Interaction of Methylene Blue with Severe Acute Respiratory Syndrome Coronavirus 2 Envelope Revealed by Molecular Modeling

Methylene blue has multiple antiviral properties against Severe Acute Respiratory Syndrome-related Coronavirus 2 (SARS-CoV-2). The ability of methylene blue to inhibit different stages of the virus life cycle, both in light-independent and photodynamic processes, is used in clinical practice. At the same time, the molecular aspects of the interactions of methylene blue with molecular components of coronaviruses are not fully understood. Here, we use Brownian dynamics to identify methylene blue binding sites on the SARS-CoV-2 envelope. The local lipid and protein composition of the coronavirus envelope plays a crucial role in the binding of this cationic dye. Viral structures targeted by methylene blue include the S and E proteins and negatively charged lipids. We compare the obtained results with known experimental data on the antiviral effects of methylene blue to elucidate the molecular basis of its activity against coronaviruses.

Analysing Sources of Error in Total Internal Reflection Microscopy (TIRM) Experiments and Data Analysis

Many phenomena observed in synthetic and biological colloidal suspensions are dominated by the static interaction energies and the hydrodynamic interactions that act both between individual particles and also between colloids and macroscopic interfaces. This calls for methods that allow precise measurements of the corresponding forces. One method used for this purpose is total internal reflection microscopy (TIRM), which has been employed for around three decades to measure in particular the interactions between a single particle suspended in a liquid and a solid surface. However, given the importance of the observable variables, it is crucial to understand the possibilities and limitations of the method. In this paper, we investigate the influence of technically unavoidable noise effects and an inappropriate choice of particle size and sampling time on TIRM measurement results. Our main focus is on the measurement of diffusion coefficients and drift velocities, as the influence of error sources on dynamic properties has not been investigated so far. We find that detector shot noise and prolonged sampling times may cause erroneous results in the steep parts of the interaction potential where forces of the order of pico-Newtons or larger act on the particle, while the effect of background noise is negligible below certain thresholds. Furthermore, noise does not significantly affect dynamic data but we find that lengthy sampling times and/or probe particles with too small a radius will cause issues. Most importantly, we observe that dynamic results are very likely to differ from the standard hydrodynamic predictions for stick boundary conditions due to partial slip.

Simulational Tests of the Rouse Model

An extensive review of literature simulations of quiescent polymer melts is given, considering results that test aspects of the Rouse model in the melt. We focus on Rouse model predictions for the mean-square amplitudes ⟨(Xp(0))2⟩ and time correlation functions ⟨Xp(0)Xp(t)⟩ of the Rouse mode Xp(t). The simulations conclusively demonstrate that the Rouse model is invalid in polymer melts. In particular, and contrary to the Rouse model, (i) mean-square Rouse mode amplitudes ⟨(Xp(0))2⟩ do not scale as sin-2(pπ/2N), N being the number of beads in the polymer. For small p (say, p≤3) ⟨(Xp(0))2⟩ scales with p as p-2; for larger p, it scales as p-3. (ii) Rouse mode time correlation functions ⟨Xp(t)Xp(0)⟩ do not decay with time as exponentials; they instead decay as stretched exponentials exp(-αtβ). β depends on p, typically with a minimum near N/2 or N/4. (iii) Polymer bead displacements are not described by independent Gaussian random processes. (iv) For p≠q, ⟨Xp(t)Xq(0)⟩ is sometimes non-zero. (v) The response of a polymer coil to a shear flow is a rotation, not the affine deformation predicted by Rouse. We also briefly consider the Kirkwood-Riseman polymer model.

The Kirkwood-Riseman Model of Polymer Solution Dynamics Is Qualitatively Correct

The Rouse model is the foundational basis of much of modern polymer physics. The period alternative, the Kirkwood-Riseman model, is rarely mentioned in modern monographs. The models are qualitatively different. The models do not agree as to how many internal modes a polymer molecule has. In the Kirkwood-Riseman model, polymers in a shear field perform whole-body rotation; in the Rouse model, polymers respond to shear with an affine deformation. We use Brownian dynamics to show that the Kirkwood-Riseman model for chain motion is qualitatively correct. Contrary to the Rouse model, in shear flow, polymer coils rotate. Rouse modes are cross-correlated. The amplitudes and relaxation rates of Rouse modes depend on the shear rate. Several alternatives to Rouse modes as collective coordinates are discussed.

Perspective: How to overcome dynamical density functional theory

We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, and machine learning nonequilibrium phenomena that occur in soft matter. To give guidance for navigating the theoretical and practical challenges that lie ahead, we discuss and exemplify the limitations of dynamical density functional theory (DDFT). Instead of the implied adiabatic sequence of equilibrium states that this approach provides as a makeshift for the true time evolution, we posit that the pending theoretical tasks lie in developing a systematic understanding of the dynamical functional relationships that govern the genuine nonequilibrium physics. While static density functional theory gives a comprehensive account of the equilibrium properties of many-body systems, we argue that power functional theory is the only present contender to shed similar insights into nonequilibrium dynamics, including the recognition and implementation of exact sum rules that result from the Noether theorem. As a demonstration of the power functional point of view, we consider an idealized steady sedimentation flow of the three-dimensional Lennard-Jones fluid and machine-learn the kinematic map from the mean motion to the internal force field. The trained model is capable of both predicting and designing the steady state dynamics universally for various target density modulations. This demonstrates the significant potential of using such techniques in nonequilibrium many-body physics and overcomes both the conceptual constraints of DDFT as well as the limited availability of its analytical functional approximations.

SARS-CoV-2 evolved variants optimize binding to cellular glycocalyx

Viral variants of concern continue to arise for SARS-CoV-2, potentially impacting both methods for detection and mechanisms of action. Here, we investigate the effect of an evolving spike positive charge in SARS-CoV-2 variants and subsequent interactions with heparan sulfate and the angiotensin converting enzyme 2 (ACE2) in the glycocalyx. We show that the positively charged Omicron variant evolved enhanced binding rates to the negatively charged glycocalyx. Moreover, we discover that while the Omicron spike-ACE2 affinity is comparable to that of the Delta variant, the Omicron spike interactions with heparan sulfate are significantly enhanced, giving rise to a ternary complex of spike-heparan sulfate-ACE2 with a large proportion of double-bound and triple-bound ACE2. Our findings suggest that SARS-CoV-2 variants evolve to be more dependent on heparan sulfate in viral attachment and infection. This discovery enables us to engineer a second-generation lateral-flow test strip that harnesses both heparin and ACE2 to reliably detect all variants of concern, including Omicron.

Interplay of Hydropathy and Heterogeneous Diffusion in the Molecular Transport within Lamellar Lipid Mesophases

Lipid mesophases are being intensively studied as potential candidates for drug-delivery purposes. Extensive experimental characterization has unveiled a wide palette of release features depending on the nature of the host lipids and of the guest molecule, as well as on the environmental conditions. However, only a few simulation works have addressed the matter, which hampers a solid rationalization of the richness of outcomes observed in experiments. Particularly, to date, there are no theoretical works addressing the impact of hydropathy on the transport of a molecule within lipid mesophases, despite the significant fraction of hydrophobic molecules among currently-available drugs. Similarly, the high heterogeneity of water mobility in the nanoscopic channels within lipid mesophases has also been neglected. To fill this gap, we introduce here a minimal model to account for these features in a lamellar geometry, and systematically study the role played by hydropathy and water-mobility heterogeneity by Brownian-dynamics simulations. We unveil a fine interplay between the presence of free-energy barriers, the affinity of the drug for the lipids, and the reduced mobility of water in determining the net molecular transport. More in general, our work is an instance of how multiscale simulations can be fruitfully employed to assist experiments in release systems based on lipid mesophases.

Microscopic model on indoor propagation of respiratory droplets

Indoor propagation of airborne diseases is yet poorly understood. Here, we theoretically study a microscopic model based on the motions of virus particles in a respiratory microdroplet, responsible for airborne transmission of diseases, to understand their indoor propagation. The virus particles are driven by a driving force that mimics force due to gushing of air by devices like indoor air conditioning along with the gravity. A viral particle within the droplet experiences viscous drag due to the droplet medium, force due to interfacial tension at the droplet boundary, the thermal forces and mutual interaction forces with the other viral particles. We use Brownian Dynamics (BD) simulations and scaling arguments to study the motion of the droplet, given by that of the center of mass of the viral assembly. The BD simulations show that in presence of the gravity force alone, the time the droplet takes to reach the ground level, defined by the gravitational potential energy being zero, from a vertical height H,t_f∼γ^-0.1 dependence, where γ is the interfacial tension. In presence of the driving force of magnitude F₀ and duration τ₀, the horizontal propagation length, Y_max from the source increase linearly with τ₀, where the slope is steeper for larger F₀. Our scaling analysis explains qualitatively well the simulation observations and show long-distance transmission of airborne respiratory droplets in the indoor conditions due to F₀ ∼ nano-dyne.

Soft representation of the square-well and square-shoulder potentials to be used in Brownian and molecular dynamics simulations

The discrete hard-sphere (HS), square-well (SW), and square-shoulder (SS) potentials have become the battle horse of molecular and complex fluids because they contain the basic elements to describe the thermodynamic, structural, and transport properties of both types of fluids. The mathematical simplicity of these discrete potentials allows us to obtain some analytical results despite the nature and complexity of the modeled systems. However, the divergent forces arising at the potential discontinuities may lead to severe issues when discrete potentials are used in computer simulations with uniform time steps. One of the few routes to avoid these technical problems is to replace the discrete potentials with continuous and differentiable forms built under strict physical criteria to capture the correct phenomenology. The match of the second virial coefficient between the discrete and the soft potentials has recently been successfully used to construct a continuous representation that mimics some physical properties of HSs (Báezet al2018J. Chem. Phys.149164907). In this paper, we report an extension of this idea to construct soft representations of the discrete SW and SS potentials. We assess the accuracy of the resulting soft potential by studying structural and thermodynamic properties of the modeled systems by using extensive Brownian and molecular dynamics computer simulations. Besides, Monte Carlo results for the original discrete potentials are used as benchmark. We have also implemented the discrete interaction models and their soft counterparts within the integral equations theory of liquids, finding that the most widely used approximations predict almost identical results for both potentials.

Multi-Scale Modelling of Aggregation of TiO2 Nanoparticle Suspensions in Water

Titanium dioxide nanoparticles have risen concerns about their possible toxicity and the European Food Safety Authority recently banned the use of TiO₂ nano-additive in food products. Following the intent of relating nanomaterials atomic structure with their toxicity without having to conduct large-scale experiments on living organisms, we investigate the aggregation of titanium dioxide nanoparticles using a multi-scale technique: starting from ab initio Density Functional Theory to get an accurate determination of the energetics and electronic structure, we switch to classical Molecular Dynamics simulations to calculate the Potential of Mean Force for the connection of two identical nanoparticles in water; the fitting of the latter by a set of mathematical equations is the key for the upscale. Lastly, we perform Brownian Dynamics simulations where each nanoparticle is a spherical bead. This coarsening strategy allows studying the aggregation of a few thousand nanoparticles. Applying this novel procedure, we find three new molecular descriptors, namely, the aggregation free energy and two numerical parameters used to correct the observed deviation from the aggregation kinetics described by the Smoluchowski theory. Ultimately, molecular descriptors can be fed into QSAR models to predict the toxicity of a material knowing its physicochemical properties, enabling safe design strategies.

Modeling Brownian Microparticle Trajectories in Lab-on-a-Chip Devices with Time Varying Dielectrophoretic or Optical Forces

Lab-on-a-chip (LOC) devices capable of manipulating micro/nano-sized samples have spurred advances in biotechnology and chemistry. Designing and analyzing new and more advanced LOCs require accurate modeling and simulation of sample/particle dynamics inside such devices. In this work, we present a generalized computational physics model to simulate particle/sample trajectories under the influence of dielectrophoretic or optical forces inside LOC devices. The model takes into account time varying applied forces, Brownian motion, fluid flow, collision mechanics, and hindered diffusion caused by hydrodynamic interactions. We develop a numerical solver incorporating the aforementioned physics and use it to simulate two example cases: first, an optical trapping experiment, and second, a dielectrophoretic cell sorter device. In both cases, the numerical results are found to be consistent with experimental observations, thus proving the generality of the model. The numerical solver can simulate time evolution of the positions and velocities of an arbitrarily large number of particles simultaneously. This allows us to characterize and optimize a wide range of LOCs. The developed numerical solver is made freely available through a GitHub repository so that researchers can use it to develop and simulate new designs.

What Binds Cationic Photosensitizers Better: Brownian Dynamics Reveals Key Interaction Sites on Spike Proteins of SARS-CoV, MERS-CoV, and SARS-CoV-2

We compared the electrostatic properties of the spike proteins (S-proteins) of three coronaviruses, SARS-CoV, MERS-CoV, and SARS-CoV-2, and their interactions with photosensitizers (PSs), octacationic octakis(cholinyl)zinc phthalocyanine (Zn-PcChol₈₊) and monocationic methylene blue (MB). We found a major common PS binding site at the connection of the S-protein stalk and head. The molecules of Zn-PcChol₈₊ and MB also form electrostatic encounter complexes with large area of negative electrostatic potential at the head of the S-protein of SARS-CoV-2, between fusion protein and heptad repeat 1 domain. The top of the SARS-CoV spike head demonstrates a notable area of electrostatic contacts with Zn-PcChol₈₊ and MB that corresponds to the N-terminal domain. The S-protein protomers of SARS-CoV-2 in “open” and “closed” conformations demonstrate different ability to attract PS molecules. In contrast with Zn-PcChol₈₊, MB possesses the ability to penetrate inside the pocket formed as a result of SARS-CoV-2 receptor binding domain transition into the “open” state. The existence of binding site for cationic PSs common to the S-proteins of SARS-CoV, SARS-CoV-2, and MERS-CoV creates prospects for the wide use of this type of PSs to combat the spread of coronaviruses.

Protein Transport through Nanopores Illuminated by Long-Time-Scale Simulations

The transport of molecules through nanoscale confined space is relevant in biology, biosensing, and industrial filtration. Microscopically modeling transport through nanopores is required for a fundamental understanding and guiding engineering, but the short duration and low replica number of existing simulation approaches limit statistically relevant insight. Here we explore protein transport in nanopores with a high-throughput computational method that realistically simulates hundreds of up to seconds-long protein trajectories by combining Brownian dynamics and continuum simulation and integrating both driving forces of electroosmosis and electrophoresis. Ionic current traces are computed to enable experimental comparison. By examining three biological and synthetic nanopores, our study answers questions about the kinetics and mechanism of protein transport and additionally reveals insight that is inaccessible from experiments yet relevant for pore design. The discovery of extremely frequent unhindered passage can guide the improvement of biosensor pores to enhance desired biomolecular recognition by pore-tethered receptors. Similarly, experimentally invisible nontarget adsorption to pore walls highlights how to improve recently developed DNA nanopores. Our work can be expanded to pressure-driven flow to model industrial nanofiltration processes.

Vitrification is a spontaneous non-equilibrium transition driven by osmotic pressure

Persistent dynamics in colloidal glasses suggest the existence of a non-equilibrium driving force for structural relaxation during glassy aging. But the implicit assumption in the literature that colloidal glasses form within the metastable state bypasses the search for a driving force for vitrification and glassy aging and its connection with a metastable state. The natural relation of osmotic pressure to number-density gradients motivates us to investigate the osmotic pressure as this driving force. We use dynamic simulation to quench a polydisperse hard-sphere colloidal liquid into the putative glass region while monitoring structural relaxation and osmotic pressure. Following quenches to various depths in volume fractionϕ(whereϕ_RCP≈ 0.678 for 7% polydispersity), the osmotic pressure overshoots its metastable value, then decreases with age toward the metastable pressure, driving redistribution of coordination number and interparticle voids that smooths structural heterogeneity with age. For quenches to 0.56 ⩽ϕ⩽ 0.58, accessible post-quench volume redistributes with age, allowing the glass to relax into a strong supercooled liquid and easily reach a metastable state. At higher volume fractions, 0.59 ⩽ϕ< 0.64, this redistribution encounters a barrier that is subsequently overcome by osmotic pressure, allowing the system to relax toward the metastable state. But forϕ⩾ 0.64, the overshoot is small compared to the high metastable pressure; redistribution of volume stops as particles acquire contacts and get stuck, freezing the system far from the metastable state. Overall, the osmotic pressure drives structural rearrangements responsible for both vitrification and glassy age-relaxation. The connection of energy, pressure, and structure identifies the glass transition, 0.63 <ϕ_g⩽ 0.64. We leverage the connection of osmotic pressure to energy density to put forth the mechanistic view that relaxation of structural heterogeneity in colloidal glasses occurs via individual particle motion driven by osmotic pressure, and is a spontaneous energy minimization process that drives the glass off and back to the metastable state.

A Novel Hybrid Monte Carlo Algorithm for Sampling Path Space

To sample from complex, high-dimensional distributions, one may choose algorithms based on the Hybrid Monte Carlo (HMC) method. HMC-based algorithms generate nonlocal moves alleviating diffusive behavior. Here, I build on an already defined HMC framework, hybrid Monte Carlo on Hilbert spaces (Beskos, et al. Stoch. Proc. Applic. 2011), that provides finite-dimensional approximations of measures π, which have density with respect to a Gaussian measure on an infinite-dimensional Hilbert (path) space. In all HMC algorithms, one has some freedom to choose the mass operator. The novel feature of the algorithm described in this article lies in the choice of this operator. This new choice defines a Markov Chain Monte Carlo (MCMC) method that is well defined on the Hilbert space itself. As before, the algorithm described herein uses an enlarged phase space Π having the target π as a marginal, together with a Hamiltonian flow that preserves Π. In the previous work, the authors explored a method where the phase space π was augmented with Brownian bridges. With this new choice, π is augmented by Ornstein–Uhlenbeck (OU) bridges. The covariance of Brownian bridges grows with its length, which has negative effects on the acceptance rate in the MCMC method. This contrasts with the covariance of OU bridges, which is independent of the path length. The ingredients of the new algorithm include the definition of the mass operator, the equations for the Hamiltonian flow, the (approximate) numerical integration of the evolution equations, and finally, the Metropolis–Hastings acceptance rule. Taken together, these constitute a robust method for sampling the target distribution in an almost dimension-free manner. The behavior of this novel algorithm is demonstrated by computer experiments for a particle moving in two dimensions, between two free-energy basins separated by an entropic barrier.

The Photosensitizer Octakis(cholinyl)zinc Phthalocyanine with Ability to Bind to a Model Spike Protein Leads to a Loss of SARS-CoV-2 Infectivity In Vitro When Exposed to Far-Red LED

Photodynamic inactivation of pathogenic microorganisms can be successfully used to eradicate pathogens in localized lesions, infected liquid media, and on various surfaces. This technique utilizes the photosensitizer (PS), light, and molecular oxygen to produce reactive oxygen species that kill pathogens. Here, we used the PS, water soluble octakis(cholinyl)zinc phthalocyanine (Zn-PcChol8+), to inactivate an initial 4.75-5.00 IgTCID50/mL titer of SARS-CoV-2, thereby preventing viral infection when tested in Vero E6 cell cultures. Zn-PcChol8+ in a minimally studied concentration, 1 µM and LED 3.75 J/cm2, completely destroyed the infectivity of SARS-CoV-2. To detect possible PS binding sites on the envelope of SARS-CoV-2, we analyzed electrostatic potential and simulated binding of Zn-PcChol8+ to the spike protein of this coronavirus by means of Brownian dynamics software, ProKSim (Protein Kinetics Simulator). Most of the Zn-PcChol8+ molecules formed clusters at the upper half of the stalk within a vast area of negative electrostatic potential. Positioning of the PS on the surface of the spike protein at a distance of no more than 10 nm from the viral membrane may be favorable for the oxidative damage. The high sensitivity of SARS-CoV-2 to photodynamic inactivation by Zn-PcChol8+ is discussed with respect to the application of this PS to control the spread of COVID-19.

Atomistic Basis of Microtubule Dynamic Instability Assessed Via Multiscale Modeling

Microtubule “dynamic instability,” the abrupt switching from assembly to disassembly caused by the hydrolysis of GTP to GDP within the β subunit of the αβ-tubulin heterodimer, is necessary for vital cellular processes such as mitosis and migration. Despite existing high-resolution structural data, the key mechanochemical differences between the GTP and GDP states that mediate dynamic instability behavior remain unclear. Starting with a published atomic-level structure as an input, we used multiscale modeling to find that GTP hydrolysis results in both longitudinal bond weakening (~ 4 k_BT) and an outward bending preference (~ 1.5 k_BT) to both drive dynamic instability and give rise to the microtubule tip structures previously observed by light and electron microscopy. More generally, our study provides an example where atomic level structural information is used as the sole input to predict cellular level dynamics without parameter adjustment.

Evaporation-driven self-assembly of binary and ternary colloidal polymer nanocomposites for abrasion resistant applications

We harness the self-assembly of aqueous binary latex/silica particle blends during drying to fabricate films segregated by size in the vertical direction. We report for the first time the experimental drying of ternary colloidal dispersions and demonstrate how a ternary film containing additional small latex particles results in improved surface stability and abrasion resistance compared with a binary film. Through atomic force microscopy (AFM) and energy-dispersive X-ray spectroscopy (EDX), we show that the vertical distribution of filler particles and the surface morphologies of the films can be controlled by altering the evaporation rate and silica volume fraction. We report the formation of various silica superstructures at the film surface, which we attribute to a combination of diffusiophoresis and electrostatic interactions between particles. Brownian dynamics simulations of the final stages of solvent evaporation provide further evidence for this formation mechanism. We show how an additional small latex particle population results in an increased abrasion resistance of the film without altering its morphology or hardness. Our work provides a method to produce water-based coatings with enhanced abrasion resistance as well as valuable insights into the mechanisms behind the formation of colloidal superstructures.

Predicting the effects of dATP on cardiac contraction using multiscale modeling of the sarcomere

2'-deoxy-ATP (dATP) is a naturally occurring small molecule that has shown promise as a therapeutic because it significantly increases cardiac myocyte force development even at low dATP/ATP ratios. To investigate mechanisms by which dATP alters myosin crossbridge dynamics, we used Brownian dynamics simulations to calculate association rates between actin and ADP- or dADP-bound myosin. These rates were then directly incorporated in a mechanistic Monte Carlo Markov Chain model of cooperative sarcomere contraction. A unique combination of increased powerstroke and detachment rates was required to match experimental steady-state and kinetic data for dATP force production in rat cardiac myocytes when the myosin attachment rate in the model was constrained by the results of a Brownian dynamics simulation. Nearest-neighbor cooperativity was seen to contribute to, but not fully explain, the steep relationship between dATP/ATP ratio and steady-state force-development observed at lower dATP concentrations. Dynamic twitch simulations performed using measured calcium transients as inputs showed that the effects of dATP on the crossbridge alone were not sufficient to explain experimentally observed enhancement of relaxation kinetics by dATP treatment. Hence, dATP may also affect calcium handling even at low concentrations. By enabling the effects of dATP on sarcomere mechanics to be predicted, this multi-scale modeling framework may elucidate the molecular mechanisms by which dATP can have therapeutic effects on cardiac contractile dysfunction.

Tracer Diffusion in Tightly-Meshed Homogeneous Polymer Networks: A Brownian Dynamics Simulation Study

We report Brownian dynamics simulations of tracer diffusion in regularly crosslinked polymer networks in order to elucidate the transport of a tracer particle in polymer networks. The average mesh size of homogeneous polymer networks is varied by assuming different degrees of crosslinking or swelling, and the size of a tracer particle is comparable to the average mesh size. Simulation results show subdiffusion of a tracer particle at intermediate time scales and normal diffusion at long times. In particular, the duration of subdiffusion is significantly prolonged as the average mesh size decreases with increasing degree of crosslinking, for which long-time diffusion occurs via the hopping processes of a tracer particle after undergoing rattling motions within a cage of the network mesh for an extended period of time. On the other hand, the cage dynamics and hopping process are less pronounced as the mesh size decreases with increasing polymer volume fractions. The interpretation is provided in terms of fluctuations in network mesh size: at higher polymer volume fractions, the network fluctuations are large enough to allow for collective, structural changes of network meshes, so that a tracer particle can escape from the cage, whereas, at lower volume fractions, the fluctuations are so small that a tracer particle remains trapped within the cage for a significant period of time before making infrequent jumps out of the cage. This work suggests that fluctuation in mesh size, as well as average mesh size itself, plays an important role in determining the dynamics of molecules and nanoparticles that are embedded in tightly meshed polymer networks.

A Multi-Scale Study of Water Dynamics under Confinement, Exploiting Numerical Simulations in Relation to NMR Relaxometry, PGSE and NMR Micro-Imaging Experiments: An Application to the Clay/Water Interface

Water mobility within the porous network of dense clay sediments was investigated over a broad dynamical range by using 2H nuclear magnetic resonance spectroscopy. Multi-quanta 2H NMR spectroscopy and relaxation measurements were first performed to identify the contributions of the various relaxation mechanisms monitoring the time evolution of the nuclear magnetisation of the confined heavy water. Secondly, multi-quanta spin-locking NMR relaxation measurements were then performed over a broad frequency domain, probing the mobility of the confined water molecules on a time-scale varying between microseconds and milliseconds. Thirdly, 1H NMR pulsed-gradient spin-echo attenuation experiments were performed to quantify water mobility on a time-scale limited by the NMR transverse relaxation time of the confined NMR probe, typically a few milliseconds. Fourthly, the long living quantum state of the magnetisation of quadrupolar nuclei was exploited to probe a two-time correlation function at a time-scale reaching one second. Finally, magnetic resonance imaging measurements allow probing the same dynamical process on time-scales varying between seconds and several hours. In that context, multi-scale modelling is required to interpret these NMR measurements and extract information on the influences of the structural properties of the porous network on the apparent mobility of the diffusing water molecules. That dual experimental and numerical approach appears generalizable to a large variety of porous networks, including zeolites, micelles and synthetic or biological membranes.

Application of the Brown dynamics fluctuation-dissipation theorem to the study of Plasmodium berghei transporter protein PbAQP

In this article, the Brownian dynamics fluctuation-dissipation theorem (BD-FDT) is applied to the study of transport of neutral solutes across the cellular membrane of Plasmodium berghei (Pb), a disease-causing parasite. Pb infects rodents and causes symptoms in laboratory mice that are comparable to human malaria caused by Plasmodium falciparum (Pf). Due to the relative ease of its genetic engineering, P. berghei has been exploited as a model organism for the study of human malaria. P. berghei expresses one type of aquaporin (AQP), PbAQP, and, in parallel, P. falciparum expresses PfAQP. Either PbAQP or PfAQP is a multifunctional channel protein in the plasma membrane of the rodent/human malarial parasite for homeostasis of water, uptake of glycerol, and excretion of some metabolic wastes across the cell membrane. This FDT-study of the channel protein PbAQP is to elucidate how and how strongly it interacts with water, glycerol, and erythritol. It is found that erythritol, which binds deep inside the conducting pore of PbAQP/PfAQP, inhibits the channel protein's functions of conducting water, glycerol etc. This points to the possibility that erythritol, a sugar substitute, may inhibit the malarial parasites in rodents and in humans.

Chromatosome Structure and Dynamics from Molecular Simulations

Chromatosomes are fundamental units of chromatin structure that are formed when a linker histone protein binds to a nucleosome. The positioning of the linker histone on the nucleosome influences the packing of chromatin. Recent simulations and experiments have shown that chromatosomes adopt an ensemble of structures that differ in the geometry of the linker histone-nucleosome interaction. In this article we review the application of Brownian, Monte Carlo, and molecular dynamics simulations to predict the structure of linker histone-nucleosome complexes, to study the binding mechanisms involved, and to predict how this binding affects chromatin fiber structure. These simulations have revealed the sensitivityof the chromatosome structure to variations in DNA and linker histone sequence, as well as to posttranslational modifications, thereby explaining the structural variability observed in experiments. We propose that a concerted application of experimental and computational approaches will reveal the determinants of chromatosome structural variability and how it impacts chromatin packing.

Coarse-graining molecular dynamics: stochastic models with non-Gaussian force distributions

Incorporating atomistic and molecular information into models of cellular behaviour is challenging because of a vast separation of spatial and temporal scales between processes happening at the atomic and cellular levels. Multiscale or multi-resolution methodologies address this difficulty by using molecular dynamics (MD) and coarse-grained models in different parts of the cell. Their applicability depends on the accuracy and properties of the coarse-grained model which approximates the detailed MD description. A family of stochastic coarse-grained (SCG) models, written as relatively low-dimensional systems of nonlinear stochastic differential equations, is presented. The nonlinear SCG model incorporates the non-Gaussian force distribution which is observed in MD simulations and which cannot be described by linear models. It is shown that the nonlinearities can be chosen in such a way that they do not complicate parametrization of the SCG description by detailed MD simulations. The solution of the SCG model is found in terms of gamma functions.

Colloidal Flatlands Confronted with Urge for the Third Dimension

Two-dimensional sheets are a relatively neglected form of soft matter, interesting because of their capability to deform into the third dimension with little energy cost. Here, we confront colloidal sheets with an abruptly imposed potential tending to produce strings normal to the plane. Experimentally, this is implemented first by using ultrasound-induced acoustic levitation to produce planar sheets and then by abruptly imposing AC electric fields that introduce dipolar interactions. Seeking to identify the microscopic mechanisms underlying the observed collective behavior, we find that the patterns quantified from our fast confocal experimental imaging are reproduced by our Brownian dynamics simulations. We follow the evolution of these patterns, including their structure factor, from start to final steady state, and from successful parametrization we predict simulation phases not yet observed in experiment. The transient-state evolution toward final outcome includes monocrystalline hexagonal lattice, polycrystalline body-centered tetragonal lattice with grain boundaries, interconnected rings, serpentine zigzag chains, and columns vertical to the plane, and a "fat worm" serpentine pattern. To explain the counterintuitive findings presented here, we map dependence on softness of the confining potential.

Spatial Stochastic Intracellular Kinetics: A Review of Modelling Approaches

Models of chemical kinetics that incorporate both stochasticity and diffusion are an increasingly common tool for studying biology. The variety of competing models is vast, but two stand out by virtue of their popularity: the reaction-diffusion master equation and Brownian dynamics. In this review, we critically address a number of open questions surrounding these models: How can they be justified physically? How do they relate to each other? How do they fit into the wider landscape of chemical models, ranging from the rate equations to molecular dynamics? This review assumes no prior knowledge of modelling chemical kinetics and should be accessible to a wide range of readers.

Rule-Based Modeling Using Wildcards in the Smoldyn Simulator

Many biological molecules exist in multiple variants, such as proteins with different posttranslational modifications, DNAs with different sequences, and phospholipids with different chain lengths. Representing these variants as distinct species, as most biochemical simulators do, leads to the problem that the number of species, and chemical reactions that interconvert them, typically increase combinatorially with the number of ways that the molecules can vary. This can be alleviated by "rule-based modeling methods," in which software generates the chemical reaction network from relatively simple "rules." This chapter presents a new approach to rule-based modeling. It is based on wildcards that match to species names, much as wildcards can match to file names in computer operating systems. It is much simpler to use than the formal rule-based modeling approaches developed previously but can lead to unintended consequences if not used carefully. This chapter demonstrates rule-based modeling with wildcards through examples for signaling systems, protein complexation, polymerization, nucleic acid sequence copying and mutation, the "SMILES" chemical notation, and others. The method is implemented in Smoldyn, a spatial and stochastic biochemical simulator, for both generate-first and on-the-fly expansion, meaning whether the reaction network is generated before or during the simulation.

Preferential Localization of the Bacterial Nucleoid

Prokaryotes do not make use of a nucleus membrane to segregate their genetic material from the cytoplasm, so that their nucleoid is potentially free to explore the whole volume of the cell. Nonetheless, high resolution images of bacteria with very compact nucleoids show that such spherical nucleoids are invariably positioned at the center of mononucleoid cells. The present work aims to determine whether such preferential localization results from generic (entropic) interactions between the nucleoid and the cell membrane or instead requires some specific mechanism, like the tethering of DNA at mid-cell or periodic fluctuations of the concentration gradient of given chemical species. To this end, we performed numerical simulations using a coarse-grained model based on the assumption that the formation of the nucleoid results from a segregative phase separation mechanism driven by the de-mixing of the DNA and non-binding globular macromolecules. These simulations show that the abrupt compaction of the DNA coil, which takes place at large crowder density, close to the jamming threshold, is accompanied by the re-localization of the DNA coil close to the regions of the bounding wall with the largest curvature, like the hemispherical caps of rod-like cells, as if the DNA coil were suddenly acquiring the localization properties of a solid sphere. This work therefore supports the hypothesis that the localization of compact nucleoids at regular cell positions involves either some anchoring of the DNA to the cell membrane or some dynamical localization mechanism.

High-Resolution Nanoparticle Sizing with Maximum A Posteriori Nanoparticle Tracking Analysis

The rapid and efficient characterization of polydisperse nanoparticle dispersions remains a challenge within nanotechnology and biopharmaceuticals. Current methods for particle sizing, such as dynamic light scattering, analytical ultracentrifugation, and field-flow fractionation, can suffer from a combination of statistical biases, difficult sample preparation, insufficient sampling, and ill-posed data analysis. As an alternative, we introduce a Bayesian method that we call maximum a posteriori nanoparticle tracking analysis (MApNTA) for estimating the size distributions of nanoparticle samples from high-throughput single-particle tracking experiments. We derive unbiased statistical models for two observable quantities in a typical nanoparticle trajectory-the mean square displacement and the trajectory length-as a function of the particle size and calculate size distributions using maximum a posteriori (MAP) estimation with cross validation to mildly regularize solutions. We show that this approach infers nanoparticle size distributions with high resolution by performing extensive Brownian dynamics simulations and experiments with mono- and polydisperse solutions of gold nanoparticles as well as single-walled carbon nanotubes. We further demonstrate particular utility for characterizing minority components and impurity populations and highlight this ability with the identification of an impurity in a commercially produced gold nanoparticle sample. Modern algorithms such as MApNTA should find widespread use in the routine characterization of complex nanoparticle dispersions, allowing for significant advances in nanoparticle synthesis, separation, and functionalization.

Synergy of topoisomerase and structural-maintenance-of-chromosomes proteins creates a universal pathway to simplify genome topology

Topological entanglements severely interfere with important biological processes. For this reason, genomes must be kept unknotted and unlinked during most of a cell cycle. Type II topoisomerase (TopoII) enzymes play an important role in this process but the precise mechanisms yielding systematic disentanglement of DNA in vivo are not clear. Here we report computational evidence that structural-maintenance-of-chromosomes (SMC) proteins-such as cohesins and condensins-can cooperate with TopoII to establish a synergistic mechanism to resolve topological entanglements. SMC-driven loop extrusion (or diffusion) induces the spatial localization of essential crossings, in turn catalyzing the simplification of knots and links by TopoII enzymes even in crowded and confined conditions. The mechanism we uncover is universal in that it does not qualitatively depend on the specific substrate, whether DNA or chromatin, or on SMC processivity; we thus argue that this synergy may be at work across organisms and throughout the cell cycle.

Living Supramolecular Polymerization of Rod-Coil Block Copolymers: Kinetics, Origin of Uniformity, and Its Implication

We conduct Brownian dynamics simulations to explore the kinetics of living supramolecular polymerization using seeded growth of rod-coil block copolymers as a model system. We model the kinetics of supramolecular polymerization by developing kinetic theory for classical living covalent polymerization with length-dependent rate coefficients. The rate coefficient in the proposed kinetics theory decreases with increasing cylindrical micelle length, which is attributed to micelle rigidity and unique diffusion behavior. Like living covalent polymerization, living supramolecular polymerization can produce low-dispersity assemblies with rigidity via different mechanisms. The results nicely explain the available experimental observations.

Swimming to Stability: Structural and Dynamical Control via Active Doping

External fields can decidedly alter the free energy landscape of soft materials and can be exploited as a powerful tool for the assembly of targeted nanostructures and colloidal materials. Here, we use computer simulations to demonstrate that nonequilibrium internal fields or forces-forces that are generated by driven components within a system-in the form of active particles can precisely modulate the dynamical free energy landscape of a model soft material, a colloidal gel. Embedding a small fraction of active particles within a gel can provide a unique pathway for the dynamically frustrated network to circumvent the kinetic barriers associated with reaching a lower free energy state through thermal fluctuations alone. Moreover, by carefully tuning the active particle properties (the propulsive swim force and persistence length) in comparison to those of the gel, the active particles may induce depletion-like forces between the constituent particles of the gel despite there being no geometric size asymmetry between the particles. These resulting forces can rapidly push the system toward disparate regions of phase space. Intriguingly, the state of the material can be altered by tuning macroscopic transport properties such as the solvent viscosity. Our findings highlight the potential wide-ranging structural and kinetic control facilitated by varying the dynamical properties of a remarkably small fraction of driven particles embedded in a host material.

Phase Behavior of Bowl-Shaped Colloids: Order and Dynamics in Plastic Crystals and Glasses

Charged fluorescent bowl-shaped colloids consisting of a polystyrene core surrounded by a poly(N-isopropylmethacrylamide) shell are obtained by nanoengineering spherical composite microgels. The phase diagram of these soft bowl-shaped colloids interacting through long-range Yukawa-type interactions is investigated using confocal laser scanning microscopy. The bowl-shaped structure leads to marked differences in phase-behavior compared to their spherical counterpart. With increasing number density, a transition from a fluid to a plastic crystal phase, with freely rotating particles, followed by a glass-like state is observed. It is found that the anisotropic bowl shape frustrates crystallization and slows down crystallization kinetics and causes the glass-like transition to shift to a significantly lower volume fraction than for the spheres. Quantitative analysis of the positional and orientational order demonstrates that the plastic crystal phase exhibits quasi-long range translational order and orientational disorder, while in the disordered glass-like phase the long-range translational order vanishes and short-range rotational order appears, dictated by the specific bowl shape. It is further shown that the different structural transitions are characterized by decoupling of the translational and orientational dynamics.

A spatio-temporal model reveals self-limiting FcɛRI cross-linking by multivalent antigens

Aggregation of cell surface receptor proteins by multivalent antigens is an essential early step for immune cell signalling. A number of experimental and modelling studies in the past have investigated multivalent ligand-mediated aggregation of IgE receptors (FcɛRI) in the plasma membrane of mast cells. However, understanding of the mechanisms of FcɛRI aggregation remains incomplete. Experimental reports indicate that FcɛRI forms relatively small and finite-sized clusters when stimulated by a multivalent ligand. By contrast, modelling studies have shown that receptor cross-linking by a trivalent ligand may lead to the formation of large receptor superaggregates that may potentially give rise to hyperactive cellular responses. In this work, we have developed a Brownian dynamics-based spatio-temporal model to analyse FcɛRI aggregation by a trivalent antigen. Unlike the existing models, which implemented non-spatial simulation approaches, our model explicitly accounts for the coarse-grained site-specific features of the multivalent species (molecules and complexes). The model incorporates membrane diffusion, steric collisions and sub-nanometre-scale site-specific interaction of the time-evolving species of arbitrary structures. Using the model, we investigated temporal evolution of the species and their diffusivities. Consistent with a recent experimental report, our model predicted sharp decay in species mobility in the plasma membrane in response receptor cross-linking by a multivalent antigen. We show that, due to such decay in the species mobility, post-stimulation receptor aggregation may become self-limiting. Our analysis reveals a potential regulatory mechanism suppressing hyperactivation of immune cells in response to multivalent antigens.

Model-based image analysis of a tethered Brownian fibre for shear stress sensing

The measurement of fluid dynamic shear stress acting on a biologically relevant surface is a challenging problem, particularly in the complex environment of, for example, the vasculature. While an experimental method for the direct detection of wall shear stress via the imaging of a synthetic biology nanorod has recently been developed, the data interpretation so far has been limited to phenomenological random walk modelling, small-angle approximation, and image analysis techniques which do not take into account the production of an image from a three-dimensional subject. In this report, we develop a mathematical and statistical framework to estimate shear stress from rapid imaging sequences based firstly on stochastic modelling of the dynamics of a tethered Brownian fibre in shear flow, and secondly on a novel model-based image analysis, which reconstructs fibre positions by solving the inverse problem of image formation. This framework is tested on experimental data, providing the first mechanistically rational analysis of the novel assay. What follows further develops the established theory for an untethered particle in a semi-dilute suspension, which is of relevance to, for example, the study of Brownian nanowires without flow, and presents new ideas in the field of multi-disciplinary image analysis.

The auxiliary region method: a hybrid method for coupling PDE- and Brownian-based dynamics for reaction-diffusion systems

Reaction-diffusion systems are used to represent many biological and physical phenomena. They model the random motion of particles (diffusion) and interactions between them (reactions). Such systems can be modelled at multiple scales with varying degrees of accuracy and computational efficiency. When representing genuinely multiscale phenomena, fine-scale models can be prohibitively expensive, whereas coarser models, although cheaper, often lack sufficient detail to accurately represent the phenomenon at hand. Spatial hybrid methods couple two or more of these representations in order to improve efficiency without compromising accuracy. In this paper, we present a novel spatial hybrid method, which we call the auxiliary region method (ARM), which couples PDE- and Brownian-based representations of reaction-diffusion systems. Numerical PDE solutions on one side of an interface are coupled to Brownian-based dynamics on the other side using compartment-based 'auxiliary regions'. We demonstrate that the hybrid method is able to simulate reaction-diffusion dynamics for a number of different test problems with high accuracy. Furthermore, we undertake error analysis on the ARM which demonstrates that it is robust to changes in the free parameters in the model, where previous coupling algorithms are not. In particular, we envisage that the method will be applicable for a wide range of spatial multi-scales problems including filopodial dynamics, intracellular signalling, embryogenesis and travelling wave phenomena.

Prediction and analysis of analytical ultracentrifugation experiments for heterogeneous macromolecules and nanoparticles based on Brownian dynamics simulation

In the prediction of sedimentation profiles in analytical ultracentrifugation, the counterflow due to diffusion must be taken into account for a proper analysis of experimental data in the determination of molecular properties. This is usually achieved by numerical solution of the Lamm equation. This paper presents an alternative approach, in which the displacement of the solute in the cell, resulting from the opposite effects of ultracentrifugal force and diffusional drift, is described by Brownian dynamics simulation of the solute particles. The formalism is developed for heterogeneous solutes, composed of several species, and implemented in computational schemes and tools. The accuracy of the procedure is verified by comparison with other methods based on the Lamm equation, and its efficiency is illustrated. The possibilities offered by the Brownian dynamics methods in the determination of solute properties and sample composition are demonstrated.

RPYFMM: Parallel Adaptive Fast Multipole Method for Rotne-Prager-Yamakawa Tensor in Biomolecular Hydrodynamics Simulations

RPYFMM is a software package for the efficient evaluation of the potential field governed by the Rotne-Prager-Yamakawa (RPY) tensor interactions in biomolecular hydrodynamics simulations. In our algorithm, the RPY tensor is decomposed as a linear combination of four Laplace interactions, each of which is evaluated using the adaptive fast multipole method (FMM) [1] where the exponential expansions are applied to diagonalize the multipole-to-local translation operators. RPYFMM offers a unified execution on both shared and distributed memory computers by leveraging the DASHMM library [2, 3]. Preliminary numerical results show that the interactions for a molecular system of 15 million particles (beads) can be computed within one second on a Cray XC30 cluster using 12, 288 cores, while achieving approximately 54% strong-scaling efficiency.

HIERARCHICAL ORTHOGONAL MATRIX GENERATION AND MATRIX-VECTOR MULTIPLICATIONS IN RIGID BODY SIMULATIONS

In this paper, we apply the hierarchical modeling technique and study some numerical linear algebra problems arising from the Brownian dynamics simulations of biomolecular systems where molecules are modeled as ensembles of rigid bodies. Given a rigid body p consisting of n beads, the 6×3n transformation matrix Z that maps the force on each bead to p's translational and rotational forces (a 6 × 1 vector), and V the row space of Z, we show how to explicitly construct the (3n - 6) × 3n matrix Q ˜ consisting of (3n - 6) orthonormal basis vectors of V ⊥ (orthogonal complement of V) using only O ( n log n ) operations and storage. For applications where only the matrix-vector multiplicationsQ ˜ V andQ ˜ T V are needed, we introduce asymptotically optimal O ( n ) hierarchical algorithms without explicitly forming Q ˜ . Preliminary numerical results are presented to demonstrate the performance and accuracy of the numerical algorithms.

Inchworm movement of two rings switching onto a thread by biased Brownian diffusion represent a three-body problem

The coordinated motion of many individual components underpins the operation of all machines. However, despite generations of experience in engineering, understanding the motion of three or more coupled components remains a challenge, known since the time of Newton as the "three-body problem." Here, we describe, quantify, and simulate a molecular three-body problem of threading two molecular rings onto a linear molecular thread. Specifically, we use voltage-triggered reduction of a tetrazine-based thread to capture two cyanostar macrocycles and form a [3]pseudorotaxane product. As a consequence of the noncovalent coupling between the cyanostar rings, we find the threading occurs by an unexpected and rare inchworm-like motion where one ring follows the other. The mechanism was derived from controls, analysis of cyclic voltammetry (CV) traces, and Brownian dynamics simulations. CVs from two noncovalently interacting rings match that of two covalently linked rings designed to thread via the inchworm pathway, and they deviate considerably from the CV of a macrocycle designed to thread via a stepwise pathway. Time-dependent electrochemistry provides estimates of rate constants for threading. Experimentally derived parameters (energy wells, barriers, diffusion coefficients) helped determine likely pathways of motion with rate-kinetics and Brownian dynamics simulations. Simulations verified intercomponent coupling could be separated into ring-thread interactions for kinetics, and ring-ring interactions for thermodynamics to reduce the three-body problem to a two-body one. Our findings provide a basis for high-throughput design of molecular machinery with multiple components undergoing coupled motion.

In-plane and out-of-plane rotational motion of individual chain molecules in steady shear flow of polymer melts and solutions

Recent nonequilibrium molecular dynamics (NEMD) simulations of mildly entangled C₄₀₀H₈₀₂ and moderately entangled C₇₀₀H₁₄₀₂ linear polyethylene melts undergoing steady shear flow have revealed that several inconsistencies between theory and experiment could be rectified by consideration of the rotational motion of individual polymer chains that occurs at moderate to high flow strengths. In this study, we investigated the configurational dynamics of the individual molecular chains that allow these once-entangled, long-chain molecules to execute retraction/extension semi-periodic cycles in response to the imposed shear via NEMD simulations. Brownian dynamics simulations were also performed to extract dynamical and configurational information about the similar cycles of polymer chain behavior that occur in dilute solutions of macromolecular chain liquids dissolved in low molecular weight solvents. Results revealed that the configurational motions of the individual chains in both melt and solution were essentially the same and governed by a single timescale that scaled exponentially with the magnitude of the shear rate. This configurational motion contained both in-plane and out-of-plane components with respect to the flow-gradient plane, with the out-of-plane component playing a much larger role during the retraction phase of the cycle than during the extension phase. This was determined to be caused by the enhancement of the retraction motion by the out-of-plane entropic Brownian forces; however, these entropic forces were detrimental to the in-plane hydrodynamic diffusive forces during the extension phase of the cycle and were thus suppressed. Consequently, the configuration of a rotating chain was significantly more compact during the retraction stage than during the extension stage, wherein the latter phase most molecules were more preferentially distributed in the flow-gradient plane.

Macromolecular crowding directs the motion of small molecules inside cells

It is now well established that cell interiors are significantly crowded by macromolecules, which impede diffusion and enhance binding rates. However, it is not fully appreciated that levels of crowding are heterogeneous, and can vary substantially between subcellular regions. In this article, starting from a microscopic model, we derive coupled nonlinear partial differential equations for the concentrations of two populations of large and small spherical particles with steric volume exclusion. By performing an expansion in the ratio of the particle sizes, we find that the diffusion of a small particle in the presence of large particles obeys an advection–diffusion equation, with a reduced diffusion coefficient and a velocity directed towards less crowded regions. The interplay between advection and diffusion leads to behaviour that differs significantly from Brownian diffusion. We show that biologically plausible distributions of macromolecules can lead to highly non-Gaussian probability densities for the small particle position, including asymmetrical and multimodal densities. We confirm all our results using hard-sphere Brownian dynamics simulations.

A model-based analysis of tissue targeting efficacy of nanoparticles

Tissue targeting is a critical challenge for systemic delivery of drug nanocarriers. To overcome this challenge, major research efforts have been undertaken to design ligand-conjugated nanoparticles. However, limited work has been done to quantitatively assess the effectiveness of such approach. In this work, using a mechanistic spatio-temporal model, I investigate the effectiveness of ligand-directed tissue targeting. By applying an approach from the colloidal filtration theory, I develop a Brownian dynamics model of nanoparticle-cell interaction. The model incorporates a single cell and its surrounding flow field. It considers both specific (receptor-mediated) and non-specific (bare cell surface-mediated) recognition of nanoparticles subject to convective and diffusive motion. Using the model, I investigate how the specific and non-specific interactions compare in determining the overall targeting efficacy. My analysis provides some interesting findings that contradict the general notion that effective targeting is possible based upon the differential receptor expression in cancer and non-cancer cells. I show that such strategy may yield only a marginal gain in the targeting efficacy. Moreover, non-specific interaction may have an important influence on particle recognition by cells even at high receptor expression levels.

A multiscale modeling study of particle size effects on the tissue penetration efficacy of drug-delivery nanoparticles

BACKGROUND

Particle size is a key parameter for drug-delivery nanoparticle design. It is believed that the size of a nanoparticle may have important effects on its ability to overcome the transport barriers in biological tissues. Nonetheless, such effects remain poorly understood. Using a multiscale model, this work investigates particle size effects on the tissue distribution and penetration efficacy of drug-delivery nanoparticles.

RESULTS

We have developed a multiscale spatiotemporal model of nanoparticle transport in biological tissues. The model implements a time-adaptive Brownian Dynamics algorithm that links microscale particle-cell interactions and adhesion dynamics to tissue-scale particle dispersion and penetration. The model accounts for the advection, diffusion, and cellular uptakes of particles. Using the model, we have analyzed how particle size affects the intra-tissue dispersion and penetration of drug delivery nanoparticles. We focused on two published experimental works that investigated particle size effects in in vitro and in vivo tissue conditions. By analyzing experimental data reported in these two studies, we show that particle size effects may appear pronounced in an in vitro cell-free tissue system, such as collagen matrix. In an in vivo tissue system, the effects of particle size could be relatively modest. We provide a detailed analysis on how particle-cell interactions may determine distribution and penetration of nanoparticles in a biological tissue.

CONCLUSION

Our work suggests that the size of a nanoparticle may play a less significant role in its ability to overcome the intra-tissue transport barriers. We show that experiments involving cell-free tissue systems may yield misleading observations of particle size effects due to the absence of advective transport and particle-cell interactions.

A Multiscale Algorithm for Spatiotemporal Modeling of Multivalent Protein-Protein Interaction

This article introduces a multiscale framework for spatiotemporal modeling of protein-protein interaction. Cellular protein molecules represent multivalent species that contain modular features, such as binding domains and phosphorylation motifs. The binding and transformations of these features occur at a small time and spatial scale. On the other hand, space and time involved in protein diffusion, colocalization, and formation of complexes could be relatively large. Here, we present an agent-based framework integrated with a multiscale Brownian Dynamics (BD) simulation algorithm. The framework employs spatial graphs to describe multivalent molecules and complexes with their site-specific details. By implementing a time-adaptive feature, the BD algorithm enables efficient computation while capturing the site-specific interactions of the diffusing species at the sub-nanometer scale. We demonstrate these capabilities by modeling two multivalent molecules, one representing a ligand and the other a receptor, in a two-dimensional plane (cell membrane). Using the model, we show that the algorithm can accelerate computation by orders of magnitudes in both concentrated and dilute regimes. We also show that the algorithm enables robust model predictions against a wide range of selection of time step sizes.

Probing Photothermal Effects on Optically Trapped Gold Nanorods by Simultaneous Plasmon Spectroscopy and Brownian Dynamics Analysis

Plasmonic gold nanorods are prime candidates for a variety of biomedical, spectroscopy, data storage, and sensing applications. It was recently shown that gold nanorods optically trapped by a focused circularly polarized laser beam can function as extremely efficient nanoscopic rotary motors. The system holds promise for applications ranging from nanofluidic flow control and nanorobotics to biomolecular actuation and analysis. However, to fully exploit this potential, one needs to be able to control and understand heating effects associated with laser trapping. We investigated photothermal heating of individual rotating gold nanorods by simultaneously probing their localized surface plasmon resonance spectrum and rotational Brownian dynamics over extended periods of time. The data reveal an extremely slow nanoparticle reshaping process, involving migration of the order of a few hundred atoms per minute, for moderate laser powers and a trapping wavelength close to plasmon resonance. The plasmon spectroscopy and Brownian analysis allows for separate temperature estimates based on the refractive index and the viscosity of the water surrounding a trapped nanorod. We show that both measurements yield similar effective temperatures, which correspond to the actual temperature at a distance of the order 10-15 nm from the particle surface. Our results shed light on photothermal processes on the nanoscale and will be useful in evaluating the applicability and performance of nanorod motors and optically heated nanoparticles for a variety of applications.

The Effect of Thermal Fluctuation on the Receptor-Mediated Adhesion of a Cell Membrane to an Elastic Substrate

Mechanics of the bilayer membrane play an important role in many biological and bioengineering problems such as cell-substrate and cell-nanomaterial interactions. In this work, we study the effect of thermal fluctuation and the substrate elasticity on the cell membrane-substrate adhesion. We model the adhesion of a fluctuating membrane on an elastic substrate as a two-step reaction comprised of the out-of-plane membrane fluctuation and the receptor-ligand binding. The equilibrium closed bond ratio as a function of substrate rigidity was computed by developing a coupled Fourier space Brownian dynamics and Monte Carlo method. The simulation results show that there exists a crossover value of the substrate rigidity at which the closed bond ratio is maximal.

Modulation of Asymmetric Flux in Heterotypic Gap Junctions by Pore Shape, Particle Size and Charge

Gap junction channels play a vital role in intercellular communication by connecting cytoplasm of adjoined cells through arrays of channel-pores formed at the common membrane junction. Their structure and properties vary depending on the connexin isoform(s) involved in forming the full gap junction channel. Lack of information on the molecular structure of gap junction channels has limited the development of computational tools for single channel studies. Currently, we rely on cumbersome experimental techniques that have limited capabilities. We have earlier reported a simplified Brownian dynamics gap junction pore model and demonstrated that variations in pore shape at the single channel level can explain some of the differences in permeability of heterotypic channels observed in in vitro experiments. Based on this computational model, we designed simulations to study the influence of pore shape, particle size and charge in homotypic and heterotypic pores. We simulated dye diffusion under whole cell voltage clamping. Our simulation studies with pore shape variations revealed a pore shape with maximal flux asymmetry in a heterotypic pore. We identified pore shape profiles that match the in silico flux asymmetry results to the in vitro results of homotypic and heterotypic gap junction formed out of Cx43 and Cx45. Our simulation results indicate that the channel's pore-shape established flux asymmetry and that flux asymmetry is primarily regulated by the sizes of the conical and/or cylindrical mouths at each end of the pore. Within the set range of particle size and charge, flux asymmetry was found to be independent of particle size and directly proportional to charge magnitude. While particle charge was vital to creating flux asymmetry, charge magnitude only scaled the observed flux asymmetry. Our studies identified the key factors that help predict asymmetry. Finally, we suggest the role of such flux asymmetry in creating concentration imbalances of messenger molecules in cardiomyocytes. We also assess the potency of fibroblasts in aggravating such imbalances through Cx43-Cx45 heterotypic channels in fibrotic heart tissue.