Engineering of a synthetic quadrastable gene network to approach Waddington landscape and cell fate determination.

The process of cell fate determination has been depicted intuitively as cells travelling and resting on a rugged landscape, which has been probed by various theoretical studies. However, few studies have experimentally demonstrated how underlying gene regulatory networks shape the landscape and hence orchestrate cellular decision-making in the presence of both signal and noise. Here we tested different topologies and verified a synthetic gene circuit with mutual inhibition and auto-activations to be quadrastable, which enables direct study of quadruple cell fate determination on an engineered landscape. We show that cells indeed gravitate towards local minima and signal inductions dictate cell fates through modulating the shape of the multistable landscape. Experiments, guided by model predictions, reveal that sequential inductions generate distinct cell fates by changing landscape in sequence and hence navigating cells to different final states. This work provides a synthetic biology framework to approach cell fate determination and suggests a landscape-based explanation of fixed induction sequences for targeted differentiation.

A geometrical approach to control and controllability of nonlinear dynamical networks.

In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control.

Data-based reconstruction of complex geospatial networks, nodal positioning and detection of hidden nodes.

Given a complex geospatial network with nodes distributed in a two-dimensional region of physical space, can the locations of the nodes be determined and their connection patterns be uncovered based solely on data? We consider the realistic situation where time series/signals can be collected from a single location. A key challenge is that the signals collected are necessarily time delayed, due to the varying physical distances from the nodes to the data collection centre. To meet this challenge, we develop a compressive-sensing-based approach enabling reconstruction of the full topology of the underlying geospatial network and more importantly, accurate estimate of the time delays. A standard triangularization algorithm can then be employed to find the physical locations of the nodes in the network. We further demonstrate successful detection of a hidden node (or a hidden source or threat), from which no signal can be obtained, through accurate detection of all its neighbouring nodes. As a geospatial network has the feature that a node tends to connect with geophysically nearby nodes, the localized region that contains the hidden node can be identified.

Uncovering hidden nodes in complex networks in the presence of noise.

Ascertaining the existence of hidden objects in a complex system, objects that cannot be observed from the external world, not only is curiosity-driven but also has significant practical applications. Generally, uncovering a hidden node in a complex network requires successful identification of its neighboring nodes, but a challenge is to differentiate its effects from those of noise. We develop a completely data-driven, compressive-sensing based method to address this issue by utilizing complex weighted networks with continuous-time oscillatory or discrete-time evolutionary-game dynamics. For any node, compressive sensing enables accurate reconstruction of the dynamical equations and coupling functions, provided that time series from this node and all its neighbors are available. For a neighboring node of the hidden node, this condition cannot be met, resulting in abnormally large prediction errors that, counterintuitively, can be used to infer the existence of the hidden node. Based on the principle of differential signal, we demonstrate that, when strong noise is present, insofar as at least two neighboring nodes of the hidden node are subject to weak background noise only, unequivocal identification of the hidden node can be achieved.

Engineering of regulated stochastic cell fate determination.

Both microbes and multicellular organisms actively regulate their cell fate determination to cope with changing environments or to ensure proper development. Here, we use synthetic biology approaches to engineer bistable gene networks to demonstrate that stochastic and permanent cell fate determination can be achieved through initializing gene regulatory networks (GRNs) at the boundary between dynamic attractors. We realize this experimentally by linking a synthetic GRN to a natural output of galactose metabolism regulation in yeast. Combining mathematical modeling and flow cytometry, we show that our engineered systems are bistable and that inherent gene expression stochasticity does not induce spontaneous state transitioning at steady state. Mathematical analysis predicts that stochastic cell fate determination in this case can only be realized when gene expression fluctuation occurs on or near attractor basin boundaries (the points of instability). Guided by numerical simulations, experiments are designed and performed with quantitatively diverse gene networks to test model predictions, which are verified by both flow cytometry and single-cell microscopy. By interfacing rationally designed synthetic GRNs with background gene regulation mechanisms, this work investigates intricate properties of networks that illuminate possible regulatory mechanisms for cell differentiation and development that can be initiated from points of instability.

Forecasting synchronizability of complex networks from data.

Given a complex networked system whose topology and dynamical equations are unknown, is it possible to foresee that a certain type of collective dynamics can potentially emerge in the system, provided that only time-series measurements are available? We address this question by focusing on a commonly studied type of collective dynamics, namely, synchronization in coupled dynamical networks. We demonstrate that, using the compressive-sensing paradigm, even when the coupling strength is not uniform so that the network is effectively weighted, the full topology, the coupling weights, and the nodal dynamical equations can all be uncovered accurately. The reconstruction accuracy and data requirement are systematically analyzed, in a process that includes a validation of the reconstructed eigenvalue spectrum of the underlying coupling matrix. A master stability function (MSF), the fundamental quantity determining the network synchronizability, can then be calculated based on the reconstructed dynamical system, the accuracy of which can be assessed as well. With the coupling matrix and MSF fully uncovered, the emergence of synchronous dynamics in the network can be anticipated and controlled. To forecast the collective dynamics on complex networks is an extremely challenging problem with significant applications in many disciplines, and our work represents an initial step in this important area.

Detecting hidden nodes in complex networks from time series.

We develop a general method to detect hidden nodes in complex networks, using only time series from nodes that are accessible to external observation. Our method is based on compressive sensing and we formulate a general framework encompassing continuous- and discrete-time and the evolutionary-game type of dynamical systems as well. For concrete demonstration, we present an example of detecting hidden nodes from an experimental social network. Our paradigm for detecting hidden nodes is expected to find applications in a variety of fields where identifying hidden or black-boxed objects based on a limited amount of data is of interest.