Estimating the Continuous-Time Dynamics of Energy and Fat Metabolism in Mice

The mouse has become the most popular organism for investigating molecular mechanisms of body weight regulation. But understanding the physiological context by which a molecule exerts its effect on body weight requires knowledge of energy intake, energy expenditure, and fuel selection. Furthermore, measurements of these variables made at an isolated time point cannot explain why body weight has its present value since body weight is determined by the past history of energy and macronutrient imbalance. While food intake and body weight changes can be frequently measured over several weeks (the relevant time scale for mice), correspondingly frequent measurements of energy expenditure and fuel selection are not currently feasible. To address this issue, we developed a mathematical method based on the law of energy conservation that uses the measured time course of body weight and food intake to estimate the underlying continuous-time dynamics of energy output and net fat oxidation. We applied our methodology to male C57BL/6 mice consuming various ad libitum diets during weight gain and loss over several weeks and present the first continuous-time estimates of energy output and net fat oxidation rates underlying the observed body composition changes. We show that transient energy and fat imbalances in the first several days following a diet switch can account for a significant fraction of the total body weight change. We also discovered a time-invariant curve relating body fat and fat-free masses in male C57BL/6 mice, and the shape of this curve determines how diet, fuel selection, and body composition are interrelated

Understanding dynamics using sensitivity analysis: caveat and solution

<p>Abstract</p> <p>Background</p> <p>Parametric sensitivity analysis (PSA) has become one of the most commonly used tools in computational systems biology, in which the sensitivity coefficients are used to study the parametric dependence of biological models. As many of these models describe dynamical behaviour of biological systems, the PSA has subsequently been used to elucidate important cellular processes that regulate this dynamics. However, in this paper, we show that the PSA coefficients are not suitable in inferring the mechanisms by which dynamical behaviour arises and in fact it can even lead to incorrect conclusions.</p> <p>Results</p> <p>A careful interpretation of parametric perturbations used in the PSA is presented here to explain the issue of using this analysis in inferring dynamics. In short, the PSA coefficients quantify the integrated change in the system behaviour due to persistent parametric perturbations, and thus the dynamical information of when a parameter perturbation matters is lost. To get around this issue, we present a new sensitivity analysis based on impulse perturbations on system parameters, which is named impulse parametric sensitivity analysis (iPSA). The inability of PSA and the efficacy of iPSA in revealing mechanistic information of a dynamical system are illustrated using two examples involving switch activation.</p> <p>Conclusions</p> <p>The interpretation of the PSA coefficients of dynamical systems should take into account the persistent nature of parametric perturbations involved in the derivation of this analysis. The application of PSA to identify the controlling mechanism of dynamical behaviour can be misleading. By using impulse perturbations, introduced at different times, the iPSA provides the necessary information to understand how dynamics is achieved, i.e. which parameters are essential and when they become important.</p

Signaling Cascades Modulate the Speed of Signal Propagation through Space

Cells are not mixed bags of signaling molecules. As a consequence, signals must travel from their origin to distal locations. Much is understood about the purely diffusive propagation of signals through space. Many signals, however, propagate via signaling cascades. Here, we show that, depending on their kinetics, cascades speed up or slow down the propagation of signals through space, relative to pure diffusion.We modeled simple cascades operating under different limits of Michaelis-Menten kinetics using deterministic reaction-diffusion equations. Cascades operating far from enzyme saturation speed up signal propagation; the second mobile species moves more quickly than the first through space, on average. The enhanced speed is due to more efficient serial activation of a downstream signaling module (by the signaling molecule immediately upstream in the cascade) at points distal from the signaling origin, compared to locations closer to the source. Conversely, cascades operating under saturated kinetics, which exhibit zero-order ultrasensitivity, can slow down signals, ultimately localizing them to regions around the origin.Signal speed modulation may be a fundamental function of cascades, affecting the ability of signals to penetrate within a cell, to cross-react with other signals, and to activate distant targets. In particular, enhanced speeds provide a way to increase signal penetration into a cell without needing to flood the cell with large numbers of active signaling molecules; conversely, diminished speeds in zero-order ultrasensitive cascades facilitate strong, but localized, signaling

Modeling the Effects of Cell Cycle M-phase Transcriptional Inhibition on Circadian Oscillation

Circadian clocks are endogenous time-keeping systems that temporally organize biological processes. Gating of cell cycle events by a circadian clock is a universal observation that is currently considered a mechanism serving to protect DNA from diurnal exposure to ultraviolet radiation or other mutagens. In this study, we put forward another possibility: that such gating helps to insulate the circadian clock from perturbations induced by transcriptional inhibition during the M phase of the cell cycle. We introduced a periodic pulse of transcriptional inhibition into a previously published mammalian circadian model and simulated the behavior of the modified model under both constant darkness and light–dark cycle conditions. The simulation results under constant darkness indicated that periodic transcriptional inhibition could entrain/lock the circadian clock just as a light–dark cycle does. At equilibrium states, a transcriptional inhibition pulse of certain periods was always locked close to certain circadian phases where inhibition on Per and Bmal1 mRNA synthesis was most balanced. In a light–dark cycle condition, inhibitions imposed at different parts of a circadian period induced different degrees of perturbation to the circadian clock. When imposed at the middle- or late-night phase, the transcriptional inhibition cycle induced the least perturbations to the circadian clock. The late-night time window of least perturbation overlapped with the experimentally observed time window, where mitosis is most frequent. This supports our hypothesis that the circadian clock gates the cell cycle M phase to certain circadian phases to minimize perturbations induced by the latter. This study reveals the hidden effects of the cell division cycle on the circadian clock and, together with the current picture of genome stability maintenance by circadian gating of cell cycle, provides a more comprehensive understanding of the phenomenon of circading gating of cell cycle

Precise Regulation of Gene Expression Dynamics Favors Complex Promoter Architectures

Promoters process signals through recruitment of transcription factors and RNA polymerase, and dynamic changes in promoter activity constitute a major noise source in gene expression. However, it is barely understood how complex promoter architectures determine key features of promoter dynamics. Here, we employ prototypical promoters of yeast ribosomal protein genes as well as simplified versions thereof to analyze the relations among promoter design, complexity, and function. These promoters combine the action of a general regulatory factor with that of specific transcription factors, a common motif of many eukaryotic promoters. By comprehensively analyzing stationary and dynamic promoter properties, this model-based approach enables us to pinpoint the structural characteristics underlying the observed behavior. Functional tradeoffs impose constraints on the promoter architecture of ribosomal protein genes. We find that a stable scaffold in the natural design results in low transcriptional noise and strong co-regulation of target genes in the presence of gene silencing. This configuration also exhibits superior shut-off properties, and it can serve as a tunable switch in living cells. Model validation with independent experimental data suggests that the models are sufficiently realistic. When combined, our results offer a mechanistic explanation for why specific factors are associated with low protein noise in vivo. Many of these findings hold for a broad range of model parameters and likely apply to other eukaryotic promoters of similar structure

Drug-Induced Regulation of Target Expression

Drug perturbations of human cells lead to complex responses upon target binding. One of the known mechanisms is a (positive or negative) feedback loop that adjusts the expression level of the respective target protein. To quantify this mechanism systems-wide in an unbiased way, drug-induced differential expression of drug target mRNA was examined in three cell lines using the Connectivity Map. To overcome various biases in this valuable resource, we have developed a computational normalization and scoring procedure that is applicable to gene expression recording upon heterogeneous drug treatments. In 1290 drug-target relations, corresponding to 466 drugs acting on 167 drug targets studied, 8% of the targets are subject to regulation at the mRNA level. We confirmed systematically that in particular G-protein coupled receptors, when serving as known targets, are regulated upon drug treatment. We further newly identified drug-induced differential regulation of Lanosterol 14-alpha demethylase, Endoplasmin, DNA topoisomerase 2-alpha and Calmodulin 1. The feedback regulation in these and other targets is likely to be relevant for the success or failure of the molecular intervention

Decoupling Environment-Dependent and Independent Genetic Robustness across Bacterial Species

The evolutionary origins of genetic robustness are still under debate: it may arise as a consequence of requirements imposed by varying environmental conditions, due to intrinsic factors such as metabolic requirements, or directly due to an adaptive selection in favor of genes that allow a species to endure genetic perturbations. Stratifying the individual effects of each origin requires one to study the pertaining evolutionary forces across many species under diverse conditions. Here we conduct the first large-scale computational study charting the level of robustness of metabolic networks of hundreds of bacterial species across many simulated growth environments. We provide evidence that variations among species in their level of robustness reflect ecological adaptations. We decouple metabolic robustness into two components and quantify the extents of each: the first, environmental-dependent, is responsible for at least 20% of the non-essential reactions and its extent is associated with the species' lifestyle (specialized/generalist); the second, environmental-independent, is associated (correlation = ∼0.6) with the intrinsic metabolic capacities of a species—higher robustness is observed in fast growers or in organisms with an extensive production of secondary metabolites. Finally, we identify reactions that are uniquely susceptible to perturbations in human pathogens, potentially serving as novel drug-targets

Exact Hybrid Particle/Population Simulation of Rule-Based Models of Biochemical Systems

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This "network-free" approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of "partial network expansion" into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility. © 2014 Hogg et al

Growth landscape formed by perception and import of glucose in yeast

An important challenge in systems biology is to quantitatively describe microbial growth using a few measurable parameters that capture the essence of this complex phenomenon. Two key events at the cell membrane—extracellular glucose sensing and uptake—initiate the budding yeast’s growth on glucose. However, conventional growth models focus almost exclusively on glucose uptake. Here we present results from growth-rate experiments that cannot be explained by focusing on glucose uptake alone. By imposing a glucose uptake rate independent of the sensed extracellular glucose level, we show that despite increasing both the sensed glucose concentration and uptake rate, the cell’s growth rate can decrease or even approach zero. We resolve this puzzle by showing that the interaction between glucose perception and import, not their individual actions, determines the central features of growth, and characterize this interaction using a quantitative model. Disrupting this interaction by knocking out two key glucose sensors significantly changes the cell’s growth rate, yet uptake rates are unchanged. This is due to a decrease in burden that glucose perception places on the cells. Our work shows that glucose perception and import are separate and pivotal modules of yeast growth, the interaction of which can be precisely tuned and measured.National Institutes of Health (U.S.). Pioneer AwardNatural Sciences and Engineering Research Council of Canada (NSERC). Graduate Fellowshi