BOSS BIOLOGICAL OPERATIONS MODELED THROUGH STOCHASTIC SIMULATION By

BOSS: BIOLOGICAL OPERATIONS MODELED THROUGH STOCHASTIC SIMULATION By: Logan Brosemer, Juliana Hong, Raashmi Krishnasamy, Danial Nasirullah, Rosalie Sowers, Madeleine Taylor-Mc. Grane, and Nalini Ramanathan

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

ORDINARY DIFFERENTIAL EQUATIONS VS. STOCHASTIC SIMULATION ALGORITHMS ODE SSA ● Ordinary Differential Equations ● Deterministic ● Static equations ● Continuous timescale ● Efficiently depicts large-scale systems ● Stochastic Simulation Algorithms ● Probabilistic ● Factors that vary according to probabilities ● Randomness ● Accurately depicts small-scale systems

DIFFUSION EXAMPLE A 1 A 2 Reaction Scheme

Model of Simple Cellular Diffusion Ordinary Differential Equations Stochastic Simulation Algorithm

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

WHY GILLESPIE? ● No “Master Equation” ● Efficient ● Simple

How Gillespie Works Loops through two actions ● Finds next reaction ○ Propensities ○ Number of Molecules ○ Random number ● Finds time of next reaction ○ Propensity ○ Random number

OUTPUT

DEMONSTRATION OF BOSS

TEST CASES 1. Simple Diffusion Across a Cell Membrane 2. Lotka-Volterra 3. HIV-1 Protease Examples a. T 1 and T 2 b. E 3, E 4 and E 5

LOTKA-VOLTERRA: WOLVES AND RABBITS Equations: R -> 2 R [k 1] R + W -> 2 W [k 2] W -> nil ● ● [k 3] k values = rate constant of event k 1 = rabbit birth k 2 = rabbit consumption and wolf birth k 3 = wolf death BOSS created a graph that matches the typical cyclic pattern of Lotka-Volterra Systems.

OUR MAIN APPLICATION: HIV-1 PROTEASE http: //en. wikipedia. org/wiki/HIV-1_protease

HIV-1 PROTEASE: AN OVERVIEW ● General Information o HIV -1 - Human Immunodeficiency Virus Type 1 o HIV-1 Protease - enzyme that plays a crucial role in the replication of HIV-1 o 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: § G 48 V § L 90 M § G 48 V/L 90 M

DIFFERENT TEST GROUPS ● T 1 and T 2 Groups o focused on “base cases” o T 1 - tested different inhibitors on Wild Type and Mutant Type HIV-1 Protease o T 2 - tested one substrate on Wild Type ● E 3, E 4, and E 5 Groups o experimental groups - “inductive cases” o E 3 - change in number of molecules o E 4 - one substrate and different inhibitors on Wild Type o E 5 - one inhibitor, one substrate, different mutated forms of HIV protease

MICHAELIS-MENTEN SYSTEM OF EQUATIONS Substrate 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

T 1 AND T 2 DATA T 1: Inhibitor Alone T 2: Substrate Alone

E 3: NUMBER OF MOLECULES AND FLUCTUATION Small Number: Large Number:

E 4: TESTING DIFFERENT INHIBITORS Ritonavir (Best Inhibitor): Nelfinavir (Worst In hibitor): Little Product Produced A Lot of Product Still Produced Little product produced A lot of product produced

E 5: MUTATIONS AND INHIBITOR ACTIVITY G 48 V/L 90 M: A lot of product produced Inhibitor no longer effective with mutation Wild Type: L 90 M: Less product produced Inhibitor still effective (even despite mutation in L 90 M)

DISCUSSION Future Developments ● ● Extensive testing Graphical user interface Internal unit conversion capabilities Tau-leaping Applications to Other Systems

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:

THANK YOU!