Session K35: Physics of Sensorimotor Neural Circuits I

Neural relativity principle

Olfaction is the final frontier of our senses - the one that is still almost completely mysterious to us. Despite extensive genetic and perceptual data, and a strong push to solve the neural coding problem, fundamental questions about the sense of smell remain unresolved. Unlike vision and hearing, where relatively straightforward relationships between stimulus features and neural responses have been foundational to our understanding sensory processing, it has been difficult to quantify the properties of odorant molecules that lead to olfactory percepts. In a sense, we do not have olfactory analogs of ``red'', ``green'' and ``blue''. The seminal work of Linda Buck and Richard Axel identified a diverse family of about 1000 receptor molecules that serve as odorant sensors in the nose. However, the properties of smells that these receptors detect remain a mystery. I will review our current understanding of the molecular properties important to the olfactory system. I will also describe a theory that explains how odorant identity can be preserved despite substantial changes in the odorant concentration.   

Molecular Cooperativity Governs Diverse and Monoallelic Olfactory Receptor Expression

Multiple-objective optimization is common in biological systems. In the mammalian olfactory system, each sensory neuron stochastically expresses only one out of up to thousands of olfactory receptor (OR) gene alleles; at organism level the types of expressed ORs need to be maximized. The molecular mechanism of this Nobel-Prize winning puzzle remains unresolved after decades of extensive studies. Existing models focus only on monoallele activation, and cannot explain recent observations in mutants, especially the reduced global diversity of expressed ORs in G9a/GLP knockouts. In this work we integrated existing information on OR expression, and proposed an evolutionarily optimized three-layer regulation mechanism, which includes zonal segregation, epigenetic and enhancer competition coupled to a negative feedback loop. This model not only recapitulates monoallelic OR expression, but also elucidates how the olfactory system maximizes and maintains the diversity of OR expression. The model is validated by several experimental results, and particularly underscores cooperativity and synergy as a general design principle of multi-objective optimization in biology.   

Derivation of Neural Circuits from the Similarity Matching Principle

Our brains analyze high-dimensional datasets streamed by our sensory organs in multiple stages. Sensory cortices, for example, perform tasks like dimensionality reduction, sparse feature discovery and clustering. To model these tasks we pursue an approach analogous to use of action principles in physics and propose a new family of objective functions based on the principle of similarity matching. From these objective functions we derive online distributed algorithms that can be implemented by biological neural networks resembling cortical circuits. Our networks can adapt to changes in the number of latent dimensions or the number of clusters in the input dataset. Furthermore, we formulate minimax optimization problems from which we derive online algorithms with two classes of neurons identified with principal neurons and interneurons in biological circuits. In addition to bearing resemblance to biological circuits, our algorithms are competitive for Big Data applications.   

The dynamics of neuronal redundancy in decision making

We propose two temporal phases of collective computation in a visual motion direction discrimination task by analyzing recordings from 169 neural channels in the prefrontal cortex of macaque monkeys. Phase I is a distributed phase in which uncertainty is substantially reduced by pooling information from many cells. Phase II is a redundant phase in which numerous single cells contain all the information present at the population level in Phase I. A dynamic distributed model connects low redundancy to a slow timescale of information aggregation, and provides a common explanation for both behaviors that differs only in the degree of recurrent excitation. We attribute the slow timescale of information accumulation to critical slowing down near the transition to a memory-carrying collective state. We suggest that this dynamic of slow distributed accumulation followed by fast collective propagation is a generic feature of robust collective computing systems related to consensus formation.   

Mathematical Relationships between Neuron Morphology and Neurite Growth Dynamics in {\it Drosophila melanogaster} Larva Class IV Sensory Neurons

The morphology of neurons is diverse and reflects the diversity of neuronal functions, yet the principles that govern neuronal morphogenesis are unclear. In an effort to better understand neuronal morphogenesis we will be focusing on the development of the dendrites of class IV sensory neuron in {\it Drosophila melanogaster}. In particular we attempt to determine how the the total length, and the number of branches of dendrites are mathematically related to the dynamics of neurite growth and branching. By imaging class IV neurons during early embryogenesis we are able to measure the change in neurite length $l(t)$ as a function of time $v(t) = dl/dt$. We found that the distribution of $v(t)$ is well characterized by a hyperbolic secant distribution, and that the addition of new branches per unit time is well described by a Poisson process. Combining these measurements with the assumption that branching occurs with equal probability anywhere along the dendrite we were able to construct a mathematical model that provides reasonable agreement with the observed number of branches, and total length of the dendrites of the class IV sensory neuron.   

An investigation into the induced electric fields from transcranial magnetic stimulation.

Transcranial magnetic stimulation (TMS) is a promising tool for noninvasive brain stimulation that has been approved by the FDA for the treatment of major depressive disorder. To stimulate the brain, TMS uses large, transient pulses of magnetic field to induce an electric field in the head. This transient magnetic field is large enough to cause the depolarization of cortical neurons and initiate a synaptic signal transmission. For this study, 50 unique head models were created from MRI images. Previous simulation studies have primarily used a single head model, and thus give a limited image of the induced electric field from TMS. This study uses finite element analysis simulations on 50 unique, heterogeneous head models to better investigate the relationship between TMS and the electric field induced in brain tissues. Results showed a significant variation in the strength of the induced electric field in the brain, which can be reasonably predicted by the distance from the TMS coil to the stimulated brain. Further, it was seen that some models had high electric field intensities in over five times as much brain volume as other models.   

A Robust Feedforward Model of the Olfactory System

Most natural odors have sparse molecular composition. This makes the principles of compressing sensing potentially relevant to the structure of the olfactory code. Yet, the largely feedforward organization of the olfactory system precludes reconstruction using standard compressed sensing algorithms. To resolve this problem, recent theoretical work has proposed that signal reconstruction could take place as a result of a low dimensional dynamical system converging to one of its attractor states. The dynamical aspects of optimization, however, would slow down odor recognition and were also found to be susceptible to noise. Here we describe a feedforward model of the olfactory system that achieves both strong compression and fast reconstruction that is also robust to noise. A key feature of the proposed model is a specific relationship between how odors are represented at the glomeruli stage, which corresponds to a compression, and the connections from glomeruli to Kenyon cells, which in the model corresponds to reconstruction. We show that provided this specific relationship holds true, the reconstruction will be both fast and robust to noise, and in particular to failure of glomeruli. The predicted connectivity rate from glomeruli to the Kenyon cells can be tested experimentally.   

Animal-to-Animal Variation in Odor Preference and Neural Representation of Odors

Across any population of animals, individuals exhibit diverse behaviors and reactions to sensory stimuli like tastes and odors. While idiosyncratic behavior is ubiquitous, its biological basis is poorly understood. In this talk, I will present evidence that individual fruit flies (Drosophila melanogaster) display idiosyncratic olfactory behaviors and discuss our ongoing efforts to map these behavioral differences to variation in neural circuits. Using a high-throughput, single-fly assay for odor preference, we have demonstrated that highly inbred flies display substantial animal-to-animal variability, beyond that expected from experimental error, and that these preferences persist over days. Using in vivo two-photon calcium imaging, we are beginning to examine the idiosyncrasy of neural coding in the fly olfactory pathway and find that the odor responses of individual processing channels in the antennal lobe can vary substantially from fly to fly. These results imply that individual differences in neural coding may be used to predict the idiosyncratic behavior of an individual - a hypothesis we are currently testing by imaging neural activity from flies after measuring their odor preferences.   

Robust spatial memory maps in flickering neuronal networks: a topological model.

It is widely accepted that the hippocampal place cells provide a substrate of the neuronal representation of the environment---the ``cognitive map''. However, hippocampal network, as any other network in the brain is transient: thousands of hippocampal neurons die every day and the connections formed by these cells constantly change due to various forms of synaptic plasticity. What then explains the remarkable reliability of our spatial memories? We propose a computational approach to answering this question based on a couple of insights. First, we propose that the hippocampal cognitive map is fundamentally topological, and hence it is amenable to analysis by topological methods. We then apply several novel methods from homology theory, to understand how dynamic connections between cells influences the speed and reliability of spatial learning. We simulate the rat's exploratory movements through different environments and study how topological invariants of these environments arise in a network of simulated neurons with ``flickering'' connectivity. We find that despite transient connectivity the network of place cells produces a stable representation of the topology of the environment.   

Inference of pain stimulus level from stereotypical behavioral response of \textit{C.elegans} allows quantification of effects of anesthesia and mutation

In animals, we must infer the pain level from experimental characterization of behavior. This is not trivial since behaviors are very complex and multidimensional. To establish \textit{C.elegans} as a model for pain research, we propose for the first time a quantitative model that allows inference of a thermal nociceptive stimulus level from the behavior of an individual worm. We apply controlled levels of pain by locally heating worms with an infrared laser and capturing the subsequent behavior. We discover that the behavioral response is a product of stereotypical behavior and a nonlinear function of the strength of stimulus. The same stereotypical behavior is observed in normal, anesthetized and mutated worms. From this result we build a Bayesian model to infer the strength of laser stimulus from the behavior. This model allows us to measure the efficacy of anaesthetization and mutation by comparing the inferred strength of stimulus. Based on the measured nociceptive escape of over 200 worms, our model is able to significantly differentiate normal, anaesthetized and mutated worms with 40 worm samples.   

\textit{Drosophila} photo-taxis and odor-taxis are mediated by a shared computational pathway

In natural environments, the Drosophila larva makes navigational decisions based on variable and conflicting sensory inputs. How larvae respond to multi-modal stimuli and how their neural circuits integrate and prioritize multi-sensory information remains unknown. To identify larval navigational computations we developed a high-throughput reverse-correlation assay. We provided larvae with visual and optogenetically induced fictive olfactory stimuli and measured the correlation between the presented stimulus and evoked turn decisions. We used this technique to fit parameters of a Linear-Nonlinear-Poisson model describing computations underlying turn decisions. For uni-modal inputs, the parameterized model allowed us to predict the behavior of populations of larvae responding to novel stimulus presentations. For multi-modal inputs, our assay showed that larvae linearly combine olfactory and visual signals upstream of the decision to turn. We verified this prediction using controlled combinations of stimuli. We studied other navigational decisions that determine the size and directions of turns and found that larvae integrated odor and light according to the same rule in all cases. These results suggest that photo-taxis and odor-taxis are mediated by a shared computational pathway.