BOSS: BIOLOGICAL OPERATIONS MODELED THROUGH STOCHASTIC SIMULATION

By: Logan Brosemer, Juliana Hong, Raashmi Krishnasamy, Danial Nasirullah,

Rosalie Sowers, Madeleine Taylor-McGrane, 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● 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

DIFFUSION EXAMPLE

Reaction SchemeA1

A2

Ordinary Differential Equations Stochastic Simulation Algorithm

Model of Simple Cellular Diffusion

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 WorksLoops 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. T1 and T2

b. E3, E4 and E5

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.

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 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

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

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

T1 AND T2 DATA

T1: Inhibitor Alone T2: Substrate Alone

E3: NUMBER OF MOLECULES AND FLUCTUATION

Small Number: Large Number:

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

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

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!