Epigenetic factor competition reshapes the EMT landscape.

The emergence of and transitions between distinct phenotypes in isogenic cells can be attributed to the intricate interplay of epigenetic marks, external signals, and gene-regulatory elements. These elements include chromatin remodelers, histone modifiers, transcription factors, and regulatory RNAs. Mathematical models known as gene-regulatory networks (GRNs) are an increasingly important tool to unravel the workings of such complex networks. In such models, epigenetic factors are usually proposed to act on the chromatin regions directly involved in the expression of relevant genes. However, it has been well-established that these factors operate globally and compete with each other for targets genome-wide. Therefore, a perturbation of the activity of a regulator can redistribute epigenetic marks across the genome and modulate the levels of competing regulators. In this paper, we propose a conceptual and mathematical modeling framework that incorporates both local and global competition effects between antagonistic epigenetic regulators, in addition to local transcription factors, and show the counterintuitive consequences of such interactions. We apply our approach to recent experimental findings on the epithelial-mesenchymal transition (EMT). We show that it can explain the puzzling experimental data, as well as provide verifiable predictions.

Distributed Implementation of Boolean Functions by Transcriptional Synthetic Circuits.

Starting in the early 2000s, sophisticated technologies have been developed for the rational construction of synthetic genetic networks that implement specified logical functionalities. Despite impressive progress, however, the scaling necessary in order to achieve greater computational power has been hampered by many constraints, including repressor toxicity and the lack of large sets of mutually orthogonal repressors. As a consequence, a typical circuit contains no more than roughly seven repressor-based gates per cell. A possible way around this scalability problem is to distribute the computation among multiple cell types, each of which implements a small subcircuit, which communicate among themselves using diffusible small molecules (DSMs). Examples of DSMs are those employed by quorum sensing systems in bacteria. This paper focuses on systematic ways to implement this distributed approach, in the context of the evaluation of arbitrary Boolean functions. The unique characteristics of genetic circuits and the properties of DSMs require the development of new Boolean synthesis methods, distinct from those classically used in electronic circuit design. In this work, we propose a fast algorithm to synthesize distributed realizations for any Boolean function, under constraints on the number of gates per cell and the number of orthogonal DSMs. The method is based on an exact synthesis algorithm to find the minimal circuit per cell, which in turn allows us to build an extensive database of Boolean functions up to a given number of inputs. For concreteness, we will specifically focus on circuits of up to 4 inputs, which might represent, for example, two chemical inducers and two light inputs at different frequencies. Our method shows that, with a constraint of no more than seven gates per cell, the use of a single DSM increases the total number of realizable circuits by at least 7.58-fold compared to centralized computation. Moreover, when allowing two DSM's, one can realize 99.995% of all possible 4-input Boolean functions, still with at most 7 gates per cell. The methodology introduced here can be readily adapted to complement recent genetic circuit design automation software. A toolbox that uses the proposed algorithm was created and made available at https://github.com/sontaglab/DBC/.

Stochastic analysis of genetic feedback controllers to reprogram a pluripotency gene regulatory network.

Cellular reprogramming is traditionally accomplished through an open loop (OL) control approach, wherein key transcription factors (TFs) are injected in cells to steer the state of the pluripotency (PL) gene regulatory network (GRN), as encoded by TFs concentrations, to the pluripotent state. Due to the OL nature of this approach, the concentration of TFs cannot be accurately controlled. Recently, a closed loop (CL) feedback control strategy was proposed to overcome this problem with promising theoretical results. However, previous analyses of the controller were based on deterministic models. It is well known that cellular systems are characterized by substantial stochasticity, especially when molecules are in low copy number as it is the case in reprogramming problems wherein the gene copy number is usually one or two. Hence, in this paper, we analyze the Chemical Master Equation (CME) for the reaction model of the PL GRN with and without the feedback controller. We computationally and analytically investigate the performance of the controller in biologically relevant parameter regimes where stochastic effects dictate system dynamics. Our results indicate that the feedback control approach still ensures reprogramming even when both the PL GRN and the controller are stochastic.

Stochastic multistationarity in a model of the hematopoietic stem cell differentiation network.

A central issue in the analysis of multi-stable systems is that of controlling the relative size of the basins of attraction of alternative states through suitable choices of system parameters. We are interested here mainly in the stochastic version of this problem, that of shaping the stationary probability distribution of a Markov chain so that various alternative modes become more likely than others. Although many of our results are more general, we were motivated by an important biological question, that of cell differentiation. In the mathematical modeling of cell differentiation, it is common to think of internal states of cells (quanfitied by activation levels of certain genes) as determining the different cell types. Specifically, we study here the "PU.1/GATA-1 circuit" which is involved in the control of the development of mature blood cells from hematopoietic stem cells (HSCs). All mature, specialized blood cells have been shown to be derived from multipotent HSCs. Our first contribution is to introduce a rigorous chemical reaction network model of the PU.1/GATA-1 circuit, which incorporates current biological knowledge. We then find that the resulting ODE model of these biomolecular reactions is incapable of exhibiting multistability, contradicting the fact that differentiation networks have, by definition, alternative stable steady states. When considering instead the stochastic version of this chemical network, we analytically construct the stationary distribution, and are able to show that this distribution is indeed capable of admitting a multiplicity of modes. Finally, we study how a judicious choice of system parameters serves to bias the probabilities towards different stationary states. We remark that certain changes in system parameters can be physically implemented by a biological feedback mechanism; tuning this feedback gives extra degrees of freedom that allow one to assign higher likelihood to some cell types over others.