Dynamical Systems seminars

Living cells contain millions of enzymes and proteins, which carry out multiple reactions simultaneously. To optimize these processes, cells compartmentalize reactions in membraneless liquid condensates. Certain features of cellular condensates can be explained by principles of liquid-liquid phase separation studied in material science. However, biological condensates exist in the inherently out of equilibrium environment of a living cell, being driven by force-generating microscopic processes. These cellular conditions are fundamentally different than the equilibrium conditions of liquid-liquid phase separation studied in materials science and physics. How condensates function in the active riotous environment of a cell is essential for understanding of cellular functions, as well as to the onset of neurodegenerative diseases. Currently, we lack model systems that enable rigorous studies of these processes. Living cells are too complex for quantitative analysis, while reconstituted equilibrium condensates fail to capture the non-equilibrium environment of biological cells. To bridge this gap, we reconstituted a DNA based membraneless condensates in an active environment that mimics the conditions of a living cell. We combine condensates with a reconstituted network of cytoskeletal filaments and molecular motors, and study how the mechanical interactions change the phase behavior and dynamics of membraneless structures. Studying these composite materials elucidates the fundamental physics rules that govern the behavior of liquid-liquid phase separation away from equilibrium while providing insight into the mechanism of condensate phase separation in cellular environments.

When listening to music, we typically lock onto and move to a beat (1-6 Hz). Behavioral studies on such synchronization (Repp 2005) abound, yet the neural mechanisms remain poorly understood. Some models hypothesize an array of self-sustaining entrainable neural oscillators that resonate when forced with rhythmic stimuli (Large et al. 2010). In contrast, our formulation focuses on event time estimation and plasticity: a neuronal beat generator that adapts its intrinsic frequency and phase to match the extermal rhythm. The model quickly learns new rhythms, within a few cycles as found in human behavior. When the stimulus is removed the beat generator continues to produce the learned rhythm in accordance with a synchronization continuation task.

Dr. Rajan and her lab design neural network models based on experimental data, and reverse-engineer them to figure out how brain circuits function in health and disease. They recently developed a powerful framework for tracing neural paths across multiple brain regions— called Current-Based Decomposition (CURBD). This new approach enables the computation of excitatory and inhibitory input currents that drive a given neuron, aiding in the discovery of how entire populations of neurons behave across multiple interacting brain regions. Dr. Rajan’s team has applied this method to studying the neural underpinnings of behavior. As an example, when CURBD was applied to data gathered from an animal model often used to study depression- and anxiety-like behaviors (i.e., learned helplessness) the underlying biology driving adaptive and maladaptive behaviors in the face of stress was revealed. With this framework Dr. Rajan's team probes for mechanisms at work across brain regions that support both healthy and disease states-- as well as identify key divergences from multiple different nervous systems, including zebrafish, mice, non-human primates, and humans.

Cells and microorganisms produce and consume all sorts of chemicals, from nutrients to signalling molecules. The same happens at the nanoscale inside cells themselves, where enzymes catalyse the production and consumption of the chemicals needed for life. In this work, we have found a generic mechanism by which such chemically-active particles, be it cells or enzymes or engineered synthetic colloids, can "sense" each other and ultimately self- organize in a multitude of ways. A peculiarity of these chemical-mediated interactions is that they break action-reaction symmetry : for example, one particle may be repelled from a second particle, which is in turn attracted to the first one, so that it ends up "chasing" it. Such chasing interactions allow for the formation of large clusters of particles that "swim" autonomously. Regarding enzymes, we find that they can spontaneously aggregate into clusters with precisely the right composition, so that the product of one enzyme is passed on, without lack or excess, to the next enzyme in the metabolic cascade.

Sylvia Serfaty studies the many-particle limit of systems driven by Coulomb or Riesz interactions through gradient flows or analogous conservative dynamics, possibly with added random diffusion. The Riesz interaction has inverse-distance exponent s between d−2 and d in dimension d. The talk presents convergence, as the number of particles tends to infinity, to the expected mean-field evolution. It also discusses deriving the Vlasov–Poisson equation from Newtonian dynamics in the monokinetic case and related results for Ginzburg–Landau vortex dynamics.

Constraints on control-dependent processing have become a fundamental concept in general theories of cognition that explain human behavior in terms of rational adaptations to these constraints. However, theories miss a rationale for why such constraints would exist in the first place. Recent work suggests that constraints on the allocation of control facilitate flexible task switching at the expense of the stability needed to support goal-directed behavior in face of distraction. We formulate this problem in a dynamical system, in which control signals are represented as attractors and in which constraints on control allocation limit the depth of these attractors. We derive formal expressions of the stability-flexibility tradeoff, showing that constraints on control allocation improve cognitive flexibility but impair cognitive stability. We provide evidence that human participants adapt higher constraints on the allocation of control as the demand for flexibility increases but that participants deviate from optimal constraints. In continuing work, we are investigating how collaborative performance of a group of individuals can benefit from individual differences defined in terms of balance between cognitive stability and flexibility.

Despite the recent success of deep learning in artificial intelligence, the lack of biological plausibility and labeled data in natural learning still poses a challenge in understanding biological learning. At the other extreme lies Hebbian learning, the simplest local and unsupervised one, yet considered to be computationally less efficient. In this talk, I would introduce a novel method to infer the form of Hebbian learning from in vivo data. Applying the method to the data obtained from the monkey inferior temporal cortex for the recognition task indicates how Hebbian learning changes the dynamic properties of the circuits and may promote brain oscillation. Notably, recent electrophysiological data observed in rodent V1 showed that the effect of visual experience on direction selectivity was similar to that observed in monkey data and provided strong validation of asymmetric changes of feedforward and recurrent synaptic strengths inferred from monkey data. This may suggest a general learning principle underlying the same computation, such as familiarity detection across different features represented in different brain regions.

Active particles which are self-propelled by converting energy into mechanical motion represent an expanding research realm in physics and chemistry. For micron-sized particles moving in a liquid (``microswimmers''), most of the basic features have been described by using the model of overdamped active Brownian motion [1]. However, for macroscopic particles or microparticles moving in a gas, inertial effects become relevant such that the dynamics is underdamped. Therefore, recently, active particles with inertia have been described by extending the active Brownian motion model to active Langevin dynamics which include inertia [2]. In this talk, recent developments of active particles with inertia (``microflyers'', ``hoppers'' or ``runners'') are summarized including: inertial delay effects between particle velocity and self-propulsion direction [3], tuning of the long-time self-diffusion by the moment of inertia [3], the influence of inertia on motility-induced phase separation and the cluster growth exponent [4], and the formation of active micelles (“rotelles”) by using inertial active surfactants. References [1] C. Bechinger, R. di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, G. Volpe, Reviews of Modern Physics 88, 045006 (2016). [2] H. Löwen, Journal of Chemical Physics 152, 040901 (2020). [3] C. Scholz, S. Jahanshahi, A. Ldov, H. Löwen, Nature Communications 9, 5156 (2018). [4] S. Mandal, B. Liebchen, H. Löwen, Physical Review Letters 123, 228001 (2019). [5] C. Scholz, A. Ldov, T. Pöschel, M. Engel, H. Löwen, Surfactants and rotelles in active chiral fluids, will be published

This talk will focus on different aspects of the Local Field Potential (LFP) signal. Classically, LFP fluctuations are related to changes in the functional state of the cortex. Yet, the mechanisms linking LFP changes with the state of the cortex are not well understood. The presentation will start with a brief explanation of the main oscillatory components of the LFP signal, how these different oscillatory components are generated at cortical microcircuits, and how their dynamics can be studied across multiple areas. Thereafter, a case study of a patient with akinetic mutism will be presented, linking cortical states with the behavior of the patient, as well as some preliminary results about how the LF cortical microcircuit dynamic changes modulate different cortical states and how these changes are reflected in the LFP signal

The ability to simultaneously record the activity from tens to thousands to tens of thousands of neurons has allowed us to analyze the computational role of population activity as opposed to single neuron activity. Recent work on a variety of cortical areas suggests that neural function may be built on the activation of population-wide activity patterns, the neural modes, rather than on the independent modulation of individual neural activity. These neural modes, the dominant covariation patterns within the neural population, define a low dimensional neural manifold that captures most of the variance in the recorded neural activity. We refer to the time-dependent activation of the neural modes as their latent dynamics, and argue that latent cortical dynamics within the manifold are the fundamental and stable building blocks of neural population activity. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2021-03-17. Recording duration: 00:47:16.

Rajanlab designs neural network models constrained by experimental data, and reverse engineers them to figure out how brain circuits function in health and disease. Recently, we have been developing a powerful new theory-based framework for “in-vivo tract tracing” from multi-regional neural activity collected experimentally. We call this framework CURrent-Based Decomposition (CURBD). CURBD employs recurrent neural networks (RNNs) directly constrained, from the outset, by time series measurements acquired experimentally, such as Ca2+ imaging or electrophysiological data. Once trained, these data-constrained RNNs let us infer matrices quantifying the interactions between all pairs of modeled units. Such model-derived “directed interaction matrices” can then be used to separately compute excitatory and inhibitory input currents that drive a given neuron from all other neurons. Therefore different current sources can be de-mixed – either within the same region or from other regions, potentially brain-wide – which collectively give rise to the population dynamics observed experimentally. Source de-mixed currents obtained through CURBD allow an unprecedented view into multi-region mechanisms inaccessible from measurements alone. We have applied this method successfully to several types of neural data from our experimental collaborators, e.g., zebrafish (Deisseroth lab, Stanford), mice (Harvey lab, Harvard), monkeys (Rudebeck lab, Sinai), and humans (Rutishauser lab, Cedars Sinai), where we have discovered both directed interactions brain wide and inter-area currents during different types of behaviors. With this powerful framework based on data-constrained multi-region RNNs and CURrent Based Decomposition (CURBD), we ask if there are conserved multi-region mechanisms across different species, as well as identify key divergences.

Granular matter can serve as a prototype for exploring the rich physics of many-body systems driven far from equilibrium. This talk will outline a new direction for granular physics with macroscopic particles, where acoustic levitation compensates the forces due to gravity and eliminates frictional interactions with supporting surfaces in order to focus on particle interactions. Levitating small particles by intense ultrasound fields in air makes it possible to manipulate and control their positions and assemble them into larger aggregates. The small air viscosity implies that the regime of underdamped dynamics can be explored, where inertial effects are important, in contrast to typical colloids in a liquid, where inertia can be neglected. Sound scattered off individual, levitated solid particles gives rise to controllable attractive forces with neighboring particles. I will discuss some of the key concepts underlying acoustic levitation, describe how detuning an acoustic cavity can introduce active fluctuations that control the assembly statistics of small levitated particles clusters, and give examples of how interactions between neighboring levitated objects can be controlled by their shape.

Rhythmic activity in the brain has been reported in relation to a wide range of cognitive processes. Changes in the rhythmic activity have been related to pathological states. These observations raise the question of the origin of these rhythms: can the mechanisms responsible for generation of these rhythms and that allow the propagation of the rhythmic signal be acquired via a process of learning? In my talk I will focus on spike timing dependent plasticity (STDP) and examine under what conditions this unsupervised learning rule can facilitate the propagation of rhythmic activity downstream in the central nervous system. Next, the I will apply the theory of STDP to the whisker system and demonstrate how STDP can shape the distribution of preferred phases of firing in a downstream population. Interestingly, in both these cases STDP dynamics does not relax to a fixed-point solution, rather the synaptic weights remain dynamic. Nevertheless, STDP allows for the system to retain its functionality in the face of continuous remodeling of the entire synaptic population.

During learning, populations of neurons alter their connectivity and activity patterns, enabling the brain to construct a model of the external world. Conventional wisdom holds that the durability of a such a model is reflected in the stability of neural responses and the stability of synaptic connections that form memory engrams. However, recent experimental findings have challenged this idea, revealing that neural population activity in circuits involved in sensory perception, motor planning and spatial memory continually change over time during familiar behavioural tasks. This continual change suggests significant redundancy in neural representations, with many circuit configurations providing equivalent function. I will describe recent work that explores the consequences of such redundancy for learning and for task representation. Despite large changes in neural activity, we find cortical responses in sensorimotor tasks admit a relatively stable readout at the population level. Furthermore, we find that redundancy in circuit connectivity can make a task easier to learn and compensate for deficiencies in biological learning rules. Finally, if neuronal connections are subject to an unavoidable level of turnover, the level of plasticity required to optimally maintain a memory is generally lower than the total change due to turnover itself, predicting continual reconfiguration of an engram.

Distinct synapses influence one another when they undergo changes, with unclear consequences for neuronal dynamics and function. Here we show that synapses can interact such that excitatory currents are naturally normalised and balanced by inhibitory inputs. This happens when classical spike-timing dependent synaptic plasticity rules are extended by additional mechanisms that incorporate the influence of neighbouring synaptic currents and regulate the amplitude of efficacy changes accordingly. The resulting control of excitatory plasticity by inhibitory activation, and vice versa, gives rise to quick and long-lasting memories as seen experimentally in receptive field plasticity paradigms. In models with additional dendritic structure, we observe experimentally reported clustering of co-active synapses that depends on initial connectivity and morphology. Finally, in recurrent neural networks, rich and stable dynamics with high input sensitivity emerge, providing transient activity that resembles recordings from the motor cortex. Our model provides a general framework for codependent plasticity that frames individual synaptic modifications in the context of population-wide changes, allowing us to connect micro-level physiology with behavioural phenomena.

Regulation of information flow in the brain is critical for many forms of behavior. In the process of sensory based decision-making, decisions about future actions are held in memory until enacted, making them potentially vulnerable to distracting sensory input. Therefore, gating of information flow from sensory to motor areas could protect memory from interference during decision-making, but the underlying network mechanisms are not understood. I will present our recent experimental and modeling work describing how information flow from the sensory cortex can be gated by state-dependent frontal cortex dynamics during decision-making in mice. Our results show that communication between brain regions can be regulated via attractor dynamics, which control the degree of commitment to an action, and reveal a novel mechanism of gating of neural information.

Rigidity is the ability of a system to resist imposed stresses before ultimately undergoing failure. However, disordered materials often contain both rigid and floppy subregions that complicate the utility of taking system-wide averages. I will talk about 3 frameworks capable of connecting the internal structure of disordered materials to their rigidity and/or failure under loading, and describe how my collaborators and I have applied these frameworks to laboratory data on laser-cut lattices and idealized granular materials. These are, in order of increasing physics content: (1) centrality within an adjacency matrix describing its connectivity, (2) Maxwell constraint counting on the full network of frictional contact forces, and (3) the vibrational modes of a synthetic dynamical matrix (Hessian). The first two rely primarily on topology, and the second two contrast the utility of considering interparticle forces (Coulomb failure) vs. the energy landscape. All three methods, while successfully elucidating the origins of rigidity and brittle vs. ductile failure, also provide interesting counterpoints regarding how much information is enough to make predictions.

We study the dynamics of (inhibitory) balanced networks at varying (i) the level of symmetry in the synaptic connectivity; and (ii) the ariance of the synaptic efficacies (synaptic gain). We find three regimes of activity. For suitably low synaptic gain, regardless of the level of symmetry, there exists a unique stable fixed point. Using a cavity-like approach, we develop a quantitative theory that describes the statistics of the activity in this unique fixed point, and the conditions for its stability. Increasing the synaptic gain, the unique fixed point destabilizes, and the network exhibits chaotic activity for zero or negative levels of symmetry (i.e., random or antisymmetric). Instead, for positive levels of symmetry, there is multi-stability among a large number of marginally stable fixed points. In this regime, ergodicity is broken and the network exhibits non-exponential relaxational dynamics. We discuss the potential relevance of such a “glassy” phase to explain some features of cortical activity.

fMRI results have shown that the supplementary motor area (SMA) and the basal ganglia, most often discussed in their roles in generating action, are engaged by beat-based timing even in the absence of movement. Some have argued that the motor system is “recruited” by beat-based timing tasks due to the presence of motor-like timescales, but a deeper understanding of the roles of these motor structures is lacking. Reviewing a body of motor neurophysiology literature and drawing on the “active inference” framework, I argue that we can see the motor and timing functions of these brain areas as examples of dynamic sub-second prediction informed by sensory event timing. I hypothesize that in both cases, sub-second dynamics in SMA predict the progress of a temporal process outside the brain, and direct pathway activation in basal ganglia selects temporal and sensory predictions for the upcoming interval -- the only difference is that in motor processes, these predictions are made manifest through motor effectors. If we can unify our understanding of beat-based timing and motor control, we can draw on the substantial motor neuroscience literature to make conceptual leaps forward in the study of predictive timing and musical rhythm.