UNIVERSITY OF CALIFORNIA, SAN DIEGO BERKLIEY DAVIS - IRVINE LOS ANGELES - MERCED - RIVERSIDE SAN DIEGO - SAN FRANCISCO SANTA BARBARA - SANTA CRUZ Gabriel A. Silva, Professor of Bioengineering and Neurosciences Jacobs Faculty Endowed Scholar in Engineering Founding Director, Center for Engineered Natural Intelligence University of California San Diego Mailing address Department of Bioengineering University of California. San Diego 9500 Gilman Drive MC 0412 La Iolla, California 92093-0412 Telephone: 858.822.4591 Email: gsilanucsdedu Web Mathematical Neuroscience UCSD Center for Engineered Natural Intelligence August 5, 2019 Kevin Murphy, MD Vice Chair, Department of Radiation Medicine University of California San Diego Re: Invitation to join the Center for Engineered Natural Intelligence Dear Prof. Murphy, Following up on our discussions, it is with great pleasure that I invite you to formally join the Center for Engineered Natural Intelligence (CENI). As you are aware, CENI is focused on advancing a systems neuroscience understanding of the brain and relevant neurological and neurodevelopmental disorders. At the same time, we are exploring the development of new directions in machine learning by applying of computational, theoretical, and systems neuroscience to novel algorithms and related hardware. We look forward to having you join us. Sincerely, Gabriel A. Silva Measuring Deviations of the Refraction Ratio in Autism Brain Networks undergoing as a Physiological Basis for Observed Clinical Outcomes Gabriel A. Silva Jacobs Faculty Endowed Scholar in Engineering Department of Bioengineering and Department of Neurosciences Director, Center for Engineered Natural Intelligence Email: gsilva@ucsd.edu The refraction ratio: Measuring optimally efficient dynamic signaling in neurons The mechanisms underlying the successful integration and rapid transmission of information in individual neurons and networks of neurons rely on complex interactions between structural and dynamical properties. For a long time, the prevailing hypotheses was that neurons were morphologically structurally) designed to optimize for the least amount of cellular material necessary in order to conserve energy and cellular resources. In particular, a number of studies have argued that wiring minimization principles that maximize the conservation of material underlie the morphological design of neurons and even the broader anatomical organization responsible for functional maps in the neocortex, such as the intracortical wiring underlying functional maps in mammalian visual cortex. However, more recent work has shown that neurons are not minimized for wiring length, but at the same tine are not designed to signal as fast at they could either. Instead, they are designed somewhere in between the two extremes of minimum wiring (path) and fastest signaling. They use more material than minimal construction costs would allow in order to increase conduction velocities that decrease temporal costs, while at the same time they do not signal as fast as they could if the wiring design was optimized strictly for speed, thereby offsetting the material. Recent work has shown that there exists a trade?off between the time it takes action potentials to reach synaptic terminals (temporal cost) and the amount of cellular material associated with the wiring path length of the neuron's morphology (material cost). This trade-off can be interpreted as a balance between as fast as possible signaling while keeping material and cellular costs within reason. In other words, the temporal latency associated with action potentials propagating from the soma (cell body) to the synaptic terminals should be minimized in order to achieve signaling that is fast enough to maximize communication, while at the same time wiring should be minimized in order to conserve the amount of cellular and energy resources used by the neuron in its construction. However, to the best of our knowledge, no one has ever discovered or even proposed Where this spatial-temporal trade-off lies. In other words, what the criteria or principle is that is being optimized in the design of neurons that reflects the balance between structure (morphology) and dynamics (signaling latencies). Identifying what this principle is however, is critical to ultimately understanding why neurons are designed the way they are, and the effect it has on a neuron's ability to represent and process information in the brain. This would allow many other seemingly unrelated neurobiological results that involve considerations of neuronal structure-function relationships to be understood within this new context. As a result, completely disconnected results, models, and interpretations of data would have an underlying ?constraint? that nature necessitates they conform to. In turn this would have a huge impact on our understanding of the brain as a system. We have mathematically shown that optimal ef?cient signaling between connected node pairs in geometric networks necessitates a ratio between the signaling latency on the edge and the internal dynamics of individual nodes that approaches unity. We call this ratio the refraction ratio. We then showed that Basket cell neurons are designed to optimize the refraction ratio between the refractory period of their membrane, and action potential latencies (delays) between the initial segment where action potentials start at the base of the cell body and the synaptic terminals where they end. Given signaling latencies along the convoluted path resulting from the morphological geometry of the axon arbor, the ratio of the signaling latency to the membrane refractory period approaches a value of unity for each individual axonal branch. We computed this ratio for nearly 12,000 independent axonal branches independent statistical data points). These data demonstrate that Basket cell neurons approach the theoretically predicted ideal refraction ratio. The interpretation of our results suggests that the convoluted paths taken by axons and axonal branches re?ect a design compensation by the neuron to slow down signaling latencies in order to optimize the refraction ratio. Because the cell does not have direct control over the biophysics responsible for producing the membrane refractory period, it us es axonal morphology (structure) to ensure that an optimized refraction ratio is almost always preserved by the time action potentials reach synaptic terminals. An optimized ratio re?ects a balance between the temporal constraints associated with the biophysics of the membrane, and the amount of time it takes action potentials (the signals) to travel down the axonal branch. It serves to maximize the amount of information individual branches can support. As we have previously shown in computational numerical simulations, a deviation of this ratio in geometric networks can result in the complete breakdown of signaling dynamics. root vertex VB. branching vertex Vr :lerminal vertex Output Vertex venex in edge . .generlc edge root vertex - I branching vertex I termmal vertex Figure 1. Deriving axonal network tree graphs from morphological reconstructions. (A) Representative three dimensional morphological reconstruction of one of the basket cells in our dataset from rat neocortex. Dendritic arbors are in green, axonal arbors in black [data from (B) Graph-based model of the geometric network of an axon and its arborizations. Vertices in the graph are labeled as follows: root vertex vR is located at the initial segment of the axon at the soma; branching vertices vB corresponding to branch points along the axons; terminal vertices VT were synaptic terminals of the axon arborizations. Vertices between branch points re?ect measurement points in the original reconstruction, and are denoted as ve,n with identifying the edge and the speci?c axonal point within that edge. The computation of the convoluted geometric distance between the root vertex VR and a selected terminal vertex st was determined by the sum of all edge distances between ve,n pairs forming the total path that connected the two vertices. The total distance approximates well the edge path length integral (see the Methods) of the tortuous path connecting the axon initial segment to a synaptic terminal in a real neuron (see panel A). (C) Reduced adjacency matrix mapping the connectivity between branching points along the axon tree of the neuron visualized in A. (D) Three dimensional graph of the same axon arbor mapped onto a minimized length network where only root vertex and terminal vertices are considered. The edges connecting the vertices had equal to the shortest path length, the Euclidean distance. (E) Biograph of the reduced network of the axon arbor in A, described by the adjacency matrix in C. Each labeled box in the graph stands for an identi?cation number of the reported vertex. Root vertex in yellow, branching vertices in green, and terminal vertices in red. A 30 i 1000i @500 100 200 300 400 500 Refraction Ratio Refraction ratio 20 3 i ~15600Ratio medians 400 800 1200 160 Refraction Ratio Refraction ratio Figure 2. Basket cell neurons display optimized refraction ratios (A) Distribution of the refraction ratio for all branches forming the axon arbor for a single neuron, for all paths p(vR VT connecting the root vertex at the initial segment vR to the synaptic terminals VT . The inset shows an example of one axonal branch path from this cell. The refraction ratio was computed independently for each axonal branch for all branches of the axon tree. The x-axes represents values of the computed refraction ratio, while the y?axes shows the number or count of individual axonal branches. (B) Distribution of the refraction ratio for the full dataset of 57 basket cells. All axonal branches variables, (1 1,575) from all the neurons are independent and the value of the refraction ratio corresponding to each of them was used to build the distribution. Inset: zoomed view of the data with the refraction ratios axis up to a value of 50. (C) The peak of the distribution shown in occurred at 0.56, while the median had a value of 0.92. The median value of all medians computed for each of the 57 neurons in the dataset had a value of 0.91 (see the discussion in the main text). Inset: histogram of the median values of the refraction ratio distribution independently computed for each of the 57 neurons. The computed mean of the median ratio distribution had a value of 1.01 with 49 neurons (86% of the entire dataset) within one standard deviation, 1.01 i- 0.61 (p i 10). (D) Distribution of the refraction ratio for the entire dataset (same data shown in panel B) but with x-axis extending out to the full range of values in order to show the few outliers (indicated by the red arrows). Inset: zoomed in View of the main plot out to a refraction ratio of 60 which captures the range over which most of the outliers were found. Note how the branch count steeply decreases from the peak. The distribution of refraction ratio values, the number and width of each bin, was obtained by dividing the full range of the computed refraction ratio by the smallest value of the ratio in order to obtain reasonable bin sizes. Hypothesis: A breakdown in the ef?ciency of dynamic signaling in autism networks can be measured by changes in the refraction ratio We ?rst hypothesize that from a systems perspective, the associated with autism spectrum disorder (ASD) is the result of inef?cient dynamic signaling between populations of neurons re?ecting inef?cient communication between different functional parts of the brain. This breakdown results due to inef?cient signaling at the level of individual neurons that translates across hierarchies of neuronal organization, from neurons to networks to the connectivity across brain regions. The functional manifestation of this signaling breakdown in brain networks result in the cognitive and clinical hallmarks associated with ASD and objective empirical markers measurable on the electroencephalogram (EEG We propose that such a network dynamics breakdown can be measured as a change in the refraction ratio away from near optimal values. And again, we hypothesize that changes in the refraction ratio are spatially multi-scale, in the sense that deviations from optimality can be measured at different networks scales: ?rst, at the scale of individual neurons from ASD patients, and secondly, at the scale of networks of populations of neurons between brain regions. We suggest that while genetic, molecular and cellular changes are responsible for changes in the internal dynamics and function of affected neurons, it is changes in the dynamics of neurons and populations of neurons detectable using our analysis that are physiologically the basis for the defects in how ASD cellular networks process information. This is an inherent consequence of the effect of the geometry and structure of ASD networks and how their geometry affects their ability for dynamic signaling that cannot be studied or even de?ned at the molecular, cellular, or genetic scales. It is a consequence of the effects of how molecular, cellular, and genetic processes shape ASD networks, but it can only be investigated in the networks themselves. For example, identifying a specific mutation and the resultant miss-folding of the protein that gene encodes represent ?broken? network building block components that may have varying degrees of functional consequences. But understanding how those components affect the dynamics of the network and the resultant effect on the ability of the network to process information is a very different problem than the identi?cation of faulty components in the ?rst place. In fact, simply identifying such components do es not guarantee that a causal understanding will be achieved about the eventual effects they may have. We also note that the emphasis of our hypothesis is on how ASD networks process information as a result of dynamic changes in the interplay between geometry and signaling dynamics. It is not focused on changes associated with the connectivity or ?re~wiring? of ASD networks, i.e. what cells are connected to what other cells, which has been the dominant view point in the literature to date. This project proposes to extend appropriate quantitative methods to measure the refraction ratio in ASD patients before and after undergoing stimulation protocols developed by the Murphy lab. This work is complimentary and will be able to directly take advantage of the ability to do simultaneous measurements and stimulation, and provides a physiological basis for the clinical results being observed with the modified protocols. Budget Draft Personnel Graduate student salary tuition and fees (12 months) Postdoc 1. Senior software engineer Software engineer Gabriel Silva summer salary 3 months Total Equipment and Resources Computational resources (San Diego Super Computer Center) Totals (year 1) Two year project total $62,500 $70,000 $90,000 $75,000 $90,000 $3875,000 $50,000 $437500 $875,000