Analysis of binding kinetics and mass transport in SPR-based biosensor using the Generalized Integral Transform Technique and the Markov Chain Monte Carlo Method.

In this chapter we present application of a Markov chain Monte Carlo (MCMC) method, within the Bayesian framework, for the identification of nonhomogeneities or inclusions in a medium through the solution of an inverse heat conduction problem. Such identification involves estimation of the spatially-dependent thermophysical properties. Two different approaches are presented in conjunction with the MCMC method, namely: (1) a nodal approach, which locally linearizes the inverse problem by using temperature measurements for the computation of the sensitivity matrix, and (2) an expansion of unknown spatially-dependent thermo-physical properties in terms of Eigen functions, which is used in conjunction with the Generalized Integral Transform Technique (GITT).

The interaction between the SARS-CoV-2 virus Spike protein receptor binding domain (RBD) and the ACE2 cell surface protein is required for viral infection of cells. Mutations in the RBD are present in SARS-CoV-2 variants of concern that have emerged independently worldwide. For example, the B.1.1.7 lineage has a mutation (N501Y) in its Spike RBD that enhances binding to ACE2. There are also ACE2 alleles in humans with mutations in the RBD binding site. Here we perform a detailed affinity and kinetics analysis of the effect of five common RBD mutations (K417N, K417T, N501Y, E484K, and S477N) and two common ACE2 mutations (S19P and K26R) on the RBD/ACE2 interaction. We analysed the effects of individual RBD mutations and combinations found in new SARS-CoV-2 Alpha (B.1.1.7), Beta (B.1.351), and Gamma (P1) variants. Most of these mutations increased the affinity of the RBD/ACE2 interaction. The exceptions were mutations K417N/T, which decreased the affinity. Taken together with other studies, our results suggest that the N501Y and S477N mutations enhance transmission primarily by enhancing binding, the K417N/T mutations facilitate immune escape, and the E484K mutation enhances binding and immune escape.

Decision letter: Effects of common mutations in the SARS-CoV-2 Spike RBD and its ligand, the human ACE2 receptor on binding affinity and kinetics

Human angiotensin-converting enzyme 2 (ACE2) is a functional receptor for SARS coronavirus (SARS-CoV). Here we identify the SARS-CoV spike (S)-protein-binding site on ACE2. We also compare S proteins of SARS-CoV isolated during the 2002–2003 SARS outbreak and during the much less severe 2003–2004 outbreak, and from palm civets, a possible source of SARS-CoV found in humans. All three S proteins bound to and utilized palm-civet ACE2 efficiently, but the latter two S proteins utilized human ACE2 markedly less efficiently than did the S protein obtained during the earlier human outbreak. The lower affinity of these S proteins could be complemented by altering specific residues within the S-protein-binding site of human ACE2 to those of civet ACE2, or by altering S-protein residues 479 and 487 to residues conserved during the 2002–2003 outbreak. Collectively, these data describe molecular interactions important to the adaptation of SARS-CoV to human cells, and provide insight into the severity of the 2002–2003 SARS epidemic.

In many applications in flows through porous media, one needs to determine the properties of subsurface to detect, monitor, or predict the actions of natural or induced forces. Here, we focus on two important subsurface properties: rock permeability and porosity. A Bayesian approach using a Markov Chain Monte Carlo (MCMC) algorithm is well suited for reconstructing the spatial distribution of permeability and porosity, and quantifying associated uncertainty in these properties. A crucial step in this approach is the computation of a likelihood function, which involves solving a possibly nonlinear system of partial differential equations. The computation time for the likelihood function limits the number of MCMC iterations that can be performed in a practical period of time. This affects the consistency of the posterior distribution of permeability and porosity obtained by MCMC exploration. To speed-up the posterior exploration, we can use a prefetching technique, which relies on the fact that multiple likelihoods of possible states into the future in an MCMC chain can be computed ahead of time. In this paper, we show that the prefetching technique implemented on multiple processors can make the Bayesian approach computationally tractable for subsurface characterization and prediction of porous media flows.

This work deals with the simultaneous estimation of spatially variable thermal conductivity and diffusivity for one-dimensional heat conduction in heterogeneous media. The direct problem solution is analytically obtained via integral transforms and the related eigenvalue problem is solved by the Generalized Integral Transform Technique (GITT). The inverse problem is handled by Bayesian inference through a Markov Chain Monte Carlo (MCMC) method. Instead of seeking the function estimation in the form of a sequence of local values for the thermal properties, an alternative approach is utilized here, which is based on the eigenfunction expansion of the thermal conductivity and diffusivity themselves. Then, the unknown parameters become the corresponding expansion coefficients. In addition, the inverse analysis is performed on the transformed temperature field, instead of employing the actual local temperature measurements, thus promoting a significant data reduction through the integral transformation of the experimental measurements. A demonstration experiment is built involving a partially heated thin bakelite plate. Temperature measurements obtained via infrared thermography are used in the inverse analysis.

Inverse analysis with integral transformed temperature fields: Identification of thermophysical properties in heterogeneous media

Inverse analysis of forced convection in micro-channels with slip flow via integral transforms and Bayesian inference

When seawater streams around risers, it causes vortex-induced vibrations (VIV), which occur in two forms: in-line (IL) and cross-flow (CF). Accurate prediction of coupled IL and CF VIV behaviors is essential for designing risers. To investigate the VIV of marine risers used in deep-sea oil and gas transportation, this study analyzed the coupled CF and IL VIV characteristics of the riser with axially time-varying tension under the combined effects of internal flow and oceanic linear shear flow. The work established the vibration control equation for the riser considering internal flow velocity, axial top tension, and bending stiffness, which is based on Euler-Bernoulli beam theory. The double Van der Pol diffusion wake oscillator model was used to simulate the vortex-induced forces from the ocean currents, and the internal fluid was considered as a single-phase incompressible liquid. Using the Generalized Integral Transform Technique (GITT), the coupled system of nonlinear partial differential equations was further transformed into a system of nonlinear ordinary differential equations for numerical solution. A parametric study was conducted to analyze the impact of current velocity, internal flow velocity, and diffusion term on the VIV responses, including structural displacement, structural frequency, displacement envelope, and displacement evolution. Numerical results indicate that the vibration modes of the riser are influenced by both CF and IL directions, and the effect of IL can not be ignored. The diffusion term has a significant impact on the vibrations of the riser. The number of vibration modes of the riser is mainly influenced by the increasing current velocity, and for a given current velocity, the vibration of the riser becomes chaotic when the dimensionless internal fluid velocity increased within a certain range.

Proteomic identification of protein interactions with membrane associated molecules in their native membrane environment pose a challenge because of technical problems of membrane handling. We investigate the possibility of employing membrane nanodiscs for harboring the membrane associated molecule to tackle the challenges. Nanodiscs are stable, homogenous pieces of membrane with a discoidal shape. They are stabilized by an encircling amphipatic protein with an engineered epitope tag. In the present study we employ the epitope tag of the nanodiscs for detection and co-immunoprecipitation of interaction partners of the glycolipid ganglioside GM1 harbored by nanodiscs. Highly specific binding activity for nanodisc-GM1 immobilized on sensorchips was observed by surface plasmon resonance in culture media from enterotoxigenic Escherischia coli. To isolate the interaction partner(s) from enterotoxigenic Escherischia coli, GM1-nanodiscs were employed for co-immunoprecipitation. The B subunit of heat labile enterotoxin was identified as a specific interaction partner by mass spectrometry, thus demonstrating that nanodisc technology is useful for highly specific detection and identification of interaction partners to specific lipids embedded in a membrane bilayer.

The generalized integral transform technique (GITT) is an hybrid numerical‐analytical method that has been successfully applied in convection‐diffusion problems, where the original potentials are replaced by eigenexpansion series, and the system of partial differential equations is transformed into a finite system of ordinary differential equations, allowing to obtain an error controlled solution without any kind of grid generation. This paper aims at the application of GITT to the transient version of the classical differentially heated square cavity problem, considering fluid properties as functions of temperature. Comparing results to some previously reported data for constant fluid properties validates the computational procedure. The solution for variable fluid properties with Boussinesq approximation is presented for several values of inclinations, at Rayleigh number of 103 and a Prandtl number of 0.71, demonstrating GITT capability of capturing circulating cells formation and evolution at a low Rayleigh number. New correlations for leaning angle and aspect ratio are presented.

Simultaneous estimation of space-variable thermal conductivity and heat capacity in heterogeneous samples of nanocomposites is dealt with by employing a combination of the generalized integral transform technique (GITT), for the direct problem solution, Bayesian inference as implemented with the Markov chain Monte Carlo (MCMC) method, for the inverse analysis and infrared thermography, for the temperature measurements. Another aspect of the proposed approach is the integral transformation of the thermographic experimental data along the space variable, which allows for a significant data compression since the inverse analysis is undertaken within the transformed field. Results are presented for the covalidation of the experiment with a homogeneous polyester plate, as well as for a plate made of polyester–alumina nanoparticles composite with abrupt variation of the filler concentration.

This work illustrates the use of Bayesian inference in the estimation of spatially variable thermal conductivity for one-dimensional heat conduction in heterogeneous media, such as particle-filled composites and other two-phase dispersed systems, by employing a Markov chain Monte Carlo (MCMC) method, through the implementation of the Metropolis-Hastings algorithm. The direct problem solution is obtained analytically via integral transforms, and the related eigenvalue problem is solved by the generalized integral transform technique (GITT), offering a fast, precise, and robust solution for the transient temperature field, which are desirable features for the implementation of the inverse analysis. Instead of seeking the function estimation in the form of a sequence of local values for the thermal conductivity, an alternative approach is proposed here, which is based on the eigenfunction expansion of the thermal conductivity itself. Then, the unknown parameters become the corresponding series coefficients. Simulated temperatures obtained via integral transforms are used in the inverse analysis. From the prescription of the concentration distribution of the dispersed phase, available correlations for the thermal conductivity are employed to produce the simulated results with high precision in the direct problem solution, while eigenfunction expansions with reduced number of terms are employed in the inverse analysis itself, in order to avoid the so-called inverse crime. Both Gaussian and noninformative uniform distributions were used as priors for comparison purposes. In addition, alternative correlations for the thermal conductivity that yield different predictions are also employed as Gaussian priors for the algorithm in order to test the inverse analysis robustness.

This work presents the combined use of the integral transform method, for the direct problem solution, and of Bayesian inference, for the inverse problem analysis, in the simultaneous estimation of spatially variable thermal conductivity and thermal capacity for one-dimensional heat conduction within heterogeneous media. The direct problem solution is analytically obtained via integral transforms and the related eigenvalue problem is solved by the generalized integral transform technique (GITT), offering a fast, precise, and robust solution for the transient temperature field. The inverse problem analysis employs a Markov chain Monte Carlo (MCMC) method, through the implementation of the Metropolis-Hastings sampling algorithm. Instead of seeking the functions estimation in the form of local values for the thermal conductivity and capacity, an alternative approach is employed based on the eigenfunction expansion of the thermophysical properties themselves. Then, the unknown parameters become the corresponding series coefficients for the properties eigenfunction expansions. Simulated temperatures obtained via integral transforms are used in the inverse analysis, for a prescribed concentration distribution of the dispersed phase in a heterogeneous media such as particle filled composites. Available correlations for the thermal conductivity and theory of mixtures relations for the thermal capacity are employed to produce the simulated results with high precision in the direct problem solution, while eigenfunction expansions with reduced number of terms are employed in the inverse analysis itself, in order to avoid the inverse crime. Gaussian distributions were used as priors for the parameter estimation procedure. In addition, simulated results with different randomly generated errors were employed in order to test the inverse analysis robustness.

ABSTRACTApart from being induced by internal and external flow, vibration of free-spanning pipelines is also constrained by the soil that supports the span on both ends. A wake oscillator model is chosen to describe the vortex shedding acting on the pipeline, and the soil spring is adopted to describe the pipe–soil interaction at the span shoulders. A semi-analytical solution – the generalised integral transform technique (GITT) – is used to study the dynamic response of free-spanning submarine pipelines. With this method, the coupled fluid-structure system of partial differential equations is transformed into a system of second-order ordinary differential equations in temporal variable. Parametric studies are carried out to analyse the influence of different internal and external flow velocities, and different soil stiffness. GITT is proved to be a fast and accurate approach for analysing the dynamic response of free-spanning submarine pipelines considering the influence of the current and the internal flow, as well as the effect of the soil.