitogenesis, it can mediate an all-or-none cell fate switch to influence pattern formation in various tissues during development. Furthermore, while in some contexts continuous Notch signaling is required, in others a transient Notch signal is sufficient to influence cell fate decisions. However, the signaling mechanisms that underlie these diverse behaviors in different cellular contexts have not been understood. Notch1 along with two downstream transcription factors hes1 and RBP-Jk forms an intricate network of positive and negative feedback loops, and we have implemented a systems biology approach to computationally study this gene regulation network. Our results indicate that the system exhibits bistability and is capable of switching states at a critical level of Notch signaling initiated by its ligand Delta in a particular range of parameter values. In this mode, transient activation of Delta is also capable of inducing prolonged high expression of Hes1, mimicking the “ON” state depending on the intensity and duration of the signal. Furthermore, this system is highly sensitive to certain model parameters and can transition from functioning as a bistable switch to an oscillator by tuning a single parameter value. This parameter, the transcriptional repression constant of hes1, can thus qualitatively govern the behavior of the signaling network. In addition, we find that the system is able to dampen and reduce the effects of biological noise that arise from stochastic effects in gene expression for systems that respond quickly to Notch signaling.

This work thus helps our understanding of an important cell fate control system and begins to elucidate how this context dependent signaling system can be modulated in different cellular settings to exhibit entirely different behaviors.

The Notch signaling pathway is an evolutionarily conserved signaling system that is involved in various cell fate decisions, both during development of an organism and during adulthood. While the same core circuit functions in various different cellular contexts, it has experimentally been shown to elicit varied behaviors and responses. On the one hand, it functions as a cellular oscillator critical for somitogenesis, whereas in other situations, it can function as a cell fate switch to pattern developing tissue, for example in the Drosophila eye. Furthermore, malfunctioning of Notch signaling is implicated in various cancers. To better understand the underlying mechanisms that allow the network to function distinctly in different contexts, we have mathematically modeled the behavior of the Notch network, encompassing the Notch gene along with two of its downstream effector transcription factors, which together form a network of positive and negative feedback loops. Our results indicate that the qualitative and quantitative behavior of the system can readily be tuned based on key parameters to reflect its multiple roles. Furthermore, our results provide insights into alterations in the signaling system that lead to malfunction and hence disease, which could be used to identify potential drug targets for therapy.

Genetic noise control via protein oligomerization

BACKGROUND

Gene expression in a cell entails random reaction events occurring over disparate time scales. Thus, molecular noise that often results in phenotypic and population-dynamic consequences sets a fundamental limit to biochemical signaling. While there have been numerous studies correlating the architecture of cellular reaction networks with noise tolerance, only a limited effort has been made to understand the dynamic role of protein-protein interactions.

RESULTS

We have developed a fully stochastic model for the positive feedback control of a single gene, as well as a pair of genes (toggle switch), integrating quantitative results from previous in vivo and in vitro studies. In particular, we explicitly account for the fast binding-unbinding kinetics among proteins, RNA polymerases, and the promoter/operator sequences of DNA. We find that the overall noise-level is reduced and the frequency content of the noise is dramatically shifted to the physiologically irrelevant high-frequency regime in the presence of protein dimerization. This is independent of the choice of monomer or dimer as transcription factor and persists throughout the multiple model topologies considered. For the toggle switch, we additionally find that the presence of a protein dimer, either homodimer or heterodimer, may significantly reduce its random switching rate. Hence, the dimer promotes the robust function of bistable switches by preventing the uninduced (induced) state from randomly being induced (uninduced).

CONCLUSION

The specific binding between regulatory proteins provides a buffer that may prevent the propagation of fluctuations in genetic activity. The capacity of the buffer is a non-monotonic function of association-dissociation rates. Since the protein oligomerization per se does not require extra protein components to be expressed, it provides a basis for the rapid control of intrinsic or extrinsic noise. The stabilization of regulatory circuits and epigenetic memory in general is of direct implications to organism fitness. Our results also suggest possible avenues for the design of synthetic gene circuits with tunable robustness for a wide range of engineering purposes.

OptCircuit: an optimization based method for computational design of genetic circuits

Background

Recent years has witnessed an increasing number of studies on constructing simple synthetic genetic circuits that exhibit desired properties such as oscillatory behavior, inducer specific activation/repression, etc. It has been widely acknowledged that that task of building circuits to meet multiple inducer-specific requirements is a challenging one. This is because of the incomplete description of component interactions compounded by the fact that the number of ways in which one can chose and interconnect components, increases exponentially with the number of components.

Results

In this paper we introduce OptCircuit, an optimization based framework that automatically identifies the circuit components from a list and connectivity that brings about the desired functionality. Multiple literature sources are used to compile a comprehensive compilation of kinetic descriptions of promoter-protein pairs. The dynamics that govern the interactions between the elements of the genetic circuit are currently modeled using deterministic ordinary differential equations but the framework is general enough to accommodate stochastic simulations. The desired circuit response is abstracted as the maximization/minimization of an appropriately constructed objective function. Computational results for a toggle switch example demonstrate the ability of the framework to generate the complete list of circuit designs of varying complexity that exhibit the desired response. Designs identified for a genetic decoder highlight the ability of OptCircuit to suggest circuit configurations that go beyond the ones compatible with digital logic-based design principles. Finally, the results obtained from the concentration band detector example demonstrate the ability of OptCircuit to design circuits whose responses are contingent on the level of external inducer as well as pinpoint parameters for modification to rectify an existing (non-functional) biological circuit and restore functionality.

Conclusion

Our results demonstrate that OptCircuit framework can serve as a design platform to aid in the construction and finetuning of integrated biological circuits.

Executable cell biology

Computational modeling of biological systems is becoming increasingly important in efforts to better understand complex biological behaviors. In this review, we distinguish between two types of biological models--mathematical and computational--which differ in their representations of biological phenomena. We call the approach of constructing computational models of biological systems 'executable biology', as it focuses on the design of executable computer algorithms that mimic biological phenomena. We survey the main modeling efforts in this direction, emphasize the applicability and benefits of executable models in biological research and highlight some of the challenges that executable biology poses for biology and computer science. We claim that for executable biology to reach its full potential as a mainstream biological technique, formal and algorithmic approaches must be integrated into biological research. This will drive biology toward a more precise engineering discipline.

Methods for simulating the dynamics of complex biological processes

In this chapter, we provide the basic information required to understand the central concepts in the modeling and simulation of complex biochemical processes. We underline the fact that most biochemical processes involve sequences of interactions between distinct entities (molecules, molecular assemblies), and also stress that models must adhere to the laws of thermodynamics. Therefore, we discuss the principles of mass-action reaction kinetics, the dynamics of equilibrium and steady state, and enzyme kinetics, and explain how to assess transition probabilities and reactant lifetime distributions for first-order reactions. Stochastic simulation of reaction systems in well-stirred containers is introduced using a relatively simple, phenomenological model of microtubule dynamic instability in vitro. We demonstrate that deterministic simulation [by numerical integration of coupled ordinary differential equations (ODE)] produces trajectories that would be observed if the results of many rounds of stochastic simulation of the same system were averaged. In Section V, we highlight several practical issues with regard to the assessment of parameter values. We draw some attention to the development of a standard format for model storage and exchange, and provide a list of selected software tools that may facilitate the model building process, and can be used to simulate the modeled systems.

Biology by design: reduction and synthesis of cellular components and behaviour

Biological research is experiencing an increasing focus on the application of knowledge rather than on its generation. Thanks to the increased understanding of cellular systems and technological advances, biologists are more frequently asking not only 'how can I understand the structure and behaviour of this biological system?', but also 'how can I apply that knowledge to generate novel functions in different biological systems or in other contexts?' Active pursuit of the latter has nurtured the emergence of synthetic biology. Here, we discuss the motivation behind, and foundational technologies enabling, the development of this nascent field. We examine some early successes and applications while highlighting the challenges involved. Finally, we consider future directions and mention non-scientific considerations that can influence the field's growth.

The response of the metabolic network of the red blood cell to pyruvate kinase deficiency

The response of the metabolic network of human red blood cell is investigated using the E-Cell simulation system when pyruvate kinase (PK) is deficient. The results that several downstream metabolites of the glycolysis pathway accumulate are in a good agreement with experimental data reported in literatures. This accumulation results in the reaction that phosphoglycerate kinase (PGK) catalyzes reversing its direction. Mathematical analysis to the simulation results shows that the PGK-catalyzing reaction reversing its direction happens simultaneously with an abrupt change of the second derivative of the ATP quantity.

Transcription factor profiling in individual hematopoietic progenitors by digital RT-PCR

We report here a systematic, quantitative population analysis of transcription factor expression within developmental progenitors, made possible by a microfluidic chip-based "digital RT-PCR" assay that can count template molecules in cDNA samples prepared from single cells. In a survey encompassing five classes of early hematopoietic precursor, we found markedly heterogeneous expression of the transcription factor PU.1 in hematopoietic stem cells and divergent patterns of PU.1 expression within flk2- and flk2+ common myeloid progenitors. The survey also revealed significant differences in the level of the housekeeping transcript GAPDH across the surveyed populations, which demonstrates caveats of normalizing expression data to endogenous controls and underscores the need to put gene measurement on an absolute, copy-per-cell basis.

Systems interface biology

The field of systems biology has attracted the attention of biologists, engineers, mathematicians, physicists, chemists and others in an endeavour to create systems-level understanding of complex biological networks. In particular, systems engineering methods are finding unique opportunities in characterizing the rich behaviour exhibited by biological systems. In the same manner, these new classes of biological problems are motivating novel developments in theoretical systems approaches. Hence, the interface between systems and biology is of mutual benefit to both disciplines.

A fluctuation method to quantify in vivo fluorescence data

Quantitative in vivo measurements are essential for developing a predictive understanding of cellular behavior. Here we present a technique that converts observed fluorescence intensities into numbers of molecules. By transiently expressing a fluorescently tagged protein and then following its dilution during growth and division, we observe asymmetric partitioning of fluorescence between daughter cells at each division. Such partition asymmetries are set by the actual numbers of proteins present, and thus provide a means to quantify fluorescence levels. We present a Bayesian algorithm that infers from such data both the fluorescence conversion factor and an estimate of the measurement error. Our algorithm works for arbitrarily sized data sets and handles consistently any missing measurements. We verify the algorithm with extensive simulation and demonstrate its application to experimental data from Escherichia coli. Our technique should provide a quantitative internal calibration to systems biology studies of both synthetic and endogenous cellular networks.

Stochastic regulation in early immune response

Living cells may be considered noisy or stochastic biochemical reactors. In eukaryotic cells, in which the number of protein or mRNA molecules is relatively large, the stochastic effects originate primarily in regulation of gene activity. Transcriptional activity of a gene can be initiated by transactivator molecules binding to the specific regulatory site(s) in the target gene. The stochasticity of activator binding and dissociation is amplified by transcription and translation, since target gene activation results in a burst of mRNAs molecules, and each copy of mRNA then serves as a template for numerous protein molecules. In this article, we reformulate our model of the NF-kappaB regulatory module to analyze a single cell regulation. Ordinary differential equations, used for description of fast reaction channels of processes involving a large number of molecules, are combined with a stochastic switch to account for the activity of the genes involved. The stochasticity in gene transcription causes simulated cells to exhibit large variability. Moreover, none of them behaves like an average cell. Although the average mRNA and protein levels remain constant before tumor necrosis factor (TNF) stimulation, and stabilize after a prolonged TNF stimulation, in any single cell these levels oscillate stochastically in the absence of TNF and keep oscillating under the prolonged TNF stimulation. However, in a short period of approximately 90 min, most cells are synchronized by the TNF signal, and exhibit similar kinetics. We hypothesize that this synchronization is crucial for proper activation of early genes controlling inflammation. Our theoretical predictions of single cell kinetics are supported by recent experimental studies of oscillations in NF-kappaB signaling made on single cells.

Dizzy: stochastic simulation of large-scale genetic regulatory networks

We describe Dizzy, a software tool for stochastically and deterministically modeling the spatially homogeneous kinetics of integrated large-scale genetic, metabolic, and signaling networks. Notable features include a modular simulation framework, reusable modeling elements, complex kinetic rate laws, multi-step reaction processes, steady-state noise estimation, and spatial compartmentalization.

Transcriptional stochasticity in gene expression

Due to the small number of copies of molecular species involved, such as DNA, mRNA and regulatory proteins, gene expression is a stochastic phenomenon. In eukaryotic cells, the stochastic effects primarily originate in regulation of gene activity. Transcription can be initiated by a single transcription factor binding to a specific regulatory site in the target gene. Stochasticity of transcription factor binding and dissociation is then amplified by transcription and translation, since target gene activation results in a burst of mRNA molecules, and each mRNA copy serves as a template for translating numerous protein molecules. In the present paper, we explore a mathematical approach to stochastic modeling. In this approach, the ordinary differential equations with a stochastic component for mRNA and protein levels in a single cells yield a system of first-order partial differential equations (PDEs) for two-dimensional probability density functions (pdf). We consider the following examples: Regulation of a single auto-repressing gene, and regulation of a system of two mutual repressors and of an activator-repressor system. The resulting PDEs are approximated by a system of many ordinary equations, which are then numerically solved.

Phenotype analysis using network motifs derived from changes in regulatory network dynamics

The intrinsic dynamic response of a transcriptional regulatory network depends directly on molecular interactions in the cellular transcription, translation, and degradation machineries. These interactions can be incorporated into dynamic mathematical models of the biochemical system using the biophysical relationship with the model parameters. Modifications of such interactions bring changes to the biological behavior of the cells, and therefore, many normal and pathological cellular states depend on them. It is important for analysis, prediction, diagnosis, and treatment of cellular function to have an experimentally derived model with parameters that adequately represent the molecular interactions of interest. Finding the model and parameters of a transcriptional regulatory network is a difficult task that has been approached at different levels and with different techniques. We develop here a new analysis method (based on previous work on network inference, modeling, and parameter identification) that finds the most changed parameters from yeast oligonucleotide microarray expression patterns in cases where a phenotype difference exists between two samples. We then relate and examine the changed parameters with their associated genes, corresponding genetic functional categories, and particular subnetworks and connectivities. The biophysical bases for these changes are also identified by studying the relationship of the changed parameters with the transcription, translation, and degradation mechanisms. The method is improved to cases where there are two or more transcription factors influencing transcription, and a statistical analysis is performed to give a measurement of the uniqueness and robustness of the parameter fit.

Linking physiological and genetic analyses of the control of leaf growth under changing environmental conditions

Decrease in leaf growth rate under water deficit can be seen as an adaptive process. The analysis of its genetic variability is therefore important in the context of drought tolerance. Several mechanisms are widely believed to drive the reduction in leaf growth rate under water deficit, namely leaf carbon balance, incomplete turgor maintenance, and decrease in cell wall plasticity or in cell division rate, with contributions from hormones such as abscisic acid or ethylene. Each of these mechanisms is still controversial, and involves several families of genes. It is argued that gene regulatory networks are not feasible for modelling such complex systems. Leaf growth can be modelled via response curves to environmental conditions, which are considered as ‘meta-mechanisms’ at a higher degree of organisation. Response curves of leaf elongation rate to meristem temperature, atmospheric vapour pressure deficit, and soil water status were established in recombinant inbred lines (RILs) of maize in experiments carried out in the field and in the greenhouse. A quantitative trait locus (QTL) analysis was conducted on the slopes of these responses. Each parameter of the ecophysiological model could then be computed as the sum of QTL effects, allowing calculation of parameters of new RILs, either virtual or existing. Leaf elongation rates of new RILS were simulated and were similar to measurements in a growth chamber experiment. This opens the way to the simulation of virtual genotypes, known only by their alleles, in any climatic scenario. Each genotype is therefore represented by a set of response parameters, valid in a large range of conditions and deduced from the alleles at QTLs.

A model for restriction point control of the mammalian cell cycle

Inhibition of protein synthesis by cycloheximide blocks subsequent division of a mammalian cell, but only if the cell is exposed to the drug before the "restriction point" (i.e. within the first several hours after birth). If exposed to cycloheximide after the restriction point, a cell proceeds with DNA synthesis, mitosis and cell division and halts in the next cell cycle. If cycloheximide is later removed from the culture medium, treated cells will return to the division cycle, showing a complex pattern of division times post-treatment, as first measured by Zetterberg and colleagues. We simulate these physiological responses of mammalian cells to transient inhibition of growth, using a set of nonlinear differential equations based on a realistic model of the molecular events underlying progression through the cell cycle. The model relies on our earlier work on the regulation of cyclin-dependent protein kinases during the cell division cycle of yeast. The yeast model is supplemented with equations describing the effects of retinoblastoma protein on cell growth and the synthesis of cyclins A and E, and with a primitive representation of the signaling pathway that controls synthesis of cyclin D.

MOLECULAR NETWORKS IN MODEL SYSTEMS

Model organisms, especially the budding yeast, are leading systems in the transformation of biology into an information science. With the availability of genome sequences and genome-scale data generation technologies, the extraction of biological insight from complex integrated molecular networks has become a major area of research. Here I examine key concepts and review research developments. I propose specific areas of research effort to drive network analysis in directions that will promote modeling with increasing predictive power.

Mathematical Modeling of Complex Regulatory Networks

Cellular regulation comprises overwhelmingly complex interactions between genes and proteins that ultimately will only be rendered understandable by employing formal approaches. Developing large-scale mathematical models of such systems in an efficient and reliable way, however, requires careful evaluation of structuring principles for the models, of the description of the system dynamics, and of the experimental data basis for adjusting the models to reality. We discuss these three aspects of model development using the example of cell cycle regulation in yeast and suggest that capturing complex dynamic networks is feasible despite incomplete (quantitative) biological knowledge.

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.

Data-based model and parameter evaluation in dynamic transcriptional regulatory networks

Finding the causality and strength of connectivity in transcriptional regulatory networks from time-series data will provide a powerful tool for the analysis of cellular states. Presented here is the design of tools for the evaluation of the network's model structure and parameters. The most effective tools are found to be based on evolution strategies. We evaluate models of increasing complexity, from lumped, algebraic phenomenological models to Hill functions and thermodynamically derived functions. These last functions provide the free energies of binding of transcription factors to their operators, as well as cooperativity energies. Optimization results based on published experimental data from a synthetic network in Escherichia coli are presented. The free energies of binding and cooperativity found by our tools are in the same physiological ranges as those experimentally derived in the bacteriophage lambda system. We also use time-series data from high-density oligonucleotide microarrays of yeast meiotic expression patterns. The algorithm appropriately finds the parameters of pairs of regulated regulatory yeast genes, showing that for related genes an overall reasonable computation effort is sufficient to find the strength and causality of the connectivity of large numbers of them.

Bayesian decomposition: analyzing microarray data within a biological context

The detection and correct identification of cancer, especially at an early stage, are vitally important for patient survival and quality of life. Since signaling pathways play critical roles in cancer development and metastasis, methods that reliably assess the activity of these pathways are critical to understand cancer and the response to therapy. Bayesian Decomposition (BD) identifies signatures of expression that can be linked directly to signaling pathway activity, allowing the changes in mRNA levels to be used as downstream indicators of pathway activity. Here, we demonstrate this ability by identifying the downstream expression signal associated with the mating response in Saccharomyces cerevisiae and showing that this signal disappears in deletion mutants of genes critical to the MAPK signaling cascade used to trigger the response. We also show the use of BD in the context of supervised learning, by analyzing the Mus musculus tissue-specific data set provided by Project Normal. The algorithm correctly removes routine metabolic processes, allowing tissue-specific signatures of expression to be identified. Gene ontology is used to interpret these signatures. Since a number of modern therapeutics specifically target signaling proteins, it is important to be able to identify changes in signaling pathways in order to use microarray data to interpret cancer response. By removing routine metabolic signatures and linking specific signatures to signaling pathway activity, BD makes it possible to link changes in microarray results to signaling pathways.

Cytoscape: a software environment for integrated models of biomolecular interaction networks

Cytoscape is an open source software project for integrating biomolecular interaction networks with high-throughput expression data and other molecular states into a unified conceptual framework. Although applicable to any system of molecular components and interactions, Cytoscape is most powerful when used in conjunction with large databases of protein-protein, protein-DNA, and genetic interactions that are increasingly available for humans and model organisms. Cytoscape's software Core provides basic functionality to layout and query the network; to visually integrate the network with expression profiles, phenotypes, and other molecular states; and to link the network to databases of functional annotations. The Core is extensible through a straightforward plug-in architecture, allowing rapid development of additional computational analyses and features. Several case studies of Cytoscape plug-ins are surveyed, including a search for interaction pathways correlating with changes in gene expression, a study of protein complexes involved in cellular recovery to DNA damage, inference of a combined physical/functional interaction network for Halobacterium, and an interface to detailed stochastic/kinetic gene regulatory models.

Pleiotropy, homeostasis, and functional networks based on assays of cardiovascular traits in genetically randomized populations

A major problem in studying biological traits is understanding how genes work together to provide organismal structures and functions. Conventional reductionist paradigms attribute functions to particular proteins, motifs, and amino acids. An equally important but harder problem involves the synthesis of data at fundamental levels of biological systems to understand functionality at higher levels. We used subtle, naturally occurring, multigenic variation of cardiovascular (CV) properties in a panel of genetically randomized strains that are derived from the A/J and C57BL/6J strains of mice to perturb CV functions in nonpathologic ways. In this proof-of-concept study, computational analysis correctly identified the known relations among CV properties and revealed functionality at higher levels of the CV system. The network was then used to account for pleiotropies and homeostatic responses in single gene mutant mice and in mice treated with a pharmacologic agent (anesthesia). The CV network accounted for functional dependencies in complementary ways to the insights obtained from genetic networks and biochemical pathways. These networks are therefore an important approach for defining and characterizing functional relations in complex biological systems in health and disease.

The Engineering of Gene Regulatory Networks

The rapid accumulation of genetic information and advancement of experimental techniques have opened a new frontier in biomedical engineering. With the availability of well-characterized components from natural gene networks, the stage has been set for the engineering of artificial gene regulatory networks with sophisticated computational and functional capabilities. In these efforts, the ability to construct, analyze, and interpret qualitative and quantitative models is becoming increasingly important. In this review, we consider the current state of gene network engineering from a combined experimental and modeling perspective. We discuss how networks with increased complexity are being constructed from simple modular components and how quantitative deterministic and stochastic modeling of these modules may provide the foundation for accurate in silico representations of gene regulatory network function in vivo.

On schemes of combinatorial transcription logic

Cells receive a wide variety of cellular and environmental signals, which are often processed combinatorially to generate specific genetic responses. Here we explore theoretically the potentials and limitations of combinatorial signal integration at the level of cis-regulatory transcription control. Our analysis suggests that many complex transcription-control functions of the type encountered in higher eukaryotes are already implementable within the much simpler bacterial transcription system. Using a quantitative model of bacterial transcription and invoking only specific protein-DNA interaction and weak glue-like interaction between regulatory proteins, we show explicit schemes to implement regulatory logic functions of increasing complexity by appropriately selecting the strengths and arranging the relative positions of the relevant protein-binding DNA sequences in the cis-regulatory region. The architectures that emerge are naturally modular and evolvable. Our results suggest that the transcription regulatory apparatus is a "programmable" computing machine, belonging formally to the class of Boltzmann machines. Crucial to our results is the ability to regulate gene expression at a distance. In bacteria, this can be achieved for isolated genes via DNA looping controlled by the dimerization of DNA-bound proteins. However, if adopted extensively in the genome, long-distance interaction can cause unintentional intergenic cross talk, a detrimental side effect difficult to overcome by the known bacterial transcription-regulation systems. This may be a key factor limiting the genome-wide adoption of complex transcription control in bacteria. Implications of our findings for combinatorial transcription control in eukaryotes are discussed.

Statistical bioinformatic methods in microbial genome analysis

It is probable that, increasingly, genome investigations are going to be based on statistical formalization. This review summarizes the state of art and potentiality of using statistics in microbial genome analysis. First, I focus on recent advances in functional genomics, such as finding genes and operons, identifying gene conversion events, detecting DNA replication origins and analysing regulatory sites. Then I describe how to use phylogenetic methods in genome analysis and methods for genome-wide scanning for positively selected amino acids. I conclude with speculations on the future course of genome statistical modeling.

Virtual plants: modelling as a tool for the genomics of tolerance to water deficit

Modelling can simulate the responses of virtual plants carrying diverse combinations of alleles under different scenarios of abiotic stress. The main difficulty is mathematically expressing the genetic variability of responses to environmental conditions. Modelling via gene regulatory networks is not feasible for such complex systems, but plants can be modelled using response curves to environmental conditions that are 'meta mechanisms' at plant level. Each genotype is represented by a set of response parameters that are valid under a wide range of conditions. Transgenesis of one function experimentally affected one response parameter only. Transgenic plants or plants carrying any combination of quantitative trait loci might therefore be simulated and tested under different climatic scenarios, before genetic manipulations are performed.