Seamless Modeling of Complex Biological Processes using DPD
Many biological processes take place at the cellular and subcellular levels, where the continuum deterministic description is no longer valid and hence stochastic effects have to be considered. To this end, mesoscopic methods with stochastic terms are attracting increasing attention as a promising approach for tackling challenging problems in bioengineering and biotechnology. We proposed a new framework that seamlessly integrates four key components of blood clotting namely, blood rheology, cell mechanics, coagulation kinetics and transport of species and platelet adhesive dynamics. We used tDPD as the base solver, while a coarse-grained representation of blood cell's (e.g., red blood cell and platelet) membrane accounts for its mechanics. This new multiscale particle-based methodology helps us probe synergistic mechanisms of thrombus formation, and can open new directions in addressing other biological processes from subcellular to macroscopic scales.
Dissipative Particle Dynamics
Dissipative particle dynamics (DPD) has proven itself as one of the most popular particle-based hydrodynamics approach to model fluid and suspending cells at the mesoscale. DPD simplifies atomistic simulations dramatically by using a single coarse-grained particle to represent an entire cluster of molecules, where the effects of unresolved degrees of freedom are approximated by stochastic forces. Similarly to the molecular dynamics (MD), a DPD system consists of many interacting particles and their dynamics are computed by time integration of Newton's equation of motion. However, in contrast to MD, DPD has soft interaction potentials allowing for larger integration time steps. With larger spatial and temporal scales, DPD modeling can be used to investigate hydrodynamics in larger systems, which are beyond the capability of conventional atomistic simulations. We have successfully applied DPD to model proteins, healthy and diseased cells (e.g., sickle or malaria infected red blood cells), and blood plasma in a seamless fashion. The classic DPD method is a minimally working version for mesoscopic simulations of fluids. Due to the lack of necessary degrees of freedom, it cannot be used for some specific problems e.g., heat flow in non-isothermal systems and liquid-vapor interface in two-phase fluid systems. To this end, several extensions of the DPD method have been developed.
An extension of the classic DPD framework is transport dissipative particle dynamics (tDPD). In the tDPD model, each particle is associated with extra variables for carrying concentrations (e.g., of oxygen) to describe the evolution of concentration fields. We studied kinetics of the coagulation cascade (a chain of enzymatic reaction necessary for platelet activation) in blood flow described by advection-diffusion-reaction (ADR) partial differential equations for the reactants. tDPD provides an economical way to solve ADR equations with a large number of species at subcellular scales. For instance, we showed that in a coagulation kinetics problem with 23 ADR equations, the additional computational cost of tDPD is the same as the flow solver, unlike the continuum model requiring 23 Helmholtz solvers making the additional computational cost over ten times higher than a pure Navier-Stokes solver!
