BOSS: Biological Operations modeled through Stochastic Simulation
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Transcript of BOSS: Biological Operations modeled through Stochastic Simulation
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BOSS: BIOLOGICAL OPERATIONS MODELED THROUGH STOCHASTIC SIMULATION
By: Logan Brosemer, Juliana Hong, Raashmi Krishnasamy, Danial Nasirullah,
Rosalie Sowers, Madeleine Taylor-McGrane, and Nalini Ramanathan
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INTRODUCTION
Objectives:
1. Research stochastic simulation
2. Develop a simulator using the Gillespie method
3. Test our simulator, BOSS, on several biological systems:
o Simple diffusion across a cell membrane
o Lotka-Volterra system
o HIV-1 protease substrate binding and inhibition
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ORDINARY DIFFERENTIAL EQUATIONS VS. STOCHASTIC SIMULATION ALGORITHMS
ODE● Ordinary Differential
Equations● Deterministic● Static equations● Continuous timescale● Efficiently depicts large-
scale systems
SSA● Stochastic Simulation
Algorithms● Probabilistic● Factors that vary according
to probabilities● Randomness● Accurately depicts small-
scale systems
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DIFFUSION EXAMPLE
Reaction SchemeA1
A2
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Ordinary Differential Equations Stochastic Simulation Algorithm
Model of Simple Cellular Diffusion
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INPUT● i = iterations● t = time ● of = output frequency● Molecules = initial molecule
counts● Reactions = reactions and
rates● Output = names of output files
for each molecule● Plot = whether or not data will
be plotted
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WHY GILLESPIE?● No “Master Equation”● Efficient● Simple
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How Gillespie WorksLoops through two actions
● Finds next reaction○ Propensities○ Number of Molecules○ Random number
● Finds time of next reaction○ Propensity○ Random number
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OUTPUT
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DEMONSTRATION OF BOSS
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TEST CASES
1. Simple Diffusion Across a Cell Membrane
2. Lotka-Volterra
3. HIV-1 Protease Examples
a. T1 and T2
b. E3, E4 and E5
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LOTKA-VOLTERRA: WOLVES AND RABBITSEquations:
R -> 2R [k1]
R + W -> 2W [k2]
W -> nil [k3]
● k values = rate constant of event● k1 = rabbit birth● k2 = rabbit consumption and wolf
birth● k3 = wolf death
BOSS created a graph that matches the typical cyclic pattern of Lotka-Volterra Systems.
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OUR MAIN APPLICATION: HIV-1 PROTEASE
http://en.wikipedia.org/wiki/HIV-1_protease
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HIV-1 PROTEASE: AN OVERVIEW● General Information
o HIV -1 - Human Immunodeficiency Virus Type 1o HIV-1 Protease - enzyme that plays a crucial role in the replication of
HIV-1o No cure for virus, drugs that inhibit HIV-1 Protease are currently being
tested● HIV Protease Mutations and Drug Resistance
o Mutations in the enzyme → changes shape of enzyme → resistance to specific inhibitors
o Some mutated versions of HIV-1 Protease: G48V L90M G48V/L90M
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DIFFERENT TEST GROUPS
● T1 and T2 Groups
o focused on “base cases”
o T1 - tested different inhibitors on Wild Type and Mutant Type HIV-1
Protease
o T2 - tested one substrate on Wild Type
● E3, E4, and E5 Groups
o experimental groups - “inductive cases”
o E3 - change in number of molecules
o E4 - one substrate and different inhibitors on Wild Type
o E5 - one inhibitor, one substrate, different mutated forms of HIV
protease
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MICHAELIS-MENTEN SYSTEM OF EQUATIONSSubstrate Equations:
Enzyme + Substrate→ Enzyme-Substrate Complex [Kon] Enzyme-Substrate Complex→ Enzyme + Substrate [Koff]Enzyme-Substrate Complex→ Enzyme + Product [Kcat]
Inhibitor Equations:Enzyme + Inhibitor → Enzyme-Inhibitor Complex [Kon]Enzyme-Inhibitor Complex→ Enzyme + Inhibitor [Koff]
● Kon = rate constant of creation of ES or EI● Koff = rate constant of dissociation of ES or EI● Kcat= rate constant of catalysis
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T1 AND T2 DATA
T1: Inhibitor Alone T2: Substrate Alone
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E3: NUMBER OF MOLECULES AND FLUCTUATION
Small Number: Large Number:
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E4: TESTING DIFFERENT INHIBITORS
Ritonavir (Best Inhibitor): Nelfinavir (Worst Inhibitor):
Little Product Produced
A Lot of Product Still Produced
Little product produced A lot of product produced
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E5: MUTATIONS AND INHIBITOR ACTIVITY
G48V/L90M: Wild Type: L90M:
A lot of product produced Less product produced
Inhibitor still effective (even despite mutation in L90M)Inhibitor no longer effective with mutation
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DISCUSSION
Future Developments● Extensive testing● Graphical user interface● Internal unit conversion capabilities● Tau-leaping
Applications to Other Systems
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ACKNOWLEDGEMENTS
We would like to acknowledge the following individuals and groups…
● Dr. Markus Dittrich● Maria Cioffi● Dr. Gordon Rule● Dr. Barry Luokkala● PGSS Alumni Association and Donors● Corporate Sponsors:
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THANK YOU!