Competition and synergy of Arp2/3 and formins in nucleating actin waves.

Actin assembly and dynamics are crucial for maintaining cell structure and changing physiological states. The broad impact of actin on various cellular processes makes it challenging to dissect the specific role of actin regulatory proteins. Using actin waves that propagate on the cortex of mast cells as a model, we discovered that formins (FMNL1 and mDia3) are recruited before the Arp2/3 complex in actin waves. GTPase Cdc42 interactions drive FMNL1 oscillations, with active Cdc42 and the constitutively active mutant of FMNL1 capable of forming waves on the plasma membrane independently of actin waves. Additionally, the delayed recruitment of Arp2/3 antagonizes FMNL1 and active Cdc42. This antagonism is not due to competition for monomeric actin but rather for their common upstream regulator, active Cdc42, whose levels are negatively regulated by Arp2/3 via SHIP1 recruitment. Collectively, our study highlights the complex feedback loops in the dynamic control of the actin cytoskeletal network.

Emergent perceptual biases from state-space geometry in trained spiking recurrent neural networks.

A stimulus held in working memory is perceived as contracted toward the average stimulus. This contraction bias has been extensively studied in psychophysics, but little is known about its origin from neural activity. By training recurrent networks of spiking neurons to discriminate temporal intervals, we explored the causes of this bias and how behavior relates to population firing activity. We found that the trained networks exhibited animal-like behavior. Various geometric features of neural trajectories in state space encoded warped representations of the durations of the first interval modulated by sensory history. Formulating a normative model, we showed that these representations conveyed a Bayesian estimate of the interval durations, thus relating activity and behavior. Importantly, our findings demonstrate that Bayesian computations already occur during the sensory phase of the first stimulus and persist throughout its maintenance in working memory, until the time of stimulus comparison.

Identifying behavioral links to neural dynamics of multifiber photometry recordings in a mouse social behavior network.

Objective.Distributed hypothalamic-midbrain neural circuits help orchestrate complex behavioral responses during social interactions. Given rapid advances in optical imaging, it is a fundamental question how population-averaged neural activity measured by multi-fiber photometry (MFP) for calcium fluorescence signals correlates with social behaviors is a fundamental question. This paper aims to investigate the correspondence between MFP data and social behaviors.Approach:We propose a state-space analysis framework to characterize mouse MFP data based on dynamic latent variable models, which include a continuous-state linear dynamical system and a discrete-state hidden semi-Markov model. We validate these models on extensive MFP recordings during aggressive and mating behaviors in male-male and male-female interactions, respectively.Main results:Our results show that these models are capable of capturing both temporal behavioral structure and associated neural states, and produce interpretable latent states. Our approach is also validated in computer simulations in the presence of known ground truth.Significance:Overall, these analysis approaches provide a state-space framework to examine neural dynamics underlying social behaviors and reveals mechanistic insights into the relevant networks.

Temporal information in the anterior cingulate cortex relates to accumulated experiences.

Anterior cingulate cortex (ACC) activity is important for operations that require the ability to integrate multiple experiences over time, such as rule learning, cognitive flexibility, working memory, and long-term memory recall. To shed light on this, we analyzed neuronal activity while rats repeated the same behaviors during hour-long sessions to investigate how activity changed over time. We recorded neuronal ensembles as rats performed a decision-free operant task with varying reward likelihoods at three different response ports (n = 5). Neuronal state space analysis revealed that each repetition of a behavior was distinct, with more recent behaviors more similar than those further apart in time. ACC activity was dominated by a slow, gradual change in low-dimensional representations of neural state space aligning with the pace of behavior. Temporal progression, or drift, was apparent on the top principal component for every session and was driven by the accumulation of experiences and not an internal clock. Notably, these signals were consistent across subjects, allowing us to accurately predict trial numbers based on a model trained on data from a different animal. We observed that non-continuous ramping firing rates over extended durations (tens of minutes) drove the low-dimensional ensemble representations. 40% of ACC neurons' firing ramped over a range of trial lengths and combinations of shorter duration ramping neurons created ensembles that tracked longer durations. These findings provide valuable insights into how the ACC, at an ensemble level, conveys temporal information by reflecting the accumulation of experiences over extended periods.

Exploring the Effects of Instruction and Game Design on Youth Soccer Players' Skill Involvement and Cooperative Team Behaviour.

Objectives: The relationship between task constraints and player behaviors is of interest to coaches tasked with designing practice to optimize learning. This study aims to compare the skill involvements and cooperative team behavior of teams of youth soccer players engaged in a goal exaggeration and/or a prescriptive coach instruction condition compared to a free-play control condition. Methods: Twenty male soccer players aged 12-15 participated in small-sided games under four conditions: free-play, goal exaggeration, prescriptive coach instruction, and combination over four weeks. Using video footage, teams' collective skill involvements (shot, pass, dribble) and passing network characteristics (closeness, density, and betweenness) were measured for each game. Results: A Friedmans rank test identified that playing conditions resulted in significant differences in attempted dribbles (p < .001), goals scored (p < .001), network density (p = .001), closeness (p < .001) and betweenness (p = .002). Teams attempted to dribble the most in the free-play and goal-exaggeration conditions, and the most goals were scored in the goal-exaggeration and combination conditions. Additionally, teams exhibited more well-connected passing networks (i.e. higher density, higher closeness, and lower betweenness values) in the combination condition and higher network density in the explicit instruction condition. Conclusions: The results of this study indicate that coach instruction may be more associated with cooperative team behavior, whereas free-play or manipulating task constraints in the absence of instruction may be associated with players attempting more individual actions.

Similarity in evoked responses does not imply similarity in macroscopic network states.

It is commonplace in neuroscience to assume that if two tasks activate the same brain areas in the same way, then they are recruiting the same underlying networks. Yet computational theory has shown that the same pattern of activity can emerge from many different underlying network representations. Here we evaluated whether similarity in activation necessarily implies similarity in network architecture by comparing region-wise activation patterns and functional correlation profiles from a large sample of healthy subjects (N = 242). Participants performed two executive control tasks known to recruit nearly identical brain areas, the color-word Stroop task and the Multi-Source Interference Task (MSIT). Using a measure of instantaneous functional correlations, based on edge time series, we estimated the task-related networks that differed between incongruent and congruent conditions. We found that the two tasks were much more different in their network profiles than in their evoked activity patterns at different analytical levels, as well as for a wide range of methodological pipelines. Our results reject the notion that having the same activation patterns means two tasks engage the same underlying representations, suggesting that task representations should be independently evaluated at both node and edge (connectivity) levels.

As a dynamical system, the brain can encode information at the module (e.g., brain regions) or the network level (e.g., connections between brain regions). This means that two tasks can produce the same pattern of activation, but differ in their network profile. Here we tested this using two tasks with largely similar cognitive requirements. Despite producing nearly identical macroscopic activation patterns, the two tasks produced different functional network profiles. These findings confirm prior theoretical work that similarity in task activation does not imply the same similarity in underlying network states.

Time-dependent ligand-receptor binding kinetics and functionality in a heterodimeric receptor model.

GPCRs heteromerize both in CNS and non-CNS regions. The cell uses receptor heteromerization to modulate receptor functionality and to provide fine tuning of receptor signaling. In order for pharmacologists to explore these mechanisms for therapeutic purposes, quantitative receptor models are needed. We have developed a time-dependent model of the binding kinetics and functionality of a preformed heterodimeric receptor involving two drugs. Two cases were considered: both or only one of the drugs are in excess with respect to the total concentration of the receptor. The latter case can be applied to those situations in which a drug causes unwanted side effects that need to be reduced by decreasing its concentration. The required efficacy can be maintained by the allosteric effects mutually exerted by the two drugs in the two-drug combination system. We discuss this concept assuming that the drug causing unwanted side effects is an opioid and that analgesia is the therapeutic effect. As additional points, allosteric modulation by endogenous compounds and synthetic bivalent ligands was included in the study. Receptor heteromerization offers a mechanistic understanding and quantification of the pharmacological effects elicited by combinations of two drugs at different doses and with different efficacies and cooperativity effects, thus providing a conceptual framework for drug combination therapy.

Generation of genetic codes with 2-adic codon algebra and adaptive dynamics.

This is a brief review on modeling genetic codes with the aid of 2-adic dynamical systems. In this model amino acids are encoded by the attractors of such dynamical systems. Each genetic code is coupled to the special class of 2-adic dynamics. We consider the discrete dynamical systems, These are the iterations of a function F:Z2→Z2, where Z2 is the ring of 2-adic numbers (2-adic tree). A genetic code is characterized by the set of attractors of a function belonging to the code generating functional class. The main mathematical problem is to reduce degeneration of dynamic representation and select the optimal generating function. Here optimality can be treated in many ways. One possibility is to consider the Lipschitz functions playing the crucial role in general theory of iterations. Then we minimize the Lip-constant. The main issue is to find the proper biological interpretation of code-functions. One can speculate that the evolution of the genetic codes can be described in information space of the nucleotide-strings endowed with ultrametric (treelike) geometry. A code-function is a fitness function; the solutions of the genetic code optimization problem are attractors of the code-function. We illustrate this approach by generation of the standard nuclear and (vertebrate) mitochondrial genetics codes.

Recurrent flow patterns as a basis for two-dimensional turbulence: Predicting statistics from structures.

A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space [Hopf, Commun. Appl. Maths 1, 303 (1948)]. The chaotic dynamics are shaped by the unstable simple invariant solutions populating the inertial manifold. The hope has been to turn this picture into a predictive framework where the statistics of the flow follow from a weighted sum of the statistics of each simple invariant solution. Two outstanding obstacles have prevented this goal from being achieved: 1) paucity of known solutions and 2) the lack of a rational theory for predicting the required weights. Here, we describe a method to substantially solve these problems, and thereby provide compelling evidence that the probability density functions (PDFs) of a fully developed turbulent flow can be reconstructed with a set of unstable periodic orbits. Our method for finding solutions uses automatic differentiation, with high-quality guesses constructed by minimizing a trajectory-dependent loss function. We use this approach to find hundreds of solutions in turbulent, two-dimensional Kolmogorov flow. Robust statistical predictions are then computed by learning weights after converting a turbulent trajectory into a Markov chain for which the states are individual solutions, and the nearest solution to a given snapshot is determined using a deep convolutional autoencoder. In this study, the PDFs of a spatiotemporally chaotic system have been successfully reproduced with a set of simple invariant states, and we provide a fascinating connection between self-sustaining dynamical processes and the more well-known statistical properties of turbulence.

A mathematical framework for measuring and tuning tempo in developmental gene regulatory networks.

Embryo development is a dynamic process governed by the regulation of timing and sequences of gene expression, which control the proper growth of the organism. Although many genetic programmes coordinating these sequences are common across species, the timescales of gene expression can vary significantly among different organisms. Currently, substantial experimental efforts are focused on identifying molecular mechanisms that control these temporal aspects. In contrast, the capacity of established mathematical models to incorporate tempo control while maintaining the same dynamical landscape remains less understood. Here, we address this gap by developing a mathematical framework that links the functionality of developmental programmes to the corresponding gene expression orbits (or landscapes). This unlocks the ability to find tempo differences as perturbations in the dynamical system that preserve its orbits. We demonstrate that this framework allows for the prediction of molecular mechanisms governing tempo, through both numerical and analytical methods. Our exploration includes two case studies: a generic network featuring coupled production and degradation, with a particular application to neural progenitor differentiation; and the repressilator. In the latter, we illustrate how altering the dimerisation rates of transcription factors can decouple the tempo from the shape of the resulting orbits. We conclude by highlighting how the identification of orthogonal molecular mechanisms for tempo control can inform the design of circuits with specific orbits and tempos.

Discovering optimal kinetic pathways for self-assembly using automatic differentiation.

Macromolecular complexes are often composed of diverse subunits. The self-assembly of these subunits is inherently nonequilibrium and must avoid kinetic traps to achieve high yield over feasible timescales. We show how the kinetics of self-assembly benefits from diversity in subunits because it generates an expansive parameter space that naturally improves the "expressivity" of self-assembly, much like a deeper neural network. By using automatic differentiation algorithms commonly used in deep learning, we searched the parameter spaces of mass-action kinetic models to identify classes of kinetic protocols that mimic biological solutions for productive self-assembly. Our results reveal how high-yield complexes that easily become kinetically trapped in incomplete intermediates can instead be steered by internal design of rate-constants or external and active control of subunits to efficiently assemble. Internal design of a hierarchy of subunit binding rates generates self-assembly that can robustly avoid kinetic traps for all concentrations and energetics, but it places strict constraints on selection of relative rates. External control via subunit titration is more versatile, avoiding kinetic traps for any system without requiring molecular engineering of binding rates, albeit less efficiently and robustly. We derive theoretical expressions for the timescales of kinetic traps, and we demonstrate our optimization method applies not just for design but inference, extracting intersubunit binding rates from observations of yield-vs.-time for a heterotetramer. Overall, we identify optimal kinetic protocols for self-assembly as a powerful mechanism to achieve efficient and high-yield assembly in synthetic systems whether robustness or ease of "designability" is preferred.

Exploring Simplicity Bias in 1D Dynamical Systems.

Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input-output maps. This phenomenon is known as simplicity bias. By viewing the parameters of dynamical systems as inputs, and the resulting (digitised) trajectories as outputs, we study simplicity bias in the logistic map, Gauss map, sine map, Bernoulli map, and tent map. We find that the logistic map, Gauss map, and sine map all exhibit simplicity bias upon sampling of map initial values and parameter values, but the Bernoulli map and tent map do not. The simplicity bias upper bound on the output pattern probability is used to make a priori predictions regarding the probability of output patterns. In some cases, the predictions are surprisingly accurate, given that almost no details of the underlying dynamical systems are assumed. More generally, we argue that studying probability-complexity relationships may be a useful tool when studying patterns in dynamical systems.

Linking fast and slow: The case for generative models.

A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable longer, more naturalistic neuronal recordings. The implicit opportunity for understanding the self-organised brain calls for new analysis methods that link temporal scales: from the order of milliseconds over which neuronal dynamics evolve, to the order of minutes, days, or even years over which experimental observations unfold. This review article demonstrates how hierarchical generative models and Bayesian inference help to characterise neuronal activity across different time scales. Crucially, these methods go beyond describing statistical associations among observations and enable inference about underlying mechanisms. We offer an overview of fundamental concepts in state-space modeling and suggest a taxonomy for these methods. Additionally, we introduce key mathematical principles that underscore a separation of temporal scales, such as the slaving principle, and review Bayesian methods that are being used to test hypotheses about the brain with multiscale data. We hope that this review will serve as a useful primer for experimental and computational neuroscientists on the state of the art and current directions of travel in the complex systems modelling literature.

Mathematical Modeling of Photo- and Thermomorphogenesis in Plants.

Increased day lengths and warm conditions inversely affect plant growth by directly modulating nuclear phyB, ELF3, and COP1 levels. Quantitative measures of the hypocotyl length have been key to gaining a deeper understanding of this complex regulatory network, while similar quantitative data are the foundation for many studies in plant biology. Here, we explore the application of mathematical modeling, specifically ordinary differential equations (ODEs), to understand plant responses to these environmental cues. We provide a comprehensive guide to constructing, simulating, and fitting these models to data, using the law of mass action to study the evolution of molecular species. The fundamental principles of these models are introduced, highlighting their utility in deciphering complex plant physiological interactions and testing hypotheses. This brief introduction will not allow experimentalists without a mathematical background to run their own simulations overnight, but it will help them grasp modeling principles and communicate with more theory-inclined colleagues.

Neurobiological Causal Models of Language Processing.

The language faculty is physically realized in the neurobiological infrastructure of the human brain. Despite significant efforts, an integrated understanding of this system remains a formidable challenge. What is missing from most theoretical accounts is a specification of the neural mechanisms that implement language function. Computational models that have been put forward generally lack an explicit neurobiological foundation. We propose a neurobiologically informed causal modeling approach which offers a framework for how to bridge this gap. A neurobiological causal model is a mechanistic description of language processing that is grounded in, and constrained by, the characteristics of the neurobiological substrate. It intends to model the generators of language behavior at the level of implementational causality. We describe key features and neurobiological component parts from which causal models can be built and provide guidelines on how to implement them in model simulations. Then we outline how this approach can shed new light on the core computational machinery for language, the long-term storage of words in the mental lexicon and combinatorial processing in sentence comprehension. In contrast to cognitive theories of behavior, causal models are formulated in the "machine language" of neurobiology which is universal to human cognition. We argue that neurobiological causal modeling should be pursued in addition to existing approaches. Eventually, this approach will allow us to develop an explicit computational neurobiology of language.

Modelling motion energy in psychotherapy: A dynamical systems approach.

In this study we introduce an innovative mathematical and statistical framework for the analysis of motion energy dynamics in psychotherapy sessions. Our method combines motion energy dynamics with coupled linear ordinary differential equations and a measurement error model, contributing new clinical parameters to enhance psychotherapy research. Our approach transforms raw motion energy data into an interpretable account of therapist-patient interactions, providing novel insights into the dynamics of these interactions. A key aspect of our framework is the development of a new measure of synchrony between the motion energies of therapists and patients, which holds significant clinical and theoretical value in psychotherapy. The practical applicability and effectiveness of our modelling and estimation framework are demonstrated through the analysis of real session data. This work advances the quantitative analysis of motion dynamics in psychotherapy, offering important implications for future research and therapeutic practice.

A geometrical model of cell fate specification in the mouse blastocyst.

The lineage decision that generates the epiblast and primitive endoderm from the inner cell mass (ICM) is a paradigm for cell fate specification. Recent mathematics has formalized Waddington's landscape metaphor and proven that lineage decisions in detailed gene network models must conform to a small list of low-dimensional stereotypic changes called bifurcations. The most plausible bifurcation for the ICM is the so-called heteroclinic flip that we define and elaborate here. Our re-analysis of recent data suggests that there is sufficient cell movement in the ICM so the FGF signal, which drives the lineage decision, can be treated as spatially uniform. We thus extend the bifurcation model for a single cell to the entire ICM by means of a self-consistently defined time-dependent FGF signal. This model is consistent with available data and we propose additional dynamic experiments to test it further. This demonstrates that simplified, quantitative and intuitively transparent descriptions are possible when attention is shifted from specific genes to lineages. The flip bifurcation is a very plausible model for any situation where the embryo needs control over the relative proportions of two fates by a morphogen feedback.

Robust inference of causality in high-dimensional dynamical processes from the Information Imbalance of distance ranks.

We introduce an approach which allows detecting causal relationships between variables for which the time evolution is available. Causality is assessed by a variational scheme based on the Information Imbalance of distance ranks, a statistical test capable of inferring the relative information content of different distance measures. We test whether the predictability of a putative driven system Y can be improved by incorporating information from a potential driver system X, without explicitly modeling the underlying dynamics and without the need to compute probability densities of the dynamic variables. This framework makes causality detection possible even between high-dimensional systems where only few of the variables are known or measured. Benchmark tests on coupled chaotic dynamical systems demonstrate that our approach outperforms other model-free causality detection methods, successfully handling both unidirectional and bidirectional couplings. We also show that the method can be used to robustly detect causality in human electroencephalography data.

Understanding behavioral and cognitive dispositions as subsystem topologies within cognitive models: A proposal.

In our 2023 paper, entitled "Modeling interactions between the embodied and the narrative self: Dynamics of the self-pattern within LIDA," Kugele, Newen, Franklin, and I propose a functional description and implementation of a central element of Gallagher & Newen's pattern theory of self, which identifies an agent's self with a dynamic pattern of so-called cognitive aspects which govern their thought and behavior (Gallagher, 2013; Newen, 2018; Gallagher & Daly, 2018). The pattern theory explicitly rejects the traditional conceptualization of the self as a unitary entity with certain properties that resides within agents, with the idea of a pattern of aspects being central to its ability to account for the dynamic, yet relatively stable development of most natural agents' selves. Implementing the pattern theory within Learning Intelligent Distribution Agent revealed that, in order for a cognitive architecture to account for both the dynamic and stable nature of an agent's self-pattern, aspects of that pattern had to be realized by dispositions of the agent to either think or act in a certain way. In this commentary, I argue that this fundamental role of dispositions extends to cognitive processes in general and that cognitive systems should be understood in terms of the dynamical interactions of dispositions over time. In order to facilitate such an understanding, dispositions will have to be identified with topologies of cognitive (sub)systems. I provide an example of such a topology by reference to informational topologies in neuronal systems.

The selfish network: how the brain preserves behavioral function through shifts in neuronal network state.

Neuronal networks possess the ability to regulate their activity states in response to disruptions. How and when neuronal networks turn from physiological into pathological states, leading to the manifestation of neuropsychiatric disorders, remains largely unknown. Here, we propose that neuronal networks intrinsically maintain network stability even at the cost of neuronal loss. Despite the new stable state being potentially maladaptive, neural networks may not reverse back to states associated with better long-term outcomes. These maladaptive states are often associated with hyperactive neurons, marking the starting point for activity-dependent neurodegeneration. Transitions between network states may occur rapidly, and in discrete steps rather than continuously, particularly in neurodegenerative disorders. The self-stabilizing, metastable, and noncontinuous characteristics of these network states can be mathematically described as attractors. Maladaptive attractors may represent a distinct pathophysiological entity that could serve as a target for new therapies and for fostering resilience.