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Brain-Morphism: Astrocytes As Memory Units combra.cs.rutgers.edu Brain-morphism: Astrocytes as Memory Units Constantine Michmizos Computational Brain Lab – Rutgers University 6th Neuro Inspired Computational Elements Workshop – Intel Hillsboro, OR 2015 Computa- Neural tional Astrocytic Brain Networks 2013 Children MEG and Modeling with Autism CNS 1 m ComBra Lab‘s goal †mimic Systems 10 cm ᴥ To understand biological intelligence and translate our knowledge to artificial intelligence †restore Maps 1 cm o by developing Networks 1 mm brain-morphic †understand Computa- Neural tional Astrocytic Brain Networks computational methods Neurons 100 μm • that integrate† with the brain Synapses 1 μm from the macro (behavioral) to the micro (synaptic) scale Adapted by Molecules 1 Å Terry Sejnowski Computing for Grillner et al. Nature Neuroscience 2016 Brain Science Understanding the function of the brain Brain Science for Computing Using computational principles of the brain for generic data analysis Alan Turing, 1948 • A fascinating prelude to today’s AI • Proposed connectionist models that would today be called neural networks The Neuron as a • Randomly connected networks of Basic Information Processing Unit artificial neurons McCulloch and Pitts (1943) • Training via reinforcing successful and useful links and cutting useless ones 1948 1956 • The proposed learning rule was inspired by the infant’s brain 50 70 90 10 1957 1996 pigeons playing ping-pong - Skinner 1950 50 70 90 10 since they both contain similar elements input neurons first hidden layer 1959 2013 50 70 90 10 Capsule NNs decreased the error by a whopping 45% A capsule is a subset of neurons within a layer that outputs: 1. an instantiation parameter: is an entity present within a limited domain? 2. a vector of pose parameters: the pose of the entity relative to a canonical version A capsule replaces max pooling 1956 Dec 2017 50 70 90 10 Computing for Brain Science Understanding the function of the brain Sejnowski et al. Putting big data to good use in neuroscience Nature Neuroscience 2014 Brain Science for Computing Using computational principles of the brain for generic data analysis 50 70 90 10 1932. Edgar Adrian, Nobel Prize 1971. David Cohen, MIT 2013. Motor neurons control a robotic Single-Neuron Recordings Magnetoencephalography arm for paraplegic patients (BrainGate) Information = f (electrical activityn) eurons 1997. Deep Brain Stimulation for 2013. TMS applied to the motor alleviating Parkinson’s disease cortex induces hand movement Non-neuronal brain cells are electrically silent The other brain (glia cells) 10% neurons90% Non-neuronal brain cells are electrically silent 2000’s. Calcium Imaging allows studies of calcium signaling in hundreds of neurons and glial cells, within neuronal circuits . Santiago Ramón y Cajal’s drawing of an astrocyte Ramón y Cajal S. Something about the physiological significance of neuroglia. Revista Trimestral Micrografía 1, 3–47, 1897 2015 2015 Astrocytes A paradigm shift in Neuroscience Computational Astrocytes Astrocytes ᴥ Neuro-morphic Computing • Introducing astrocyte, A paradigm shift in Neuroscience a new computational unit into Neural Networks ᴥ Understanding astrocytes by calcium imaging ᴥ Learning by weight updating • Embed astrocytic • The third part of the synapse mechanisms into NANs introduces an orthogonal • Suggest functions for dimension to “neural” plasticity astrocytes at the network level and large time scales ᴥ Time in discrete instances • where behavior and • Astrocytes respond dynamically diseases emerge and in larger time scales than neurons, mapping neural activity into the slower behavioral scales Microglia Astrocyte Presynaptic Neuron Astrocyte Blood Vessel Colangelo et al. Neuroscience Letters 2014 Postsynaptic Neuron The Neural Modeling Paradigm Physical Phenomenon (e.g., neural firing) v(t) I(t) treat as emergent phenomenon treat as target function • Byophysics-based models • Phenomenological models • Understand the principles of • Occam’s razor/KISS principle the underlying phenomena • Level of detail is • Data drives details hypothesis/interest driven Typically higher model complexity Typically lower model complexity Adapted by Karlheinz Meier Neural Network Astrocytic Network Tripartite Synapse Neurons encode information in spike rate Neural Network To capture the dynamics of the interaction between the neuronal and the astrocytic component of the networks Step 1. Input as Spike timing 푉푗 푡 = 훿 푡 − 푡푖 푖 Step 2. Synaptic current response Mapping function between input-output 푡−푡 푡−푡 − − 푤푗 푒 휏 − 푒 4휏 , 푖푓 푡 > 푡푖 퐼푗 푡, 푡푖 = Leaky Integrate-and-Fire (LIF) Neuron 0, 푖푓 푡 ≤ 푡푖 푑푣 Step 3. Integration of synaptic current 휏 = 푣 − 푣 푡 + 푅퐼(푡) 푑푡 푟푒푠푒푡 LIF 퐼 푡 = 퐼푗(푡) 푗 푖푓 푣(푡) ≥ 푉th Step 4. Output spike 푡ℎ푒푛 푣 푡 + 1 ← 푣푟푒푠푒푡 푉표 푡 = LIF 퐼(푡) Neural Network Astrocytic Network Tripartite Synapse 푖 푎푖 = 푎0 ∗ 푛 ∗ exp − 휏푑 2+ Inter-cellular Ca wave propagation in space and time 푐푖 푟푖, 푡 = 푎푖 ∙ 푔푖 푟푖, 푡 푟푖 − 휇 ∙ 푣 ∙ 푡 푟푖 − 휇 ∙ 푣 ∙ 푡 푔푖 푟푖, 푡 = 푒푥푝 − − 푒푥푝 − 휏푑푒푐푎푦 휏푟푖푠푒 the distance of astrocyte 푖 from the origination site (푟0 ≡ 0) intracellular Ca2+ level in astrocyte 푖 at time t nM 2+ • 휏푑푒푐푎푦, 휏푟푖푠푒 control the fall and rise time of the Ca wave • 휏푑 controls the magnitude of the amplitude fall-off between astrocytes • µ captures the permeability of the cells through which the wave propagates s with speed 푣 - lumping together all the sub-mechanisms of gap-junctional and extracellular communication • n is the normalization constant for biexponential function, which is a function μm of the rise and decay parameter Neural Network Astrocytic Network Tripartite Synapse Isyn Neural Network Astrocytic Network Tripartite Synapse 푑푥 푧 = − 1 − 푓 ∙ 푢 ∙ 푥 ∙ 훿 푡 − 푡푠푝 푑푡 휏푟푒푐 푑푦 푦 = − + 1 − 푓 ∙ 푢 ∙ 푥 ∙ 훿 푡 − 푡푠푝 푑푡 휏푖푛 푑푧 푦 푧 = − 푑푡 휏푖푛 휏푟푒푐 synaptic synaptic M. Tsodyks, A. Uziel, and H. Markram Synchrony generation in recurrent networks with current strength frequency-dependent synapses J. Neurosci. 2000 Isyn = A ∙ y(t) 푥 + 푦 + 푧 = 1 are the fractions of synaptic 휏푖푛 is the characteristic time of postsynaptic currents (PSCs) decay resources in a recovered, active, inactive state 푢 is the fraction of 푥 released when a spike 휏푟푒푐 is the recovery time from synaptic depression arrives at the synapse at time 푡푠푝 Neural Network Astrocytic Network Tripartite Synapse 푑푥 푧 = − 1 − 푓 ∙ 푢 ∙ 푥 ∙ 훿 푡 − 푡푠푝 푑푡 휏푟푒푐 푑푦 푦 = − + 1 − 푓 ∙ 푢 ∙ 푥 ∙ 훿 푡 − 푡 I 푠푝 Isynsyn 푑푡 휏푖푛 푑푧 푦 푧 = − 푑푡 휏푖푛 휏푟푒푐 Isyn = A ∙ y(t) 푑푓 푓 = − + 1 − 푓 ∙ 휅 ∙ 훩 푐푖 푟푖, 푡 − 푐푡ℎ푟푒푠ℎ 푑푡 휏퐶푎 휏퐶푎 is the decay constant of 푓 푓 is the gating variable 휅 controls the rise time of 푓 It models Ca2+-dependent presynaptic inhibition 푥 + 푦 + 푧 = 1 are the fractions of synaptic 휏푖푛 is the characteristic time of postsynaptic currents (PSCs) decay resources in a recovered, active, inactive state 훩(푥) Heaviside function 2+ 푢 is the fraction of 푥 released when a spike 휏푟푒푐 is the recovery time from 푐푡ℎ푟푒푠ℎ is [intracellular Ca ] needed synaptic depression to activate 푓 arrives at the synapse at time 푡푠푝 Neural Network Astrocytic Network Tripartite Synapse Astrocytes inject into the post-synaptic neuron a slow-injected current (SICs) I SICs Isynsyn • are well fit to bi-exponential distributions • have a rapid rise time (on the order of tens of ms) Upon reaching a Ca2+ peak, an • have a comparatively larger decay time (on the order of hundreds of ms) astrocyte releases glio- • are correlated with Ca2+ wave peaks in both time and amplitude transmitters that lead to 휇퐴 NMDAR-mediated SICs, with I = 2.11 ∙ ∙ 푙푛 푤 ∙ 훩 푙푛 푤 the SIC amplitude being astro 푐푚2 logarithmically proportional to 2+ the Ca wave amplitude. 푤 = 푐푖 푟푖, 푡 푛 푀 − 196.69 푡 푡 ISIC 푡 = Iastro 푐푖 푟푖, 푡 = cpeak 푒푥푝 − 푆퐼퐶 − 푒푥푝 − 푆퐼퐶 휏푑푒푐푎푦 휏푟푖푠푒 Neural Network Astrocytic Network Tripartite Synapse 푑푥 푧 = − 1 − 푓 ∙ 푢 ∙ 푥 ∙ 훿 푡 − 푡푠푝 푑푡 휏푟푒푐 푑푦 푦 = − + 1 − 푓 ∙ 푢 ∙ 푥 ∙ 훿 푡 − 푡푠푝 푑푡 휏푖푛 IIsyn syn 푑푧 푦 푧 = − 푑푡 휏푖푛 휏푟푒푐 I = A ∙ y(t) 푑푓 푓 syn = − + 1 − 푓 ∙ 휅 ∙ 훩 푐푖 푟푖, 푡 − 푐푡ℎ푟푒푠ℎ 푑푡 휏퐶푎 휇퐴 I = 2.11 ∙ ∙ 푙푛 푤 ∙ 훩 푙푛 푤 astro 푐푚2 푤 = 푐푖 푟푖, 푡 푛 푀 − 196.69 푡 푡 ISIC 푡 = Iastro 푐푖 푟푖, 푡 = cpeak 푒푥푝 − 푆퐼퐶 − 푒푥푝 − 푆퐼퐶 휏푑푒푐푎푦 휏푟푖푠푒 Putting a Neural-Astrocytic Network to Sleep Probabilistic neural connections, with a Gaussian fall-off m 2 2 푃μ 푟 푖푗 = 푃푚푎푥푒푥푝 − 푟푖푗 2휎 • 푟푖푗 the distance between neurons 푖 and 푗 • 푃푚푎푥 and 휎 are the peak and width of the probabilityμm distribution • No function – just basal Oscillations emerge as a network property neural activity Local Sleep in Awake Rats, Nature 2011 Bryant et al. Nature Reviews, 2004 "This hypothesis was reinforced by a recent modelling study showing that intercellular Ca2+ signaling potentially can introduce slow oscillation in neurons [our Ref]. Our experimental data strongly supports this hypothesis by demonstrating that increasing astrocytic influence on neurons indeed drives them to join the oscillatory activity (Fig. 5C). In this context it is also important to note, that the ratio of astrocytes involved in the SWA was found to start decreasing right after virtually all neurons joined the simultaneous activity (Figs 4 and 5). This observation further supports the view that astrocytic activity corresponds to the generation or maintenance, rather than termination of SWA." brain oscillations are still lacking a mechanistic origin • Rhythmic or repetitive electrical activity generated spontaneouslyPublications on or "Oscillations" in response per to Year stimuli by the neurons 2500 • Studied for 100 years (EEG, MEG, fMRI, PET, MER) 2000 • Encode and process brain information flow 1500 • Communication through coherence: interregional communication # Papers 1000 is established when the oscillatory activity between neuronal 500 pools is coherent (Fries 2005; 2009) 0• Related to all aspects of human behavior 1889 1909 1929 1949 1969 1989 2009 • cognitive, sensory, and motor tasks Year • All brain diseases are associated with oscillatory imbalances Source: PubMed Introducing function into a Neural-Astrocytic Network NAN Hopfield Nets • The idea of memories as energy minima was proposed by I.A.
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