FULLY NONLINEAR MODELING AND ANALYSIS OF PRECISION MEMBRANES

Collision Probability with Gaussian Mixture Orbit Uncertainty

Approximation of Optimal Impulsive Flyby Transfer with Terminal Inspection Constraints

The cation diffusion facilitator (CDF) family of metal ion transporters plays important roles in zinc transport at all phylogenetic levels. In this report, we describe a novel interaction between two members of the CDF family in Saccharomyces cerevisiae. One CDF member in yeast, Msc2p, was shown recently to be involved in zinc transport into the endoplasmic reticulum (ER) and required for ER function. We describe here a newly recognized CDF family member in yeast, Zrg17p. ZRG17 was previously identified as a zinc-regulated gene controlled by the zinc-responsive Zap1p transcription factor. A zrg17 mutant exhibits the same zinc-suppressible phenotypes as an msc2 mutant, including an induction of the unfolded protein response in low zinc. Moreover, a significant fraction of the total Zrg17p protein appears to localize to the ER. Their common phenotypes and localization suggested that these two proteins function together to mediate zinc transport into the ER. Consistent with this hypothesis, Msc2p and Zrg17p physically interact with each other, as determined by co-immunoprecipitation. Therefore, we propose that Msc2p and Zrg17p form a heteromeric zinc transport complex in the ER membrane. We also demonstrate that ZnT5 and ZnT6, mammalian homologues of Msc2p and Zrg17p, functionally interact as well. These results suggest that heteromeric complexes formed by different CDF members may be a common phenomenon for this ubiquitous family of metal ion transporters.

Molecular selection, ion exclusion, and water permeation are well known regulatory mechanisms in aquaporin. Water permeability was found to be diverse in different subgroups of plasma membrane intrinsic proteins (PIPs), even though the residues surrounding the water holes remained the same across the subgroups. Upon homology modeling and structural comparison, a conserved Ala/Ile(Val) residue difference was identified in helix 2 that affected the conformation of the NPA region and consequently influenced the water permeability. The residue difference was found to be conservative within the two subgroups of PIPs in rice as well as in other plants. Functional tests further confirmed the prediction via site-directed mutagenesis where replacement of Ala(103) or Ala(102) in respective OsPIP1;1 or OsPIP1;3 with Val yielded 7.0- and 2.2-fold increases in water transportation, and substitution of Ile(98) or Val(95) in respective OsPIP2;3 or OsPIP2;7 with Ala resulted in 73 or 52% reduction of water transportation. Based on structural analyses and molecular dynamics simulations, we proposed that the difference in water permeability was attributed to the orientation variations of helix 2 that modified water-water and water-protein interactions.

In the last 25 years, mathematical and numerical modeling of cardiovascular problems has experienced a spectacular progress. Moving progressively from the stage of idealized models supporting traditional in vitro and in vivo approaches – basically with proofs of concept – Cardiovascular Mathematics has been transforming into a unique tool for patient-specific analysis. This has been made possible by the strong integration with imaging devices. Nowadays, the work pipeline starting from a medical image in the Digital Imaging and Communications in Medicine (DICOM) format to retrieve the patient-specific geometry of an artery or the left ventricle to be used as computational domain in a numerical simulation is well established. This has initiated a paradigm shift in the interactions between mathematicians, bioengineers, and medical doctors. The latter are progressively getting used to in silico analysis as an important component of their research [3]. The introduction of numerical procedures as a part of an established clinical routine and more in general of a consolidated support to the decision-making process of physicians still requires some steps both in terms of infrastructures (to bring computational tools to the operating room or the bedside) and methods. In particular, the quality of the numerical results needs to be assessed and certified. The reliability of simulations calls for an accurate quantification and possibly reduction of uncertainty. In this scenario and in view of terrific advancements of measuring techniques, an important research line – quite established in other fields – is data assimilation [4,6,9], that is, the integration of numerical simulations and measurements. We may say that numerical models provide a background knowledge (based on physical principles and constitutive laws, not patient-specific), whereas measures give a foreground (individual) information; accuracy of in silico procedures relies on the correct integration of these two levels of knowledge of the problem [9,10]. As a matter of fact, numerical models depend on parameters and boundary/initial conditions. Their knowledge is in practice usually incomplete, inaccurate, and noisy. In some cases, the sensitivity itself of the final results to these parameters is unclear and needs to be quantified. Such an uncertainty may be significantly reduced by the availability of patient-specific measures; on the other hand, the quality of measures can be strongly enhanced by comparison with mathematical models (after all, noise is in general not educated, it does not know PDEs . . . ) [4,5,7,8,9,11]. We think therefore that, in the future, a crucial step for the clinical application of Cardiovascular Mathematics will be the passage from numerical simulation to data assimilation. To be concrete, borrowing a motto by Michel Fortin supporting mesh adaptivity in finite element simulations, stating that a ‘grid should not be considered a data, but an unknown of the problem’, we think that many parameters currently tuned on the basis of nonpatient specific criteria (even in patient-specific geometries) should be considered part of the unknowns to be found by assimilation procedures.

Causality: Perceiving the Causes of Visual Events

Crystal structures of the xenobiotic metabolizing cytochrome P450 2B4 have demonstrated markedly different conformations in the presence of imidazole inhibitors or in the absence of ligand. However, knowledge of the plasticity of the enzyme in solution has remained scant. Thus, hydrogen-deuterium exchange mass spectrometry (DXMS) was utilized to probe the conformations of ligand-free P450 2B4 and the complex with 4-(4-chlorophenyl)imidazole (4-CPI) or 1-biphenyl-4-methyl-1H-imidazole (1-PBI). The results of DXMS indicate that the binding of 4-CPI slowed the hydrogen-deuterium exchange rate over the B'- and C-helices and portions of the F-G-helix cassette compared with P450 2B4 in the absence of ligands. In contrast, there was little difference between the ligand-free and 1-PBI-bound exchange sets. In addition, DXMS suggests that the ligand-free P450 2B4 is predominantly open in solution. Interestingly, a new high resolution structure of ligand-free P450 2B4 was obtained in a closed conformation very similar to the 4-CPI complex. Molecular dynamics simulations performed with the closed ligand-free structure as the starting point were used to probe the energetically accessible conformations of P450 2B4. The simulations were found to equilibrate to a conformation resembling the 1-PBI-bound P450 2B4 crystal structure. The results indicate that conformational changes observed in available crystal structures of the promiscuous xenobiotic metabolizing cytochrome P450 2B4 are consistent with its solution structural behavior.

Towards modeling spatiotemporal processes in metal–organic frameworks

Inverse problem solution is an integral part of data interpretation for well testing in petroleum reservoirs. In case of two-phase well tests with water injection, forward problem is based on the multiphase flow model in porous media and solved numerically. The inverse problem is based on a misfit or likelihood objective function. Adjoint methods have proved robust and efficient for gradient calculation of the objective function in this type of problems. However, if time-lapse electrical resistivity measurements during the well test are included in the objective function, both the forward and inverse problems become multiphysical, and straightforward application of the adjoint method is problematic. In this paper we present a novel adjoint algorithm for the inverse problems considered. It takes into account the structure of cross dependencies between flow and electrical equations and variables, as well as specifics of the equations (mixed parabolic-hyperbolic for flow and elliptic for electricity), numerical discretizations and grids, and measurements in the inverse problem. Decomposition is proposed for the adjoint problem which makes possible step-wise solution of the electric adjoint equations, like in the forward problem, after which a cross-term is computed and added to the right-hand side of the flow adjoint equations at this timestep. The overall procedure provides accurate gradient calculation for the multiphysical objective function while preserving robustness and efficiency of the adjoint methods. Example cases of the adjoint gradient calculation are presented and compared to straightforward difference-based gradient calculation in terms of accuracy and efficiency.

Bacterial translation initiation factor IF2 promotes ribosomal subunit association, recruitment, and binding of fMet-tRNA to the ribosomal P-site and initiation dipeptide formation. Here, we present the solution structures of GDP-bound and apo-IF2-G2 of Bacillus stearothermophilus and provide evidence that this isolated domain binds the 50 S ribosomal subunit and hydrolyzes GTP. Differences between the free and GDP-bound structures of IF2-G2 suggest that domain reorganization within the G2-G3-C1 regions underlies the different structural requirements of IF2 during the initiation process. However, these structural signals are unlikely forwarded from IF2-G2 to the C-terminal fMet-tRNA binding domain (IF2-C2) because the connected IF2-C1 and IF2-C2 modules show completely independent mobility, indicating that the bacterial interdomain connector lacks the rigidity that was found in the archaeal IF2 homolog aIF5B.

BackgroundThe aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes.MethodsWhile other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field.ResultsIt starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method.ConclusionSolving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.

Researchers have investigated the dynamics of oscillation of a single-link assistive manipulator and carried out vibration analysis of the same due to its great application in real life. Thus, studying the dynamics of flexible assistive robots and developing the model is indeed an interesting research topic. It is possible that the exact solution to the equations associated with such a single-link manipulator does not always exist. We used a numerical method, viz., Galerkin’s method to solve the governing differential equations of the problem, and the corresponding frequency of oscillation was calculated. This is known as the forward problem. On the other hand, the inverse problem is to compute values of the unknowns when the frequency is known by experiment, but the values of the remaining parameters are not known. With this backdrop, the purpose of this chapter is to investigate forward and inverse problems related to single-link robotic manipulators using Euler’s beam theory to define the system dynamics. Firstly, the frequencies of the first four modes of vibration have been calculated. Furthermore, the frequency is assumed to be known (experimental outcome), and the inverse case is studied using Young’s modulus and density of the material of manufacturing of the manipulator as unknown parameters. Besides, the system of single-link manipulators has been studied in uncertain environments using fuzzy theory for forward and inverse problems.

Multidomain kinases such as c-Src and c-Abl are regulated by complex allosteric interactions involving their noncatalytic SH3 and SH2 domains. Here we show that enhancing natural allosteric control of kinase activity by SH3/linker engagement has long-range suppressive effects on the kinase activity of the c-Abl core. Surprisingly, enhanced SH3/linker interaction also dramatically sensitized the Bcr-Abl tyrosine kinase associated with chronic myelogenous leukemia to small molecule inhibitors that target either the active site or the myristic acid binding pocket in the kinase domain C-lobe. Dynamics analyses using hydrogen exchange mass spectrometry revealed a remarkable allosteric network linking the SH3 domain, the myristic acid binding pocket, and the active site of the c-Abl core, providing a structural basis for the biological observations. These results suggest a rational strategy for enhanced drug targeting of Bcr-Abl and other multidomain kinase systems that use multiple small molecules to exploit natural mechanisms of kinase control.

Many materials (e.g., rubber or biologic tissues) are "nearly" incompressible and often assumed to be incompressible in their constitutive equations. This assumption hinders realistic analyses of wave motion including acoustoelasticity. In this study, this constraint is relaxed and the reflected waves from nearly incompressible, hyper-elastic materials are examined. Specifically, reflection coefficients are considered from the interface of water and uni-axially prestretched rubber. Both forward and inverse problems are experimentally and analytically studied with the incident wave perpendicular to the interface. In the forward problem, the wave reflection coefficient at the interface is evaluated with strain energy functions for nearly incompressible materials in order to compute applied strain. For the general inverse problem, mathematical relations are derived that identify both uni-axial strains and normalized material constants from reflected wave data. The validity of this method of analysis is demonstrated via an experiment with stretched rubber. Results demonstrate that applied strains and normalized material coefficients can be simultaneously determined from the reflected wave data alone if they are collected at several different (but unknown) levels of strain. This study therefore indicates that acoustoelasticity, with an appropriate constitutive formulation, can determine strain and material properties in hyper-elastic, nearly incompressible materials.

'Acoustic probes have shown promise to be quite effective in determining the solid content in solid-liquid suspensions. However, the presence of small amounts of gas in the waste slurries stored in tanks across the DOE complex prevents straightforward application for characterization of these slurries. The proposed research will develop an acoustic probe for monitoring particle size and volume fraction in slurries in the absence and the presence of gas bubbles. Theoretical Analysis Accomplished: Attenuation of sound waves depends on the size distribution of the solids and the volume fraction of solids. These can in principle be calculated from attenuation measured over a range of frequencies. However, small amounts of bubbles distort the measured attenuation. A typical result from theoretical analysis for the attenuation of solid- gas-liquid systems is given in Figure 1. The total attenuation of a sound wave v(o) equals the sum of contributions by a large number of ''bins'' of particle sizes. This notion yields the following equation for the (hitherto) unknown number density of solid particles as a function of particle radius N(a): j k(o,a)N(a)da = v(o), where the kernel k(o,a) is obtained from analysis. If N(a) is given, the above equation is used to calculate the attenuation v(o). This is referred to as solving the ''forward problem''. Solving for N(a) with v(o) given is the ''inverse problem''. A complication that one faces when trying to solve the inverse problem is that the stated problem is mathematically ill-posed, i.e., small fluctuations in v(o) cause large fluctuations in the result for the number density. Therefore the problem needs to be ''regularized'', i.e., the stated problem needs to be changed slightly such as to make it well-posed. This has been done by others for gas-liquid systems in the past. This approach is currently being applied in the present project to solid-liquid systems. As is shown in Figure 2, it successfully recovers the number density that has been used in the forward problem to generate attenuation data. Having this solution technique giving reliable results for the inverse problems of both gas-liquid and solid-liquid systems, the authors shall apply this method in the near future to solid-gas-liquid systems.'