Revealing the SARS-CoV-2 Spike Protein and Specific Antibody Immune Complex Formation Mechanism for Precise Evaluation of Antibody Affinity.

The profound understanding and detailed evaluation of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike (SCoV2-S) protein and specific antibody interaction mechanism is of high importance in the development of immunosensors for COVID-19. In the present work, we studied a model system of immobilized SCoV2-S protein and specific monoclonal antibodies by molecular dynamics of immune complex formation in real time. We simultaneously applied spectroscopic ellipsometry and quartz crystal microbalance with dissipation to reveal the features and steps of the immune complex formation. We showed direct experimental evidence based on acoustic and optical measurements that the immune complex between covalently immobilized SCoV2-S and specific monoclonal antibodies is formed in two stages. Based on these findings it was demonstrated that applying a two-step binding mathematical model for kinetics analysis leads to a more precise determination of interaction rate constants than that determined by the 1:1 Langmuir binding model. Our investigation showed that the equilibrium dissociation constants (KD) determined by a two-step binding model and the 1:1 Langmuir model could differ significantly. The reported findings can facilitate a deeper understanding of antigen-antibody immune complex formation steps and can open a new way for the evaluation of antibody affinity towards corresponding antigens.

Enhancing search efficiency through diffusive echo.

Despite having been studied for decades, first passage processes remain an active area of research. In this article, we examine a particle diffusing in an annulus with an inner absorbing boundary and an outer reflective boundary. We obtain analytic expressions for the joint distribution of the hitting time and the hitting angle in two and three dimensions. For certain configurations, we observe a "diffusive echo," i.e., two well-defined maxima in the first passage time distribution to a targeted position on the absorbing boundary. This effect, which results from the interplay between the starting location and the environmental constraints, may help to significantly increase the efficiency of the random search by generating a high, sustained flux to the targeted position over a short period. Finally, we examine the corresponding one-dimensional system for which there is no well-defined echo. In a confined system, the flux integrated over all target positions always displays a shoulder. This does not, however, guarantee the presence of an echo in the joint distribution.

Weak clogging in constricted channel flow.

We investigate simple models of a monodisperse system of soft, frictionless disks flowing through a two-dimensional microchannel in the presence of a single or a double constriction using Brownian dynamics simulation. After a transient time, a stationary state is observed with an increase in particle density before the constriction and a depletion after it. For a constriction width to particle diameter ratio of less than 3, the mean particle velocity is reduced compared to the unimpeded flow and it falls to zero for ratios of less than 1. At low temperatures, the particle mean velocity may vary nonmonotonically with the constriction width. The associated intermittent behavior is due to the formation of small arches of particles with a finite lifetime. The distribution of the interparticle exit times rises rapidly at short times followed by an exponential decay with a large characteristic time, while the cascade size distribution displays prominent peaks for specific cluster sizes. Although the dependence of the mean velocity on the separation of two constrictions is not simple, the mean flow velocity of a system with a single constriction provides an upper envelope for the system with two constrictions. We also examine the orientation of the leading pair of particles in front of the constriction(s). With a single constriction in the intermittent regime, there is a strong preference for the leading pair to be orientated perpendicular to the flow. When two constrictions are present, orientations parallel to the flow are much more likely at the second constriction.

The Iris billiard: Critical geometries for global chaos.

We introduce the Iris billiard that consists of a point particle enclosed by a unit circle around a central scattering ellipse of fixed elongation (defined as the ratio of the semi-major to the semi-minor axes). When the ellipse degenerates to a circle, the system is integrable; otherwise, it displays mixed dynamics. Poincaré sections are presented for different elongations. Recurrence plots are then applied to the long-term chaotic dynamics of trajectories launched from the unstable period-2 orbit along the semi-major axis, i.e., one that initially alternately collides with the ellipse and the circle. We obtain numerical evidence of a set of critical elongations at which the system undergoes a transition to global chaos. The transition is characterized by an endogenous escape event, E, which is the first time a trajectory launched from the unstable period-2 orbit misses the ellipse. The angle of escape, θesc, and the distance of the closest approach, dmin, of the escape event are studied and are shown to be exquisitely sensitive to the elongation. The survival probability that E has not occurred after n collisions is shown to follow an exponential distribution.

Evaluation of affinity sensor response kinetics towards dimeric ligands linked with spacers of different rigidity: Immobilized recombinant granulocyte colony-stimulating factor based synthetic receptor binding with genetically engineered dimeric analyte derivatives.

The modelling of protein-protein binding kinetics is important for the development of affinity-sensors and the prediction of signaling protein based drug efficiency. Therefore, in this research we have evaluated the binding kinetics of several genetically designed protein models: (i) three different ligands based on granulocyte colony-stimulating factor GCSF homo-dimeric derivatives linked by differed by linkers of different length and flexibility; (ii) an antibody-like receptor (GCSF-R) based on two GCSF-receptor sites immobilized to Fc domains, which are common parts of protein structures forming antibodies. Genetically engineered GCSF-R is similar to an antibody because it, like the antibody, has two binding sites, which both selectively bind with GCSF ligands. To design the affinity sensor model studied here, GCSF-R was immobilized on a thin gold layer via self-assembled monolayer conjugated with Protein-G. Binding kinetics between immobilized GCSF-R and all three different recombinant GCSF-based homo-dimeric derivatives were evaluated by total internal reflection ellipsometry. Association constants were determined by fitting mathematical models to the experimental data. It was clearly observed that both (i) affinity and (ii) binding kinetics depend on the length and flexibility of the linker that connects both domains of a GCSF-based ligand. The fastest association between immobilized GCSF-R and GCSF-based ligands was observed for ligands whose GCSF domains were interconnected by the longest and the most flexible linker. Here we present ellipsometry-based measurements and models of the interaction kinetics that advance the understanding of bidentate-receptor-based immunosensor action and enables us to predict the optimal linker structure for the design of GCSF-based medications.

Recurrence dynamics of particulate transport with reversible blockage: From a single channel to a bundle of coupled channels.

We model a particulate flow of constant velocity through confined geometries, ranging from a single channel to a bundle of N_{c} identical coupled channels, under conditions of reversible blockage. Quantities of interest include the exiting particle flux (or throughput) and the probability that the bundle is open. For a constant entering flux, the bundle evolves through a transient regime to a steady state. We present analytic solutions for the stationary properties of a single channel with capacity N≤3 and for a bundle of channels each of capacity N=1. For larger values of N and N_{c}, the system's steady state behavior is explored by numerical simulation. Depending on the deblocking time, the exiting flux either increases monotonically with intensity or displays a maximum at a finite intensity. For large N we observe an abrupt change from a state with few blockages to one in which the bundle is permanently blocked and the exiting flux is due entirely to the release of blocked particles. We also compare the relative efficiency of coupled and uncoupled bundles. For N=1 the coupled system is always more efficient, but for N>1 the behavior is more complex.

Granular silo flow of inelastic dumbbells: Clogging and its reduction.

We study the discharge of inelastic, two-dimensional dumbbells through an orifice in the bottom wall of a silo using discrete element method (DEM) simulations. As with spherical particles, clogging may occur due to the formation of arches of particles around the orifice. The clogging probability decreases with increasing orifice width in both cases. For a given width, however, the clogging probability is much higher for the nonspherical particles due to their arbitrary orientations and the possibility of geometrical interlocking. We also examine the effect of placing a fixed, circular obstacle above the orifice. The clogging probability depends strongly on the vertical and lateral position of the obstacle, as well as its size. By suitably placing the obstacle the clogging probability can be significantly reduced compared to a system with no obstacle. We attempt to elucidate the clogging reduction mechanism by examining the packing fraction, granular temperature, and velocity distributions of the particles in the vicinity of the orifice.

Stochastic models of multi-channel particulate transport with blockage.

Particle conveying channels may be bundled together. The limited carrying capacity of the constituent channels may cause the bundle to be subject to blockages. If coupled, the blockage of one channel causes an increase in the flux entering the others, leading to a cascade of failures. Once all the channels are blocked, no additional particles may enter the system. If the blockages are of finite duration, the system reaches a steady state with an exiting flux that is reduced compared to the incoming one. We propose a stochastic model consisting of N c channels, each with a blocking threshold of N particles. Particles enter the system's open channels according to a Poisson process, with an equally distributed input flux of intensity Λ. In an open channel the leading particle exits at a rate µ and a blocked channel unblocks at a rate [Formula: see text], where [Formula: see text]. We present and explain the methodology of an analytical description of the behavior of bundled channels. This leads to exact expressions for the steady-state output flux, for [Formula: see text], which promises to extend to arbitrary N c and N. The results are applied to compare the efficiency of conveying a particulate stream of intensity Λ using a single, high capacity (HC) channel with multiple channels of a proportionately reduced low capacity (LC). The HC channel is more efficient at low input intensities, while the multiple LC channels have a higher throughput at high intensities. We also compare [Formula: see text] coupled channels, each of capacity N = 2 with the corresponding number of independent channels of the same capacity. For [Formula: see text], if [Formula: see text], the coupled channels are always more efficient. Otherwise the independent channels are more efficient for sufficiently large Λ.

Route optimisation and solving Zermelo's navigation problem during long distance migration in cross flows.

The optimum path to follow when subjected to cross flows was first considered over 80 years ago by the German mathematician Ernst Zermelo, in the context of a boat being displaced by ocean currents, and has become known as the 'Zermelo navigation problem'. However, the ability of migrating animals to solve this problem has received limited consideration, even though wind and ocean currents cause the lateral displacement of flyers and swimmers, respectively, particularly during long-distance journeys of 1000s of kilometres. Here, we examine this problem by combining long-distance, open-ocean marine turtle movements (obtained via long-term GPS tracking of sea turtles moving 1000s of km), with a high resolution basin-wide physical ocean model to estimate ocean currents. We provide a robust mathematical framework to demonstrate that, while turtles eventually arrive at their target site, they do not follow the optimum (Zermelo's) route. Even though adult marine turtles regularly complete incredible long-distance migrations, these vertebrates primarily rely on course corrections when entering neritic waters during the final stages of migration. Our work introduces a new perspective in the analysis of wildlife tracking datasets, with different animal groups potentially exhibiting different levels of complexity in goal attainment during migration.

Effect of dynamic and static friction on an asymmetric granular piston.

We investigate the influence of dry friction on an asymmetric, granular piston of mass M, composed of two materials, undergoing inelastic collisions with bath particles of mass m. Numerical simulations of the Boltzmann-Lorentz equation reveal the existence of two scaling regimes depending on the friction strength. In the large friction limit, we introduce an exact model giving the asymptotic behavior of the Boltzmann-Lorentz equation. For small friction and for large mass ratio M/m, we derive a Fokker-Planck equation for which the exact solution is also obtained. Static friction attenuates the motor effect and results in a discontinuous velocity distribution.

Analysis of a class of granular motors in the brownian limit.

We analyze the dynamics of heterogeneous granular particles immersed in a bath of thermalized particles, which are candidates for granular motors, with a mechanical approach. We first apply the method to the previously introduced asymmetric piston and show that it gives the exact drift velocity in the brownian limit. We also obtain results for the efficiency of the motor and compare with numerical simulations. Finally, we introduce a chiral rotor model and discuss opportunities for observing a real granular motor.

Kinetics and equilibrium of multicomponent adsorption on chiraly templated surfaces.

In this contribution we propose a simple model of adsorption of a binary (racemic) mixture on a chiraly templated surface. As an example, the adsorption of a liquid mixture of enantiomers on a chiral stationary phase (CSP) is considered. In particular, we study the effect of the lateral interactions in the adsorbed phase on the kinetic and equilibrium isotherms of the enantiomers. Additionally, we investigate the influence of the composition of the surface on the performance of the CSP in the presence of the lateral interactions. To that end, the adsorption of the mixture is modeled by using Monte Carlo simulations as well as by applying an analytical approach involving rate equations coupled with the Mean Field Approximation (MFA). The predictions of the theory are found to be in good agreement with the results of the simulations.

Anisotropic energy distribution in three-dimensional vibrofluidized granular systems.

We examine the energy flows in a three-dimensional model of a granular system consisting of N inelastic hard spheres contained in an open cylinder of radius R under the influence of gravity. Energy is supplied to the system in the vertical direction by a vibrating base and is transferred to the perpendicular directions through particle-particle collisions. We examine how the local and global dissipation of energy by particle-particle and particle-wall collisions depends on the number of particles, the velocity of the vibrating base, and the restitution coefficients.

Mass and size effects in three-dimensional vibrofluidized granular mixtures.

We examine the steady state properties of binary systems of driven inelastic hard spheres. The spheres, which move under the influence of gravity, are contained in a vertical cylinder with a vibrating base. We computed the trajectories of the spheres using an event-driven molecular dynamics algorithm. In the first part of the study, we chose simulation parameters that match those of experiments published by Wildman and Parker. Various properties computed from the simulation including the density profile, granular temperature, and circulation pattern are in good qualitative agreement with the experiments. We then studied the effect of varying the mass ratio and the size ratio independently while holding the other parameters constant. The mass and size ratio are shown to affect the distribution of the energy. The changes in the energy distributions affect the packing fraction and temperature of each component. The temperature of the heavier component has a nonlinear dependence on the mass of the lighter component, while the temperature of the lighter component is approximately proportional to its mass. The temperature of both components is inversely dependent on the size of the smaller component.