Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

New Forms of Collaboration Between the Social and Natural Sciences Could Become Necessary for Understanding Rapid Collective Transitions in Social Systems

Human societies are complex systems and as such have tipping points. They can rapidly transit from one mode of operation to another and thereby change the way they function as a whole. Such transitions appear as financial or economic crises, rapid swings in collective opinion, political regime shifts, or revolutions. In physics collective transitions are known as phase transitions; for example, water exists in states of liquid, ice, and vapor. A few variables determine which state is realized: temperature, pressure, and volume. For social systems it is less clear what determines collective social states. A better understanding of social tipping points would allow us to tackle some of the big challenges more systematically, such as polarization, loss of social cohesion, fragmentation, or the green transition. The physics concept of universality might be key to understanding some tipping points in human societies and why agent-based models (ABMs) might make sense for identifying the transition points. If universality exists in social systems there is hope that relatively simple ABMs will be sufficient for understanding collective social systems in transition; if it does not exist, highly detailed computational models will be unavoidable. Both are possible. Both need new forms of collaboration between the social and natural sciences, and new types of data will be essential.

Double transition in kinetic exchange opinion models with activation dynamics

In this work, we study a model of opinion dynamics considering activation/deactivation of agents. In other words, individuals are not static and can become inactive and drop out from the discussion. A probability [Formula: see text] governs the deactivation dynamics, whereas social interactions are ruled by kinetic exchanges, considering competitive positive/negative interactions. Inactive agents can become active due to interactions with active agents. Our analytical and numerical results show the existence of two distinct non-equilibrium phase transitions, with the occurrence of three phases, namely ordered (ferromagnetic-like), disordered (paramagnetic-like) and absorbing phases. The absorbing phase represents a collective state where all agents are inactive, i.e. they do not participate in the dynamics, inducing a frozen state. We determine the critical value [Formula: see text] above which the system is in the absorbing phase independently of the other parameters. We also verify a distinct critical behaviour for the transitions among different phases. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

Dynamics of diffusive cell signaling relays

In biological contexts as diverse as development, apoptosis, and synthetic microbial consortia, collections of cells or subcellular components have been shown to overcome the slow signaling speed of simple diffusion by utilizing diffusive relays, in which the presence of one type of diffusible signaling molecule triggers participation in the emission of the same type of molecule. This collective effect gives rise to fast-traveling diffusive waves. Here, in the context of cell signaling, we show that system dimensionality – the shape of the extracellular medium and the distribution of cells within it – can dramatically affect the wave dynamics, but that these dynamics are insensitive to details of cellular activation. As an example, we show that neutrophil swarming experiments exhibit dynamical signatures consistent with the proposed signaling motif. We further show that cell signaling relays generate much steeper concentration profiles than does simple diffusion, which may facilitate neutrophil chemotaxis.

Optical waveguiding by atomic entanglement in multilevel atom arrays

The optical properties of subwavelength arrays of atoms or other quantum emitters have attracted significant interest recently. For example, the strong constructive or destructive interference of emitted light enables arrays to function as nearly perfect mirrors, support topological edge states, and allow for exponentially better quantum memories. In these proposals, the assumed atomic structure was simple, consisting of a unique electronic ground state. Within linear optics, the system is then equivalent to a periodic array of classical dielectric particles, whose periodicity supports the emergence of guided modes. However, it has not been known whether such phenomena persist in the presence of hyperfine structure, as exhibited by most quantum emitters. Here, we show that waveguiding can arise from rich atomic entanglement as a quantum many-body effect and elucidate the necessary conditions. Our work represents a significant step forward in understanding collective effects in arrays of atoms with realistic electronic structure.

New Trends in Statistical Physics of Complex Systems

A challenging frontier in physics concerns the study of complex and disordered systems. [...].

Collective Behavior of Place and Non-place Neurons in the Hippocampal Network

Discussions of the hippocampus often focus on place cells, but many neurons are not place cells in any given environment. Here we describe the collective activity in such mixed populations, treating place and non-place cells on the same footing. We start with optical imaging experiments on CA1 in mice as they run along a virtual linear track and use maximum entropy methods to approximate the distribution of patterns of activity in the population, matching the correlations between pairs of cells but otherwise assuming as little structure as possible. We find that these simple models accurately predict the activity of each neuron from the state of all the other neurons in the network, regardless of how well that neuron codes for position. Our results suggest that understanding the neural activity may require not only knowledge of the external variables modulating it but also of the internal network state.

The dynamics of information-driven coordination phenomena: A transfer entropy analysis

Data from social media provide unprecedented opportunities to investigate the processes that govern the dynamics of collective social phenomena. We consider an information theoretical approach to define and measure the temporal and structural signatures typical of collective social events as they arise and gain prominence. We use the symbolic transfer entropy analysis of microblogging time series to extract directed networks of influence among geolocalized subunits in social systems. This methodology captures the emergence of system-level dynamics close to the onset of socially relevant collective phenomena. The framework is validated against a detailed empirical analysis of five case studies. In particular, we identify a change in the characteristic time scale of the information transfer that flags the onset of information-driven collective phenomena. Furthermore, our approach identifies an order-disorder transition in the directed network of influence between social subunits. In the absence of clear exogenous driving, social collective phenomena can be represented as endogenously driven structural transitions of the information transfer network. This study provides results that can help define models and predictive algorithms for the analysis of societal events based on open source data.

Public goods in relation to competition, cooperation, and spite

Public goods and common-pool resources are fundamental features of biological and social systems, and pose core challenges in achieving sustainability; for such situations, the immediate interests of individuals and the societies in which they are embedded are in potential conflict, involving game-theoretic considerations whose resolution need not serve the collective good. Evolution has often confronted such dilemmas--e.g., in bacterial biofilms--in the challenges of cancer, in nitrogen fixation and chelation, in the production of antibiotics, and in collective action problems across animal groups; there is much to learn from the Darwinian resolution of these situations for how to address problems our societies face today. Addressing these problems involves understanding the emergence of cooperative agreements, from reciprocal altruism and insurance arrangements to the social norms and more formal institutions that maintain societies. At the core are the issues of how individuals and societies discount the future and the interests of others, and the degree that individual decisions are influenced by regard for others. Ultimately, as Garrett Hardin suggested, the solution to problems of the commons is in "mutual coercion, mutually agreed upon," and hence in how groups of individuals form and how they arrive at decisions that ultimately benefit all.