Dynamical simulations of virus wrapping and budding

T. Ruiz-Herrero1, M. F. Hagan2, E. Velasco1

1. Universidad Autónoma de Madrid, Madrid, Spain2. Brandeis University, Waltham, MA, USA

INTRODUCTION

Budding

exiting the cell

acquiring membrane coating

Attachment to the cell membraneWrappingFusion of the final neck

Budding steps

T. RUIZ-HERRERO 1/13

COARSE GRAINING

polar head Hydrophilic tail

T. RUIZ-HERRERO 2/13

MEMBRANE MODEL:cooke model

Vrep

Vbond

Vbend

Vatrr

[Cooke et al, Phys. Rev. E, 72 (2205)]

T. RUIZ-HERRERO 3/13

MEMBRANE MODEL CHARACTERISTICS

● Broad range of fluidity● Easily tunable● Good agreement with measurements: rigidity, diffusion, density

ωC

κ/ε0

ωC

A/σ2

kBT/ε0=1.1 [from Cooke et al,Phys Rev E, 72 (2205)]

Area per molecule Bending rigidity

T. RUIZ-HERRERO 4/13

MEMBRANE PARTICLE INTERACTION AND SIMULATION CHARACTERISTICS

s=R-σ/2

Simulation characteristics: Important parameters:

• Molecular dynamics simulation R • NPT ensamble ε• Langevin thermostat kBT/ε=1.1 ωc κ,ρ• Andersen barostat P=0• Verlet algorithm

s

Membrane-particle interaction

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SIMULATIONS RESULTS: MAIN BEHAVIORS

WRAPPING NON-WRAPPING

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MEMBRANE BREAKING

SYSTEM BEHAVIOR 1: NON-WRAPPING

/0=1e3 /0=5e3

/0=1e4/0=3e4

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SYSTEM BEHAVIOR 2: WRAPPING

/0=5e2 /0=5e3 /0=1.5e4

/0=1.55e4 /0=1.6e4 /0=1.65e4

T. RUIZ-HERRERO 8/13

SYSTEM BEHAVIOR 3: MEMBRANE BREAKING

/0=5.5e3 /0=6e3 /0=7e3

/=7.5e3 /0=9.5e3 /0=1e4

T. RUIZ-HERRERO 9/13

PHASE DIAGRAMS

ε/ε0

In general, good agreement between simulations and theorySubtle dependence on bending coefficientFor small epsilons deviation from theory

/ε0

R/σ=10

R/σ

ε/ε0

/kBT=12.5

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ELASTIC THEORY

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ENERGY MAPS AND BUDDING PATHWAYS

Penetration[σ]Penetration[σ]

Penetration[σ]

θ[rad] θ[rad]

θ[rad]

ε/ε0=0.7 ε/ε0=0.9

ε/ε0=1.1

T. RUIZ-HERRERO 12/13

BUDDING DYNAMICS: TIME SCALES AND PENETRATION

Penetration vs time

• steepness of the budding pathway ---> process speed • strenght adhesion energy ---> maximum penetration

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