1 / 52

Spatial Stochastic Simulators

Spatial Stochastic Simulators. Kim “Avrama” Blackwell George Mason University Krasnow Institute of Advanced Studies. Diverse Numbers of Molecules Spatially Inhomogeneous. G protein coupled receptors Diffusion required for signal interaction. Glutamate receptors 1  M  60 molecules

sphipps
Download Presentation

Spatial Stochastic Simulators

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Spatial Stochastic Simulators Kim “Avrama” Blackwell George Mason University Krasnow Institute of Advanced Studies

  2. Diverse Numbers of MoleculesSpatially Inhomogeneous G protein coupled receptors Diffusion required for signal interaction Glutamate receptors 1 M  60 molecules molecular interactions occur stochastically Small number of molecules in spines Large number of molecules in system Kotaleski and Blackwell 2010

  3. Spatial Stochastic Simulators • Particle based • Smoldyn, MCell, CDS • Individual molecules are represented as point-based particles, which diffuse random distance and random direction at each time step • If two reacting molecules pass near each other they may react • Computations increase with number of molecules Diffusion Association Dissociation b Membrane

  4.   Mcell (First and oldest) Transparent • Geometry from volumetric imaging data using Blender (www.blender.org) • Mesh elements may be reflective, transparent, or absorptive • Surface or volume diffusion • Ray tracing determines whether molecules would have collided during (fixed) time step • Reaction rules depend on order of reaction, and whether surface or volume molecules involved (Kerr et al. SIAM J Sci Comput 2008) Reflective

  5. MCell Diffusion • Diffusion distance from probability density: • Radial distance from uniformly distributed random variable X: • Speed computations by storing values of X in look-up table • Direction: uniformly distributed random variable [0,2π)

  6. Mcell – STDP example • Calmodulin activation versus spike timing • Do NMDA receptors and VDCC produce different calmodulin profiles? • Neuron model to determine voltage-dependent open probability of VDCC and NMDA • MCell model with calmodulin, calbindin, NCX and PMCA • Model: Keller et al. PLoS One 2008, tutorial: http://www.mcell.org/tutorials/

  7. MCell Model NMDAR Pre-synaptic Terminal Spine Head Spine Neck Dendrite VDCC Calcium binding Proteins (cytosol) Pumps (Membrane)

  8. UnpairedStimuli • Calcium differs due to channel distribution Keller et al. PLoS One 2008

  9. Paired Stimuli EPSP-AP AP-EPSP • Calcium depends on timing of AP versus glutamate release Keller et al. PLoS One 2008

  10. CDS • Particle based simulator with event driven algorithm • All possible collisions are detected during short dt • If collision detected, the exact collision time is calculated • Earliest collision (or reaction events) are simulated one-by-one until dt • Particles have volume, thus can simulate crowding and volume exclusion • http://nba.uth.tmc.edu/cds/content/download.htm • Includes users guide

  11. CDS Example • Morphology from triangular meshes • CaMKII diffusion out of spine depends on morphology (b) and also binding targets and F-actin • Byrne et al. J Comput Neuro 2011

  12. Smoldyn • Particle simulation algorithm Relatively easy to learn/use stand-alone software • http://www.smoldyn.org/ • incorporated into Moose (Genesis 3) and VCell • http://vcell.org/index.html

  13. Stochastic (non-spatial) Simulators Gillespie (Exact Stochastic Simulation Algorithm) Propensity of reaction aj Kf Np • Propensity of any reaction, a0 =  aj • Next reaction occurs with exponential distribution with mean a0: • Identity of reaction selected randomly, based on propensity • Computations increase with number of molecules

  14. ad2 a2 + ad1 ad4 a1 + ad3 Extensions to SSA • Spatial Gillespie, e.g. Fange et al. 2010, PNAS • Morphology is subdivided into small compartments • Propensity of diffusion calculated from diffusion coefficient, ad D  Nd • Diffusion considered as another reaction • Tau leap – non-spatial • Allow multiple reaction events, Kj, to occur for each reaction at each time step, , according to Poisson:

  15. Hybrid Models • Partition the reaction-diffusion space into two or more sets of reactions (and diffusion) • Each set is simulated differently • Diffusion – deterministic, reactions – stochastic • Fast reactions - deterministic, slow reactions – stochastic • “Critical” reactions - exact stochastic, non-critical reactions – tau leap

  16. STEPS • Spatial extension of exact stochastic simulation algorithm • Tetrahedral meshes allows realistic geometries • Diffusion constant can vary between compartments • Simulations are specified in python, witih morphology, reactions and simulations specified independently (for ideal control of simulation experiments) • http://steps.sourceforge.net/STEPS/default.php

  17. STEPS-Cerebellar LTD Calcium Buffers Calcium Pumps AMPA Receptor calcium Protein Phosphatase 5 PKC Raf Raf-act Protein Phosphatase 2A Arachidonic Acid Positive Feedback Loop MEK MapKinase Phosphatase 1 ERK cPLA2 Protein Phosphatase 1 Inactivation, dephosphorylation Activation, phosphorylation

  18. Steps-Single Spine Model • Average of multiple simulations reveals graded induction of LTD • Single runs reveals bistability at intermediate calcium Time (min) Antunes et al. J Neurosci 2012

  19. Steps – continued development • Steps has integrated electrical activity and realistic morphology • Chen W, De Schutter E. Python-based geometry preparation and simulation visualization toolkits for STEPS. Front Neuroinform. 2014 Apr 11;8:37. • Hepburn I, Cannon R, De Schutter E. Efficient calculation of the quasi-static electrical potential on a tetrahedral mesh and its implementation in STEPS. Front Comput Neurosci. 2013 Oct 29;7:129.

  20. NeuroRD • Spatial extension to Gillespie tau leap • Multiple reaction events and diffusion events can occur during each time step • Morphology is subdivided into small compartments • Designed for rapid, approximate simulation of large scale models • Numerous reactions and compartments • Large numbers of molecules

  21. NeuroRD – Mesoscopic • Subdivide dendrites and spines into sub-volumes • Pre-calculate the probability that one molecule leaves the compartment or reacts • Look-up tables store the probability that j out of N molecules leave a compartment or react • At each time step, for each molecule, choose a random number to determine the number, j, molecules out of N leaving or reacting

  22. NeuroRD - Validation • An approximation, to allow large scale simulations • Agrees with Smoldyn, and deterministic solution for reaction-diffusion system Molecule A Molecule B Oliveira et al. 2010, PLoS One

  23. NeuroRD • NeuroRD is up to 60 times faster than Smoldyn • Computations increase linearly with number of compartments, but not molecules Oliveira et al. 2010, PLoS One

  24. Which Molecules Discriminate Temporal Pattern? Dopamine interacts with Acetylcholine, which activates Gq coupled pathways 2AG (LTD) and PKC (Chemical LTP) Kim et al. PLoS Comp Biol 2013

  25. 0.5 m 2 m Morphology • Single spine • Multiple spines Submembrane Submembrane

  26. Temporal Specificity? Theta burst enhances PKC more than 2AG LTP results because PKC effect dominates Kim et al. PLoS Comp Biol 2013

  27. Molecular Signature Ratio of PKC:2AG is robust to variation in least constrained parameters Kim et al. PLoS Comp Biol 2013

  28. Little Spatial Specificity for 2AG Kim et al. PLoS Comp Biol 2013

  29. High Spatial Specificity for PKC Kim et al. PLoS Comp Biol 2013

  30. Variable Spatial Specificity Ratio of PKC to 2AG suggests that TBS will produce LTP at activated synapse, and LTD nearby Kim et al. PLoS Comp Biol 2013

  31. NeuroRD • Model specification allows good experimental design, with separate files for • Reactions • Spatial morphology • Initial conditions • Stimulation • Output specification • Top level file which specifies reactions, morphology, initial conditions, output specs, time step and spatial grid, random seed Tissue Experiment Simulation control

  32. NeuroRD – Morphology File • Specify start and end of each segment • Specification includes id, region type, location (x,y,z), radius, and optional label <Segment id="seg1" region="dendrite"> <start x="1.0" y="1.0" z="0.0" r="5.0" /> <end x="1.0" y="11.0" z="0.0" r="5.0" label="pointA"/> </Segment> • Additional segments start on a previous segment • Branching is possible – see branching.tar

  33. NeuroRD – Morphology File • Randomly distribute spines on dendrite • Shape of spine prototype (multiple allowed) <SpineType id="mushroom"> <Section width="0.2" at="0.0" regionClass="neck"/> <Section width="0.2" at="0.2" regionClass="neck"/> <Section width="0.2" at="0.3" regionClass="head"/> <Section width="0.6" at="0.4" regionClass="head"/> <Section width="0.6" at="0.5" regionClass="PSD"/> <Section width="0.2" at="0.6" label="pointA"/> </SpineType> • Distribution <SpineAllocation id="saA" spineType="mushroom" region="dendrite" lengthDensity="0.6"/>

  34. NeuroRD – Morphology + Spines

  35. NeuroRD – Reaction File • Define each species that has either a reaction pool or conservepool • Include diffusion constant, which can be 0 <Specie name="mGluR" id="mGluR" kdiff="0" kdiffunit = "mu2/s"/> • Specify Reactions • First order – single reactant and product • Second order – two reactants or two products

  36. NeuroRD – Reaction File • Include forward and backward rate constants <Reaction name = "glu+mGluR--glu-mGluR reac" id="glu+mGluR--glumGluR_id"> <Reactant specieID="glu" /> <Reactant specieID="mGluR" /> <Product specieID="glu-mGluR" /> <forwardRate> 5e-03 </forwardRate> <reverseRate> 50e-03 </reverseRate> <Q10> 0.2 </Q10> </Reaction>

  37. NeuroRD – Initial Condition File • Four types of initial conditions • General concentration of molecule in entire morphology: <NanoMolarity specieID="mGluR" value="5e3" /> • Region specific concentration <ConcentrationSet region="PSD" > followed by <NanoMolarity specieID=“IP3" value=“30" /> • Overrides general concentration

  38. NeuroRD – Initial Condition File • Surface Density of membrane molecules • Overrides concentration specifications • Can be specific region <PicoSD specieID="PLC" value="2.5" />

  39. NeuroRD – Stimulation File • Stimulation used to inject molecules • Temporary fix until software is integrated with software for simulating neuron electrical activity and ion channels • Specify molecule and injection site <InjectionStim specieID="Ca" injectionSite="pointA"> • To inject at several spines, called sa1: <InjectionStim specieID="a" injectionSite="sa1[3,4,5].pointA"> • To inject at all spines, called sa1: <InjectionStim specieID="a" injectionSite="sa1[0:2].pointA">

  40. NeuroRD – Stimulation File • Repetitive trains can be created • Specify onset time, duration, rate (amplitude) • Optional: period and end used for train • Optional: InterTrain Interval, numTrains to repeat train onset end duration rate InterTrainInterval period

  41. NeuroRD – Output Specification • Specify dt for output, species and compartment <OutputSet filename = "dt1" region="dendrite" dt="1.0"> <OutputSpecie name="glu" /> <OutputSpecie name="IP3" /> </OutputSet> • Multiple outputSets can be specified • Sample slowly changing molecules less frequently • Sample glutamate receptors from PSD only

  42. NeuroRD – Model file • Specify all the other files <reactionSchemeFile>Purkreactions</reactionSchemeFile> <morphologyFile>Purkmorph</morphologyFile> <stimulationFile>Purkstim</stimulationFile> <initialConditionsFile>Purkic</initialConditionsFile> <outputSchemeFile>Purkio</outputSchemeFile> • Specify some other parameters, such as algorithm variations and random seed • Indicate total simulation time, time step and largest compartment size

  43. NeuroRD – running simulation Java -jar stochdiff2.1.9.jar Model_mglur_diff.xml • Morphology output file: Model_mglur_diff.out-mesh.txt • Ascii output file • name of model file -- .out –output set name - conc.txt Model_mglur_diff.out-dt1-conc.txt Version 3, with faster and more accurate algorithm, will be released very soon (https://github.com/neurord/stochdiff) Current users guide (readme) and software available from: http://krasnow1.gmu.edu/CENlab/software.html

  44. Smoldyn Example • Great (and simple) instructions on installing for linux (in README.txt) • 2 page quick start guide, > 100 page user manual • SmoldynModular.txt re-arranges and adds a few comments • Nice visualization built in • mglur-ip3 model: • mglur-ip3-smoldyn-um-surf.txt • mglur-ip3-smoldyn-um.txt • Results not the same (and should not be)

  45. Smoldyn - Reactions • Define diffusion constants, and one directional reactions • SPECIFY AFTER SYSTEM VOLUME • Table 3.4.1 difc Glu_mGluR(all) 10 (all): diffusion constant can depend on state • Table 3.7.1, 3.8.2 reaction GGmGlufor Glu_mGluR(front) + Gabg(front) -> GGmGluR(front) D5f reaction GGmGlubak GGmGluR(front) -> Glu_mGluR(front) + Gabg(front) D5b

  46. Smoldyn - Morphology • Three parts to morphology spec • System space: dimensions, and outermost boundaries in each dimension • Table 3.3.1 • MUST COME FIRST IN FILE • Surfaces - Table 3.7.1 • SPECIFY AFTER MOLECULES • Sphere is simplest, cuboid requires specification of dim*2 rectangular surfaces • Specify molecules interaction with surface • Compartments – Table 3.9.1 • SPECIFY AFTER SURFACES

  47. Smoldyn- initial conditions • Must come after molecules, surfaces and compartments • Table 3.4.1 • Initialize not just molecules, but molecule state • Cytosolic: • compartment_mol K_IP3_init IP3(fsoln) inside • Surface molecules: • surface_mol K_Glu_mGluR Glu_mGluR(front) membrane all all

  48. Smoldyn • Output and simulation • Simulation time • Must be specified before text output • Graphical output • Specify color and display size of molecules • Text output • Which molecules, frequency of output, name of output file • Injection not possible

  49. VCell • Quite easy for single compartment simulations • Much more difficult for membrane simulations • Download the user interface, need to get an account • Software hosted by UConn • Introduction about capabilities: Spatial (and non-spatial), deterministic or stochastic • http://vcell.org/vcell_software/intro_cap.html?current=three • Quick start guide to introduce how to simulate models in VCell. Very little about creating new models, but large database of models available • http://vcell.org/vcell_software/user_guide.html?current=four

  50. GUI Interface File>New>Biomodel Physiology: • Species (Rxn) • Reactions (Rxn) • Structures (Morphology) Applications: • Stimulation protocols (Stim) • Geometry (Morphology) • Simulation • Methods (solvers), time

More Related