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)

A robust method for designing multistable systems by embedding bistable subsystems

Although multistability is an important dynamic property of a wide range of complex systems, it is still a challenge to develop mathematical models for realising high order multistability using realistic regulatory mechanisms. To address this issue, we propose a robust method to develop multistable mathematical models by embedding bistable models together. Using the GATA1-GATA2-PU.1 module in hematopoiesis as the test system, we first develop a tristable model based on two bistable models without any high cooperative coefficients, and then modify the tristable model based on experimentally determined mechanisms. The modified model successfully realises four stable steady states and accurately reflects a recent experimental observation showing four transcriptional states. In addition, we develop a stochastic model, and stochastic simulations successfully realise the experimental observations in single cells. These results suggest that the proposed method is a general approach to develop mathematical models for realising multistability and heterogeneity in complex systems

Chaos synchronization between linearly coupled chaotic systems

Abstract This paper investigates the chaos synchronization between two linearly coupled chaotic systems. Some sufficient conditions of global asymptotic synchronization are attained from rigorously mathematical theory. Also, a new method for analyzing the stability of synchronization solution is presented. Using this method, some sufficient conditions of linear stability of the synchronization chaotic solution are gained. The influence of coupling coefficients on chaos synchronization is further studied for three typical chaotic systems: Lorenz system, Chen system, and newly found L€ u u system.

Geometric Characteristics of Dynamic Correlations for Combinatorial Regulation in Gene Expression Noise

Knowing which mode of combinatorial regulation (typically, AND or OR logic operation) that a gene employs is important for determining its function in regulatory networks. Here, we introduce a dynamic cross-correlation function between the output of a gene and its upstream regulator concentrations for signatures of combinatorial regulation in gene expression noise. We find that the correlation function is always upwards convex for the AND operation whereas downwards convex for the OR operation, whichever sources of noise (intrinsic or extrinsic or both). In turn, this fact implies a means for inferring regulatory synergies from available experimental data. The extensions and applications are discussed.Comment: 4 pages, 3 figures, and supporting materia

Synchronization and clustering of synthetic genetic networks: A role for cis-regulatory modules

The effect of signal integration through cis-regulatory modules (CRMs) on synchronization and clustering of populations of two-component genetic oscillators coupled by quorum sensing is in detail investigated. We find that the CRMs play an important role in achieving synchronization and clustering. For this, we investigate 6 possible cis-regulatory input functions (CRIFs) with AND, OR, ANDN, ORN, XOR, and EQU types of responses in two possible kinds of cell-to-cell communications: activator-regulated communication (i.e., the autoinducer regulates the activator) and repressor-regulated communication (i.e., the autoinducer regulates the repressor). Both theoretical analysis and numerical simulation show that different CRMs drive fundamentally different cellular patterns, such as complete synchronization, various cluster-balanced states and several cluster-nonbalanced states.Comment: 30 pages, 8 figure

External Stimuli Mediate Collective Rhythms: Artificial Control Strategies

The artificial intervention of biological rhythms remains an exciting challenge. Here, we proposed artificial control strategies that were developed to mediate the collective rhythms emerging in multicellular structures. Based on noisy repressilators and by injecting a periodic control amount to the extracellular medium, we introduced two typical kinds of control models. In one, there are information exchanges among cells, where signaling molecules receive the injected stimulus that freely diffuses toward/from the intercellular medium. In the other, there is no information exchange among cells, but signaling molecules also receive the stimulus that directionally diffuses into each cell from the common environment. We uncovered physical mechanisms for how the stimulus induces, enhances or ruins collective rhythms. We found that only when the extrinsic period is close to an integer multiplicity of the averaged intrinsic period can the collective behaviors be induced/enhanced; otherwise, the stimulus possibly ruins the achieved collective behaviors. Such entrainment properties of these oscillators to external signals would be exploited by realistic living cells to sense external signals. Our results not only provide a new perspective to the understanding of the interplays between extrinsic stimuli and intrinsic physiological rhythms, but also would lead to the development of medical therapies or devices