Biophysically inspired model for functionalized nanocarrier adhesion to cell surface: roles of protein expression and mechanical factors

Rational nanoparticle design: Optimization using insights from experiments and mathematical models

Polymeric nanoparticles are highly tunable drug delivery systems that show promise in targeting therapeutics to specific sites within the body. Rational nanoparticle design can make use of mathematical models to organize and extend experimental data, allowing for optimization of nanoparticles for particular drug delivery applications. While rational nanoparticle design is attractive from the standpoint of improving therapy and reducing unnecessary experiments, it has yet to be fully realized. The difficulty lies in the complexity of nanoparticle structure and behavior, which is added to the complexity of the physiological mechanisms involved in nanoparticle distribution throughout the body. In this review, we discuss the most important aspects of rational design of polymeric nanoparticles. Ultimately, we conclude that many experimental datasets are required to fully model polymeric nanoparticle behavior at multiple scales. Further, we suggest ways to consider the limitations and uncertainty of experimental data in creating nanoparticle design optimization schema, which we call quantitative nanoparticle design frameworks.

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.

Targeting vascular inflammation through emerging methods and drug carriers

Acute inflammation is a common dangerous component of pathogenesis of many prevalent conditions with high morbidity and mortality including sepsis, thrombosis, acute respiratory distress syndrome (ARDS), COVID-19, myocardial and cerebral ischemia-reperfusion, infection, and trauma. Inflammatory changes of the vasculature and blood mediate the course and outcome of the pathology in the tissue site of insult, remote organs and systemically. Endothelial cells lining the luminal surface of the vasculature play the key regulatory functions in the body, distinct under normal vs. pathological conditions. In theory, pharmacological interventions in the endothelial cells might enable therapeutic correction of the overzealous damaging pro-inflammatory and pro-thrombotic changes in the vasculature. However, current agents and drug delivery systems (DDS) have inadequate pharmacokinetics and lack the spatiotemporal precision of vascular delivery in the context of acute inflammation. To attain this level of precision, many groups design DDS targeted to specific endothelial surface determinants. These DDS are able to provide specificity for desired tissues, organs, cells, and sub-cellular compartments needed for a particular intervention. We provide a brief overview of endothelial determinants, design of DDS targeted to these molecules, their performance in experimental models with focus on animal studies and appraisal of emerging new approaches. Particular attention is paid to challenges and perspectives of targeted therapeutics and nanomedicine for advanced management of acute inflammation.

Biophysical Considerations in the Rational Design and Cellular Targeting of Flexible Polymeric Nanoparticles

How nanoparticle (NP) mechanical properties impact multivalent ligand-receptor-mediated binding to cell surfaces, the avidity, propensity for internalization, and effects due to crowding remains unknown or unquantified. Through computational analyses, the effects of NP composition from soft, deformable NPs to rigid spheres, effect of tethers, the crowding of NPs at the membrane surface, and the cell membrane properties such as cytoskeletal interactions are addressed. Analyses of binding mechanisms of three distinct NPs that differ in type and rigidity (core-corona flexible NP, rigid NP, and rigid-tethered NP) but are otherwise similar in size and ligand surface density are reported; moreover, for the case of flexible NP, NP stiffness is tuned by varying the internal crosslinking density. Biophysical modeling of NP binding to membranes together with thermodynamic analysis powered by free energy calculations is employed, and it is shown that efficient cellular targeting and uptake of NP functionalized with targeting ligand molecules can be shaped by factors including NP flexibility and crowding, receptor-ligand binding avidity, state of the membrane cytoskeleton, and curvature inducing proteins. Rational design principles that confer tension, membrane excess area, and cytoskeletal sensing properties to the NP which can be exploited for cell-specific targeting of NP are uncovered.

Quantifying and controlling bond multivalency for advanced nanoparticle targeting to cells

Nanoparticles have drawn intense interest as delivery agents for diagnosing and treating various cancers. Much of the early success was driven by passive targeting mechanisms such as the enhanced permeability and retention (EPR) effect, but this has failed to lead to the expected clinical successes. Active targeting involves binding interactions between the nanoparticle and cancer cells, which promotes tumor cell-specific accumulation and internalization. Furthermore, nanoparticles are large enough to facilitate multiple bond formation, which can improve adhesive properties substantially in comparison to the single bond case. While multivalent binding is universally believed to be an attribute of nanoparticles, it is a complex process that is still poorly understood and difficult to control. In this review, we will first discuss experimental studies that have elucidated roles for parameters such as nanoparticle size and shape, targeting ligand and target receptor densities, and monovalent binding kinetics on multivalent nanoparticle adhesion efficiency and cellular internalization. Although such experimental studies are very insightful, information is limited and confounded by numerous differences across experimental systems. Thus, we focus the second part of the review on theoretical aspects of binding, including kinetics, biomechanics, and transport physics. Finally, we discuss various computational and simulation studies of nanoparticle adhesion, including advanced treatments that compare directly to experimental results. Future work will ideally continue to combine experimental data and advanced computational studies to extend our knowledge of multivalent adhesion, as well as design the most powerful nanoparticle-based agents to treat cancer.

A Dynamic, Supramolecular View on the Multivalent Interaction between Influenza Virus and Host Cell

Understanding how influenza viruses traverse the mucus and recognize host cells is critical for evaluating their zoonotic potential, and for prevention and treatment of the disease. The surface of the influenza A virus is covered with the receptor-binding protein hemagglutinin and the receptor-cleaving enzyme neuraminidase, which jointly control the interactions between the virus and the host cell. These proteins are organized in closely spaced trimers and tetramers to facilitate multivalent interactions with sialic acid-terminated glycans. This review shows that the individually weak multivalent interactions of influenza viruses allow superselective binding, virus-induced recruitment of receptors, and the formation of dynamic complexes that facilitate molecular walking. Techniques to measure the avidity and receptor specificity of influenza viruses are reviewed, and the pivotal role of multivalent interactions with their emergent properties in crossing the mucus and entering host cells is discussed. A model is proposed for the initiation of cell entry through virus-induced receptor clustering. The multivalent interactions of influenza viruses are maintained in a dynamic regime by a functional balance between binding and cleaving.

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.

Targeting drug delivery in the vascular system: Focus on endothelium

The bloodstream is the main transporting pathway for drug delivery systems (DDS) from the site of administration to the intended site of action. In many cases, components of the vascular system represent therapeutic targets. Endothelial cells, which line the luminal surface of the vasculature, play a tripartite role of the key target, barrier, or victim of nanomedicines in the bloodstream. Circulating DDS may accumulate in the vascular areas of interest and in off-target areas via mechanisms bypassing specific molecular recognition, but using ligands of specific vascular determinant molecules enables a degree of precision, efficacy, and specificity of delivery unattainable by non-affinity DDS. Three decades of research efforts have focused on specific vascular targeting, which have yielded a multitude of DDS, many of which are currently undergoing a translational phase of development for biomedical applications, including interventions in the cardiovascular, pulmonary, and central nervous systems, regulation of endothelial functions, host defense, and permeation of vascular barriers. We discuss the design of endothelial-targeted nanocarriers, factors underlying their interactions with cells and tissues, and describe examples of their investigational use in models of acute vascular inflammation with an eye on translational challenges.

Binding of a Brownian nanoparticle to a thermally fluctuating membrane surface

We investigate the Brownian dynamics of a nanoparticle bound to a thermally undulating elastic membrane. The ligand-functionalized nanoparticle is assumed to interact monovalently with the receptor expressed on the membrane. In order to resolve the nanoparticle transient motion subject to the instantaneous membrane configuration in a consistent manner, we employ a set of coupled Langevin equations that simultaneously incorporate the hydrodynamic effects, ligand-receptor binding interaction, intramembrane elastic forces, and thermal fluctuations. We show that the presence of a deformable, elastic fluid membrane not only affects the dynamics of a bound nanoparticle but also alters the effective binding potential felt by the nanoparticle. In contrast to a nanoparticle bound to a flat surface, the oscillatory characteristics of the nanoparticle velocity autocorrelation function are suppressed and transition to an anticorrelated long-time tail. Moreover, the nanoparticle position fluctuation becomes more coherent with that of the membrane binding site, and the width of the distribution of the nanoparticle distance from the membrane decreases with increasing membrane bending rigidity. By introducing a locally harmonic, bistable potential as an effective potential for the ligand-receptor pair, the rate of nanoparticle transitioning between two bound states is facilitated by membrane undulations as a result of stronger positional variations associated with the nanoparticle.

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.

Cross-linker-Modulated Nanogel Flexibility Correlates with Tunable Targeting to a Sterically Impeded Endothelial Marker

Deformability of injectable nanocarriers impacts rheological behavior, drug loading, and affinity target adhesion. Here, we present atomic force microscopy (AFM) and spectroscopy measurements of nanocarrier Young's moduli, tune the moduli of deformable nanocarriers with cross-linkers, and demonstrate vascular targeting behavior that correlates with Young's modulus. Homobifunctional cross-linkers were introduced into lysozyme-dextran nanogels (NGs). Single particle-scale AFM measurements determined NG moduli varying from ∼50-150 kPa for unmodified NGs or NGs with a short hydrophilic cross-linker (2,2'-(ethylenedioxy)bis(ethylamine), EOD) to ∼350 kPa for NGs modified with a longer hydrophilic cross-linker (4,9-dioxa-1,12-dodecanediamine, DODD) to ∼10 MPa for NGs modified with a longer hydrophobic cross-linker (1,12-diaminododecane, DAD). Cross-linked NGs were conjugated to antibodies for plasmalemma vesicle associated protein (PLVAP), a caveolar endothelial marker that cannot be accessed by rigid particles larger than ∼100 nm. In previous work, 150 nm NGs effectively targeted PLVAP, where rigid particles of similar diameter did not. EOD-modified NGs targeted PLVAP less effectively than unmodified NGs, but more effectively than DODD or DAD modified NGs, which both yielded low levels of targeting, resembling results previously obtained with polystyrene particles. Cross-linked NGs were also conjugated to antibodies against intracellular adhesion molecule-1 (ICAM-1), an endothelial marker accessible to large rigid particles. Cross-linked NGs and unmodified NGs targeted uniformly to ICAM-1. We thus demonstrate cross-linker modification of NGs, AFM determination of NG mechanical properties varying with cross-linker, and tuning of specific sterically constrained vascular targeting behavior in correlation with cross-linker-modified NG mechanical properties.

Nanoparticle transport phenomena in confined flows

Nanoparticles submerged in confined flow fields occur in several technological applications involving heat and mass transfer in nanoscale systems. Describing the transport with nanoparticles in confined flows poses additional challenges due to the coupling between the thermal effects and fluid forces. Here, we focus on the relevant literature related to Brownian motion, hydrodynamic interactions and transport associated with nanoparticles in confined flows. We review the literature on the several techniques that are based on the principles of non-equilibrium statistical mechanics and computational fluid dynamics in order to simultaneously preserve the fluctuation-dissipation relationship and the prevailing hydrodynamic correlations. Through a review of select examples, we discuss the treatments of the temporal dynamics from the colloidal scales to the molecular scales pertaining to nanoscale fluid dynamics and heat transfer. As evident from this review, there, indeed has been little progress made in regard to the accurate modeling of heat transport in nanofluids flowing in confined geometries such as tubes. Therefore the associated mechanisms with such processes remain unexplained. This review has revealed that the information available in open literature on the transport properties of nanofluids is often contradictory and confusing. It has been very difficult to draw definitive conclusions. The quality of work reported on this topic is non-uniform. A significant portion of this review pertains to the treatment of the fluid dynamic aspects of the nanoparticle transport problem. By simultaneously treating the energy transport in ways discussed in this review as related to momentum transport, the ultimate goal of understanding nanoscale heat transport in confined flows may be achieved.

Multivalent Binding of a Ligand-Coated Particle: Role of Shape, Size, and Ligand Heterogeneity

We utilize a multiscale modeling framework to study the effect of shape, size, and ligand composition on the efficacy of binding of a ligand-coated particle to a substrate functionalized with the target receptors. First, we show how molecular dynamics along with steered molecular dynamics calculations can be used to accurately parameterize the molecular-binding free energy and the effective spring constant for a receptor-ligand pair. We demonstrate this for two ligands that bind to the α₅β₁-domain of integrin. Next, we show how these effective potentials can be used to build computational models at the meso- and continuum-scales. These models incorporate the molecular nature of the receptor-ligand interactions and yet provide an inexpensive route to study the multivalent interaction of receptors and ligands through the construction of Bell potentials customized to the molecular identities. We quantify the binding efficacy of the ligand-coated-particle in terms of its multivalency, binding free-energy landscape, and the losses in the configurational entropies. We show that 1) the binding avidity for particle sizes less than 350 nm is set by the competition between the enthalpic and entropic contributions, whereas that for sizes above 350 nm is dominated by the enthalpy of binding; 2) anisotropic particles display higher levels of multivalent binding compared to those of spherical particles; and 3) variations in ligand composition can alter binding avidity without altering the average multivalency. The methods and results presented here have wide applications in the rational design of functionalized carriers and also in understanding cell adhesion.

Stiffness can mediate balance between hydrodynamic forces and avidity to impact the targeting of flexible polymeric nanoparticles in flow

We report computational investigations of deformable polymeric nanoparticles (NPs) under colloidal suspension flow and adhesive environment. We employ a coarse-grained model for the polymeric NP and perform Brownian dynamics (BD) simulations with hydrodynamic interactions and in the presence of wall-confinement, particulate margination, and wall-adhesion for obtaining NP microstructure, shape, and anisotropic and inhomogeneous transport properties for different NP stiffness. These microscopic properties are utilized in solving the Fokker-Planck equation to obtain the spatial distribution of NP subject to shear, margination due to colloidal microparticles, and confinement due to a vessel wall. Comparing our computational results for the amount of NP margination to the near-wall adhesion regime with those of our binding experiments in cell culture under shear, we found quantitative agreement on shear-enhanced binding, the effect of particulate volume fraction, and the effect of NP stiffness. For the experimentally realized polymeric NP, our model predicts that the shear and volume fraction mediated enhancement in targeting has a hydrodynamic transport origin and is not due to a multivalent binding effect. However, for ultrasoft polymeric NPs, our model predicts a substantial increase in targeting due to multivalent binding. Our results are also in general agreement with experiments of tissue targeting measurements in vivo in mice, however, one needs to exercise caution in extending the modeling treatment to in vivo conditions owing to model approximations. The reported combined computational approach and results are expected to enable fine-tuning of design and optimization of flexible NP in targeted drug delivery applications.

Multivalent Ligand Binding to Cell Membrane Antigens: Defining the Interplay of Affinity, Valency, and Expression Density

Nature uses multivalency to govern many biological processes. The development of macromolecular and cellular therapies has largely been dependent on engineering similar polyvalent interactions to enable effective targeting. Such therapeutics typically utilize high-affinity binding domains that have the propensity to recognize both antigen-overexpressing tumors and normal-expressing tissues, leading to "on-target, off-tumor" toxicities. One strategy to improve these agents' selectivity is to reduce the binding affinity, such that biologically relevant interactions between the therapeutic and target cell will only exist under conditions of high avidity. Preclinical studies have validated this principle of avidity optimization in the context of chimeric antigen receptor (CAR) T cells; however, a rigorous analysis of this approach in the context of soluble multivalent targeting scaffolds has yet to be undertaken. Using a modular protein nanoring capable of displaying ≤8 fibronectin domains with engineered specificity for a model antigen, epithelial cell adhesion molecule (EpCAM), this study demonstrates that binding affinity and ligand valency can be optimized to afford discrimination between EpCAM^High (2.8-3.8 × 10⁶ antigens/cell) and EpCAM^Low (5.2 × 10⁴ to 2.2 × 10⁵ antigens/cell) tissues both in vitro and in vivo.

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.

Biophysics of membrane curvature remodeling at molecular and mesoscopic lengthscales

At the micron scale, where cell organelles display an amazing complexity in their shape and organization, the physical properties of a biological membrane can be better-understood using continuum models subject to thermal (stochastic) undulations. Yet, the chief orchestrators of these complex and intriguing shapes are a specialized class of membrane associating often peripheral proteins called curvature remodeling proteins (CRPs) that operate at the molecular level through specific protein-lipid interactions. We review multiscale methodologies to model these systems at the molecular as well as at the mesoscopic and cellular scales, and also present a free energy perspective of membrane remodeling through the organization and assembly of CRPs. We discuss the morphological space of nearly planar to highly curved membranes, methods to include thermal fluctuations, and review studies that model such proteins as curvature fields to describe the emergent curved morphologies. We also discuss several mesoscale models applied to a variety of cellular processes, where the phenomenological parameters (such as curvature field strength) are often mapped to models of real systems based on molecular simulations. Much insight can be gained from the calculation of free energies of membranes states with protein fields, which enable accurate mapping of the state and parameter values at which the membrane undergoes morphological transformations such as vesiculation or tubulation. By tuning the strength, anisotropy, and spatial organization of the curvature-field, one can generate a rich array of membrane morphologies that are highly relevant to shapes of several cellular organelles. We review applications of these models to budding of vesicles commonly seen in cellular signaling and trafficking processes such as clathrin mediated endocytosis, sorting by the ESCRT protein complexes, and cellular exocytosis regulated by the exocyst complex. We discuss future prospects where such models can be combined with other models for cytoskeletal assembly, and discuss their role in understanding the effects of cell membrane tension and the mechanics of the extracellular microenvironment on cellular processes.

Excess area dependent scaling behavior of nano-sized membrane tethers

Thermal fluctuations in cell membranes manifest as an excess area ([Formula: see text]) which governs a multitude of physical process at the sub-micron scale. We present a theoretical framework, based on an in silico tether pulling method, which may be used to reliably estimate [Formula: see text] in live cells. We perform our simulations in two different thermodynamic ensembles: (i) the constant projected area and (ii) the constant frame tension ensembles and show the equivalence of our results in the two. The tether forces estimated from our simulations compare well with our experimental measurements for tethers extracted from ruptured GUVs and HeLa cells. We demonstrate the significance and validity of our method by showing that all our calculations performed in the initial tether formation regime (i.e. when the length of the tether is comparable to its radius) along with experiments of tether extraction in 15 different cell types collapse onto two unified scaling relationships mapping tether force, tether radius, bending stiffness κ, and membrane tension σ. We show that [Formula: see text] is an important determinant of the radius of the extracted tether, which is equal to the characteristic length [Formula: see text] for [Formula: see text], and is equal to [Formula: see text] for [Formula: see text]. We also find that the estimated excess area follows a linear scaling behavior that only depends on the true value of [Formula: see text] for the membrane, based on which we propose a self-consistent technique to estimate the range of excess membrane areas in a cell.

Ligand Characteristics Important to Avidity Interactions of Multivalent Nanoparticles

Multivalent interactions involve the engagement of multiple ligand-receptor pairs and are important in synthetic biology as design paradigms for targeted nanoparticles (NPs). However, little is known about the specific ligand parameters important to multivalent interactions. We employed a series of oligonucleotides as ligands conjugated to dendrimers as nanoparticles, and used complementary oligonucleotides on a functionalized SPR surface to measure binding. We compared the effect of ligand affinity to ligand number on the avidity characteristics of functionalized NPs. Changing the ligand affinity, either by changing the temperature of the system or by substitution noncomplementary base pairs into the oligonucleotides, had little effect on multivalent interaction; the overall avidity, number of ligands required for avidity per particle, and the number of particles showing avidity did not significantly change. We then made NP conjugates with the same oligonucleotide using an efficient copper-free click chemistry that resulted in essentially all of the NPs in the population exceeding the threshold ligand value. The particles exceeding the threshold ligand number again demonstrated high avidity interactions. This work validates the concept of a threshold ligand valence and suggests that the number of ligands per nanoparticle is the defining factor in achieving high avidity interactions.

Effect of wall-mediated hydrodynamic fluctuations on the kinetics of a Brownian nanoparticle

The reactive flux formalism (Chandler 1978 J. Chem. Phys.68, 2959-2970. (doi:10.1063/1.436049)) and the subsequent development of methods such as transition path sampling have laid the foundation for explicitly quantifying the rate process in terms of microscopic simulations. However, explicit methods to account for how the hydrodynamic correlations impact the transient reaction rate are missing in the colloidal literature. We show that the composite generalized Langevin equation (Yu et al. 2015 Phys. Rev. E91, 052303. (doi:10.1103/PhysRevE.91.052303)) makes a significant step towards solving the coupled processes of molecular reactions and hydrodynamic relaxation by examining how the wall-mediated hydrodynamic memory impacts the two-stage temporal relaxation of the reaction rate for a nanoparticle transition between two bound states in the bulk, near-wall and lubrication regimes.