Adilson E. Motter

Aleksandar Haber, Ferenc Molnar, Adilson E. Motter

A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system. However, network states are usually unknown, and only a fraction of the state variables are directly measurable. The observability problem concerns reconstructing the network state from this limited information. Here, we propose a general optimization-based approach for observing the states of nonlinear networks and for optimally selecting the observed variables. Our results reveal several fundamental limitations in network observability, such as the trade-off between the fraction of observed variables and the observation length on one side, and the estimation error on the other side. We also show that owing to the crucial role played by the dynamics, purely graph- theoretic observability approaches cannot provide conclusions about one's practical ability to estimate the states. We demonstrate the effectiveness of our methods by finding the key components in biological and combustion reaction networks from which we determine the full system state. Our results can lead to the design of novel sensing principles that can greatly advance prediction and control of the dynamics of such networks.

Reka Albert, John Baillieul, Adilson E. Motter

The emerging field at the intersection of quantitative biology, network modeling, and control theory has enjoyed significant progress in recent years. This Special Issue brings together a selection of papers on complementary approaches to observe, identify, and control biological and biologically inspired networks. These approaches advance the state of the art in the field by addressing challenges common to many such networks, including high dimensionality, strong nonlinearity, uncertainty, and limited opportunities for observation and intervention. Because these challenges are not unique to biological systems, it is expected that many of the results presented in these contributions will also find applications in other domains, including physical, social, and technological networks.

Arthur N. Montanari, Francesco Bullo, Dmitry Krotov et al.

Recent advances at the intersection of control theory, neuroscience, and machine learning have revealed novel mechanisms by which dynamical systems perform computation. These advances encompass a wide range of conceptual, mathematical, and computational ideas, with applications for model learning and training, memory retrieval, data-driven control, and optimization. This tutorial focuses on neuro-inspired approaches to computation that aim to improve scalability, robustness, and energy efficiency across such tasks, bridging the gap between artificial and biological systems. Particular emphasis is placed on energy-based dynamical models that encode information through gradient flows and energy landscapes. We begin by reviewing classical formulations, such as continuous-time Hopfield networks and Boltzmann machines, and then extend the framework to modern developments. These include dense associative memory models for high-capacity storage, oscillator-based networks for large-scale optimization, and proximal-descent dynamics for composite and constrained reconstruction. The tutorial demonstrates how control-theoretic principles can guide the design of next-generation neurocomputing systems, steering the discussion beyond conventional feedforward and backpropagation-based approaches to artificial intelligence.

Thomas P. Wytock, Adilson E. Motter

Recent developments in synthetic biology, next-generation sequencing, and machine learning provide an unprecedented opportunity to rationally design new disease treatments based on measured responses to gene perturbations and drugs to reprogram cells. The main challenges to seizing this opportunity are the incomplete knowledge of the cellular network and the combinatorial explosion of possible interventions, both of which are insurmountable by experiments. To address these challenges, we develop a transfer learning approach to control cell behavior that is pre-trained on transcriptomic data associated with human cell fates, thereby generating a model of the network dynamics that can be transferred to specific reprogramming goals. The approach combines transcriptional responses to gene perturbations to minimize the difference between a given pair of initial and target transcriptional states. We demonstrate our approach's versatility by applying it to a microarray dataset comprising >9,000 microarrays across 54 cell types and 227 unique perturbations, and an RNASeq dataset consisting of >10,000 sequencing runs across 36 cell types and 138 perturbations. Our approach reproduces known reprogramming protocols with an AUROC of 0.91 while innovating over existing methods by pre-training an adaptable model that can be tailored to specific reprogramming transitions. We show that the number of gene perturbations required to steer from one fate to another increases with decreasing developmental relatedness and that fewer genes are needed to progress along developmental paths than to regress. These findings establish a proof-of-concept for our approach to computationally design control strategies and provide insights into how gene regulatory networks govern phenotype.

Thomas P. Wytock, Adilson E. Motter

The relationship between microscopic observations and macroscopic behavior is a fundamental open question in biophysical systems. Here, we develop a unified approach that---in contrast with existing methods---predicts cell type from macromolecular data even when accounting for the scale of human tissue diversity and limitations in the available data. We achieve these benefits by applying a k-nearest-neighbors algorithm after projecting our data onto the eigenvectors of the correlation matrix inferred from many observations of gene expression or chromatin conformation. Our approach identifies variations in epigenotype that impact cell type, thereby supporting the cell type attractor hypothesis and representing the first step toward model-independent control strategies in biological systems.

Eduardo G. Altmann, Zakary L. Whichard, Adilson E. Motter

The word-stock of a language is a complex dynamical system in which words can be created, evolve, and become extinct. Even more dynamic are the short-term fluctuations in word usage by individuals in a population. Building on the recent demonstration that word niche is a strong determinant of future rise or fall in word frequency, here we introduce a model that allows us to distinguish persistent from temporary increases in frequency. Our model is illustrated using a 10^8-word database from an online discussion group and a 10^11-word collection of digitized books. The model reveals a strong relation between changes in word dissemination and changes in frequency. Aside from their implications for short-term word frequency dynamics, these observations are potentially important for language evolution as new words must survive in the short term in order to survive in the long term.