Multiscale computational models in physical systems biology of intracellular trafficking

Abstract

In intracellular trafficking, a definitive understanding of the interplay between protein binding and membrane morphology remains incomplete. The authors describe a computational approach by integrating coarse-grained molecular dynamics (CGMD) simulations with continuum Monte Carlo (CM) simulations of the membrane to study protein-membrane interactions and the ensuing membrane curvature. They relate the curvature field strength discerned from the molecular level to its effect at the cellular length-scale. They perform thermodynamic integration on the CM model to describe the free energy landscape of vesiculation in clathrin-mediated endocytosis. The method presented here delineates membrane morphologies and maps out the free energy changes associated with membrane remodeling due to varying coat sizes, coat curvature strengths, membrane bending rigidities, and tensions; furthermore several constraints on mechanisms underlying clathrin-mediated endocytosis have also been identified, Their CGMD simulations have revealed the importance of PIP2 for stable binding of proteins essential for curvature induction in the bilayer and have provided a molecular basis for the positive curvature induction by the epsin N-terminal homology (EIMTH) domain. Calculation of the free energy landscape for vesicle budding has identified the critical size and curvature strength of a clathrin coat required for nucleation and stabilisation of a mature vesicle.

Fig. 1

Monte Carlo moves for the membrane model and illustration of the various curvature fields a Triangulated membrane patch‐vertex shift and link flip MC moves b Curvature field functions for epsin and clathrin

Fig. 2

Atomic and coarse grain structures of epsin‐ENTH domain with and without the membrane a Crystal structure of ENTH domain in complex with Ins(1,4,5)P₃ b Molecular model of ENTH domain interacting with the bilayer c Side view of four ENTH domains (lower panel) and one ENTH domain (top panel) on a bilayer

Fig. 3

Calculations for vesicle budding using TI at κ = 10 k_B T a Representative morphologies for varying C ₀ b Free energy change with respect to C ₀ c Change in excess membrane area with respect to C ₀ Results are reported for a coat radius of r ₀ = 4.55a ₀ in (4)

Fig. 4

Influence of coat size on vesicle budding at κ = 10 k_B T a Morphologies for different values of C ₀ for a coat radius of r ₀ = 3.25a ₀ b Morphologies for different values of C ₀ for a coat radius of r ₀ = 6.5a ₀ c Free energy of vesicle nucleation and its dependence on coat radius, r ₀

Fig. 5

Influence of membrane bending rigidity on vesicle budding a Free energy of vesicle nucleation and its dependence on membrane bending rigidity, κ b Morphologies for different values of C ₀ for a coat radius of r ₀ = 4.55a ₀ and membrane bending rigidity of κ = 20k_B T c Morphologies for different values of C ₀ for a coat radius of r ₀ = 3.25a ₀ and membrane bending rigidity of κ = 20k_B T

Fig. 6

Effect of the membrane excess area on the free energy and membrane morphology a Change in free energy as a function of excess area for four values of the induced curvature b Radius of the neck of a bud as a function of excess area for four values of the induced curvature c Representative snapshots of the membrane conformation for the values of A /A _p marked A, B, and C in top left panel

Fig. 7

Quantification of bilayer deformation and curvature in CGMD simulations: control simulations of free bilayer without protein (c,f,i,l); simulations of bilayer with one bound ENTH domain (b,e,h,k); simulations of bilayer with four ENTH domains bound (a,d,g,j)

Fig. 8

Map of spontaneous curvature (C₀) for 64 × 64 nm² bilayer systems containing either four or one ENTH domains compared to control The colour scale describes the spontaneous curvature map over with pixel area of 10 nm² Filled black circles represent locations of ENTH domains

Fig. 9

Free energy landscape ΔF₀ for different coat sizes for κ = 10 k_B T and 20 k_B T