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Early development of Drosophila melanogaster (fruit fly) facilitated by the gap gene network has been shown to be incredibly robust, and the same patterns emerge even when the process is seriously disrupted. We investigate this robustness using a previously developed computational framework called DSGRN (Dynamic Signatures Generated by Regulatory Networks). Our mathematical innovations include the conceptual extension of this established modeling technique to enable modeling of spatially monotone environmental effects, as well as the development of a collection of graph theoretic robustness scores for network models. This allows us to rank order the robustness of network models of cellular systems where each cell contains the same genetic network topology but operates under a parameter regime that changes continuously from cell to cell. We demonstrate the power of this method by comparing the robustness of two previously introduced network models of gap gene expression along the anterior–posterior axis of the fruit fly embryo, both to each other and to a random sample of networks with same number of nodes and edges. We observe that there is a substantial difference in robustness scores between the two models. Our biological insight is that random network topologies are in general capable of reproducing complex patterns of expression, but that using measures of robustness to rank order networks permits a large reduction in hypothesis space for highly conserved systems such as developmental networks. 

Isothermal DNA amplification reactions are used in a broad variety of applications, from diagnostic assays to DNA circuits, with greater speed and less complexity than established PCR technologies. We recently reported a unique, high gain, biphasic isothermal DNA amplification reaction, called the Ultrasensitive DNA Amplification Reaction (UDAR). Here we present a detailed analysis of the UDAR reaction pathways that initiates with a first phase followed by a nonlinear product burst, which is caused by an autocatalytic secondary reaction. The experimental reaction output was reproduced using an ordinary differential equation model based on detailed reaction mechanisms. This model provides insight on the relative importance of each reaction mechanism during both phases, which could aid in the design of product output during DNA amplification reactions. 

Large programs of dynamic gene expression, like cell cyles and circadian rhythms, are controlled by a relatively small “core” network of transcription factors and post-translational modifiers, working in concerted mutual regulation. Recent work suggests that system-independent, quantitative features of the dynamics of gene expression can be used to identify core regulators. We introduce an approach of iterative network hypothesis reduction from time-series data in which increasingly complex features of the dynamic expression of individual, pairs, and entire collections of genes are used to infer functional network models that can produce the observed transcriptional program. The culmination of our work is a computational pipeline, I terative N etwork H ypoth e sis Re ductio n from T emporal Dynamics (Inherent dynamics pipeline), that provides a priority listing of targets for genetic perturbation to experimentally infer network structure. We demonstrate the capability of this integrated computational pipeline on synthetic and yeast cell-cycle data. 

We demonstrate a modeling and computational framework that allows for rapid screening of thousands of potential network designs for particular dynamic behavior. To illustrate this capability we consider the problem of hysteresis, a prerequisite for construction of robust bistable switches and hence a cornerstone for construction of more complex synthetic circuits. We evaluate and rank most three node networks according to their ability to robustly exhibit hysteresis where robustness is measured with respect to parameters over multiple dynamic phenotypes. Focusing on the highest ranked networks, we demonstrate how additional robustness and design constraints can be applied. We compare our results to more traditional methods based on specific parameterization of ordinary differential equation models and demonstrate a strong qualitative match at a small fraction of the computational cost.