A yeast synthetic network for in vivo assessment of reverse-engineering and modeling approaches.

Systems biology approaches are extensively used to model and reverse engineer gene regulatory networks from experimental data. Conversely, synthetic biology allows "de novo" construction of a regulatory network to seed new functions in the cell. At present, the usefulness and predictive ability of modeling and reverse engineering cannot be assessed and compared rigorously. We built in the yeast Saccharomyces cerevisiae a synthetic network, IRMA, for in vivo "benchmarking" of reverse-engineering and modeling approaches. The network is composed of five genes regulating each other through a variety of regulatory interactions; it is negligibly affected by endogenous genes, and it is responsive to small molecules. We measured time series and steady-state expression data after multiple perturbations. These data were used to assess state-of-the-art modeling and reverse-engineering techniques. A semiquantitative model was able to capture and predict the behavior of the network. Reverse engineering based on differential equations and Bayesian networks correctly inferred regulatory interactions from the experimental data.

Model-based feedback control of live zebrafish behavior via interaction with a robotic replica.

The possibility of regulating the behavior of live animals using biologically-inspired robots has attracted the interest of biologists and engineers for over twenty-five years. From early work on insects to recent endeavors on mammals, we have witnessed fascinating applications that have pushed forward our understanding of animal behavior along new directions. Despite significant progress, most of the research has focused on open-loop control systems, in which robots execute predetermined actions, independent of the animal behavior. We integrate mathematical modeling of social behavior toward the design of realistic feedback laws for robots to interact with a live animal. In particular, we leverage recent advancements in data-driven modeling of zebrafish behavior. Ultimately, we establish a novel robotic platform that allows real-time actuation of a biologically-inspired 3D-printed zebrafish replica to implement model-based control of animal behavior. We demonstrate our approach through a series of experiments, designed to elucidate the appraisal of the replica by live subjects with respect to conspecifics and to quantify the biological value of closed-loop control.

On distributed coordination in networks of cyber-physical systems.

This paper is concerned with the study of the global emerging behavior in complex networks where each node can be modeled as a cyber-physical system. We recast the problem of characterizing the behavior of such systems as a stability problem and give two technical results to assess this property. We then illustrate the effectiveness of our approach by considering two testbed examples arising in applications where networks, arising from Internet of Things applications, need to be designed so as to fulfill a given task.

Entrainment and synchronization in networks of Rayleigh-van der Pol oscillators with diffusive and Haken-Kelso-Bunz couplings.

We analyze a network of non-identical Rayleigh-van der Pol (RvdP) oscillators interconnected through either diffusive or nonlinear coupling functions. The work presented here extends existing results on the case of two nonlinearly coupled RvdP oscillators to the problem of considering a network of three or more of them. Specifically, we study synchronization and entrainment in networks of heterogeneous RvdP oscillators and contrast the effects of diffusive linear coupling strategies with the nonlinear Haken-Kelso-Bunz coupling, originally introduced to study human bimanual experiments. We show how convergence of the error among the nodes' trajectories toward a bounded region is possible with both linear and nonlinear coupling functions. Under the assumption that the network is connected, simple, and undirected, analytical results are obtained to prove boundedness of the error when the oscillators are coupled diffusively. All results are illustrated by way of numerical examples and compared with the experimental findings available in the literature on synchronization of people rocking chairs, confirming the effectiveness of the model we propose to capture some of the features of human group synchronization observed experimentally in the previous literature.

Synchronization and local convergence analysis of networks with dynamic diffusive coupling.

In this paper, we address the problem of achieving synchronization in networks of nonlinear units coupled by dynamic diffusive terms. We present two types of couplings consisting of a static linear term, corresponding to the diffusive coupling, and a dynamic term which can be either the integral or the derivative of the sum of the mismatches between the states of neighbouring agents. The resulting dynamic coupling strategy is a distributed proportional-integral (PI) or a proportional-derivative (PD) law that is shown to be effective in improving the network synchronization performance, for example, when the dynamics at nodes are nonidentical. We assess the stability of the network by extending the classical Master Stability Function approach to the case where the links are dynamic ones of PI/PD type. We validate our approach via a set of representative examples including networks of chaotic Lorenz and networks of nonlinear mechanical systems.

In-vivo real-time control of protein expression from endogenous and synthetic gene networks.

We describe an innovative experimental and computational approach to control the expression of a protein in a population of yeast cells. We designed a simple control algorithm to automatically regulate the administration of inducer molecules to the cells by comparing the actual protein expression level in the cell population with the desired expression level. We then built an automated platform based on a microfluidic device, a time-lapse microscopy apparatus, and a set of motorized syringes, all controlled by a computer. We tested the platform to force yeast cells to express a desired fixed, or time-varying, amount of a reporter protein over thousands of minutes. The computer automatically switched the type of sugar administered to the cells, its concentration and its duration, according to the control algorithm. Our approach can be used to control expression of any protein, fused to a fluorescent reporter, provided that an external molecule known to (indirectly) affect its promoter activity is available.

Data-driven stochastic modelling of zebrafish locomotion.

In this work, we develop a data-driven modelling framework to reproduce the locomotion of fish in a confined environment. Specifically, we highlight the primary characteristics of the motion of individual zebrafish (Danio rerio), and study how these can be suitably encapsulated within a mathematical framework utilising a limited number of calibrated model parameters. Using data captured from individual zebrafish via automated visual tracking, we develop a model using stochastic differential equations and describe fish as a self propelled particle moving in a plane. Based on recent experimental evidence of the importance of speed regulation in social behaviour, we extend stochastic models of fish locomotion by introducing experimentally-derived processes describing dynamic speed regulation. Salient metrics are defined which are then used to calibrate key parameters of coupled stochastic differential equations, describing both speed and angular speed of swimming fish. The effects of external constraints are also included, based on experimentally observed responses. Understanding the spontaneous dynamics of zebrafish using a bottom-up, purely data-driven approach is expected to yield a modelling framework for quantitative investigation of individual behaviour in the presence of various external constraints or biological assays.

Predicting and understanding human action decisions during skillful joint-action using supervised machine learning and explainable-AI.

This study investigated the utility of supervised machine learning (SML) and explainable artificial intelligence (AI) techniques for modeling and understanding human decision-making during multiagent task performance. Long short-term memory (LSTM) networks were trained to predict the target selection decisions of expert and novice players completing a multiagent herding task. The results revealed that the trained LSTM models could not only accurately predict the target selection decisions of expert and novice players but that these predictions could be made at timescales that preceded a player's conscious intent. Importantly, the models were also expertise specific, in that models trained to predict the target selection decisions of experts could not accurately predict the target selection decisions of novices (and vice versa). To understand what differentiated expert and novice target selection decisions, we employed the explainable-AI technique, SHapley Additive explanation (SHAP), to identify what informational features (variables) most influenced modelpredictions. The SHAP analysis revealed that experts were more reliant on information about target direction of heading and the location of coherders (i.e., other players) compared to novices. The implications and assumptions underlying the use of SML and explainable-AI techniques for investigating and understanding human decision-making are discussed.

Distributed control for geometric pattern formation of large-scale multirobot systems.

Introduction: Geometric pattern formation is crucial in many tasks involving large-scale multi-agent systems. Examples include mobile agents performing surveillance, swarms of drones or robots, and smart transportation systems. Currently, most control strategies proposed to achieve pattern formation in network systems either show good performance but require expensive sensors and communication devices, or have lesser sensor requirements but behave more poorly. Methods and result: In this paper, we provide a distributed displacement-based control law that allows large groups of agents to achieve triangular and square lattices, with low sensor requirements and without needing communication between the agents. Also, a simple, yet powerful, adaptation law is proposed to automatically tune the control gains in order to reduce the design effort, while improving robustness and flexibility. Results: We show the validity and robustness of our approach via numerical simulations and experiments, comparing it, where possible, with other approaches from the existing literature.

Ratiometric control of cell phenotypes in monostrain microbial consortia.

We address the problem of regulating and keeping at a desired balance the relative numbers between cells exhibiting a different phenotype within a monostrain microbial consortium. We propose a strategy based on the use of external control inputs, assuming each cell in the community is endowed with a reversible, bistable memory mechanism. Specifically, we provide a general analytical framework to guide the design of external feedback control strategies aimed at balancing the ratio between cells whose memory is stabilized at either one of two equilibria associated with different cell phenotypes. We demonstrate the stability and robustness properties of the control laws proposed and validate them in silico, implementing the memory element via a genetic toggle-switch. The proposed control framework may be used to allow long-term coexistence of different populations, with both industrial and biotechnological applications. As a representative example, we consider the realistic agent-based implementation of our control strategy to enable cooperative bioproduction of a dimer in a monostrain microbial consortium.

Control-Based Continuation: A New Approach to Prototype Synthetic Gene Networks.

Control-Based Continuation (CBC) is a general and systematic method to carry out the bifurcation analysis of physical experiments. CBC does not rely on a mathematical model and thus overcomes the uncertainty introduced when identifying bifurcation curves indirectly through modeling and parameter estimation. We demonstrate, in silico, CBC applicability to biochemical processes by tracking the equilibrium curve of a toggle switch, which includes additive process noise and exhibits bistability. We compare the results obtained when CBC uses a model-free and model-based control strategy and show that both can track stable and unstable solutions, revealing bistability. We then demonstrate CBC in conditions more representative of an in vivo experiment using an agent-based simulator describing cell growth and division, cell-to-cell variability, spatial distribution, and diffusion of chemicals. We further show how the identified curves can be used for parameter estimation and discuss how CBC can significantly accelerate the prototyping of synthetic gene regulatory networks.

Global entrainment of transcriptional systems to periodic inputs.

This paper addresses the problem of providing mathematical conditions that allow one to ensure that biological networks, such as transcriptional systems, can be globally entrained to external periodic inputs. Despite appearing obvious at first, this is by no means a generic property of nonlinear dynamical systems. Through the use of contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all their solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific cases of models of transcriptional systems as well as constructs of interest in synthetic biology. A self-contained exposition of all needed results is given in the paper.

Derivation, identification and validation of a computational model of a novel synthetic regulatory network in yeast.

Systems biology aims at building computational models of biological pathways in order to study in silico their behaviour and to verify biological hypotheses. Modelling can become a new powerful method in molecular biology, if correctly used. Here we present step-by-step the derivation and identification of the dynamical model of a biological pathway using a novel synthetic network recently constructed in the yeast Saccharomyces cerevisiae for In-vivo Reverse-Engineering and Modelling Assessment. This network consists of five genes regulating each other transcription. Moreover, it includes one protein-protein interaction, and its genes can be switched on by addition of galactose to the medium. In order to describe the network dynamics, we adopted a deterministic modelling approach based on non-linear differential equations. We show how, through iteration between experiments and modelling, it is possible to derive a semi-quantitative prediction of network behaviour and to better understand the biology of the pathway of interest.

Dynamic Input Deep Learning Control of Artificial Avatars in a Multi-Agent Joint Motor Task.

In many real-word scenarios, humans and robots are required to coordinate their movements in joint tasks to fulfil a common goal. While several examples regarding dyadic human robot interaction exist in the current literature, multi-agent scenarios in which one or more artificial agents need to interact with many humans are still seldom investigated. In this paper we address the problem of synthesizing an autonomous artificial agent to perform a paradigmatic oscillatory joint task in human ensembles while exhibiting some desired human kinematic features. We propose an architecture based on deep reinforcement learning which is flexible enough to make the artificial agent interact with human groups of different sizes. As a paradigmatic coordination task we consider a multi-agent version of the mirror game, an oscillatory motor task largely used in the literature to study human motor coordination.

Modeling Frequency Reduction in Human Groups Performing a Joint Oscillatory Task.

In human groups performing oscillatory tasks, it has been observed that the frequency of participants' oscillations reduces when compared to that acquired in solo. This experimental observation is not captured by the standard Kuramoto oscillators, often employed to model human synchronization. In this work, we aim at capturing this observed phenomenon by proposing three alternative modifications of the standard Kuramoto model that are based on three different biologically-relevant hypotheses underlying group synchronization. The three models are tuned, validated and compared against experiments on a group synchronization task, which is a multi-agent extension of the so-called mirror game.

Spontaneous emergence of leadership patterns drives synchronization in complex human networks.

Synchronization of human networks is fundamental in many aspects of human endeavour. Recently, much research effort has been spent on analyzing how motor coordination emerges in human groups (from rocking chairs to violin players) and how it is affected by coupling structure and strength. Here we uncover the spontaneous emergence of leadership (based on physical signaling during group interaction) as a crucial factor steering the occurrence of synchronization in complex human networks where individuals perform a joint motor task. In two experiments engaging participants in an arm movement synchronization task, in the physical world as well as in the digital world, we found that specific patterns of leadership emerged and increased synchronization performance. Precisely, three patterns were found, involving a subtle interaction between phase of the motion and amount of influence. Such patterns were independent of the presence or absence of physical interaction, and persisted across manipulated spatial configurations. Our results shed light on the mechanisms that drive coordination and leadership in human groups, and are consequential for the design of interactions with artificial agents, avatars or robots, where social roles can be determinant for a successful interaction.

Automatic synchronisation of the cell cycle in budding yeast through closed-loop feedback control.

The cell cycle is the process by which eukaryotic cells replicate. Yeast cells cycle asynchronously with each cell in the population budding at a different time. Although there are several experimental approaches to synchronise cells, these usually work only in the short-term. Here, we build a cyber-genetic system to achieve long-term synchronisation of the cell population, by interfacing genetically modified yeast cells with a computer by means of microfluidics to dynamically change medium, and a microscope to estimate cell cycle phases of individual cells. The computer implements a controller algorithm to decide when, and for how long, to change the growth medium to synchronise the cell-cycle across the population. Our work builds upon solid theoretical foundations provided by Control Engineering. In addition to providing an avenue for yeast cell cycle synchronisation, our work shows that control engineering can be used to automatically steer complex biological processes towards desired behaviours similarly to what is currently done with robots and autonomous vehicles.

Cheetah: A Computational Toolkit for Cybergenetic Control.

Advances in microscopy, microfluidics, and optogenetics enable single-cell monitoring and environmental regulation and offer the means to control cellular phenotypes. The development of such systems is challenging and often results in bespoke setups that hinder reproducibility. To address this, we introduce Cheetah, a flexible computational toolkit that simplifies the integration of real-time microscopy analysis with algorithms for cellular control. Central to the platform is an image segmentation system based on the versatile U-Net convolutional neural network. This is supplemented with functionality to robustly count, characterize, and control cells over time. We demonstrate Cheetah's core capabilities by analyzing long-term bacterial and mammalian cell growth and by dynamically controlling protein expression in mammalian cells. In all cases, Cheetah's segmentation accuracy exceeds that of a commonly used thresholding-based method, allowing for more accurate control signals to be generated. Availability of this easy-to-use platform will make control engineering techniques more accessible and offer new ways to probe and manipulate living cells.

ChipSeg: An Automatic Tool to Segment Bacterial and Mammalian Cells Cultured in Microfluidic Devices.

Extracting quantitative measurements from time-lapse images is necessary in external feedback control applications, where segmentation results are used to inform control algorithms. We describe ChipSeg, a computational tool that segments bacterial and mammalian cells cultured in microfluidic devices and imaged by time-lapse microscopy, which can be used also in the context of external feedback control. The method is based on thresholding and uses the same core functions for both cell types. It allows us to segment individual cells in high cell density microfluidic devices, to quantify fluorescent protein expression over a time-lapse experiment, and to track individual mammalian cells. ChipSeg enables robust segmentation in external feedback control experiments and can be easily customized for other experimental settings and research aims.

Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer.

We propose a method for achieving an optimal protocol of intermittent androgen suppression for the treatment of prostate cancer. Since the model that reproduces the dynamical behavior of the surrogate tumor marker, prostate specific antigen, is piecewise linear, we can obtain an analytical solution for the model. Based on this, we derive conditions for either stopping or delaying recurrent disease. The solution also provides a design principle for the most favorable schedule of treatment that minimizes the rate of expansion of the malignant cell population.