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GUM*02 tutorial session UTSA, San Antonio, Texas

GUM*02 tutorial session UTSA, San Antonio, Texas. Parameter searching in neural models Mike Vanier, Caltech. The problem:. you want to build a model of a neuron you have a body of data you know a lot about the neuron’s morphology physiology ion channel kinetics

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GUM*02 tutorial session UTSA, San Antonio, Texas

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  1. GUM*02 tutorial sessionUTSA, San Antonio, Texas Parameter searching in neural models Mike Vanier, Caltech

  2. The problem: • you want to build a model of a neuron • you have a body of data • you know a lot about the neuron’s • morphology • physiology • ion channel kinetics • but you don’t know everything!

  3. Typical preliminary data set • anatomy • rough idea of morphology • detailed reconstruction

  4. Typical preliminary data set • physiology • current clamp • synaptic potentials • potentiation • modulators

  5. Typical preliminary data set • ion channels • identities of the major types • kinetics • modulation

  6. Missing data? • ion channels • identities of ALL channels • densities (uS/(um)2) • detailed kinetics • anatomy • detailed reconstructions? variability? • physiology • voltage clamp, neuromodulators, etc. ???

  7. Harsh reality • most experiments not done with models in mind • >half of model parameters loosely constrained or unconstrained • experiments to collect model params are not very sexy

  8. A different approach • collect data set model should match • collect plausible parameters • those known to be correct • educated guesses • build model • test model performance • modify parameters until get match

  9. How to modify parameters? • manually • 10 parameters @ 5 values each: • 9765625 possible simulations • 1 sim/minute = 19 years! • use previous results to guide searching • non-linear interactions? • tedious!!!

  10. How to modify parameters? • automatically • set ranges for each parameter • define update algorithm • start parameter search • go home! • check results in a day, week, ...

  11. match function • need to quantify goodness of fit • reduce entire model to one number • 0 = perfect match • match: • spike rates • spike times • voltage waveform

  12. simple match function • inputs: different current levels • e.g. 0.05, 0.1, 0.15, 0.2, 0.25, 0.3 nA • outputs: spike times

  13. waveform match function • inputs: hyperpolarized current levels • e.g. -0.05, -0.1 nA • outputs: Vm(t)

  14. other match functions • some data might be more important to match than the rest • adaptation • bursting behavior • incorporate into more complex match functions

  15. weight early spikes more • wij: weighting params • set wi0 < wi1 < wi2 < ...

  16. harder match functions • bursting • purkinje cell, pyramidal cell • transitions btw complex behaviors • regular spiking bursting

  17. the data set • need exceptionally clean data set • noise in data set: • model will try to replicate it! • need wide range of inputs

  18. typical data set for neuron model • current clamp over wide range • hyperpolarized (passive) • depolarized (spiking)

  19. the process (1) • build model • anatomy • channel params from lit • match passive data • hyperpolarized inputs

  20. the process (2) • create match function • waveform match for hyperpolarized • spike match for depolarized • run a couple of simulations • check that results aren’t ridiculous • get into ballpark of right params

  21. the process (3) • choose params to vary • channel densities • channel kinetics • minf(V), tau(V) curves • passive params • choose parameter ranges

  22. the process (4) • select a param search method • conjugate gradient • genetic algorithm • simulated annealing • set meta-params for method

  23. the process (5) • run parameter search • periodically check best results • marvel at your own ingenuity • curse at your stupid computer • figure out why it did/didn’t work

  24. results (motivation)

  25. parameter search methods • different methods have different attributes • local or global optima? • efficiency? • depends on nature of parameter space • smooth or ragged?

  26. the shapes of space smooth ragged

  27. genesis param search methods • Conjugate gradient-descent (CG) • Genetic algorithm (GA) • Simulated annealing (SA) • Brute Force (BF) • Stochastic Search (SS)

  28. conjugate gradient (CG) • “The conjugate gradient method is based on the idea that the convergence to the solution could be accelerated if we minimize Q over the hyperplane that contains all previous search directions, instead of minimizing Q over just the line that points down gradient. To determine xi+1 we minimize Q over x0 + span(p0,p1,p2,...,pi) where the pk represent previous search directions.”

  29. no, really... • take a point in parameter space • find the line of steepest descent (gradient) • minimize along that line • repeat, sort of • along conjugate directions only • i.e. ignore subspace of previous lines

  30. CG method: good and bad • for smooth parameter spaces: • guaranteed to find local minimum • for ragged parameter spaces: • guaranteed to find local minimum ;-) • not what we want...

  31. genetic algorithm • pick a bunch of random parameter sets • a “generation” • evaluate each parameter set • create new generation • copy the most fit sets • mutate randomly, cross over • repeat until get acceptable results

  32. genetic algorithm (2) • amazingly, this often works • global optimization method • many variations • many meta-params • mutation rate • crossover type (single, double) and rate • no guarantees

  33. simulated annealing • make noise work for you! • noisy version of “simplex algorithm” • evaluate points on simplex • add noise to result based on “temperature” • move simplex through space accordingly • gradually decrease temperature to zero

  34. simulated annealing(2) • some nice properties: • guaranteed to find global optimum • but may take forever ;-) • when temp = 0, finds local minimum • how fast to decrease temperature?

  35. comparing methods (1)

  36. comparing methods (2)

  37. comparing methods (3)

  38. recommendations • Passive models: SA,CG • Small active models: SA • Large active models: SA, GA • Network models: usually SOL

  39. genesis tutorial (1) • task: • parameterize simple one-compt neuron • Na, Kdr , KM channels • objects: • paramtableGA • paramtableSA • paramtableCG

  40. genesis tutorial (2) • parameters: • gmaxof Na, Kdr , KM • KMt(v) scaling • KM minf(v) midpoint

  41. Conclusions • param search algorithms are useful • but: pitfalls, judgment • modeler must help computer • failure is not always bad! • will continue to be active research area

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