Inverse bifurcation analysis: application to simple gene systems

BACKGROUND: Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional forward problem of determining the mapping from parameter space to the space of model behavior, the inverse problem of determining model parameters to result in certain desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems. These include understanding how the robustness of qualitative behavior arises from system design as well as providing a way to engineer biological networks with qualitative properties. RESULTS: We demonstrate that certain inverse bifurcation problems of biological interest may be cast as optimization problems involving minimal distances of reference parameter sets to bifurcation manifolds. This formulation allows for an iterative solution procedure based on performing a sequence of eigen-system computations and one-parameter continuations of solutions, the latter being a standard capability in existing numerical bifurcation software. As applications of the proposed method, we show that the problem of maximizing regions of a given qualitative behavior as well as the reverse engineering of bistable gene switches can be modelled and efficiently solved

Complex and unexpected dynamics in simple genetic regulatory networks

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Modular analysis of the control of flagellar Ca2+-spike trains produced by CatSper and CaV channels in sea urchin sperm

Intracellular calcium ([Ca2+]i) is a basic and ubiquitous cellular signal controlling a wide variety of biological processes. A remarkable example is the steering of sea urchin spermatozoa towards the conspecific egg by a spatially and temporally orchestrated series of [Ca2+]i spikes. Although this process has been an experimental paradigm for reproduction and sperm chemotaxis studies, the composition and regulation of the signalling network underlying the cytosolic calcium fluctuations are hitherto not fully understood. Here, we used a differential equations model of the signalling network to assess which set of channels can explain the characteristic envelope and temporal organisation of the [Ca2+]i-spike trains. The signalling network comprises an initial membrane hyperpolarisation produced by an Upstream module triggered by the egg-released chemoattractant peptide, via receptor activation, cGMP synthesis and decay. Followed by downstream modules leading to intraflagellar pH (pHi), voltage and [Ca2+]i fluctuations. The Upstream module outputs were fitted to kinetic data on cGMP activity and early membrane potential changes measured in bulk cell populations. Two candidate modules featuring voltage-dependent Ca2+-channels link these outputs to the downstream dynamics and can independently explain the typical decaying envelope and the progressive spacing of the spikes. In the first module, [Ca2+]i-spike trains require the concerted action of a classical CaV-like channel and a potassium channel, BK (Slo1), whereas the second module relies on pHi-dependent CatSper dynamics articulated with voltage-dependent neutral sodium-proton exchanger (NHE). We analysed the dynamics of these two modules alone and in mixed scenarios. We show that the [Ca2+]i dynamics observed experimentally after sustained alkalinisation can be reproduced by a model featuring the CatSper and NHE module but not by those including the pH-independent CaV and BK module or proportionate mixed scenarios. We conclude in favour of the module containing CatSper and NHE and highlight experimentally testable predictions that would corroborate this conclusion

Gene Networks of Fully Connected Triads with Complete Auto-Activation Enable Multistability and Stepwise Stochastic Transitions

abstract: Fully-connected triads (FCTs), such as the Oct4-Sox2-Nanog triad, have been implicated as recurring transcriptional motifs embedded within the regulatory networks that specify and maintain cellular states. To explore the possible connections between FCT topologies and cell fate determinations, we employed computational network screening to search all possible FCT topologies for multistability, a dynamic property that allows the rise of alternate regulatory states from the same transcriptional network. The search yielded a hierarchy of FCTs with various potentials for multistability, including several topologies capable of reaching eight distinct stable states. Our analyses suggested that complete auto-activation is an effective indicator for multistability, and, when gene expression noise was incorporated into the model, the networks were able to transit multiple states spontaneously. Different levels of stochasticity were found to either induce or disrupt random state transitioning with some transitions requiring layovers at one or more intermediate states. Using this framework we simulated a simplified model of induced pluripotency by including constitutive overexpression terms. The corresponding FCT showed random state transitioning from a terminal state to the pluripotent state, with the temporal distribution of this transition matching published experimental data. This work establishes a potential theoretical framework for understanding cell fate determinations by connecting conserved regulatory modules with network dynamics. Our results could also be employed experimentally, using established developmental transcription factors as seeds, to locate cell lineage specification networks by using auto-activation as a cipher.The article is published at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.010287

MicroRNA-Mediated Positive Feedback Loop and Optimized Bistable Switch in a Cancer Network Involving miR-17-92

MicroRNAs (miRNAs) are small, noncoding RNAs that play an important role in many key biological processes, including development, cell differentiation, the cell cycle and apoptosis, as central post-transcriptional regulators of gene expression. Recent studies have shown that miRNAs can act as oncogenes and tumor suppressors depending on the context. The present work focuses on the physiological significance of miRNAs and their role in regulating the switching behavior. We illustrate an abstract model of the Myc/E2F/miR-17-92 network presented by Aguda et al. (2008), which is composed of coupling between the E2F/Myc positive feedback loops and the E2F/Myc/miR-17-92 negative feedback loop. By systematically analyzing the network in close association with plausible experimental parameters, we show that, in the presence of miRNAs, the system bistability emerges from the system, with a bistable switch and a one-way switch presented by Aguda et al. instead of a single one-way switch. Moreover, the miRNAs can optimize the switching process. The model produces a diverse array of response-signal behaviors in response to various potential regulating scenarios. The model predicts that this transition exists, one from cell death or the cancerous phenotype directly to cell quiescence, due to the existence of miRNAs. It was also found that the network involving miR-17-92 exhibits high noise sensitivity due to a positive feedback loop and also maintains resistance to noise from a negative feedback loop

SYSTEMS CANCER BIOLOGY AND THE CONTROLLING MECHANISMS FOR THE J-SHAPED CANCER DOSE RESPONSE: TOWARDS RELAXING THE LNT HYPOTHESIS

The hormesis phenomena or J-shaped dose response have been accepted as a com- mon phenomenon regardless of the involved biological model, endpoint measured and chemical class/physical stressor. This paper first introduced a mathematical dose response model based on systems biology approach. It links molecular-level cell cycle checkpoint control information to clonal growth cancer model to predict the possible shapes of the dose response curves of Ionizing Radiation (IR) induced tumor transformation frequency. J-shaped dose response curves have been captured with consideration of cell cycle checkpoint control mechanisms. The simulation results indicate the shape of the dose response curve relates to the behavior of the saddle-node points of the model in the bifurcation diagram. A simplified version of the model in previous work of the authors was used mathematically to analyze behaviors relating to the saddle-node points for the J-shaped dose response curve. It indicates that low-linear energy transfer (LET) is more likely to have a J-shaped dose response curve. This result emphasizes the significance of systems biology approach, which encourages collaboration of multidiscipline of biologists, toxicologists and mathematicians, to illustrate complex cancer-related events, and confirm the biphasic dose-response at low doses

Synthesis of Biological and Mathematical Methods for Gene Network Control

abstract: Synthetic biology is an emerging field which melds genetics, molecular biology, network theory, and mathematical systems to understand, build, and predict gene network behavior. As an engineering discipline, developing a mathematical understanding of the genetic circuits being studied is of fundamental importance. In this dissertation, mathematical concepts for understanding, predicting, and controlling gene transcriptional networks are presented and applied to two synthetic gene network contexts. First, this engineering approach is used to improve the function of the guide ribonucleic acid (gRNA)-targeted, dCas9-regulated transcriptional cascades through analysis and targeted modification of the RNA transcript. In so doing, a fluorescent guide RNA (fgRNA) is developed to more clearly observe gRNA dynamics and aid design. It is shown that through careful optimization, RNA Polymerase II (Pol II) driven gRNA transcripts can be strong enough to exhibit measurable cascading behavior, previously only shown in RNA Polymerase III (Pol III) circuits. Second, inherent gene expression noise is used to achieve precise fractional differentiation of a population. Mathematical methods are employed to predict and understand the observed behavior, and metrics for analyzing and quantifying similar differentiation kinetics are presented. Through careful mathematical analysis and simulation, coupled with experimental data, two methods for achieving ratio control are presented, with the optimal schema for any application being dependent on the noisiness of the system under study. Together, these studies push the boundaries of gene network control, with potential applications in stem cell differentiation, therapeutics, and bio-production.Dissertation/ThesisDoctoral Dissertation Biomedical Engineering 201

Revealing Dynamic Mechanisms of Cell Fate Decisions From Single-Cell Transcriptomic Data.

Cell fate decisions play a pivotal role in development, but technologies for dissecting them are limited. We developed a multifunction new method, Topographer, to construct a "quantitative" Waddington's landscape of single-cell transcriptomic data. This method is able to identify complex cell-state transition trajectories and to estimate complex cell-type dynamics characterized by fate and transition probabilities. It also infers both marker gene networks and their dynamic changes as well as dynamic characteristics of transcriptional bursting along the cell-state transition trajectories. Applying this method to single-cell RNA-seq data on the differentiation of primary human myoblasts, we not only identified three known cell types, but also estimated both their fate probabilities and transition probabilities among them. We found that the percent of genes expressed in a bursty manner is significantly higher at (or near) the branch point (~97%) than before or after branch (below 80%), and that both gene-gene and cell-cell correlation degrees are apparently lower near the branch point than away from the branching. Topographer allows revealing of cell fate mechanisms in a coherent way at three scales: cell lineage (macroscopic), gene network (mesoscopic), and gene expression (microscopic)