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Stochastic fluctuations can reveal the feedback signs of gene regulatory networks at the single-molecule level.

ABSTRACT: Understanding the relationship between spontaneous stochastic fluctuations and the topology of the underlying gene regulatory network is of fundamental importance for the study of single-cell stochastic gene expression. Here by solving the analytical steady-state distribution of the protein copy number in a general kinetic model of stochastic gene expression with nonlinear feedback regulation, we reveal the relationship between stochastic fluctuations and feedback topology at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations. Based on such relationship, we also develop an effective method to extract the topological information of a gene regulatory network from single-cell gene expression data. The theory is demonstrated by numerical simulations and, more importantly, validated quantitatively by single-cell data analysis of a synthetic gene circuit integrated in human kidney cells.

SUBMITTER: Jia C

PROVIDER: S-EPMC5700158 | biostudies-literature | 2017 Nov

REPOSITORIES: biostudies-literature

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Stochastic fluctuations can reveal the feedback signs of gene regulatory networks at the single-molecule level.

Jia Chen C Xie Peng P Chen Min M Zhang Michael Q MQ

Scientific reports 20171122 1

Understanding the relationship between spontaneous stochastic fluctuations and the topology of the underlying gene regulatory network is of fundamental importance for the study of single-cell stochastic gene expression. Here by solving the analytical steady-state distribution of the protein copy number in a general kinetic model of stochastic gene expression with nonlinear feedback regulation, we reveal the relationship between stochastic fluctuations and feedback topology at the single-molecule ...[more]

PMID: 29167445

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Project description:BACKGROUND: Various computational models have been of interest due to their use in the modelling of gene regulatory networks (GRNs). As a logical model, probabilistic Boolean networks (PBNs) consider molecular and genetic noise, so the study of PBNs provides significant insights into the understanding of the dynamics of GRNs. This will ultimately lead to advances in developing therapeutic methods that intervene in the process of disease development and progression. The applications of PBNs, however, are hindered by the complexities involved in the computation of the state transition matrix and the steady-state distribution of a PBN. For a PBN with n genes and N Boolean networks, the complexity to compute the state transition matrix is O(nN22n) or O(nN2n) for a sparse matrix. RESULTS: This paper presents a novel implementation of PBNs based on the notions of stochastic logic and stochastic computation. This stochastic implementation of a PBN is referred to as a stochastic Boolean network (SBN). An SBN provides an accurate and efficient simulation of a PBN without and with random gene perturbation. The state transition matrix is computed in an SBN with a complexity of O(nL2n), where L is a factor related to the stochastic sequence length. Since the minimum sequence length required for obtaining an evaluation accuracy approximately increases in a polynomial order with the number of genes, n, and the number of Boolean networks, N, usually increases exponentially with n, L is typically smaller than N, especially in a network with a large number of genes. Hence, the computational efficiency of an SBN is primarily limited by the number of genes, but not directly by the total possible number of Boolean networks. Furthermore, a time-frame expanded SBN enables an efficient analysis of the steady-state distribution of a PBN. These findings are supported by the simulation results of a simplified p53 network, several randomly generated networks and a network inferred from a T cell immune response dataset. An SBN can also implement the function of an asynchronous PBN and is potentially useful in a hybrid approach in combination with a continuous or single-molecule level stochastic model. CONCLUSIONS: Stochastic Boolean networks (SBNs) are proposed as an efficient approach to modelling gene regulatory networks (GRNs). The SBN approach is able to recover biologically-proven regulatory behaviours, such as the oscillatory dynamics of the p53-Mdm2 network and the dynamic attractors in a T cell immune response network. The proposed approach can further predict the network dynamics when the genes are under perturbation, thus providing biologically meaningful insights for a better understanding of the dynamics of GRNs. The algorithms and methods described in this paper have been implemented in Matlab packages, which are attached as Additional files.

Project description:Leukocyte migration is controlled by a leading-edge chemosensory pathway that generates the regulatory lipid phosphatidylinositol-3,4,5-trisphosphate (PIP3), a growth signal, thereby driving leading-edge expansion up attractant gradients toward sites of infection, inflammation, or tissue damage. PIP3 also serves as an important growth signal in growing cells and oncogenesis. The kinases PDK1, AKT1 or PKB, and PKCα are key components of a plasma-membrane-based PIP3 and Ca2+ signaling circuit that regulates these processes. PDK1 and AKT1 are recruited to the membrane by PIP3, whereas PKCα is recruited to the membrane by Ca2+. All three of these master kinases phosphoregulate an array of protein targets. For example, PDK1 activates AKT1, PKCα, and other AGC kinases by phosphorylation at key sites. PDK1 is believed to form PDK1-AKT1 and PDK1-PKCα heterodimers stabilized by a PDK1-interacting fragment (PIF) interaction between the PDK1 PIF pocket and the PIF motif of the AGC binding partner. Here, we present the first, to our knowledge, single-molecule studies of full-length PDK1 and AKT1 on target membrane surfaces, as well as their interaction with full-length PKCα. These studies directly detect membrane-bound PDK1-AKT1 and PDK1-PKCα heterodimers stabilized by PIF interactions formed at physiological ligand concentrations. PKCα exhibits eightfold higher PDK1 affinity than AKT1 and can competitively displace AKT1 from PDK1-AKT1 heterodimers. Ensemble activity measurements under matched conditions reveal that PDK1 activates AKT1 via a cis mechanism by phosphorylating an AKT1 molecule in the same PDK1-AKT1 heterodimer, whereas PKCα acts as a competitive inhibitor of this phosphoactivation reaction by displacing AKT1 from PDK1. Overall, the findings provide insights into the binding and regulatory interactions of the three master kinases on their target membrane and suggest that a recently described tumor suppressor activity of PKC isoforms may arise from its ability to downregulate PDK1-AKT1 phosphoactivation in the PIP3-PDK1-AKT1-mTOR pathway linked to cell growth and oncogenesis.

Project description:Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the "normal velocity" that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach.

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Stochastic fluctuations can reveal the feedback signs of gene regulatory networks at the single-molecule level.

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Stochastic fluctuations can reveal the feedback signs of gene regulatory networks at the single-molecule level.

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