Presentation on theme: "Introduction to Modeling and Computational Neuroscience using Python"— Presentation transcript:
1Introduction to Modeling and Computational Neuroscience using Python Randy HeilandResearch ScientistIndiana UniversityI wonder why. I wonder why.I wonder why I wonder.I wonder why I wonder whyI wonder why I wonder! ** Surely You're Joking, Mr. Feynman! (Adventures of a Curious Character), Richard Feynman.
3Experiment Analysis Model Simulation u’ = f(u,v) v’ = g(u,v) Mental e-07, e-05,e-08, e e-06, e-09, e-08, e-06, e-08, e-09, e-06, e-07, e-06, e+00, e-06, e-08,, e-06,e-08,e-06,e-06, e-09, e-08, e+00, e-08, e-07, e-05, e-09, e-06,[ e-07, e-08, e-08, e-08, e+00, e-09,512 electrode chipCourtesy A.LitkeExperimentMentalu’ = f(u,v)v’ = g(u,v)AnalysisModelMathematicalComputational Science is a cycle of these 4 areas. An experiment may precede or follow a model.Regarding models, we’re mostly interested in mathematical models. Simulations: computer programs to solve models Analysis: interpretation/verification of simulation dataExperiments: physical/chemical/bio/astro or even “thought” experiment (Einstein)Alan Litke’s 512-electrode chip for retina neuronsMental models: Heliocentric model of earth/sun (vs. geocentric)Analysis: we now have more data than we have computers or people’s time to analyze – and it’s growing fast! (e.g. medical devices; social n/w data; astronomy; etc etc)Step 1: …Step 2: ……Simulation Patterns,Structures,Causality…ProceduralCourtesy of Indiana University
4Modeling Using math to approximate some process (or data) (physical, biological, chemical, social, …)Typically ignore some parameters for a more“reasonable” model (e.g., for your F=ma lab, youignored friction)“ all models are wrong, but some are useful”Prof. Emer. George E. P. Box, Statistics, UW-Madison
5Simulation Execution of a model in a computer program Several computer languages: C/C++, Java, etc.Higher level languages: MATLAB, Python, etc.Solving some models may require the use of parallel computing.Possibly discuss HPC, dist’d computing, cloud computing (e.g. Amazon), GPUs, etc.
6Python language Easy to use Interpreted Powerful >>> (52*55)/3.0>>> from math import *>>> cos(pi)-1.0Easy to useInterpretedPowerfulFree (“open source”); runs on all computersUsed in many computational science tools
7Simple model in Python Average monthly temperature in Indiana (from weather.com) A function as a modellowTemp=[19,22,30,41,52,61,65,63,55,43,34,23]plot(lowTemp,'o') # ‘o’ circular pointstime = arange(0, 12, 0.1)F = 22*sin(pi/6 * (time-pi)) + 42plot(time,F)(Note that Python is “0-based indexing”)
8NeuroscienceGoal: understand relationship between neural structures and functionsHelp solve important problemsVisionMemoryAuditory…Ponder/explain interesting topicsConsciousness; self-awarenessAltruismWhy?– “Seen and hear”, 1999.(image of brain)Altruism: behavior by an animal/entity that is not beneficial to or may be harmful to itself but that benefits others of its species.
9Concepts & Terminology A neuron is a nerve cell.It contains a soma, dendrites,and axon.Soma(Combination of biology, chemistry,and physics)Microscopic imageIllustrative image
10Yes, it’s quite complexSomaScanning Electron Microscope imageSEM image: cutaway of (mouse) nerve ending and its synaptic vesicles(cellimagelibrary.org)
11The scale of a modelModels can be at different scales: molecular, cellular, multi-cellular, tissue, organ, organism, …A single neuron model is on a different space and time (“spatiotemporal”) scale than a brain region or whole brain model.
12Larger number of neurons complex signaling and networks Rich-Club Organization of the Human Connectome The Journal of Neuroscience, 2 November 2011, 31(44): Martijn P. van den Heuvel and Olaf Sporns.Rich-Club Organization of the Human Connectome.M.P. van den Heuvel and O. Sporns. J. Neuroscience,2 Nov 2011.100 billion neurons in human brain(Thanks to Journal of Neuroscience and authors for permission to use this image)
13“… it is intolerable that we do not have this information [connectional map] for the human brain. Without it there is little hope of understanding how our brains work…”(Crick 1993)1962 Nobel Prize for Physiology or MedicineQ: who knows who Francis Crick was?Hint: James Watson, Maurice Wilkins, Rosalind FranklinFrancis Crick,
14Vision: conversion of light to electrical signals Rubin’s vase: Danish psychologist Edgar Rubin, Visual perception; brain can only maintain one image (vase or face) at a time.Vase or Face? A Neural Correlate of Shape-Selective Grouping Processes in the Human Brain.Journal of Cognitive Neuroscience, Aug 2001, pg
15MemoryOne of the main hypotheses in neuroscience is that memories are encoded in the strengths of synapses between neuronsPlasticity – the ability tochange as a result of experienceSomaMathematical Foundations of Neuroscience, Ermentrout and Terman, p. 168.How is it that we can remember events from many years ago, but not what happened at 2:37 yesterday? E.g. my Grandmother’s backrubs.
16Overwhelmed yet? Let’s begin by modeling a single neuron How? Why? An electrical circuit is a good starting modelWhy?Because it is an (chemo)electrical circuit
17From your past homework The nervous system of the human body contains axons whose membranes act as small capacitors. A membrane is capable of storing 1.2 x 10-9 C of charge across a potential difference of 0.07 V before discharging nerve impulses through the body. What is the capacitance of one of these axon membranes? neuron spike
18Single neuron simulation Shows how ions are responsible for potential difference.Problem with these sims, they don’t show the math.- play the simulation to see V flip/spike
19Simplified model of a neuron RC circuit (Resistance-Capacitance)Ion transportsact as a resistor.Cell membrane acts as acapacitor.
20Leaky integrate-and-fire (LIF) model (#1) Where variables refer to membrane’s:V = potentialR = resistanceI = currentif t > t_rest; otherwise = 0Note: for those who haven’t taken Calculus (yet), dV/dt is a derivative (not division)This equation is a differential equationIt can be solved numericallyLeaky integrate is from the RC-circuit model; Fire is the delta function
21LIF in Python But it’s not very realistic… # initialize all variables for i, t in enumerate(time): # loop over desired timeif t > t_rest:V[i] = V[i-1] + (-V[i-1] + I*R) / tau * dtif V[i] >= V_threshold:V[i] = V[i] + V_spiket_rest = t + tau_refplot(time,V)Numerical integration viaforward Euler method.(Rf.But it’s not very realistic…
22Hodgkin-Huxley model (#2) 1952 (Nobel Prize 1963)Giant squid measure voltages Circuit model- complete with Python sim.The Hodgkin-Huxley model for neural dynamics is one of the most successful models in computational neuroscience. Based on voltage-clamp experiments on the squid giant axon, the model incorporates voltage-sensitive ion channels into the circuit model of the membrane to describe the generation and propagation of action potentialsElectrical circuit modelA more complicated differential equation- has both linear and nonlinear components
23What about modeling LOTS of neurons To model a brain, we want to model a network of neuronsNeed models of both the spiking behavior and the synapse (transmission between neurons)In the human brain, each neuron is connected to several thousand other neurons.
24Izhikevich model (#3) m=membrane potential; u=membrane recovery if v >= 30 mV thenv = cu = u + dm=membrane potential; u=membrane recoveryCaptures multiple types of spiking behaviorComputationally fast enough to do many neurons
25Izhikevich model (cont’d) (plus many more)Izhikevich E.M. (2003) Simple Model of Spiking Neurons. IEEE Transactions on Neural Networks, 14:
26AnalysisAfter you have a model and have run a simulation of the model, you need to analyze the resulting data. Similarly, data from an experiment needs to be analyzed.Transfer Entropy is just one such analysis technique (next slide)The Fourth Paradigm: Data-Intensive Scientific Discovery (2009)
27Visualization of analysis results Transfer Entropy (TE) measures the effect thatone neuron’s spiking has on another neuron.maxminPart of much larger TE matrixGraph displays of TE(with different thresholds)
28DIY neuroscience experiments (SpikerBox: $50-$100)♪outputinputCockroach leg (it grows back)Cockroach leg
29Sampling of Research[ers] John Beggs, Physics, Indiana U.- experimental research (“brains in a dish”) andanalysis of experimental and simulated dataSusan Amara, Neurobiology,U. of Pittsburgh,past President of Society for Neuroscience.- molecular & cellular biology of transportersOlaf Sporns, Psychological and Brain Sciences, Indiana U.- computational cognitive neuroscience; neural networks; coined “Connectome”Nancy Kopell, Mathematics, Boston U.Co-Director of Center for Biodynamics- develops models for and analysis of networks of neurons, esp. rhythms and oscillations.(Joy Hirsch)Crick & James Watson famously discovered structure of DNA… led to an entire generation of research.Nancy Ko-PELL (studied under S. Smale at UC-Berkeley)
31Summary Modeling uses math to approximate reality Modeling occurs at multiple scalesNeuroscience: understand relationship between neural structures and functionsPython lets you experiment with computational neuroscience (for free)
32IU might be of interest to you Dept of PhysicsBiophysics, BiocomplexitySchool of Informatics and ComputingComplex systems, computer science, data miningDept of Pyschological and Brain SciencesLearning, computational models of …Biology, Chemistry, …
33Thanks! Be curious. Be creative. Be nice to your neurons. Questions & short survey
34Further reading/References Vase or Face? A Neural Correlate of Shape-Selective Grouping Processes in the Human Brain. Journal of Cognitive Neuroscience, Aug 2001, pg- From Eye to Sight, Alan LitkeCraddock TJA , Tuszynski JA , Hameroff S (2012) Cytoskeletal Signaling: Is Memory Encoded in Microtubule Lattices by CaMKII Phosphorylation? PLoS Comput Biol 8(3): e doi: /journal.pcbi
35Analysis publications Simple model of spiking neurons.IEEE Transactions on Neural Networks (2003) 14:Complex network measures of brain connectivity: uses and interpretations.Neuroimage Sep;52(3):Extending Transfer Entropy Improves Identification of Effective Connectivity in a Spiking Cortical Network Model
36Self-awarenessAwareness of one’s own ability to think (humans, apes, dolphins, …)1970 “mirror test” for chimpanzeesDifficult to testI wonder why. I wonder why.I wonder why I wonder.I wonder why I wonder whyI wonder why I wonder! *Prefrontal cortex
37Effects of meditation experience on functional connectivity of distributed brain networks. Feb 2012. “Participants with more meditation experience exhibited increased connectivity within attentional networks…”
38Nerve cells are formed during fetal life and for a short time after birth. Unlike most cells, which have a fairly short lifespan, neurons in the brain live a long time. These cells can live for up to 100 years or longer. To stay healthy, living neurons must constantly maintain and repair themselves.Groups of neurons in the brain have special jobs. For example, some are involved with thinking, learning, and memory. Others are responsible for receiving information from the sensory organs (such as the eyes and ears) or the skin. Still others communicate with muscles, stimulating them into action.
39Definitions (for this talk) Model: math equation(s) to describe a process (physics,chemistry,biology,…)Simulation: computer program to solve the modelAnalysis: interpretation/verification of data from the simulation (or experiment)- Might be an algorithm instead of eqns (Stephen Wolfram)- Maybe not a computer; might be analog, e.g. an electrical circuit
40Is it possible to use more of our brain? Barry Gordon, professor of neurology and cognitive science at the Johns Hopkins University School of Medicine, repliesScientific American| Saturday, March 3, 2012 | 2Yes! Though perhaps not how you might imagine. You can't put more of your brain to work. Your whole brain is working all the time, even when you think you're just being lazy. What you can do is make it work more productively.There are two proved strategies to make your neural systems more efficient. The first strategy is to focus, which is hard to do. It is quite difficult to force your brain to stay on task and to shut off extraneous thoughts. Yet by concentrating, your brain can muster the neural tools it needs to tackle a complex problem. In fact, intense focus may be one reason why so-called savants become so extraordinary at performing extensive calculations or remembering a slew of facts.The second approach is optimization. The human brain is far from an ideal "thinking machine." Our mental processes are slow, and the accuracy of our memory is far from perfect. Our intrinsic limitations are compounded by the simple mental blunders we make; these unhelpful tendencies, however, are correctable. For instance, you can become a better problem solver by looking beyond your personal biases and blind spots to consider alternative solutions. The more you learn to recognize and seek a variety of answers, the better your brain will be at finding optimal solutions.Some proof that focus and optimization can improve the brain's performance comes from research on video gamers. Neuroscientists at the University of Rochester have shown that even novice gamers can improve cognitive skills such as perception and attention by playing action video games. These games can strengthen players' mental acuity because they require intense concentration and ruthless self-correction (otherwise, your friends shoot you!).Sometimes, however, you may think better when you're not trying so hard. (You have to consider all the alternatives.) Periods of artistic and scientific creativity—when people often tackle the biggest, most open-ended problems—usually require letting your brain meander, percolate, chill. It may not feel like you are using more of your brain when you unleash it in this way, but one virtue of the human brain is that it often does its best work when it does not seem to be working at all.
411-min lesson in Diff. Eq. Geometric interpretation Show sin(x), tangent/deriv cos(x)d/dt F(x) = cos(x)
42This confocal micrograph shows specialized cells named Purkinje cells (red) that are found in a part of the brain called the cerebellum. They send out vast numbers of branches that make connections with other cells in the cerebellum. This part of the brain co-ordinates your voluntary movements and keeps you oriented in space. It also plays a part in learning physical skills - like riding a bike or playing the piano.