Network dynamics

Cesium: A public database of evolved oscillatory reaction networks

New tools and software in systems biology require testing and validation on reaction networks with desired characteristics such as number of reactions or oscillating behaviors. Often, there is only a modest number of published models that are suitable, so researchers must generate reaction networks with the desired characteristics, a process that can be computationally expensive. To reduce these computational costs, we developed a data base of synthetic reaction networks to facilitate reuse. The current database contains thousands of networks generated using directed evolution. The network are of two types: (1) those with oscillations in species concentrations and (2) those for which no oscillation was found using directed evolution. To facilitate access to networks of interest, the database is queryable by the number of species and reactants, the presence or absence of autocatalytic and degradation reactions, and the network behavior. Our analysis of the data revealed some interesting insights, such as the population of oscillating networks possess more autocatalytic reactions compared to random control networks. In the future, this database will be expanded to include other network behaviors.

Phenotypic Heterogeneity in Tumor Progression, and Its Possible Role in the Onset of Cancer

Heterogeneity among isogenic cells/individuals has been known for at least 150 years. Even Mendel, working on pea plants, realized that not all tall plants were identical. However, Mendel was more interested in the discontinuous variation between genetically distinct individuals. The concept of environment dictating distinct phenotypes among isogenic individuals has since been shown to impact the evolution of populations in numerous examples at different scales of life. In this review, we discuss how phenotypic heterogeneity and its evolutionary implications exist at all levels of life, from viruses to mammals. In particular, we discuss how a particular disease condition (cancer) is impacted by heterogeneity among isogenic cells, and propose a potential role that phenotypic heterogeneity might play toward the onset of the disease.

Energy-based analysis of biochemical cycles using bond graphs

Thermodynamic aspects of chemical reactions have a long history in the physical chemistry literature. In particular, biochemical cycles require a source of energy to function. However, although fundamental, the role of chemical potential and Gibb's free energy in the analysis of biochemical systems is often overlooked leading to models which are physically impossible. The bond graph approach was developed for modelling engineering systems, where energy generation, storage and transmission are fundamental. The method focuses on how power flows between components and how energy is stored, transmitted or dissipated within components. Based on the early ideas of network thermodynamics, we have applied this approach to biochemical systems to generate models which automatically obey the laws of thermodynamics. We illustrate the method with examples of biochemical cycles. We have found that thermodynamically compliant models of simple biochemical cycles can easily be developed using this approach. In particular, both stoichiometric information and simulation models can be developed directly from the bond graph. Furthermore, model reduction and approximation while retaining structural and thermodynamic properties is facilitated. Because the bond graph approach is also modular and scaleable, we believe that it provides a secure foundation for building thermodynamically compliant models of large biochemical networks.

Nonlinear biochemical signal processing via noise propagation

Single-cell studies often show significant phenotypic variability due to the stochastic nature of intra-cellular biochemical reactions. When the numbers of molecules, e.g., transcription factors and regulatory enzymes, are in low abundance, fluctuations in biochemical activities become significant and such "noise" can propagate through regulatory cascades in terms of biochemical reaction networks. Here we develop an intuitive, yet fully quantitative method for analyzing how noise affects cellular phenotypes based on identifying a system's nonlinearities and noise propagations. We observe that such noise can simultaneously enhance sensitivities in one behavioral region while reducing sensitivities in another. Employing this novel phenomenon we designed three biochemical signal processing modules: (a) A gene regulatory network that acts as a concentration detector with both enhanced amplitude and sensitivity. (b) A non-cooperative positive feedback system, with a graded dose-response in the deterministic case, that serves as a bistable switch due to noise-induced ultra-sensitivity. (c) A noise-induced linear amplifier for gene regulation that requires no feedback. The methods developed in the present work allow one to understand and engineer nonlinear biochemical signal processors based on fluctuation-induced phenotypes.

Ultrasensitive response motifs: basic amplifiers in molecular signalling networks

Multi-component signal transduction pathways and gene regulatory circuits underpin integrated cellular responses to perturbations. A recurring set of network motifs serve as the basic building blocks of these molecular signalling networks. This review focuses on ultrasensitive response motifs (URMs) that amplify small percentage changes in the input signal into larger percentage changes in the output response. URMs generally possess a sigmoid input–output relationship that is steeper than the Michaelis–Menten type of response and is often approximated by the Hill function. Six types of URMs can be commonly found in intracellular molecular networks and each has a distinct kinetic mechanism for signal amplification. These URMs are: (i) positive cooperative binding, (ii) homo-multimerization, (iii) multistep signalling, (iv) molecular titration, (v) zero-order covalent modification cycle and (vi) positive feedback. Multiple URMs can be combined to generate highly switch-like responses. Serving as basic signal amplifiers, these URMs are essential for molecular circuits to produce complex nonlinear dynamics, including multistability, robust adaptation and oscillation. These dynamic properties are in turn responsible for higher-level cellular behaviours, such as cell fate determination, homeostasis and biological rhythm.

A protein turnover signaling motif controls the stimulus-sensitivity of stress response pathways

Stimulus-induced perturbations from the steady state are a hallmark of signal transduction. In some signaling modules, the steady state is characterized by rapid synthesis and degradation of signaling proteins. Conspicuous among these are the p53 tumor suppressor, its negative regulator Mdm2, and the negative feedback regulator of NFκB, IκBα. We investigated the physiological importance of this turnover, or flux, using a computational method that allows flux to be systematically altered independently of the steady state protein abundances. Applying our method to a prototypical signaling module, we show that flux can precisely control the dynamic response to perturbation. Next, we applied our method to experimentally validated models of p53 and NFκB signaling. We find that high p53 flux is required for oscillations in response to a saturating dose of ionizing radiation (IR). In contrast, high flux of Mdm2 is not required for oscillations but preserves p53 sensitivity to sub-saturating doses of IR. In the NFκB system, degradation of NFκB-bound IκB by the IκB kinase (IKK) is required for activation in response to TNF, while high IKK-independent degradation prevents spurious activation in response to metabolic stress or low doses of TNF. Our work identifies flux pairs with opposing functional effects as a signaling motif that controls the stimulus-sensitivity of the p53 and NFκB stress-response pathways, and may constitute a general design principle in signaling pathways.

Eukaryotic cells constantly synthesize new proteins and degrade old ones. While most proteins are degraded within 24 hours of being synthesized, some proteins are short-lived and exist for only minutes. Using mathematical models, we asked how rapid turnover, or flux, of signaling proteins might regulate the activation of two well-known transcription factors, p53 and NFκB. p53 is a cell cycle regulator that is activated in response to DNA damage, for example, due to ionizing radiation. NFκB is a regulator of immunity and responds to inflammatory signals like the macrophage-secreted cytokine, TNF. Both p53 and NFκB are controlled by at least one flux whose effect on activation is positive and one whose effect is negative. For p53 these are the turnover of p53 and Mdm2, respectively. For NFκB they are the TNF-dependent and -independent turnover of the NFκB inhibitor, IκB. We find that juxtaposition of a positive and negative flux allows for precise tuning of the sensitivity of these transcription factors to different environmental signals. Our results therefore suggest that rapid synthesis and degradation of signaling proteins, though energetically wasteful, may be a common mechanism by which eukaryotic cells regulate their sensitivity to environmental stimuli.

Computational tools for metabolic engineering

A great variety of software applications are now employed in the metabolic engineering field. These applications have been created to support a wide range of experimental and analysis techniques. Computational tools are utilized throughout the metabolic engineering workflow to extract and interpret relevant information from large data sets, to present complex models in a more manageable form, and to propose efficient network design strategies. In this review, we present a number of tools that can assist in modifying and understanding cellular metabolic networks. The review covers seven areas of relevance to metabolic engineers. These include metabolic reconstruction efforts, network visualization, nucleic acid and protein engineering, metabolic flux analysis, pathway prospecting, post-structural network analysis and culture optimization. The list of available tools is extensive and we can only highlight a small, representative portion of the tools from each area.

Robust L-type calcium current expression following heterozygous knockout of the Cav1.2 gene in adult mouse heart

Mechanisms that contribute to maintaining expression of functional ion channels at relatively constant levels following perturbations of channel biosynthesis are likely to contribute significantly to the stability of electrophysiological systems in some pathological conditions. In order to examine the robustness of L-type calcium current expression, the response to changes in Ca²⁺ channel Cav1.2 gene dosage was studied in adult mice. Using a cardiac-specific inducible Cre recombinase system, Cav1.2 mRNA was reduced to 11 ± 1% of control values in homozygous floxed mice and the mice died rapidly (11.9 ± 3 days) after induction of gene deletion. In these homozygous knockout mice, echocardiographic analysis showed that myocardial contractility was reduced to 14 ± 1% of control values shortly before death. For these mice, no effective compensatory changes in ion channel gene expression were triggered following deletion of both Cav1.2 alleles, despite the dramatic decay in cardiac function. In contrast to the homozygote knockout mice, following knockout of only one Cav1.2 allele, cardiac function remained unchanged, as did survival.Cav1.2mRNAexpression in the left ventricle of heterozygous knockout mice was reduced to 58 ± 3% of control values and there was a 21 ± 2% reduction in Cav1.2 protein expression. There was no significant reduction in L-type Ca²⁺ current density in these mice. The results are consistent with a model of L-type calcium channel biosynthesis in which there are one or more saturated steps, which act to buffer changes in both total Cav1.2 protein and L-type current expression.

The in silico macrophage: toward a better understanding of inflammatory disease

Macrophages function as sentinel, cell-regulatory 'hubs' capable of initiating, perpetuating and contributing to the resolution of an inflammatory response, following their activation from a resting state. Highly complex and varied gene expression programs within the macrophage enable such functional diversity. To investigate how programs of gene expression relate to the phenotypic attributes of the macrophage, the development of in silico modeling methods is needed. Such models need to cover multiple scales, from molecular pathways in cell-autonomous immunity and intercellular communication pathways in tissue inflammation to whole organism response pathways in systemic disease. Here, we highlight the potential of in silico macrophage modeling as an amenable and important yet under-exploited tool in aiding in our understanding of the immune inflammatory response. We also discuss how in silico macrophage modeling can help in future therapeutic strategies for modulating both the acute protective effects of inflammation (such as host defense and tissue repair) and the harmful chronic effects (such as autoimmune diseases).