Computational Neuroscience seminars

Many networks in the nervous system possess an abundance of inhibition, which serves to shape and stabilize neural dynamics. The neurons in such networks exhibit intricate patterns of connectivity whose structure controls the allowed patterns of neural activity. In this work, we examine inhibitory threshold-linear networks whose dynamics are constrained by an underlying directed graph. We develop a set of parameter-independent graph rules that enable us to predict features of the dynamics, such as emergent sequences and dynamic attractors, from properties of the graph. These rules provide a direct link between the structure and function of these networks, and may provide new insights into how connectivity shapes dynamics in real neural circuits.

Sensory representations are typically thought as neuronal activity patterns that encode physical attributes of the outside world. However, increasing evidence is showing that as animals learned the association between a sensory stimulus and its behavioral relevance, stimulus representation in sensory cortical areas can change. In this seminar I will present recent experiments from our lab showing that the activity in the olfactory piriform cortex (PC) of mice encodes not only odor information, but also non-olfactory variables associated with the behavioral task. By developing an associative olfactory learning task, in which animals learn to associate a particular context with an odor and a reward, we were able to record the activity of multiple neurons as the animal runs in a virtual reality corridor. By analyzing the population activity dynamics using Principal Components Analysis, we find different population trajectories evolving through time that can discriminate aspects of different trial types. By using Generalized Linear Models we further dissected the contribution of different sensory and non-sensory variables to the modulation of PC activity. Interestingly, the experiments show that variables related to both sensory and non-sensory aspects of the task (e.g., odor, context, reward, licking, sniffing rate and running speed) differently modulate PC activity, suggesting that the PC adapt odor processing depending on experience and behavior.

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 framework based on data-constrained multi-region RNNs and CURrent Based Decomposition (CURBD), we can ask if there are conserved multi-region mechanisms across different species, as well as identify key divergences.

Cortical circuits receive multiple inputs from upstream populations with non-overlapping stimulus tuning preferences. Both the feedforward and recurrent architectures of the receiving cortical layer will reflect this diverse input tuning. We study how population-wide neuronal variability propagates through a hierarchical cortical network receiving multiple, independent, tuned inputs. We present new analysis of in vivo neural data from the primate visual system showing that the number of latent variables (dimension) needed to describe population shared variability is smaller in V4 populations compared to those of its downstream visual area PFC. We successfully reproduce this dimensionality expansion from our V4 to PFC neural data using a multi-layer spiking network with structured, feedforward projections and recurrent assemblies of multiple, tuned neuron populations. We show that tuning-structured connectivity generates attractor dynamics within the recurrent PFC current, where attractor competition is reflected in the high dimensional shared variability across the population. Indeed, restricting the dimensionality analysis to activity from one attractor state recovers the low-dimensional structure inherited from each of our tuned inputs. Our model thus introduces a framework where high-dimensional cortical variability is understood as ``time-sharing’’ between distinct low-dimensional, tuning-specific circuit dynamics.

Neurons in the primary visual cortex (V1) encode the orientation and contrast of visual stimuli through changes in firing rate (Hubel and Wiesel, 1962). Their activity typically peaks at a preferred orientation and decays to zero at the orientations that are orthogonal to the preferred. This activity pattern is re-scaled by contrast but its shape is preserved, a phenomenon known as contrast invariance. Contrast-invariant selectivity is also observed at the population level in V1 (Carandini and Sengpiel, 2004). The mechanisms supporting the emergence of contrast-invariance at the population level remain unclear. How does the activity of different neurons with diverse orientation selectivity and non-linear contrast sensitivity combine to give rise to contrast-invariant population selectivity? Theoretical studies have shown that in the balance limit, the properties of single-neurons do not determine the population activity (van Vreeswijk and Sompolinsky, 1996). Instead, the synaptic dynamics (Mongillo et al., 2012) as well as the intracortical connectivity (Rosenbaum and Doiron, 2014) shape the population activity in balanced networks. We report that short-term plasticity can change the synaptic strength between neurons as a function of the presynaptic activity, which in turns modifies the population response to a stimulus. Thus, the same circuit can process a stimulus in different ways –linearly, sublinearly, supralinearly – depending on the properties of the synapses. We found that balanced networks with excitatory to excitatory short-term synaptic plasticity cannot be contrast-invariant. Instead, short-term plasticity modifies the network selectivity such that the tuning curves are narrower (broader) for increasing contrast if synapses are facilitating (depressing). Based on these results, we wondered whether balanced networks with plastic synapses (other than short-term) can support the emergence of contrast-invariant selectivity. Mathematically, we found that the only synaptic transformation that supports perfect contrast invariance in balanced networks is a power-law release of neurotransmitter as a function of the presynaptic firing rate (in the excitatory to excitatory and in the excitatory to inhibitory neurons). We validate this finding using spiking network simulations, where we report contrast-invariant tuning curves when synapses release the neurotransmitter following a power- law function of the presynaptic firing rate. In summary, we show that synaptic plasticity controls the type of non-linear network response to stimulus contrast and that it can be a potential mechanism mediating the emergence of contrast invariance in balanced networks with orientation-dependent connectivity. Our results therefore connect the physiology of individual synapses to the network level and may help understand the establishment of contrast-invariant selectivity.

Neural integrators are circuits that are able to code analog information such as spatial location or amplitude. Storing amplitude requires the network to have a large number of attractors. In classic models with recurrent excitation, such networks require very careful tuning to behave as integrators and are not robust to small mistuning of the recurrent weights. In this talk, I introduce a circuit with recurrent connectivity that is subjected to a slow subthreshold oscillation (such as the theta rhythm in the hippocampus). I show that such a network can robustly maintain many discrete attracting states. Furthermore, the firing rates of the neurons in these attracting states are much closer to those seen in recordings of animals. I show the mechanism for this can be explained by the instability regions of the Mathieu equation. I then extend the model in various ways and, for example, show that in a spatially distributed network, it is possible to code location and amplitude simultaneously. I show that the resulting mean field equations are equivalent to a certain discontinuous differential equation.

In this talk I will summarize some of our recent unpublished work on spectral coding in the larval zebrafish retina. Combining 2p imaging, hyperspectral stimulation, computational modeling and connectomics, we take a renewed look at the spectral tuning of cone photoreceptors in the live eye. We find that already cones optimally rotate natural colour space in a PCA-like fashion to disambiguate greyscale from "colour" information. We then follow this signal through the retinal layers and ultimately into the brain to explore the major spectral computations performed by the visual system at its consecutive stages. We find that by and large, zebrafish colour vision can be broken into three major spectral zones: long wavelength grey-scale-like vision, short-wavelength prey capture circuits, and spectrally diverse mid-wavelength circuits which possibly support the bulk of "true colour vision" in this tetrachromate vertebrate.

To organize various experiences in a coherent mental representation, we need to properly estimate the duration and temporal order of different events. Yet, our perception of time is noisy and vulnerable to various illusions. Studying these illusions can elucidate the mechanism by which the brain perceives time. In this talk, I will review a few studies on how the brain perceives duration of events and the temporal order between self-generated motion and sensory feedback. Combined with computational models at different levels, these experiments illustrated that the brain incorporates the prior knowledge of the statistical distribution of the duration of stimuli and the decay of memory when estimating duration of an individual event, and adjusts its perception of temporal order to changes in the statistics of the environment.

Computational and cognitive neuroscience techniques have made great strides towards describing the neural computations underlying perceptual inference and decision-making under uncertainty. These tools tell us how and why perceptual illusions occur, which brain areas may represent noisy information in a probabilistic manner, and so on. However, an understanding of the subjective, qualitative aspects of perception remains elusive: qualia, or the personal, intrinsic properties of phenomenal awareness, have remained out of reach of these computational analytic insights. Here, I propose that metacognitive computations, and the subjective feelings that go along with them, give us a solid starting point for understanding subjective experience in general. Specifically, perceptual metacognition possesses ontological and practical properties that provide a powerful and unique opportunity for studying the studying the neural and computational correlates of subjective experience using established tools of computational and cognitive neuroscience. By capitalizing on decades of developments in formal computational model comparisons as applied to the specific properties of perceptual metacognition, we are now in a privileged position to reveal new and exciting insights about how the brain constructs our subjective conscious experiences.

To make judgments, brain must be able to infer the state of the world based on often incomplete and ambiguous evidence. To probe neural circuits that perform the computations underlying such judgments, we developed a behavioral task for mice that required them to detect sustained increases in the speed of a continuously varying visual stimulus. In this talk, I will present evidence that the responses of secondary motor cortex to stimulus fluctuations in this task are consistent with updates of the animal’s state of belief that the change has occurred. These results establish a framework for mechanistic inquiries into neural circuits underlying inference during perceptual decision-making.

In a cross wind, the direction a fly moves through the air may differ from its heading direction, the direction defined by its body axis. I will present a model based on experimental results that reveals how a heading direction “compass” signal is combined with optic flow to compute and represent the direction that a fly is traveling. This provides a general framework for understand how flies perform vector computations.

It is sometimes said that there are two reasons why physics is so successful as a science. One is that it deals with very simple problems. The other is that it attempts to account only for universal aspects of systems at a desired level of description, with lower level phenomena subsumed into a small number of adjustable parameters. It is a widespread belief that this approach seems unlikely to be useful in biology, which is intimidatingly complex, where “everything has an exception”, and where there are a huge number of undetermined parameters. I will try to argue, nonetheless, that there are important, experimentally-testable aspects of biology that exhibit universality, and should be amenable to being tackled from a physics perspective. My suggestion is that this can lead to useful new insights into the existence and universal characteristics of living systems. I will try to justify this point of view by contrasting the goals and practices of the field of condensed matter physics with materials science, and then by extension, the goals and practices of the newly emerging field of “Physics of Living Systems” with biology. Specific biological examples that I will discuss include the following: Universal patterns of gene expression in cell biology Universal scaling laws in ecosystems, including the species-area law, Kleiber’s law, Paradox of the Plankton Universality of the genetic code Universality of thermodynamic utilization in microbial communities Universal scaling laws in the tree of life The question of what can be learned from studying universal phenomena in biology will also be discussed. Universal phenomena, by their very nature, shed little light on detailed microscopic levels of description. Yet there is no point in seeking idiosyncratic mechanistic explanations for phenomena whose explanation is found in rather general principles, such as the central limit theorem, that every microscopic mechanism is constrained to obey. Thus, physical perspectives may be better suited to answering certain questions such as universality than traditional biological perspectives. Concomitantly, it must be recognized that the identification and understanding of universal phenomena may not be a good answer to questions that have traditionally occupied biological scientists. Lastly, I plan to talk about what is perhaps the central question of universality in biology: why does the phenomenon of life occur at all? Is it an inevitable consequence of the laws of physics or some special geochemical accident? What methodology could even begin to answer this question? I will try to explain why traditional approaches to biology do not aim to answer this question, by comparing with our understanding of superconductivity as a physical phenomenon, and with the theory of universal computation. References Nigel Goldenfeld, Tommaso Biancalani, Farshid Jafarpour. Universal biology and the statistical mechanics of early life. Phil. Trans. R. Soc. A 375, 20160341 (14 pages) (2017). Nigel Goldenfeld and Carl R. Woese. Life is Physics: evolution as a collective phenomenon far from equilibrium. Ann. Rev. Cond. Matt. Phys. 2, 375-399 (2011).

The ability of the brain to encode and store information depends on the plastic nature of the individual synapses. The increase and decrease in synaptic strength, mediated through the structural plasticity of the spine, are important for learning, memory, and cognitive function. Dendritic spines are small structures that contain the synapse. They come in a variety of shapes (stubby, thin, or mushroom-shaped) and a wide range of sizes that protrude from the dendrite. These spines are the regions where the postsynaptic biochemical machinery responds to the neurotransmitters. Spines are dynamic structures, changing in size, shape, and number during development and aging. While spines and synapses have inspired neuromorphic engineering, the biophysical events underlying synaptic and structural plasticity of single spines remain poorly understood. Our current focus is on understanding the biophysical events underlying structural plasticity. I will discuss recent efforts from my group — first, a systems biology approach to construct a mathematical model of biochemical signaling and actin-mediated transient spine expansion in response to calcium influx caused by NMDA receptor activation and a series of spatial models to study the role of spine geometry and organelle location within the spine for calcium and cyclic AMP signaling. Second, I will discuss how mechanics of membrane-cytoskeleton interactions can give insight into spine shape region. And I will conclude with some new efforts in using reconstructions from electron microscopy to inform computational domains. I will conclude with how geometry and mechanics plays an important role in our understanding of fundamental biological phenomena and some general ideas on bio-inspired engineering.

Remarkable advances in experimental neuroscience now enable us to simultaneously observe the activity of many neurons, thereby providing an opportunity to understand how the moment by moment collective dynamics of the brain instantiates learning and cognition. However, efficiently extracting such a conceptual understanding from large, high dimensional neural datasets requires concomitant advances in theoretically driven experimental design, data analysis, and neural circuit modeling. We will discuss how the modern frameworks of high dimensional statistics and deep learning can aid us in this process. In particular we will discuss: how unsupervised tensor component analysis and time warping can extract unbiased and interpretable descriptions of how rapid single trial circuit dynamics change slowly over many trials to mediate learning; how to tradeoff very different experimental resources, like numbers of recorded neurons and trials to accurately discover the structure of collective dynamics and information in the brain, even without spike sorting; deep learning models that accurately capture the retina’s response to natural scenes as well as its internal structure and function; algorithmic approaches for simplifying deep network models of perception; optimality approaches to explain cell-type diversity in the first steps of vision in the retina.

The curse of dimensionality plagues models of reinforcement learning and decision-making. The process of abstraction solves this by constructing abstract variables describing features shared by different specific instances, reducing dimensionality and enabling generalization in novel situations. Here we characterized neural representations in monkeys performing a task where a hidden variable described the temporal statistics of stimulus-response-outcome mappings. Abstraction was defined operationally using the generalization performance of neural decoders across task conditions not used for training. This type of generalization requires a particular geometric format of neural representations. Neural ensembles in dorsolateral pre-frontal cortex, anterior cingulate cortex and hippocampus, and in simulated neural networks, simultaneously represented multiple hidden and explicit variables in a format reflecting abstraction. Task events engaging cognitive operations modulated this format. These findings elucidate how the brain and artificial systems represent abstract variables, variables critical for generalization that in turn confers cognitive flexibility.

The neurotransmitter dopamine is essential for normal reward learning and motivational arousal processes. Indeed these core functions are implicated in the major neurological and psychiatric dopamine disorders such as schizophrenia, substance abuse disorders/addiction and Parkinson's disease. Over the years, we have made significant strides in understanding the dopamine system across multiple levels of description, and I will focus on our recent advances in the computational description, and brain circuit mechanisms that facilitate the dual role of dopamine in learning and performance. I will specifically describe our recent work with imaging the activity of dopamine axons and measurements of dopamine release in mice performing various behavioural tasks. We discovered wave-like spatiotemporal activity of dopamine in the striatal region, and I will argue that this pattern of activation supports a critical computational operation; spatiotemporal credit assignment to regional striatal subexperts. Our findings provide a mechanistic description for vectorizing reward prediction error signals relayed by dopamine.

Humans spend a lifetime learning, storing and refining a repertoire of motor memories. However, it is unknown what principle underlies the way our continuous stream of sensori-motor experience is segmented into separate memories and how we adapt and use this growing repertoire. Here we develop a principled theory of motor learning based on the key insight that memory creation, updating, and expression are all controlled by a single computation – contextual inference. Unlike dominant theories of single-context learning, our repertoire-learning model accounts for key features of motor learning that had no unified explanation and predicts novel phenomena, which we confirm experimentally. These results suggest that contextual inference is the key principle underlying how a diverse set of experiences is reflected in motor behavior.