Computational Models for Nanoscale Fluid Dynamics and Transport Inspired by Nonequilibrium Thermodynamics

Multiphysics pharmacokinetic model for targeted nanoparticles

Nanoparticles (NP) are being increasingly explored as vehicles for targeted drug delivery because they can overcome free therapeutic limitations by drug encapsulation, thereby increasing solubility and transport across cell membranes. However, a translational gap exists from animal to human studies resulting in only several NP having FDA approval. Because of this, researchers have begun to turn toward physiologically based pharmacokinetic (PBPK) models to guide in vivo NP experimentation. However, typical PBPK models use an empirically derived framework that cannot be universally applied to varying NP constructs and experimental settings. The purpose of this study was to develop a physics-based multiscale PBPK compartmental model for determining continuous NP biodistribution. We successfully developed two versions of a physics-based compartmental model, models A and B, and validated the models with experimental data. The more physiologically relevant model (model B) had an output that more closely resembled experimental data as determined by normalized root mean squared deviation (NRMSD) analysis. A branched model was developed to enable the model to account for varying NP sizes. With the help of the branched model, we were able to show that branching in vasculature causes enhanced uptake of NP in the organ tissue. The models were solved using two of the most popular computational platforms, MATLAB and Julia. Our experimentation with the two suggests the highly optimized ODE solver package DifferentialEquations.jl in Julia outperforms MATLAB when solving a stiff system of ordinary differential equations (ODEs). We experimented with solving our PBPK model with a neural network using Julia's Flux.jl package. We were able to demonstrate that a neural network can learn to solve a system of ODEs when the system can be made non-stiff via quasi-steady-state approximation (QSSA). Our model incorporates modules that account for varying NP surface chemistries, multiscale vascular hydrodynamic effects, and effects of the immune system to create a more comprehensive and modular model for predicting NP biodistribution in a variety of NP constructs.

Computational models for studying physical instabilities in high concentration biotherapeutic formulations

Computational prediction of the behavior of concentrated protein solutions is particularly advantageous in early development stages of biotherapeutics when material availability is limited and a large set of formulation conditions needs to be explored. This review provides an overview of the different computational paradigms that have been successfully used in modeling undesirable physical behaviors of protein solutions with a particular emphasis on high-concentration drug formulations. This includes models ranging from all-atom simulations, coarse-grained representations to macro-scale mathematical descriptions used to study physical instability phenomena of protein solutions such as aggregation, elevated viscosity, and phase separation. These models are compared and summarized in the context of the physical processes and their underlying assumptions and limitations. A detailed analysis is also given for identifying protein interaction processes that are explicitly or implicitly considered in the different modeling approaches and particularly their relations to various formulation parameters. Lastly, many of the shortcomings of existing computational models are discussed, providing perspectives and possible directions toward an efficient computational framework for designing effective protein formulations.

A survey of multiscale modeling: Foundations, historical milestones, current status, and future prospects

Research problems in the domains of physical, engineering, biological sciences often span multiple time and length scales, owing to the complexity of information transfer underlying mechanisms. Multiscale modeling (MSM) and high-performance computing (HPC) have emerged as indispensable tools for tackling such complex problems. We review the foundations, historical developments, and current paradigms in MSM. A paradigm shift in MSM implementations is being fueled by the rapid advances and emerging paradigms in HPC at the dawn of exascale computing. Moreover, amidst the explosion of data science, engineering, and medicine, machine learning (ML) integrated with MSM is poised to enhance the capabilities of standard MSM approaches significantly, particularly in the face of increasing problem complexity. The potential to blend MSM, HPC, and ML presents opportunities for unbound innovation and promises to represent the future of MSM and explainable ML that will likely define the fields in the 21st century.

Multiscale modeling of protein membrane interactions for nanoparticle targeting in drug delivery

Nanoparticle (NP)-based imaging and drug delivery systems for systemic (e.g. intravenous) therapeutic and diagnostic applications are inherently a complex integration of biology and engineering. A broad range of length and time scales are essential to hydrodynamic and microscopic molecular interactions mediating NP (drug nanocarriers, imaging agents) motion in blood flow, cell binding/uptake, and tissue accumulation. A computational model of time-dependent tissue delivery, providing in silico prediction of organ-specific accumulation of NPs, can be leveraged in NP design and clinical applications. In this article, we provide the current state-of-the-art and future outlook for the development of predictive models for NP transport, targeting, and distribution through the integration of new computational schemes rooted in statistical mechanics and transport. The resulting multiscale model will comprehensively incorporate: (i) hydrodynamic interactions in the vascular scales relevant to NP margination; (ii) physical and mechanical forces defining cellular and tissue architecture and epitope accessibility mediating NP adhesion; and (iii) subcellular and paracellular interactions including molecular-level targeting impacting NP uptake.

Thermodynamic analysis of multivalent binding of functionalized nanoparticles to membrane surface reveals the importance of membrane entropy and nanoparticle entropy in adhesion of flexible nanoparticles

We present a quantitative model for multivalent binding of ligand-coated flexible polymeric nanoparticles (NPs) to a flexible membrane expressing receptors. The model is developed using a multiscale computational framework by coupling a continuum field model for the cell membrane with a coarse-grained model for the polymeric NPs. The NP is modeled as a self-avoiding bead-spring polymer chain, and the cell membrane is modeled as a triangulated surface using the dynamically triangulated Monte Carlo method. The nanoparticle binding affinity to a cell surface is mainly determined by the delicate balance between the enthalpic gain due to the multivalent ligand-receptor binding and the entropic penalties of various components including receptor translation, membrane undulation, and NP conformation. We have developed new methods to compute the free energy of binding, which includes these enthalpy and entropy terms. We show that the multivalent interactions between the flexible NP and the cell surface are subject to entropy-enthalpy compensation. Three different entropy contributions, namely, those due to receptor-ligand translation, NP flexibility, and membrane undulations, are all significant, although the first of these terms is the most dominant. However, both NP flexibility and membrane undulations dictate the receptor-ligand translational entropy making the entropy compensation context-specific, i.e., dependent on whether the NP is rigid or flexible, and on the state of the membrane given by the value of membrane tension or its excess area.

Nanofluid Dynamics of Flexible Polymeric Nanoparticles Under Wall Confinement

Describing the hydrodynamics of nanoparticles in fluid media poses interesting challenges due to the coupling between the Brownian and hydrodynamic forces at the nanoscale. We focus on multiscale formulations of Brownian motion and hydrodynamic interactions (HI) of a single flexible polymeric nanoparticle in confining flows using the Brownian Dynamics method. The nanoparticle is modeled as a self-avoiding freely jointed polymer chain that is subject to Brownian forces, hydrodynamics forces, and repulsive interactions with the confining wall. To accommodate the effect of the wall, the hydrodynamic lift due to the wall is included in the mobility of a bead of the polymer chain which depends on its proximity to the wall. Using the example of a flexible polymeric nanoparticle, we illustrate temporal dynamics pertaining to the colloidal scale as well as the nanoscale.

Adhesion of a polymer-grafted nanoparticle to cells explored using generalized Langevin dynamics

We model a polymer-grafted stealth nanoparticle (SNP) as a composite system consisting of a spherical core coated with a porous polymeric brush with end-ligands. Adjacent to target cells, the near-wall hydrodynamics, thermal fluctuations, and thermodynamic adhesive interactions simultaneously impact the transient motion of the SNP. Employing both the Langevin framework for the effective hard sphere dynamics and the coupled generalized Langevin framework for the nanoparticle-polymer dynamics, we comprehensively investigate the velocity and position temporal relaxations of the SNP in the absence and presence of end-to-end distance fluctuations for the tethered polymer. We demonstrate that polymer structural relaxations substantially impact the SNP adhesive dynamics, especially when the grafted polymer is more flexible. Moreover, a long-time tail with t-3/2 scaling due to polymer chain-length fluctuations is observed in the velocity autocorrelation for a bound SNP. Finally, the thermodynamic effects of membrane morphology on SNP adhesion are explored by modifying the membrane-mediated binding potential of mean force.

Motion of a nano-spheroid in a cylindrical vessel flow: Brownian and hydrodynamic interactions

We study the motion of a buoyant or a nearly neutrally buoyant nano-sized spheroid in a fluid filled tube without or with an imposed pressure gradient (weak Poiseuille flow). The fluctuating hydrodynamics approach and the deterministic method are both employed. We ensure that the fluctuation-dissipation relation and the principle of thermal equipartition of energy are both satisfied. The major focus is on the effect of the confining boundary. Results for the velocity and the angular velocity autocorrelations (VACF and AVACF), the diffusivities and the drag and the lift forces as functions of the shape, the aspect ratio, the inclination angle and the proximity to the wall are presented. For the parameters considered, the boundary modifies the VACF and AVACF such that three distinct regimes are discernible - an initial exponential decay followed by an algebraic decay culminating in a second exponential decay. The first is due to the thermal noise, the algebraic regime is due both to the thermal noise and the hydrodynamic correlations, while the second exponential decay shows the effect of momentum reflection from the confining wall. Our predictions display excellent comparison with published results for the algebraic regime (the only regime for which earlier results exist). We also discuss the role of the off-diagonal elements of the mobility and the diffusivity tensors that enable the quantifications of the degree of lift and margination of the nanocarrier. Our study covers a range of parameters that are of wide applicability in nanotechnology, microrheology and in targeted drug delivery.