Table of Contents and Schedule of Presentations

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1 The NEURON Simulation Environment Didactic Presentations Table of Contents and Schedule of Presentations NTC MLH WWL AM RMcD TM SS Ted Carnevale Michael Hines Bill Lytton Amit Majumdar Robert McDougal Tom Morse Subha Sivagnanam Hands-on exercises are indicated by an asterisk * in the Page column. Times shown are approximate, except for lunch. Monday, 6/20 Morning session Time Speaker Title Page 9:00 AM NTC Welcome to the NEURON summer course 5 Installing and configuring NEURON NTC Introduction to modeling 7 10:30 Coffee Break GUI: building and using a simple model 9 * Neurites, cables, and sections 11 10:45 MLH / NTC Interactive modeling: Hodgkin-Huxley axon 13 * 11:45 NTC Range, range variables, nodes, and nseg 15 12:00 Lunch Afternoon session 1:00 NTC Constructing branched model cells with the CellBuilder 2:00 Free time (Coffee Break at 2:30) 19 * 4:00 NTC Working with morphometric data 21 * 4:45 Daily wrapup 5:00 End of afternoon session Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 1

2 Didactic Presentations The NEURON Simulation Environment Tuesday, 6/21 Morning session Time Speaker Title Page 9:00 AM Q & A 9:15 WWL The hoc programming language 25 10:30 Coffee Break 10:45 MLH / NTC NMODL: the NEURON Model Description Language 12:30 Lunch Afternoon session 1:00 RMcD Numerical methods: accuracy, stability, speed 49 2:00 RMcD ModelDB and Model View 61 * 3:00 Coffee Break and Free time 3:45 MLH / NTC Channel Builder 75 4:45 Daily wrapup 5:00 End of afternoon session 41* Wednesday, 6/22 Morning session Time Speaker Title Page 9:00 AM Q & A 9:15 NTC Inhomogeneous channel distributions 85 * 10:30 Coffee Break 10:45 RMcD Python + NEURON 87 * 12:00 Lunch Page 2 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

3 The NEURON Simulation Environment Didactic Presentations Afternoon session 1:00 RMcD Reaction-diffusion 107 * 2:00 NTC Networks: synapses, events, and artificial spiking cells 2:30 Coffee Break 2:45 NTC Networks: synapses, events, and artificial spiking cells continued 3:30 Free time 4:45 Daily wrapup 5:00 End of afternoon session 125 * 125 * Thursday, 6/23 Morning session Time Speaker Title Page 9:00 AM Q & A 9:15 MLH / NTC Variable time steps and parameter discontinuities 10:30 Coffee Break 137 * 10:45 MLH / NTC Threads 161 * 12:00 Lunch Afternoon session 1:00 WWL Inhibitory synchronizing networks 173 * 2:45 Coffee Break and Free time 4:45 Daily wrapup 5:00 End of afternoon session Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 3

4 Didactic Presentations The NEURON Simulation Environment Friday, 6/24 Morning session Time Speaker Title Page 9:00 AM Q & A 9:15 MLH Parallel computation: distributed network models 10:45 Coffee Break 197 * 11:00 NTC Initialization 215 * 12:00 Lunch Afternoon session 1:00 AM & SS High performance computing via the Neuroscience Gateway Portal 2:30 Coffee Break 2:45 Free time 4:30 Wrapup, review, and evaluation (see last page in this booklet) 5:00 End of afternoon session 223 * Evening sessions and other material Appendix NTC Overview of creating and using NEURON models 233 MLH Ion accumulation mechanisms: a calcium pump 239 * MLH Families of simulations in parallel 243 * NTC The Impedance Tools 249 * NTC Linear Circuit Builder 257 * Translating network models to parallel hardware in NEURON (Hines & Carnevale 2008). NEURON and Python (Hines et al. 2009). before survey Receipt Survey penultimate page last page Page 4 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

6 Didactic Presentations The NEURON Simulation Environment Lipid Bilayer Physical System Membrane with no channels Model Capacitor I V C na ms 40 I V mv Simulation Representation create soma 80 Page 6 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

7 The NEURON Simulation Environment Didactic Presentations Topics 1. How to create and use models of neurons and networks of neurons How to specify anatomical and biophysical properties How to control, display, and analyze models and simulation results 2. How NEURON works 3. How to add user-defined biophysical mechanisms From Physical System to Computational Model Physical System Conceptual Model Computational Model Conceptual model a simplified representation of the physical system Computational model an accurate representation of the conceptual model Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 7

8 Didactic Presentations The NEURON Simulation Environment From Physical System to Computational Model Physical system Conceptual model Computational model v dendrite soma create soma, dendrite connect dendrite(0), soma(1) Ca1 pyramidal cell ball and stick hoc code Fundamental Concepts Signals What moves Driving force What is conserved Electrical charge carriers voltage gradient charge Chemical solute concentration gradient mass Page 8 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

9 The NEURON Simulation Environment Didactic Presentations Conservation of Charge i a i m i m i a i m i m i a C m d V m d t i ion = i a i a Example: Single Compartment Lipid bilayer (no channels) Membrane with linear ion channels (passive leak) Project goals: Use the GUI to build the model and custom interface for using it Run simulations and analyze results Change stimulus intensity and duration Adjust graphical displays of simulation results Adjust dt and Points Plotted / ms Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 9

11 The NEURON Simulation Environment Didactic Presentations Conservation of Charge i a i m i m i a i m i m i a C m d V m d t + i ion =i a i a The Model Equations c j d v j d t i ionj = k v k v j r j k v j i ionj c j r jk membrane potential in compartment j net transmembrane ionic current in compartment j membrane capacitance of compartment j axial resistance between the centers of compartment j and adjacent compartments k Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 11

12 Didactic Presentations The NEURON Simulation Environment Separating Anatomy and Biophysics from Purely Numerical Issues section a continuous length of unbranched cable Anatomical data from A.I. Gulyás Page 12 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

15 The NEURON Simulation Environment Didactic Presentations Range Variables Name Meaning Units diam diameter [µm] cm specific membrane [µf/cm 2 ] capacitance g_pas specific conductance [siemens/cm 2 ] of the pas mechanism v membrane potential [mv] range normalized position along the length of a section 0 range 1 any variable name can be used for range, e.g. x 0 physical distance physical length normalized distance 0 1 Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 15

16 Didactic Presentations The NEURON Simulation Environment Syntax: sectionname.rangevar(range) returns or sets the value of rangevar at the location corresponding to range Examples: dend.v(0.5) returns membrane potential at the middle of dend Shortcut: dend.v dend for (x) print x*l, v(x) prints physical distance and v at each point in dend where v was calculated nseg the number of points in a section at which the discretized cable equation is integrated nseg=1 nseg=2 nseg=3 Example: axon nseg = 3 To test spatial resolution forall nseg = nseg*3 and repeat the simulation Page 16 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

17 The NEURON Simulation Environment Didactic Presentations Category Variable Units Time t [ms] Voltage v [mv] Current specific i [ma/cm 2 ] (distributed) absolute [na] (point process) Capacitance specific cm [µf/cm 2 ] absolute [nf] (point process) Length diam, L [µm] Conductance specific g [S/cm 2 ] (distributed) absolute [µs] (point process) Cytoplasmic resistivity Ra [ cm] Resistance ri() [10 6 ] Concentration nai etc. [mm] Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 17

19 The NEURON Simulation Environment Didactic Presentations Example: Branched Model Cells Physical system: anatomically complex cell Conceptual model: "stick figure" Computational model: soma + dendritic cylinder(s) (and maybe an axon...) Project goals: Learn how to use CellBuilder Use session files to save and retrieve user interface (elementary project management) Test model and simulation: structural integrity discretization of space and time basilar soma oblique trunk trunk[1] tuft From hoc file generated by CellBuilder: create soma, trunk[2], oblique, tuft, basilar proc topol() { local i connect trunk(0), soma(1) connect trunk[1](0), trunk(1) connect oblique(0), trunk(1) connect tuft(0), trunk[1](1) connect basilar(0), soma(0)... Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 19

20 Didactic Presentations The NEURON Simulation Environment basilar soma oblique trunk trunk[1] tuft From hoc file generated by CellBuilder: proc geom() { forsec all { } soma { L = 30 diam = 30 } trunk { L = 400 diam = 3 } trunk[1] { L = 400 diam = 2 } oblique { L = 300 diam = 1.5 } tuft { L = 300 diam = 1 } basilar { L = 300 diam = 3 } } proc biophys() { forsec all { Ra = 160 cm = 1 } forsec dendrites { insert pas g_pas = 3e-05 e_pas = -70 } forsec apicals { insert hh gnabar_hh = gkbar_hh = gl_hh = 0 el_hh = } soma { insert hh gnabar_hh = 0.12 gkbar_hh = gl_hh = el_hh = } } Page 20 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

21 The NEURON Simulation Environment Didactic Presentations Anatomy and Empirically-based Models Quality of data histology staining, amputation, shrinkage diameter spines Data formats Detailed Morphometric Data Where to get it? DIY the kindness of strangers ModelDB NeuroMorpho.org How to get it into NEURON? standalone conversion programs import into CellBuilder Import3D tool "already in hoc" Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 21

22 Didactic Presentations The NEURON Simulation Environment Trust but verify... Qualitative tests Orphan sections and bottlenecks? insert pas, set Ra and g_pas low inject large depol current at soma examine shape plot of v Z-axis drift and backlash? examine side view of shape plot for abrupt jumps... and verify some more Quantitative tests Diameter Too large? _dmin=10 forall for i=0, n3d()-1 \ if (diam3d(i)<_dmin) _dmin=diam3d(i) print _dmin Too small? forall for i=0, n3d()-1 \ if (diam3d(i)<0.1) \ print secname(), " ", i, diam3d(i) Page 22 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

23 The NEURON Simulation Environment Didactic Presentations When it really matters... Test for systematic errors Favorite numbers? histogram of diameter measurements Other tests Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 23

The NEURON Simulation Environment Didactic Presentations Copyright

41 The NEURON Simulation Environment Didactic Presentations NMODL NEURON Model Description Language Add new membrane mechanisms to NEURON Density mechanisms Distributed Channels Ion accumulation Point Processes Electrodes Synapses Described by Differential equations Kinetic schemes Algebraic equations Benefits Specification only independent of solution method. Efficient translated into C. Compact One NMODL statement > many C statements. Interface code automatically generated. Consistent ion current/concentration interactions. Consistent Units Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 41

42 Didactic Presentations The NEURON Simulation Environment NMODL general block structure What the model looks like from outside NEURON { SUFFIX kchan USEION k READ ek WRITE ik RANGE gbar,... } What names are manipulated by this model UNITS { (mv) = (millivolt)... } PARAMETER { gbar =.036 (mho/cm2) <0, 1e9>... } STATE { n... } ASSIGNED { ik (ma/cm2)... } Initial default values for states INITIAL { rates(v) n = ninf } Calculate currents (if any) as function of v, t, states (and specify how states are to be integrated) BREAKPOINT { SOLVE deriv METHOD cnexp ik = gbar * n^4 * (v ek) } State equations DERIVATIVE deriv { rates(v) n = (ninf n)/ntau } Functions and procedures PROCEDURE rates(v(mv)) {... } Page 42 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

44 Didactic Presentations The NEURON Simulation Environment Density mechanism NEURON { SUFFIX leak NONSPECIFIC_CURRENT i RANGE i, e, g } PARAMETER { g =.001 (mho/cm2) <0, 1e9> e = 65 (millivolt) } ASSIGNED { i (milliamp/cm2) v (millivolt) } BREAKPOINT { i = g*(v e) } Point Process NEURON { POINT_PROCESS Shunt NONSPECIFIC_CURRENT i RANGE i, e, r } PARAMETER { r = 1 (gigaohm) <1e 9,1e9> e = 0 (millivolt) } ASSIGNED { i (nanoamp) v (millivolt) } BREAKPOINT { i = (.001)*(v e)/r } Density mechanism Point Process NMODL NEURON { SUFFIX leak NONSPECIFIC_CURRENT i RANGE i, e, g } SingleComp soma pas hh leak GUI NEURON { POINT_PROCESS Shunt NONSPECIFIC_CURRENT i RANGE i, e, r } SelectPointProcess Show PointProcessManager Shunt[0] at: soma(0.5) soma { insert leak g_leak =.0001 } print soma.i_leak(.5) Interpreter objref s soma s = new Shunt(.5) s.r = 2 Page 44 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

45 The NEURON Simulation Environment Ion Channel NEURON { USEION k READ ek WRITE ik } BREAKPOINT { SOLVE states METHOD cnexp ik = gbar*n*n*n*n*(v ek) } DERIVATIVE states { rate(v*1(/mv)) n = (inf n)/tau } Ion Accumulation NEURON { USEION k READ ik WRITE ko } BREAKPOINT { SOLVE state METHOD cnexp } DERIVATIVE state { ko = ik/fhspace/f*(1e8) + k*(kbath ko) } Didactic Presentations (mm) (mv) (ma/cm2) v(.5) (ms) 2 soma.ik( 0.5 ) 5 soma.ko( 0.5 ) 40 soma.ek( 0.5 ) Achase Vesicle Ach Internal Free Calcium ica Saturable Calcium Buffer STATE { Vesicle Ach Achase Ach2ase X Buffer[N] CaBuffer[N] Ca[N] } KINETIC calcium_evoked_release { : release ~ Vesicle + 3Ca[0] < > Ach (Agen, Arev) ~ Ach + Achase < > Ach2ase (Aase2, 0) : idiom for enzyme reaction ~ Ach2ase < > X + Achase (Aase2, 0) : requires two reactions : Buffering FROM i = 0 TO N 1 { ~ Ca[i] + Buffer[i] < > CaBuffer[i] (kcabuffer, kmcabuffer) } : Diffusion FROM i = 1 TO N 1 { ~ Ca[i 1] < > Ca[i] (Dca*a[i 1], Dca*b[i]) } : inward flux ~ Ca[0] << (ica) } Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 45

46 Didactic Presentations The NEURON Simulation Environment UNITS Checking NEURON { POINT_PROCESS Shunt... } PARAMETER { e = 0 (millivolt) r = 1 (gigaohm) <1e 9,1e9> } ASSIGNED { i (nanoamp) v (millivolt) } BREAKPOINT { i = (v e)/r } Units are incorrect in the "i =..." current assignment. BREAKPOINT { i = (v e)/r } The output from modlunit shunt is: Checking units of shunt.mod The previous primary expression with units: 1 12 coul/sec is missing a conversion factor and should read: (0.001)*() at line 14 in file shunt.mod i = (v e)/r<> To fix the problem replace the line with: i = (.001)*(v e)/r What conversion factor will make the following consistent? nai = ina / FARADAY * (c/radius) (um/ms) (ma/cm2) / (coulomb/mole) / (um) Page 46 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

The NEURON Simulation Environment Didactic Presentations Electronics 101 Solving a differential equation Incorporating space Numerical Methods Accuracy, stability, speed Robert A.

49 The NEURON Simulation Environment Didactic Presentations Electronics 101 Solving a differential equation Incorporating space Numerical Methods Accuracy, stability, speed Robert A. McDougal Yale School of Medicine 21 June 2016 Electronics 101 Solving a differential equation Incorporating space Hodgkin and Huxley: squid giant axon experiments Top: Alan Lloyd Hodgkin; Bottom: Andrew Fielding Huxley. Images from Wikipedia. Adapted from Pearson Education Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 49

50 Didactic Presentations The NEURON Simulation Environment Electronics 101 Solving a differential equation Incorporating space Hodgkin and Huxley equations C dv dt = g Na m 3 h V E Na )+g K n 4 V E K )+g V E ) dm dt = α m V) 1 m) β m V)m dh dt = α h V) 1 h) β h V)h dn dt = α n V) 1 n) β n V)n Top: Alan Lloyd Hodgkin; Bottom: Andrew Fielding Huxley. Images from Wikipedia. Adapted from Hodgkin and Huxley Electronics 101 Solving a differential equation Incorporating space What does it mean? Electronics 1 1 Page 50 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

51 The NEURON Simulation Environment Didactic Presentations Electronics 101 Solving a differential equation Incorporating space Current urrent is the movement of charge. In electronics, current is carried by the movement of electrons. In neurons, current flows across the membrane by the movement of ions. These ions can be positively or negatively charged. K + Na + Ca ++ Cl - Electronics 101 Solving a differential equation Incorporating space Resistors = Conductors A resistor is a material that impedes current flow. This includes essentially all materials. For those materials obeying Ohm s law, v = IR where v is the voltage drop across the resistor, I is the current, and R is the resistance this may be constant or a function of time). This may alternatively be written as I = gv where g = 1/R is the conductance. Ion channels Ion channels allow current to pass in the form of moving ions. They are therefore resistors. The resistance varies over time. Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 51

52 Didactic Presentations The NEURON Simulation Environment Electronics 101 Solving a differential equation Incorporating space Capacitors A capacitor accumulates charge according to CV = Q where Q is the charge, V is the potential, and C is the capacitance. The capacitive current is the rate at which charge is being stored on the current, dq/dt. Thus differentiating both sides of the above, we find C dv dt = dq dt = I. Cell membrane Charged ions accumulate along a neuron s membrane. It is therefore a capacitor. Electronics 101 Solving a differential equation Incorporating space Kirchoff s Current Law The algebraic sum of currents in a network of conductors meeting at a point is zero. I 1 I 2 I 3 I 4 I k = 0. k Wording from 27s circuit laws Page 52 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

53 The NEURON Simulation Environment Didactic Presentations Electronics 101 Solving a differential equation Incorporating space Putting it together: the electronics of a neuron Consider the simplified cell with three currents: I i 1 V i 2 C R i 3 By Kirchoff, Rearranging terms, we conclude: 0 = i 1 +i 2 +i 3 = I +C dv dt +gv C dv dt = gv +I. The Hodgkin-Huxley equations account for a pull on ions due to the balance of chemical and electrical gradients. This approximately acts as a battery with potential E associated with each resistor and leads to terms of the form g(v - E). Electronics 101 Solving a differential equation Incorporating space Solving a differential equation Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 53

54 Didactic Presentations The NEURON Simulation Environment Electronics 101 Solving a differential equation Incorporating space Separation of Variables Consider the differential equation C dv dt = gv +I V 0) = V 0 We can solve this for V t) by separation of variables: Therefore, dv I gv = dt C dv I gv = dt C 1 g ln I gv = t C +c 1 V = 1 g I gv = c 2 e gt I c 2 e gt. We can then solve for c 2 by plugging in V 0) = V 0 : so and thus V = 1 g Here we re assuming g is a constant. This is not true for voltage gated ion channels. V 0 = 1 g I c 2) c 2 = I gv 0 I I gv 0 )e gt. Note: This is a lot of work and is only possible because the equation is simple. This type of equation appears in leaky integrate and fire and is the basis of the cnexp solver. To solve general differential equations, we must use numerical techniques. Electronics 101 Solving a differential equation Incorporating space Explicit Euler In the Explicit Euler method, we approximate dy dt Δy Δt for some small time step Δt and estimate the function at a series of time points. Here Δy n = y n+1 y n and Δt n = t n+1 t n. Then starting from some initial point t 0 y 0 ), we approximate dy dt = f t y) as Δy n Δt n = f t n y n ) and thus and therefore Δy n = Δt n f t n y n ) Explicit Euler starts at a point, moves in the direction of the tangent line slope dy/dt) for a time Δt, then repeats. y n+1 = y n +Δt n f t n y n ). Page 54 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

55 The NEURON Simulation Environment Didactic Presentations Electronics 101 Solving a differential equation Incorporating space Explicit Euler Explicit Euler is numerically unstable If the time step in Explicit Euler is too large, the solution will be unstable: small dt 0.02 x < large dt ( 0.20 x > 0.1) 1/20 V 1 V Electronics 101 Solving a differential equation Incorporating space Implicit Euler 1.00 The Implicit Euler method is almost the same as the Explicit Euler method except instead of evaluating at f t n y n ), we evaluate at f t n+1 y n+1 ). That is, y n+1 = y n +Δt n f t n+1 y n+1 ). Note that y n+1 is on both sides, and thus we have an algebraic equation that must be solved to find y n Implicit Euler finds a new point such that if we moved in the direction of the tangent line slope dy/dt) backward in time by Δt, we would get where we started. Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 55

56 Didactic Presentations The NEURON Simulation Environment Electronics 101 Solving a differential equation Incorporating space Implicit Euler Implicit Euler is numerically stable small dt large dt ( ) /20 V 1 V As Implicit Euler is numerically stable, it is the default integration method in NEURON. Electronics 101 Solving a differential equation Incorporating space Implicit Euler Accuracy of Implicit Euler Note that the solutions found with a small dt and a large dt are different, even after the initial rapid change small dt large dt ( ) /20 V V One can prove that halving dt will approximately halve the difference between the computed value and the true value. Thus Implicit Euler is a first order method Error convergence estimates are true in the limit as dt 0. Page 56 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

57 The NEURON Simulation Environment Didactic Presentations Electronics 101 Solving a differential equation Incorporating space Crank-Nicolson Method Crank-Nicolson is stable but can oscillate NEURON also supports the second-order Crank-Nicolson method h secondorder=2). The solution is stable and converges faster than Implicit or Explicit Euler, but it can exhibit oscillations. Electronics 101 Solving a differential equation Incorporating space Staggered time steps If h secondorder=2, then membrane potentials are second order correct at time t, currents at t dt/2, and channel conductances at t +dt/2. To plot these correctly in NEURON, use a voltage axis, current axis, or state axis, respectively. ẋ = 1.4xy ẏ = xy y Single iteration y Staggered time step 1.0 x 1.0 x Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 57

58 Didactic Presentations The NEURON Simulation Environment Electronics 101 Solving a differential equation Incorporating space CVode: Variable Time Steps Variable time steps So far, we have considered numerical error as a function of the time step dt. We can instead choose an error tolerance and use that to pick a new dt at each time step. NEURON provides the CVode object for enabling variable step simulation h.cvode().atol(1e-3) 1.5 h.cvode().atol(1e-1) Electronics 101 Solving a differential equation Incorporating space Incorporating space Page 58 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

59 The NEURON Simulation Environment Didactic Presentations Electronics 101 Solving a differential equation Incorporating space i a i a x i a i m i m = i a i a c j dv j dt +i j = k v k v j r jk Electronics 101 Solving a differential equation Incorporating space Section Node v(0) v(1.5/nseg) Segment v(1) Membrane Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 59

60 Didactic Presentations The NEURON Simulation Environment Electronics 101 Solving a differential equation Incorporating space Improving accuracy by increasing nseg Improve accuracy by reducing the size of spatial compartments. In NEURON, do this by increasing nseg, the number of segments: nseg = 1 nseg = 2 nseg = 3 for sec in h.allsec(): sec.nseg *= 3 Note that you must multiply nseg by an odd number to preserve the location of the computed values, which is essential to testing convergence. Electronics 101 Solving a differential equation Incorporating space Trees can be solved stably in ) Only unstable methods can solve arbitrary shapes in ) To solve Δy = b where y and b have n entries e.g. if we want to solve for 4 variables at n/4 points) takes time proportional to: n 3 via Gaussian Elimination n log 2 7 via Strassen 1969) n if corresponds to a tree-matrix e.g. a neuron) discretized in a certain way right). McDougal et al 2013 Page 60 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

61 The NEURON Simulation Environment Didactic Presentations General issues ModelDB Other resources Stay up to date Don t reinvent the brain Using ModelDB and other archives for your research Robert A. McDougal Yale School of Medicine 21 June 2016 General issues ModelDB Other resources Stay up to date General issues Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 61

62 Didactic Presentations The NEURON Simulation Environment General issues ModelDB Other resources Stay up to date On reproducibility Non-reproducible single occurrences are of no significance to science. Karl Popper in The logic of scientific discovery, What is needed for a model to be reproducible? Model an approximation of the system of interest e.g. a model organism or a complete statement of the properties of the model in mathematical or computable form Experimental protocol what was done with the model to produce the data Science builds upon previous work; in order to do that, the previous work needs to be reproducible. General issues ModelDB Other resources Stay up to date Models are complicated 50 to % % > 100 K 3.0% 20 to % 0 to % 10 to 100K 12.1% 5 to 10K 9.1% < 0.5K 10.9% 0.5 to 1K 13.6% 10 to % 5 to % 2 to 5K 30.7% 1 to 2K 20.6% Files per Model File Size 38.5 of ModelDB models have over 20 files; 24.2 of files are over 5K. It is often hard to fully describe this complexity in a paper. Any bugs, typos, errors, or omissions might completely change the dynamics. Distributions from ModelDB, Fall A model was counted as having 0 files if it was not hosted on ModelDB. Page 62 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

63 The NEURON Simulation Environment Didactic Presentations General issues ModelDB Other resources Stay up to date Model sharing helps, but only reuse what you understand The easiest way to replicate someone else s results a first step toward building on them is to get their model code from a repository such as ModelDB. But beware: They may be solving a different problem than you with respect to species, temperature, age, etc). Their code may have bugs. To reduce the risk of problems: Read the associated paper. Compare the model and results to other similar models. Examine the model with ModelView and/or psection. Test ion channels individually. Collaborate with an experimentalist. General issues ModelDB Other resources Stay up to date ModelDB Part of the SenseLab Project Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 63

64 Didactic Presentations The NEURON Simulation Environment General issues ModelDB Other resources Stay up to date General issues ModelDB Other resources Stay up to date modeldb.yale.edu What is in ModelDB? Models for: 178 cell types 16+ species 48 ion channels, pumps, etc 135 topics Alzheimer s, STDP, etc) 1102 published models from 75 simulators 532 NEURON models Numbers are as of June 10, 2016 Page 64 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

The NEURON Simulation Environment Didactic Presentations General issues ModelDB Other resources Stay up to date Finding models Search box on the top-left of every page.

General issues ModelDB Other resources Stay up to date Anatomy of a ShowModel page 1) Search models. 2) Browse models. 3) Description of model. 4) Paper s) describing or using model.

65 The NEURON Simulation Environment Didactic Presentations General issues ModelDB Other resources Stay up to date Finding models Search box on the top-left of every page. Do full text or attribute searches. Word completions based on ModelDB entries not English) and attribute results updated as you type. Advanced search and browsing are also available. General issues ModelDB Other resources Stay up to date Anatomy of a ShowModel page 1) Search models. 2) Browse models. 3) Description of model. 4) Paper s) describing or using model. 5) Find models and papers cited by this model s paper, or that cite this model. 6) Searchable metadata. 7) Links to NeuronDB channel distributions etc within cell types). 8) Link to download the entire simulation. 9) Auto-launch a NEURON simulation requires browser configuration). 10) Simulation platform 5 minutes of remote desktop access to experiment with the model). 11) ModelView: visualize model structure. 12) 3D printable versions of cells from the model in 3DModelDB). 13) Directory browser, showing model files. 14) View pane for the currently selected file. Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 65

Didactic Presentations The NEURON Simulation Environment General issues ModelDB Other resources Stay up to date Identifying existing reuse Asterisks in the file browser indicate that the file is

66 Didactic Presentations The NEURON Simulation Environment General issues ModelDB Other resources Stay up to date Identifying existing reuse Asterisks in the file browser indicate that the file is reused in other models; click the asterisk to see a list of the other models. General issues ModelDB Other resources Stay up to date ICGenealogy: ion channel metadata When viewing most mo files describing an ion channel, an ICGenealogy button appears. Clicking this button loads the corresponding page of the ICGenealogy database which shows curated information about the channel model how it was derived, information about the underlying data, etc) and response curves. Page 66 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

print) General issues ModelDB Other resources Stay up to date McDougal et al, euroinformatics

67 The NEURON Simulation Environment Didactic Presentations General issues ModelDB Other resources Stay up to date ModelView Adapted from McDougal et al, euroinformatics 2015 online ahead of print) General issues ModelDB Other resources Stay up to date McDougal et al, euroinformatics 2015 online ahead of print) Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 67

Didactic Presentations The NEURON Simulation Environment General issues ModelDB Other resources Stay up to date McDougal et al, euroinformatics 2015 online ahead of print) General

68 Didactic Presentations The NEURON Simulation Environment General issues ModelDB Other resources Stay up to date McDougal et al, euroinformatics 2015 online ahead of print) General issues ModelDB Other resources Stay up to date McDougal et al, euroinformatics 2015 online ahead of print) Page 68 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

The NEURON Simulation Environment Didactic Presentations General issues ModelDB Other resources Stay up to date McDougal et al, euroinformatics 2015 online ahead of print) General issues ModelDB

69 The NEURON Simulation Environment Didactic Presentations General issues ModelDB Other resources Stay up to date McDougal et al, euroinformatics 2015 online ahead of print) General issues ModelDB Other resources Stay up to date How do people use ModelDB? Find a model described in a paper, download it, and experiment to understand the model s predictions. Find a model described in a paper. Use ModelView to understand the model s structure. Locate models and modeling papers on a given topic. Locate model components e.g. L-type calcium channel) for potential reuse. Search for simulator keywords e.g. FInitializeHandler) to find examples of how to use them. You can help by sharing your model code on ModelDB after publication. Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 69

70 Didactic Presentations The NEURON Simulation Environment General issues ModelDB Other resources Stay up to date Neurobiological context General issues ModelDB Other resources Stay up to date Other resources Page 70 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

The NEURON Simulation Environment Didactic Presentations General issues ModelDB Other resources Stay up to date NeuroMorpho.Org Tools Miscellaneous Import 3D NeuroMorpho.

Before using: rotate to check for z-axis errors, check to make sure the diameters are not all equal. Use the Import 3D tool to import morphologies into NEURON. For details, see: neuron.yale.

71 The NEURON Simulation Environment Didactic Presentations General issues ModelDB Other resources Stay up to date NeuroMorpho.Org Tools Miscellaneous Import 3D NeuroMorpho.Org is home to 37,712 reconstructed neurons from 158 cell types and 35 species as of June 10, Warning: not every morphology was reconstructed with the intent of being in a simulation. Before using: rotate to check for z-axis errors, check to make sure the diameters are not all equal. Use the Import 3D tool to import morphologies into NEURON. For details, see: neuron.yale.edu/neuron/docs/import3d General issues ModelDB Other resources Stay up to date Channelpedia Channelpedia.epfl.ch) Home to information about ion channels. Many channels have one or more associated models e.g. different species or cell types); all are downloadable as MOD files. Shows gating variable and channel response to voltage clamp for each model. Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 71

Didactic Presentations The NEURON Simulation Environment General issues ModelDB Other resources Stay up to date Biomodels www.ebi.ac.uk/biomodels-main) jnml BIOMD0000000073_LEMS.

Models are in SBML but can be converted to MOD files via e.g. jneuroml github.com/neuroml/jneuroml). Test converted models before using in a larger model.

72 Didactic Presentations The NEURON Simulation Environment General issues ModelDB Other resources Stay up to date Biomodels jnml BIOMD _LEMS.xml -neuron Biomodels model (SBML) LEMS model MOD file jnml -sbml-import BIOMD xml Biomodels is a systems biology model repository. Models are in SBML but can be converted to MOD files via e.g. jneuroml github.com/neuroml/jneuroml). Test converted models before using in a larger model. Edits will likely be necessary to get them to interoperate with other mechanisms. A native SBML importer for NEURON s rxd module is under development. General issues ModelDB Other resources Stay up to date Open Source Brain OpenSourceBrain.org) Open Source Brain promotes collaborative model development via github. Models are typically in NeuroML or neuroconstruct format; neuroconstruct neuroconstruct.org) converts both formats to NEURON. The conversion process places different ion channels in different MOD files, which allows extracting model components. Page 72 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

The NEURON Simulation Environment Didactic Presentations General issues ModelDB Other

org) NeuroElectro archives experimentally measured electrophysiology values for

etc. General issues ModelDB Other resources Stay up to date SenseLab senselab.med.yale.

73 The NEURON Simulation Environment Didactic Presentations General issues ModelDB Other resources Stay up to date NeuroElectro NeuroElectro.org) NeuroElectro archives experimentally measured electrophysiology values for different cell types; it shows the spread and allows comparing values across different cell types. Read the paper associated with a value to understand: species, experimental conditions, etc. General issues ModelDB Other resources Stay up to date SenseLab senselab.med.yale.edu) Locations of I A in CA1 Pyramidal SenseLab is a suite of 10 interconnected databases listed at left). ModelDB and NeuronDB at right) are the most useful for modeling. NeuronDB shows what channels are present and the inputs and outputs y cell region e.g. distal apical dendrite vs proximal apical dendrite). Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 73

74 Didactic Presentations The NEURON Simulation Environment General issues ModelDB Other resources Stay up to date Stay up to date Twitter Many groups announce new developments on Twitter, including: SenseLab including Open Source ICGenealogy Int. Neuroinformatics Coordinating Facility Page 74 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

75 The NEURON Simulation Environment Didactic Presentations Iconify NEURON Main Menu File Edit Build Tools Graph Vector Window single compartment Cell Builder NetWork Cell NetWork Builder Linear Circuit Channel Builder ChannelBuild[0] managed KSChan Close Hide Properties leak Density Mechanism NonSpecific ohmic ion current i_leak = g_leak * (v - e_leak) g is a RANGE PARAMETER Default g = 0 (S/cm2) e = 0 (mv) Select here to construct gates SingleComp Close soma pas hh leak Hide ChannelBuild[0] managed KSChan Close Properties Hide leak Channel Density Name Mechanism NonSpecific Selective for ohmic Ion... ion current i_leak Ohmic = i=g*(v-e) g_leak * (v - e_leak) g is Goldman-Hodgkin-Katz a RANGE PARAMETER Default Default gmax g = 0 (S/cm2) e = 0 (mv) HH sodium channel Select HH potassium here to construct channel gates Clone channel type Text to stdout ChannelBuild[1] managed KSChan Close Properties Hide nahh Density Mechanism na ohmic ion current ina = g_nahh * (v - ena) g = gmax * m^3 * h Default gmax = 0 (S/cm2) m = am*(1 - m) - bm*m h = ah*(1 - h) - bh*h Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 75

76 Didactic Presentations The NEURON Simulation Environment Close Default gmax = 0 (S/cm2) m = am*(1 - m) - bm*m h = ah*(1 - h) - bh*h States Transitions Properties ChannelBuildGateGUI[0] for ChannelBuild[0] Hide Select hh state or ks transition to change properties m h m^3 m = am*(1 - m) - bm*m Power 3 Fractional Conductance m fraction 1 Adjust Run infm taum m <-> m (a, b) (KSTrans[0]) Display inf, tau am = A*x/(1 - exp(-x)) where x = k*(v - d) A 1 k 0.1 d -40 bm = A*exp(k*(v - d))) ChannelBuild[0] managed KSChan Close Properties Clone channel type nahh Density Mechanism Text to stdout na ohmic ion current ina = g_nahh * (v ena) g = gmax * m^3 * h Default gmax = 0 (S/cm2) m = am*(1 m) bm*m (KSTrans[0]) am = 1*x/(1 exp( x)) where x = 0.1*(v + 40) (Vector[7]) bm = 4*exp( *(v + 65))) (Vector[8]) h = ah*(1 h) bh*h (KSTrans[1]) ah = 0.07*exp( 0.05*(v + 65))) (Vector[11]) bh = 1/(1 + exp( 0.1*( 35 v))) (Vector[12]) Hide nahh Channel Density Name Mechanism na Selective ohmic ion for Ion... current ina Ohmic = g_nahh i=g*(v-e) * ena) g = Goldman-Hodgkin-Katz gmax * m^3 * h Default gmax gmax = 0 (S/cm2) HH sodium channel m HH = am*(1 potassium m) channel bm*m h = ah*(1 h) bh*h Page 76 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

77 The NEURON Simulation Environment Didactic Presentations ah bh bh = A/(1 + exp(k*(d v)) A 1 k d EquationType alpha,beta ah bh a,b inf,tau ah bh bh = A/(1 + exp(k*(d v)) A 1 k d EquationType alpha,beta ah bh A A*exp(k*(v d))) A*x/(1 exp( x)) where x = k*(v d) A/(1 + exp(k*(d v)) KSChanBGa ah bh tauh = A*exp(k*(v d))) A 1 k d EquationType inf,tau infh tauh A A/(1 + exp(k*(d v)) Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 77

78 Didactic Presentations The NEURON Simulation Environment Close States Transitions Properties O C Hide Drag new state from left. Drag off canvas to delete O C ChannelBuildGateGUI[0] for ChannelBuild[0] C2 no gate selected Adjust Run no KSTrans selected ChannelBuildGateGUI[0] for ChannelBuild[0] Close Hide States Transitions Properties New transition pair: select source and drag to target no gate selected C v C2 O Adjust Run no KSTrans selected Page 78 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

79 The NEURON Simulation Environment Didactic Presentations Close States Transitions Properties Hide Select hh state or ks transition to change properties v v C C2 O ChannelBuildGateGUI[0] for ChannelBuild[0] O O: 3 state, 2 transitions Power 1 Fractional Conductance C2 fraction 0 O fraction 1 Adjust Run ac2o 0.6 bc2o bc2o = A A 0 EquationType alpha,beta ac2o bc2o a,b inf,tau nai nao ki ko cai cao Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 79

80 Didactic Presentations The NEURON Simulation Environment Close States Transitions Properties Hide Select hh state or ks transition to change properties v cai C C2 O ChannelBuildGateGUI[0] for ChannelBuild[0] O O: 3 state, 2 transitions Power 1 Fractional Conductance C2 fraction 0 O fraction 1 Adjust Run ac2o 0.6 bc2o ChannelBuild[0] managed KSChan Close Hide Properties kca Density Mechanism k ohmic ion current ik = g_kca * (v ek) g = gmax * O Default gmax = 0 (S/cm2) C2 + cai < > O (a, b) (KSTrans[9]) Display inf, tau ac2o = A O: 3 state, 2 transitions Page 80 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

81 The NEURON Simulation Environment Didactic Presentations Close ChannelBuild[0] managed KSChan[0] Properties Hide leak Density Mechanism NonSpecific ohmic ion current i_leak = g_leak * (v e_leak) g = gmax * O * O2 * O3 Default gmax = 0 (S/cm2) e = 0 (mv) O: 3 state, 2 transitions O2: 2 state, 1 transitions O3 = ao3*(1 O3) bo3*o3 Close O C States Transitions Properties Hide Drag new state from left. Drag off canvas to delete v v C C2 O C3 v O2 ChannelBuildGateGUI[0] for ChannelBuild[0] Change state name O3 nrniv no gate selected O3 Accept Cancel Adjust Run no KSTrans selected 1 ChannelBuild[0] managed KSChan Close Properties Hide leak Channel Density Name Mechanism NonSpecific Selective for ohmic Ion... ion current NonSpecific i_leak Ohmic = i=g*(v-e) g_leak * (v e_leak) na g is Goldman-Hodgkin-Katz a RANGE PARAMETER k Default Default gmax g = 0 (S/cm2) e = 0 Create (mv) new type HH sodium channel Select HH potassium here to construct channel gates Clone channel type Text to stdout Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 81

82 Didactic Presentations The NEURON Simulation Environment ionname charge e.g. ca 2 cl 1 nrniv Accept Cancel ChannelBuild[0] managed KSChan Close Hide Properties leak Density Mechanism cl ohmic ion current icl = g_leak * (v ecl) g is a RANGE PARAMETER Default g = 0 (S/cm2) Select here to construct gates Page 82 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

85 The NEURON Simulation Environment Didactic Presentations Spatially inhomogeneous parameters Rules None (arbitrary values) Constant over sets of sections use SectionLists (CellBuilder Subsets) A function of position Example: model with hh in apical dendrites Suppose gnabar_hh in the apical tree decreases linearly with distance from the soma. Details: 100% at tree origin, 0% at most distant termination. Copyright N.T. Carnevale and M.L. Hines, all rights reserved Page 85

86 Didactic Presentations The NEURON Simulation Environment This example: gnabar_hh = 0.12 * (1 - p) where p = L 0x /L max (normalized path distance from location x to origin 0 of apical tree) The general problem: param = f(p), where f can be any function and p is a "distance metric" such as: path length from a reference point radial distance from a reference point distance from a plane ("3D projection onto a line") An equivalent hoc idiom: forsec subset for (x,0) { rangevar_suffix(x) = f(p(x)) } Conceptualize the task 1. Specify the subset s distance metric p parameter that depends on distance function f that governs the relationship between the parameter and p 2. Verify the implementation How? hoc or Python or GUI (CellBuilder) Page 86 Copyright N.T. Carnevale and M.L. Hines, all rights reserved

Electronics 101 Solving a differential equation Incorporating space. Numerical Methods. Accuracy, stability, speed. Robert A.

Electronics 101 Solving a differential equation Incorporating space. Numerical Methods. Accuracy, stability, speed. Robert A. Numerical Methods Accuracy, stability, speed Robert A. McDougal Yale School of Medicine 21 June 2016 Hodgkin and Huxley: squid giant axon experiments Top: Alan Lloyd Hodgkin; Bottom: Andrew Fielding Huxley.