(284f) Accelerate Simulations of Multivalent Letin-Glycan Binding Process through Hybrid PDE-Kinetic Monte Carlo Model

Glycans (also called sugars, carbohydrates, or saccharides) are one of the most diverse biomolecules [1]. Its interaction with lectins (i.e. glycan-binding proteins) are of importance since glycans are involved in a number of cellular processes. Many glycans are localized on cell surfaces and mediate host-pathogen interactions, such as viral and bacterial adhesion to host cell surfaces [1]. One common feature in the glycan-lectin binding process is multivalency: a lectin often has multiple binding pockets that can bind to multiple glycan molecules on a cell surface. This accumulation of multiple binding events significantly increases the overall binding affinity [2-3]. Our prior studies have demonstrated that multivalent binding process also significantly impacts the binding kienetics [2,5]. The equilibrium half-time of lectin binding could vary from a minute to several hours In order to study dynamics of the glycan-lectin binding process and its implications on downstream signaling pathways, we have proposed on-lattice kinetic Monte Carlo (kMC) simulation frameworks to study how bacteria toxins, such as cholera toxin, bind to glycans on host cell membranes [2, 4-5]. Specifically, the binding process is represented by five discrete microscopic events: (a) attachment of a lectin from the solution phase to a cell membrane, (b) detachment of a membrane-bound lectin from the cell membrane to the solution, (c) a surface forward reaction (a membrane-bound lectin binds with an additional glycan), (d) a surface backward reaction (a membrane-bound lectin dissociates with one of its bound glycans), and (e) two-dimensional (2D) surface migration of a glycan on the cell membrane. The proposed kMC model is suitable for describing the lectin-glycan system since it can capture the intrinsic stochasticity of the process and consider effects of inhomogeneous glycan distributions on the overall binding process [5,6].

One major disadvantage of the on-lattice kMC model is the high computational cost. This is mainly due to the disparity in time scales. Specifically, the 2D glycan migration process is at least one order of magnitude more likely to occur compared to other microscopic events. As a result, during a kMC simulation, a vast majority of time will be spent on the glycan migration rather than other microscopic events (i.e., the association and dissociation between glycans and lectins), which are more important for the actual binding dynamics. Motivated by this, this study proposed a hybrid modeling approach, where the kMC model is coupled with a partial differential equation (PDE) to represent the glycan migration separately for efficient computation [7]. Under this new PDE-kMC hybrid model, a cell membrane is represented by a square simulation lattice that consists of a finite number of lattice sites, whose size is approximately equal to the surface area of a glycan’s head group [Lee et al., 2018]. Previously, unbound glycans are randomly distributed on the simulation lattice, and the location of each individual glycan is tracked over time. In the proposed PDE-kMC model, instead of treating each glycan as a discrete entity, it is now treated as a continuum variable, and only its concentration over the surface is tracked. And, its migration on the surface is now simulated by the conventional Fickian diffusion PDE. Consequently, the kMC model now only considers the non-migration microscopic events, and the PDE is solved after a kMC event is executed. Such implementation greatly reduces the computational cost associated with the kMC simulation. By comparing with the original kMC model, we will show that the proposed hybrid kMC model significantly reduces the computational time and does not compromise the accuracy of the model predictions.

References

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