1. Multiscale Modeling of Protein-Mediated Membrane Processes
Joshua Weinstein*, Mark Goulian*, & Ravi Radhakrishnan¶
Departments of Physics* and Bioengineering¶, University of Pennsylvania

2. Endocytosis: The Internalization Machinery in Cells

3. Paradigms of Membrane Curvature
McMahon, Gallop, Nature reviews, 2005

4. Imaging Endocytosis Ap180 Ford et al., Nature, 2002 Epsin Membrane
Clathrin

5. Endocytosis Machinery
Ford et al., Nature, 2002
Epsin
Clathrin
Ap180
Ap180+Clathrin
Epsin+Clathrin
Ap180+Epsin+Clathrin
Receptor Inactivation to Neurotransmitters

6. Objectives Short-term
Quantitative dynamic models for membrane invagination: Development of a multiscale approach to describe protein-membrane interaction at the mesoscale (m)
Long-term
Integrating with flow and signal transduction
Targeted Therapeutics

7. Hierarchical Multiscale Modeling
K E Gubbins et al.,
J. Phys.: Cond. Matter, 2006
Weinan E, Bjorn Engquist,
Notices of the ACM, 2003

8. Hierarchical Multiscale Modeling
Spatial Multiscale Methods (Traditional)
Boundary layer Analysis, Perturbation Theory
Multigrid Method
Domain Decomposition, Adaptive Mesh Refinement
Temporal Multiscale Methods
Separation of timescales, discrete frequency spectrum
Multiple-timestep Molecular Dynamics, -leap KMC
Free energy methods, Density of States Methods
Path-based approaches: Transition path sampling, Nudged elastic band, Stochastic String
Fast Evaluation Methods
Effective treatment of long-range interactions
Fast Multipole Method
Ewald-summation
Linear Scaling Density Functional Theory
Based on a single Lagrangian, Hamiltonian, energy function, or equation of motion

9. Hierarchical Multiscale Modeling
Coarse Graining Hamiltonians
Field-theoretic expansion based on order parameters
Frequency filtering
Effective potential for Force-matching
Effective potential for Property matching
Dynamical Coarse Graining
Time-stepping with up and down shifting
Hybrid Lagrangian, Hamiltonians
Carr-Parrinello MD, Born-Oppenheimer MD
Mixed Quantum Mechanics Molecular Mechanics
Hybrid Integrators
Mixed deterministic and Stochastic Integrators in kinetic modeling of networks
Renormalization of the Hamiltonian, Energy Function
Same
effective
phenomenology

10. Hierarchical Multiscale Modeling
Hybrid Representations (Heterogeneous Multiscale Modeling)
Decoupled Approach
Transition State Dynamics
Coupled Approaches
Integration of Disparate Representations
Non-adiabatic surface hopping dynamics
MD+Navier-Stokes (flux matching)
KMC+Diffusion field equation (flux matching)
Mixed
phenomenology
Deterministic+Stochastic
Domain Decomposotion
The hybrid multiscale approach is well suited for modeling the complexities biological systems because it enables us to leverage the strengths of pre-validated phenomenological theories in different fields and combine them together

11. Model Components for Endocytosis
Ap180
Epsin
Vesicle membrane motion
Hohenberg and Halperin, 1977
Nelson, Piran, Weinberg, 1987
Membrane
z(x,y,t) membrane coordinates;  interfacial tension;  bending rigidity; M membrane mobility,  Langevin noise; F elastic free energy; C(x,y) is the intrinsic mean curvature of the membrane
Epsin diffusion
Gillespie, 1977
Clathrin
Kinetic Monte Carlo: diffusion on a lattice

12. Epsin Localization Causes Membrane Invagination
Time-dependent Ginzburg Landau Equation Dissipative Dynamics
C(x,y)

13. Epsin-Membrane Interaction Parameters
Range (R)
r*, Surface
Density
Hardsphere exclusion
C0 (intrinsic
curvature)
Measurable quantities:
C0, D, , 
Micropipette, FRAP, Microscopy
C(x,y) is the mean intrinsic curvature of the membrane determined by epsins adsorbed on the membrane. C(x,y) is dynamically varying because of lateral diffusion of epsins

14. Hybrid Multiscale Integration
Regime 1: Deborah number De<<1
or (a2/D)/(z2/M) << 1
Regime 2: Deborah number De~1 or (a2/D)/(z2/M) ~ 1
KMC
TDGL
#=1/De
#=/t
Surface hopping switching probability
Relationship Between Lattice & Continuum Scales
Lattice  continuum: Epsin diffusion changes C0(x,y)
Continuum  lattice: Membrane curvature introduces an energy landscape for epsin diffusion R R F
C0 r
C0/t=-(1/M)F/C0=-(C0/tDiffusion,Free)F/C0
tDiffusion,Membrane/tDiffusion,Free=1/(F/C0)

15. Membrane Dynamics (Constant Temperature)
Epsin Localization
Process Spontaneous?
Activated?
F/kT
Determinants of Nucleation

16. Membrane Dynamics, R= 40nm
Membrane-Mediated Protein-Protein Spatial & Orientational Correlations
Membrane Dynamics, R= 40nm
r*=0.004, C0=20
r*=0.03, C0=20

17. No Nucleation Below Threshold Curvature and Range
Process Spontaneous?
Activated?
F/kT
Threshold
C0*=20
R*=40 nm
Localization

18. sequence Membrane Dynamics, R=60nm
Membrane-Mediated Protein-Protein Spatial & Orientational Correlations
Membrane Dynamics, R=60nm
r*=0.008, C0=10
sequence
r*=0.008, C0=40
r*=0.008, C0=60

19. Membrane Dynamics, R=80nm
Membrane-Mediated Protein-Protein Spatial & Orientational Correlations
r*=0.008, C0=30
r*=0.008, C0=50

20. Nucleation Limited by Diffusional Timescale of Association
Process Spontaneous?
Activated?
F(r)kBT ln g(r)
F/kT
C0**: 30-50
C0**> 50
Membrane Rupture?
Localization

21. Membrane-Mediated Protein-Protein Spatial & Orientational Correlations
Membrane Dynamics, R=80nm
r*=0.008, C0=30
r*=0.016, C0=30

22. Membrane-Mediated Protein-Protein Spatial & Orientational Correlations
Membrane Dynamics, R=100nm
r*=0.016, C0=30

23. Membrane-Mediated Protein-Protein Spatial & Orientational Correlations
Membrane Dynamics, R=80nm
r*=0.02, C0=5
r*=0.02, C0=10
r*=0.03, C0=20

24. Nucleation occurs following the emergence of long-ranged spatial and orientational correlations
Process Spontaneous?
Activated?
F/kT
Requirements:
Under conditions where orientational correlations persist
Under conditions that preclude a glass transition
C0*: 10-30
Localization

25. Global Phase Diagram r* C0 R GT No N NVLRO NVA GT: Glass transition
No N: No nucleation
NVLRO: Nucleation via long range order
NVA: Nucleation via association

26. Conclusions
The hybrid multiscale approach is successful in describing the dynamic processes associated with the interaction of proteins and membranes at a coarse-grained level
Membrane-mediated protein-protein repulsion and attraction effects short- and long-ranged ordering
Two modes of nucleation observed
-- NVA: Effected by large C0
-- NVLRO: Effected by persistence of orientational correlations
In the regime of small intrinsic curvature and large density, a glass transition is observed
A global phase diagram is proposed

27. Activation of Endocytosis as a Multiscale Problem
Extracellular
Molecular Dynamics
Intracellular
(MAP Kinases) Ras
Mixed Quantum Mechanics Molecular Mechanics
PLC
IP3
DAG
Raf
Ca++
PKC
MEK
Nucleus
ERK
Proliferation
KMC+TDGL

28. Acknowledgments Mr. Josh Weinstein, UG, (Co-Author)
Prof. Mark Goulian (Co-Author)
Mr. Neeraj Agrawal, PhD student, CBE
Ms. Yingting Liu, PhD Student, BE
Mr. Jeremy Weiss, UG student, BMB

29. Helfrich Free Energy Plane: H=0, K=0 1 R1>0, R2<0 H=0, K<0
C0 :Intrinsic curvature
k: Bending Modulus
k: Gaussian Curvature Modulus 2
R1>0, R2>0
H>0, K>0
Cartesian (Monge) notation: h(x,y)
H1/2[1/R1+1/R2]
K1/R11/R2
Nelson, Piran, Weinberg, 1987

30. The Variational Problem

36. 

38. r* C0 R Global State Diagram GT No N NVLRO NVA GT: Glass transition
No N: No nucleation
NVLRO: Nucleation via long range order
NVA: Nucleation via association

39. Multiscale modeling of Protein-mediated membrane dynamics
Develop a New Heterogeneous Multiscale Approach
Aim 1(a): Generalize and extend the multiscale approach
Aim 2: Determine parameters from atomistic simulations
Aim 3: Biological Application to endocytosis
Aim 1(b):
Develop a global state diagram
Dielectric experiments of Dr. Bartkowiak, Poznan, Poland
Membrane biophysical experiments of Dr. Tobias Baumgart, Penn.
Cell biology experiments of Dr. Mark Lemmon, Penn
Compare and validate
Apply
Long-term objective of integrating with flow, cytoskeleton motion, biochemical signal transduction
Long-term
Multiscale modeling of
Protein-mediated membrane dynamics

40. Clathrin

41. Epsin
Clathrin