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.

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.

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.

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.

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.

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.

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.