An implicit lipid model for efficient reaction-diffusion simulations of protein binding to surfaces of arbitrary topology

Abstract

Localization of proteins to a membrane is an essential step in a broad range of biological processes such as signaling, virion formation, and clathrin-mediated endocytosis. The strength and specificity of proteins binding to a membrane depend on the lipid composition. Single-particle reaction-diffusion methods offer a powerful tool for capturing lipid-specific binding to membrane surfaces by treating lipids explicitly as individual diffusible binding sites. However, modeling lipid particle populations is expensive. Here we present an algorithm for reversible binding of proteins to continuum surfaces with implicit lipids, providing dramatic speed-ups to many body simulations. Our algorithm can be readily integrated into most reaction-diffusion software packages. We characterize changes to kinetics that emerge from explicit versus implicit lipids as well as surface adsorption models, showing excellent agreement between our method and the full explicit lipid model. Compared to models of surface adsorption, which couple together binding affinity and lipid concentration, our implicit lipid model decouples them to provide more flexibility for controlling surface binding properties and lipid inhomogeneity, and thus reproducing binding kinetics and equilibria. Crucially, we demonstrate our method's application to membranes of arbitrary curvature and topology, modeled via a subdivision limit surface, again showing excellent agreement with explicit lipid simulations. Unlike adsorption models, our method retains the ability to bind lipids after proteins are localized to the surface (through e.g. a protein-protein interaction), which can greatly increase stability of multi-protein complexes on the surface. Our method will enable efficient cell-scale simulations involving proteins localizing to realistic membrane models, which is a critical step for predictive modeling and quantification of in vitro and in vivo dynamics. Ⅰ. Introduction:Proteins localize to membranes via multiple different binding modes, including recognition and binding to highly specific lipid head-groups (e.g. PI(4,5)P 2 ) [1], electrostatically driven adherence to negatively charged membranes [2] (as performed by many BAR-domain proteins) [3,4], and binding to membrane-inserted proteins (e.g. Ras) [5,6]. Once proteins have localized to the surface, they can be further stabilized by interactions with additional lipids or transmembrane proteins, and these subsequent binding events are effectively two dimensional (2D) in their search [6,7]. Capturing these various forms of membrane binding is critical for effective kinetic and spatial modeling of cell-scale systems with quantitative comparison to experiment, both in equilibrium and non-equilibrium systems. Because molecular modeling approaches that could capture the fundamental electrostatic or hydrophobic nature of these interactions are too expensive at this scale [8,9], rate-based approaches such as reaction-diffusion provide a powerful alternative [10][11][12][13][14]. These modeling approaches can be us...

NERDSS: a non-equilibrium simulator for multibody self-assembly at the cellular scale

“…While all NERDSS routines work within a simple rectangular volume and (if appropriate) flat membrane, the software also handles arbitrarily curved surfaces 35 . This new feature for single-particle RD 36 also includes an efficient method for surface binding using an implicit lipid model. The implicit lipid model accurately reproduces binding kinetics from the more expensive explicit lipid simulations with orders of magnitude speed-ups 36 .…”

“…This new feature for single-particle RD 36 also includes an efficient method for surface binding using an implicit lipid model. The implicit lipid model accurately reproduces binding kinetics from the more expensive explicit lipid simulations with orders of magnitude speed-ups 36 .…”

“…Simulations were run by treating the adaptor binding sites on the surface using our implicit-lipid model to speed-up the simulations 36 . This model has been shown to accurately reproduce the kinetics of binding to explicit surface sites in 3D and 2D 36 (the off-rate) unchanged. The loop cooperativity factor (applies only to clathrin-clathrin interactions) was set to f=0.001.…”

“…Molecule flexibility is a natural extension beyond rigid molecules that would improve defects and also enable better treatment of disordered regions and genomes. A particularly exciting future development is integration of NERDSS with continuum membrane models36 , to allow more realistic simulations of vesicle and virion formation dynamics and coupling of assembly to mechanical force generation. Ultimately, NERDSS has encoded as a core feature the ability to resolve relatively fast processes over long time scales, and individual proteins over long length scales, simulating otherwise intractable protein assembly dynamics.…”

The Roles of Space and Stochasticity in Computational Simulations of Cellular Biochemistry: Quantitative Analysis and Qualitative Insights

“…This is more efficient but importantly, it need not reach the same equilibrium as explicit particle simulations, because the occupancy of surface binding sites is not accounted for. Modeling explicit particles thus gives more control over the surface properties, and algorithms for binding to surfaces while accounting for site occupancy using implicit sites rival adsorption models in speed (Fu et al, 2019). Not all tools allow for all types of surface binding, hence it is important to recognize these distinctions between adsorption vs single-site binding.…”