∑k - computational & systems biology · machinery/gnm co lective dynamics gnm Å - 1 0 nm...

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Cellular Simulations:Cellular Simulations:Analytic, Finite Difference, & Monte Analytic, Finite Difference, & Monte

Carlo Approaches to ReactionCarlo Approaches to Reaction--Diffusion Diffusion SystemsSystems

Joel R. Stiles, MD, PhDJoel R. Stiles, MD, PhD

NIHNIH--NSF BBSI: Simulation and Computer NSF BBSI: Simulation and Computer Visualization of Biological Systems at Multiple Visualization of Biological Systems at Multiple

ScalesScales

June 27, 2003June 27, 2003

Monte Carlo Probabilities for Monte Carlo Probabilities for UnimolecularUnimolecular TransitionsTransitions

o0

0

o0

21

)S(

)S(1

)S(

)S...()S()S( ttn

ttktp −=++=

If this reaction proceeds for any time t from an initial concentration (S0)o, the total probability (pkt) that a single molecule in the S0 state undergoes a transition is given by the fraction of(S0)o that undergoes any transition during time t:


From this, the lifetime of S0 is exponentially distributed with a mean value given by τ:

−= ∑ tk

n

it

1o0

0

exp)S(

)S(

∑=τn

ik1

1


From:

−−= ∑ tkp

n

ikt1

exp1

o0

0

o0

21

)S(

)S(1

)S(

)S...()S()S( ttn

ttktp −=++=

−= ∑ tk

n

it

1o0

0

exp)S(

)S(

and:

we obtain:

∆

−−= ∑ tkp

n

ikt1

exp1

kt

n

kin

i

nktknn

i

ktk ppk

kpp

k

kpp =⋅=⋅= ∑

∑∑ 1

11

11 ;, �


And finally:

Interactive Interactive MCellMCell Demos:Demos:

2

Monte Carlo Probabilities for Bimolecular AssociationsMonte Carlo Probabilities for Bimolecular Associations

pbt = 1 – (1 – pb)N

H

tkpn

it ∆

=ζ≅ ∑ + o

1

)A(

tkppn

itN

bH ∆

=ζ≅=−− ∑ + o

1

)A()1(1


After integration, final analytic expressions for pt are:

( ) ( ) ( )[ ]( )( ) ( )[ ]( )

−⋅−−−−+

−−⋅+==

∑∑∑

+

+

qtkqbqb

qtkqbp

i

iti

t

exp2

1exp

)R(

1

)R(

AR 2

oo

2oo

oo

oo

)R)(A(4

and )RA(

where;R)((A) if

bq

b

−=

+−=≠

( ) ( )( )

( )( ) tk

tk

tk

tkp

i

i

i

it

i

t

o

o

o

2o

oo A)(1

)A(

A)(1

)A(

)R(

1

)R(

AR

∑∑

∑∑∑

+

+

+

+

+=

+==

oo )R()A( if =

or


Reality check:

From these equations, the probability (pt) that a single R molecule becomes bound during an arbitrarily long interval of time (t) depends on all the k+ values, (A)o, and (R)o; pt = 0 for t = 0, and for t = ∞, pt = 1 if (A)o ≥ (R)o, or pt = (A)o/(R)o if (A)o < (R)o.

( )2

1

1111 2

;

∆π

⋅σ⋅=ΧΧ⋅⋅++Χ⋅⋅=Χ⋅⋅== +++∑∑

La

EGAnsns

n

isi

n

bib D

t

N

fkfkfkfpp �


21

1 ))((2

1

∆π

= ∑ +

LETa

n

ib D

t

ANkp

Interactive Interactive MCellMCell Demos:Demos:Cells Are Complicated …Cells Are Complicated …

PSC’s Biomedical Supercomputing Initiative – An NIH Resource Center

““[[R]esultsR]esults to date show a dizzying array of signaling systems to date show a dizzying array of signaling systems acting within and between cells. … In such settings, intuition cacting within and between cells. … In such settings, intuition can an be inadequate, often giving incomplete or incorrect predictions.be inadequate, often giving incomplete or incorrect predictions. … … In the face of such complexity, computational tools must be In the face of such complexity, computational tools must be employed as a tool for understanding.” Fraser & Harland, employed as a tool for understanding.” Fraser & Harland, Cell Cell 100:41 (2000).100:41 (2000).

•• Need to accurately assess the Need to accurately assess the variabilityvariability of biological of biological systems, and their propensity to systems, and their propensity to switchswitch between between different operating modes and/or to different operating modes and/or to failfail

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Cells Are Complicated …Cells Are Complicated …


Requires: Requires: Stochastic methodsStochastic methods applied to applied to complex 3D reactioncomplex 3D reaction--diffusion diffusion andand cellscells--asas--machines machines problems problems -- largely embryonic largely embryonic due to the scope of necessary software developmentdue to the scope of necessary software development

Dramatically increasedDramatically increasedspace and time scalesspace and time scales

∆∆∆∆∆∆∆∆tt ~10~10--66 ss

MicrophysiologicalMicrophysiological (3(3--D Reaction/Diffusion) SimulationsD Reaction/Diffusion) Simulations

? How ?

QM/MMQM/MM∆∆∆∆∆∆∆∆tt ~10~10--1515 ss

Cellular StructuresMolecular LocationsMass Action Rate Constants

Molecular DiffusionMolecular MechanismsMolecular Structure

MCellMCell & & DReAMMDReAMMBuild models and Build models and use Monte Carlo SSL algorithms to couple use Monte Carlo SSL algorithms to couple

Brownian Dynamics diffusion with binding, unbinding, Brownian Dynamics diffusion with binding, unbinding, conformational changes,…conformational changes,…

Molecular & Cellular Modeling and Simulation Methods

Problem/Method

TypicalApplication

SoftwareExamples

Resolution(Scale)

SpatialRealism

StochasticRealism

TimeStep

TimeScale

Serial/Parallel

ComputerTime

Networks ofReactions/

Sets of ODEs

Metabolic orsignalingpathways

VCell, ECellGepasi

XPPAUT

N/A(cell) N/A none ms ms - hrs serial minimal

Excitation/Compartmental

Circuit

Nervesignaling

GENESISNEURONNEOSIM

µm - mm(cell -

multicell)

low -medium none ms ms - hrs usually

serialusually

low

ReactionKinetics/

Stochastic

Generegulation/

transcription

BioSpiceStochSimXPPAUT

MCell

N/A(cell) N/A high ms ms - hrs serial low

3-D ReactionDiffusion/

Finite Element

Flow models,Calcium

dynamics

VCellFIDAP

Kaskade

<µm(cell)

medium-high none µs - ms µs - sec either low - high

3-D ReactionDiffusion/

Monte Carlo

Micro-physiological

processesMCell

nm – mm(subcell -

cell)high high ps - ms µs - sec either low - high

MacromolecularMachinery/GNM

Collectivedynamics GNM Å - 100 nm

(complexes)high none N/A ps - 10 ns N/A

(analytic) minimal

Diffusion inPotential

Field/Poisson-Nernst-Planck

Electrostaticinteractions,ion channels

-----Å - nm

(membraneproteins)

high(implicitsolvent)

none N/A 10 ns parallel low -medium

MacromolecularMotions/Brownian

Dynamics (BD)

Conformationaldynamics (inflow fields)

CHARMMGROMOS

Å - nm(macro-

molecules)

high(implicitsolvent)

high 5 - 10 fs 1 - 10 ns parallel medium- high

MolecularStructure/Molecular

Dynamics (MD)

Conformationdynamics

& free energies

AMBERCHARMMGROMOS

Å(macro-

molecules)

exact(explicitsolvent)

exact 1 - 2 fs ~ ns parallel very high

MolecularStructure/Ab initio

simulations

Solution of theSchrodinger

equationGaussian98

< Å(electrons -

atoms)exact exact --- N/A parallel highest

Molecular & Cellular Modeling and Simulation MethodsMolecular & Cellular Modeling and Simulation Methods

MeshMeshGGenerationeneration

Model DesignModel Design

SimulationSimulation

AnalysisAnalysis

Various Software PackagesVarious Software Packagese.g., FormZ, XVoxTrace, NWGrid, Mesquite, LaGrit, PSC Volume Browser

DReAMMDReAMMDesign, Render & Animate MCell Models

MCellMCellGeneral Monte Carlo Simulator of Microcellular Physiology


MicrophysiologicalMicrophysiological ModelingModeling

Geometry DesignGeometry Design

MeshMeshGGenerationeneration

Skipping over …Skipping over …••Brownian Dynamics Random WalkBrownian Dynamics Random Walk

(Grid(Grid--free)free)••Monte Carlo Probabilities for:Monte Carlo Probabilities for:

UnimolecularUnimolecular TransitionsTransitionsBimolecular AssociationsBimolecular Associations

••Numerical AccuracyNumerical Accuracy••RunRun--time Optimizationstime Optimizations

4

MicrophysiologicalMicrophysiological ModelingModeling


MCellMCell simulations of miniature endplate currentssimulations of miniature endplate currents

Insight #1: Insight #1: JunctionalJunctional Folds Decrease Folds Decrease mepcmepc AmplitudeAmplitude

Skipping over …Skipping over …••Parameter Fitting for Parameter Fitting for NMJsNMJs::

Untreated; Untreated; AChEAChE Inhibited;Inhibited;AChEAChE Inhibited + Inhibited + AChRAChR Blockade Blockade

••Predicted Untreated Predicted Untreated mepcmepc ttrr

Testing Prediction for Untreated Testing Prediction for Untreated mepcmepc ttrr::Simultaneous Broadband EC and VC RecordingsSimultaneous Broadband EC and VC Recordings

Skipping over …Skipping over …••Quantitative Bandwidth Quantitative Bandwidth

DeterminationDetermination••Effect of EC Electrode Diameter Effect of EC Electrode Diameter

and Pressureand Pressure••mepcmepc Alignment and AveragingAlignment and Averaging

Insight #2: Insight #2: mepcmepc ttrr and and AChACh ExocytosisExocytosis Insight #3a: Temperature Sensitivity of Insight #3a: Temperature Sensitivity of mepcsmepcs is Mostly is Mostly Governed by Offsetting Effects on Channel GatingGoverned by Offsetting Effects on Channel Gating

5

Skipping over …Skipping over …••Experimental Determination ofExperimental Determination of

AChEAChE Site DensitySite Density••Experimental Determination ofExperimental Determination of

AChEAChE Turnover NumberTurnover Number

Insight #3b: Highly Nonlinear Sensitivity of Insight #3b: Highly Nonlinear Sensitivity of mepcmepc ttff to to AChEAChE ParametersParameters Insight #3a: Temperature Sensitivity of Insight #3a: Temperature Sensitivity of mepcsmepcs is Mostly is Mostly Governed by Offsetting Effects on Channel GatingGoverned by Offsetting Effects on Channel Gating

Patient followed from birth:

• Progressive weakness and impaired neuromuscular transmission without early degenerative endplate changes typically associated with SCCMS

• Prolonged, low amplitude synaptic currents at early and late stages

• Atypical, initially mild (focal) ultrastructural changes progressed over time

• Novel C-to-T substitution in exon 8 of the δδδδ subunit of AChR: serine to phenylalanine mutation in the second transmembrane domain (M2) that lines the ion channel

• AChR numbers not significantly reduced


Insight #4: Synaptic Insight #4: Synaptic PathophysiologyPathophysiology in a Novel Form ofin a Novel Form ofSlow Channel Congenital Slow Channel Congenital MyasthenicMyasthenic Syndrome (SCCMS)Syndrome (SCCMS)

Normal

Focal (early)

Global(late)


6


•• Typical of SCCMS, mutant neurotransmitter receptors showed Typical of SCCMS, mutant neurotransmitter receptors showed dramatically slowed deactivation (ion channel closing rate)dramatically slowed deactivation (ion channel closing rate)

•• However, However, simulations simulations of synaptic signalsof synaptic signals predictedpredicted an an additional noveladditional novel slowing of receptor activation (ion channel slowing of receptor activation (ion channel opening rateopening rate))

•• Based on model predictions, opening rate was measured and Based on model predictions, opening rate was measured and found to be decreasedfound to be decreased -- likely explains unique early course of likely explains unique early course of disease in this patientdisease in this patient


200open

AChRs1 ms

Insight #5: Insight #5: SpatioSpatio--Temporal Correlations and Synaptic NoiseTemporal Correlations and Synaptic Noise

averaged results from averaged results from MCellMCell simulations (3000 runs)simulations (3000 runs)

SpatioSpatio--Temporal Correlations and Synaptic NoiseTemporal Correlations and Synaptic Noise

Stochastic Simulation Algorithm Stochastic Simulation Algorithm ModelModel

Insight #5: Insight #5: SpatioSpatio--Temporal Correlations and Synaptic NoiseTemporal Correlations and Synaptic Noise Insight #5: Insight #5: SpatioSpatio--Temporal Correlations and Synaptic NoiseTemporal Correlations and Synaptic Noise

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Insight #5: Insight #5: SpatioSpatio--Temporal Correlations and Synaptic NoiseTemporal Correlations and Synaptic Noise Insight #5: Insight #5: SpatioSpatio--Temporal Correlations and Synaptic NoiseTemporal Correlations and Synaptic Noise

PresynapticPresynaptic calcium dynamics & neurotransmitter releasecalcium dynamics & neurotransmitter release

NormalNormal Developing/RegeneratingDeveloping/Regenerating


NormalNormal


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Developing/RegeneratingDeveloping/Regenerating


33--D reconstruction of D reconstruction of vertebrate neuromuscular vertebrate neuromuscular

junctionjunction

Synaptic topology & current variabilitySynaptic topology & current variability


Synaptic topology & Synaptic topology & current variabilitycurrent variability

Synaptic topology & current variabilitySynaptic topology & current variability Synaptic topology & current variability Synaptic topology & current variability –– synaptic synaptic AChEAChE distributiondistribution

9


Usage Scenarios:

Expanding User Group & Range of ApplicationsExpanding User Group & Range of Applications

Serial or Parallel - Look & See, Parameter Fitting, Parameter SweepMainframes Workstations Parallel Grid

Workshops1997 – Cornell Theory Center, NSF support (MCell test group)

1999 – SDSC, NSF support (MCell test group)

2001 – PSC, NCRR support (open, MCell & DReAMM)

2003 – PSC, (Drosophila neuromuscular research, MCell & DReAMM)

Outside Users:Outside Users:Registration & Download Website Maintained at PSC – UNIX, PC, Mac

>300 Registered>300 Registered

WebWeb--based Instructionbased Instructionwww.mcell.psc.eduwww.mcell.psc.edu

www.mcell.psc.edu/DReAMMwww.mcell.psc.edu/DReAMM

Developers & CollaboratorsDevelopers & Collaborators

Joel R. Stiles (PSC, CMU, Pitt)Joel R. Stiles (PSC, CMU, Pitt)Thomas M. Thomas M. BartolBartol (Computational Neurobiology Lab (Computational Neurobiology Lab

of Terrence J. of Terrence J. SejnowskiSejnowski, The Salk Institute), The Salk Institute)

Edwin E. Edwin E. SalpeterSalpeter (Physics and Astronomy, Cornell)(Physics and Astronomy, Cornell)

MCellMCell and and DReAMMDReAMM::


NSF ITR NSF ITR -- Virtual Instruments: Scalable Virtual Instruments: Scalable Software Instruments for the Grid:Software Instruments for the Grid:

Berman, F. (PI, UCSD)Berman, F. (PI, UCSD)Casanova, H. (UCSD)Casanova, H. (UCSD)DongarraDongarra, J. (U. Tenn.) , J. (U. Tenn.) EllismanEllisman, M. (UCSD), M. (UCSD)WolskiWolski, R. (UCSB), R. (UCSB)

MCellMCell Developers &Developers &

AnglisterAnglister, L., L. (Hebrew U.)(Hebrew U.)DeerinckDeerinck, T., , T., EllismanEllisman, M., M. (UCSD)(UCSD)Ford, W.Ford, W. (U. Pittsburgh)(U. Pittsburgh)Gomez, C.Gomez, C. (U. Minnesota)(U. Minnesota)KovyazinaKovyazina, I., I. ((KazanKazan U.)U.)PattilloPattillo, J., , J., MerineyMeriney, S., S. (U. Pittsburgh)(U. Pittsburgh)SalpeterSalpeter, M., M. (Cornell)(Cornell)TemizTemiz, N.A., , N.A., BaharBahar, I., I. (U. Pittsburgh)(U. Pittsburgh)Van Van HeldenHelden., D.., D. (U. Newcastle)(U. Newcastle)

MicrophysiologyMicrophysiology::

NIHNIH--NSF BBSI: Simulation and Computer Visualization of Biological SyNSF BBSI: Simulation and Computer Visualization of Biological Systems at stems at Multiple Scales Multiple Scales –– Summer Institute beginning May 2003; Pitt, PSC, Duquesne, CMUSummer Institute beginning May 2003; Pitt, PSC, Duquesne, CMU

“Computational biology today is in a state analogous to weather prediction 25 years ago, when it was not very reliable or highlyrespected. … Now we routinely rely on accurate global weather forecasting. Similarly, we foresee a new age of cell biology, when computational modeling plays an integral role in our understanding of the molecular basis of cell physiology and human disease. The impact of computational cell biology on biomedicine will be just as great as the impact of modern weather prediction on the transportation industry, the military, and civil defense.”

NARRC Working Group on Computational Cell Biology, September 10, 2002, Farmington, ConnecticutGary Borisy, Arey Professor of Cell and Molecular Biology, Northwestern; President, American Society for Cell BiologyJames Cassatt, Director of Cell and Molecular Biology and Acting Director Center for Computational Biology, NIGMS

Ann Cowan, Assistant Professor of Biochemistry and Deputy director, Center for Biomedical Imaging Technology, UConnHC.Amarnath Gupta, Associate Research Scientist, San Diego Supercomputer Center

Chris Hogue, Asst. Professor of Biochemistry and Director of Bioinformatics, U. Toronto; Director of the BIND ProjectMike Hucka, Researcher, Control and Dynamical Systems, CalTech; SBW/SBML

Ravi Iyengar, Interim Dean for Research, Rosenstiel Professor and Chair of Pharmacology and Biochemistry, Mt. Sinai Medical SchoolLeslie Loew, Professor of Physiology, UConnHC; Director, National Resource for Cell Analysis and Modeling

Robert Phair, President, Bioinformatics Services, Inc.Tom Pollard, Higgins Professor of Cell, Molecular and Developmental Biology, Yale

Brian Ray, Editor, Science STKERalph Roskies, Professor of Physics, U. Pittsburgh and Scientific Director, Pittsburgh Supercomputing Center

Dong-Guk Shin, Professor of Computer Science and Engineering, UConnJoel Stiles, Senior Scientist, Pittsburgh Supercomputing Center; MCELL

John Tyson, University Distinguished Professor of Molecular Cell Biology, Virginia TechRai Winslow, Professor of Biomedical Engineering and Director Center for Computational Medicine and Biology, Johns Hopkins

∑k - computational & systems biology · machinery/gnm co lective dynamics gnm Å - 1 0 nm...

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