Asymptotically consistent numerical approximation of hemolysis

In a previous communication, we have proposed a numerical framework for the prediction of in vitro hemolysis indices in the preselection and optimization of medical devices. This numerical methodology is based on a novel interpretation of Giersiepen-Wurzinger blood damage correlation as a volume integration of a damage function over the computational domain. We now propose an improvement of this approach based on a hyperbolic equation of blood damage that is asymptotically consistent. Consequently, while the proposed correction has yet to be proven experimentally, it has the potential to numerically predict more realistic red blood cell destruction in the case of in vitro experiments. We also investigate the appropriate computation of the shear stress scalar of the damage fraction model. Finally, we assess the validity of this consistent approach with an analytical example and with some 3D examples.     

Crustacean molt-inhibiting hormone: Structure,function, and cellular mode of action

In Crustacea, secretion of ecdysteroid molting hormones by Y-organs is regulated, at least in part, by molt-inhibiting hormone (MIH), a polypeptide neurohormone produced by neurosecretory cells of the eyestalks. This article reviews current knowledge of MIH, with particular emphasis on recent findings regarding the (a) structure of the MIH peptide and gene, (b) levels of MIH in eyestalks and hemolymph, (c) cellular mechanism of action of MIH, and (d) responsiveness of Y-organs to MIH. At least 26 MIH/MIH-like sequences have been directly determined by protein sequencing or deduced from cloned cDNA. Recent studies reveal the existence of multiple forms of MIH/MIH-like molecules among penaeids and raise the possibility that molecular polymorphism may exist more generally among MIH (type II) peptides. The hemolymphatic MIH titer has been determined for two species, a crayfish (Procambarus clarkii) and a crab (Carcinus maenas). The data are dissimilar and additional studies are needed. Composite data indicate cellular signaling pathways involving cGMP, cAMP, or both may play a role in MIH-induced suppression of ecdysteroidogenesis. Data from the two species studied in our laboratories (P. clarkii and Callinectes sapidus) strongly favor cGMP as the physiologically relevant second messenger. Ligand-binding studies show an MIH receptor exists in Y-organ plasma membranes, but the MIH receptor has not been isolated or fully characterized for any species. Such studies are critical to understanding the cellular mechanism by which MIH regulates ecdysteroidogenesis. Rates of ecdysteroid synthesis appear also to be influenced by stage-specific changes in the responsiveness of Y-organs to MIH. The changes in responsiveness result, at least in part, from changes in glandular phosphodiesterase (PDE) activity. The PDE isotype (PDE1) present in Y-organs of C. sapidus is calcium/calmodulin dependent. Thus, calcium may regulate ecdysteroidogenesis through activation of glandular PDE.     

The Lagrangian stochastic model for estimating footprint and water vapor fluxes over inhomogeneous surfaces

This study investigated a two-dimensional Lagrangian stochastic dispersion model for estimating water vapor fluxes and footprint over homogeneous and inhomogeneous surfaces. Over the homogeneous surface, particle trajectories were computed from a 2-D Lagrangian model forced by Eulerian velocity statistics determined by Monin–Obukhov similarity theory (MOST). For an inhomogeneous surface, the velocity and atmospheric stability profiles were computed using a second-order Eulerian closure model, and these local profiles were then used to drive the Lagrangian model. The model simulations were compared with water vapor flux measurements carried out above an irrigated bare soil site and an irrigated potato site. The inhomogeneity involved a step change in surface roughness, humidity, and temperature. Good agreement between eddy-correlation-measured and Lagrangian-model-predicted water vapor fluxes was found for both sites. Hence, this analysis demonstrates the practical utility of second-order closure models in conjunction with Lagrangian analysis to estimate the scalar footprint in planar inhomogeneous flows.     

Numerical simulation of blood flow in the left ventricle and aortic sinus using magnetic resonance imaging and computational fluid dynamics

Understanding cardiac blood flow patterns has many applications in analysing haemodynamics and for the clinical assessment of heart function. In this study, numerical simulations of blood flow in a patient-specific anatomical model of the left ventricle (LV) and the aortic sinus are presented. The realistic 3D geometry of both LV and aortic sinus is extracted from the processing of magnetic resonance imaging (MRI). Furthermore, motion of inner walls of LV and aortic sinus is obtained from cine-MR image analysis and is used as a constraint to a numerical computational fluid dynamics (CFD) model based on the moving boundary approach. Arbitrary Lagrangian–Eulerian finite element method formulation is used for the numerical solution of the transient dynamic equations of the fluid domain. Simulation results include detailed flow characteristics such as velocity, pressure and wall shear stress for the whole domain. The aortic outflow is compared with data obtained by phase-contrast MRI. Good agreement was found between simulation results and these measurements.     

An efficient numerical method for distributed-loop models of the urine concentrating mechanism

In this study we describe an efficient numerical method, based on the semi-Lagrangian (SL) semi-implicit (SI) method and Newton's method, for obtaining steady-state (SS) solutions of equations arising in distributed-loop models of the urine concentrating mechanism. Dynamic formulations of these models contain large systems of coupled hyperbolic partial differential equations (PDEs). The SL method advances the solutions of these PDEs in time by integrating backward along flow trajectories, thus allowing large time steps while maintaining stability. The SI approach controls stiffness arising from transtubular transport terms by averaging these terms in time along flow trajectories. An approximate SS solution of a dynamic formulation obtained via the SLSI method can be used as an initial guess for a Newton-type solver, which rapidly converges to a highly accurate numerical approximation to the solution of the ordinary differential equations that arise in the corresponding SS model formulation. In general, it is difficult to specify a priori for a Newton-type solver an initial guess that falls within the radius of convergence; however, the initial guess generated by solving the dynamic formulation via the SLSI method can be made sufficiently close to the SS solution to avoid numerical instability. The combination of the SLSI method and the Newton-type solver generates stable and accurate solutions with substantially reduced computation times, when compared to previously applied dynamic methods.     

A milestoning study of the kinetics of an allosteric transition: atomically detailed simulations of deoxy Scapharca hemoglobin

Atomically detailed simulations are used to compute the kinetics of the R-to-T transition in deoxy Scapharca hemoglobin. A computational approach called milestoning is utilized that combines 1), an efficient reaction path algorithm; and 2), a "fragment and glue" approach for classical trajectories. Milestoning computes the R-to-T transition kinetics on the microsecond timescale based on atomically detailed trajectories that rarely exceed a nanosecond. Eleven reference hypersurfaces (milestones) are constructed along the reaction coordinate, which is computed with a global path optimization algorithm. Two-hundred classical trajectories are calculated for each of the milestones to collect local distributions of first passage times. These local distributions are used in a non-Markovian theory to compute the overall timescale. Exponential enrichment of reactive trajectories, an important component of the milestoning approach, makes these calculations possible. The overall timescale of the reaction is estimated as 10 +/- 9 micros, in accord with available experimental data. The barrier is not sharp and is spread over four milestones. Even after the most significant structural changes are completed (phenylalanine F4 ring flips), highly collective and activated motions continue. The calculations suggest an additional late free energy barrier.     

A Porous Media Approach to Finite Deformation Behaviour in Soft Tissues

The present work presents a porous medium formulation for the biomechanical analysis of soft tissues. An updated Lagrangian approach is developed to study the coupled effects of low speed flows of fluid phases, in partially or fully saturated conditions, and the finite deformation occurring in the solid matrix. The procedure developed allows both for the evaluation of coupled geometric and material non-linearities. The main theoretical and computational aspects of this multiphase formulation are discussed. The finite element method is used for the numerical solution of the resulting coupled system of equations. A reference case is reported with regard to healthy and degenerative phases of intervertebral segment. Results reported allow for a detailed interpretation of the formulation reliability, also by comparison with existing experimental data. In particular, the role played by the fluid on the load carrying mechanism is pointed out, thus stressing the importance of a multiphase approach to the overall behaviour of the spinal motion segment in time.     

Efficient simulations of tubulin-driven axonal growth

This work concerns efficient and reliable numerical simulations of the dynamic behaviour of a moving-boundary model for tubulin-driven axonal growth. The model is nonlinear and consists of a coupled set of a partial differential equation (PDE) and two ordinary differential equations. The PDE is defined on a computational domain with a moving boundary, which is part of the solution. Numerical simulations based on standard explicit time-stepping methods are too time consuming due to the small time steps required for numerical stability. On the other hand standard implicit schemes are too complex due to the nonlinear equations that needs to be solved in each step. Instead, we propose to use the Peaceman–Rachford splitting scheme combined with temporal and spatial scalings of the model. Simulations based on this scheme have shown to be efficient, accurate, and reliable which makes it possible to evaluate the model, e.g. its dependency on biological and physical model parameters. These evaluations show among other things that the initial axon growth is very fast, that the active transport is the dominant reason over diffusion for the growth velocity, and that the polymerization rate in the growth cone does not affect the final axon length.     

Improved Reconstruction of In Silico Gene Regulatory Networks by Integrating Knockout and Perturbation Data

We performed computational reconstruction of the in silico gene regulatory networks in the DREAM3 Challenges. Our task was to learn the networks from two types of data, namely gene expression profiles in deletion strains (the ‘deletion data’) and time series trajectories of gene expression after some initial perturbation (the ‘perturbation data’). In the course of developing the prediction method, we observed that the two types of data contained different and complementary information about the underlying network. In particular, deletion data allow for the detection of direct regulatory activities with strong responses upon the deletion of the regulator while perturbation data provide richer information for the identification of weaker and more complex types of regulation. We applied different techniques to learn the regulation from the two types of data. For deletion data, we learned a noise model to distinguish real signals from random fluctuations using an iterative method. For perturbation data, we used differential equations to model the change of expression levels of a gene along the trajectories due to the regulation of other genes. We tried different models, and combined their predictions. The final predictions were obtained by merging the results from the two types of data. A comparison with the actual regulatory networks suggests that our approach is effective for networks with a range of different sizes. The success of the approach demonstrates the importance of integrating heterogeneous data in network reconstruction.     

Crystal structure of the GAF-B domain from human phosphodiesterase 10A complexed with its ligand, cAMP

Cyclic nucleotide phosphodiesterases (PDEs) catalyze the degradation of the cyclic nucleotides cAMP and cGMP, which are important second messengers. Five of the 11 mammalian PDE families have tandem GAF domains at their N termini. PDE10A may be the only mammalian PDE for which cAMP is the GAF domain ligand, and it may be allosterically stimulated by cAMP. PDE10A is highly expressed in striatal medium spiny neurons. Here we report the crystal structure of the C-terminal GAF domain (GAF-B) of human PDE10A complexed with cAMP at 2.1-angstroms resolution. The conformation of the PDE10A GAF-B domain monomer closely resembles those of the GAF domains of PDE2A and the cyanobacterium Anabaena cyaB2 adenylyl cyclase, except for the helical bundle consisting of alpha1, alpha2, and alpha5. The PDE10A GAF-B domain forms a dimer in the crystal and in solution. The dimerization is mainly mediated by hydrophobic interactions between the helical bundles in a parallel arrangement, with a large buried surface area. In the PDE10A GAF-B domain, cAMP tightly binds to a cNMP-binding pocket. The residues in the alpha3 and alpha4 helices, the beta6 strand, the loop between 3(10) and alpha4, and the loop between alpha4 and beta5 are involved in the recognition of the phosphate and ribose moieties. This recognition mode is similar to those of the GAF domains of PDE2A and cyaB2. In contrast, the adenine base is specifically recognized by the PDE10A GAF-B domain in a unique manner, through residues in the beta1 and beta2 strands.     

Model reduction using a posteriori analysis

Mathematical models in biology and physiology are often represented by large systems of non-linear ordinary differential equations. In many cases, an observed behaviour may be written as a linear functional of the solution of this system of equations. A technique is presented in this study for automatically identifying key terms in the system of equations that are responsible for a given linear functional of the solution. This technique is underpinned by ideas drawn from a posteriori error analysis. This concept has been used in finite element analysis to identify regions of the computational domain and components of the solution where a fine computational mesh should be used to ensure accuracy of the numerical solution. We use this concept to identify regions of the computational domain and components of the solution where accurate representation of the mathematical model is required for accuracy of the functional of interest. The technique presented is demonstrated by application to a model problem, and then to automatically deduce known results from a cell-level cardiac electrophysiology model.     

The solution structure of molt-inhibiting hormone from the Kuruma prawn Marsupenaeus japonicus

Molting in crustaceans is controlled by molt-inhibiting hormone (MIH) and ecdysteroids. It is presumed that MIH inhibits the synthesis and the secretion of ecdysteroids by the Y-organ, resulting in molt suppression. The amino acid sequence of MIH is similar to that of crustacean hyperglycemic hormone (CHH), and therefore, they form a peptide family referred to as the CHH family. Most of the CHH family peptides show no cross-activity, whereas a few peptides show multiple hormonal activities. To reveal the structural basis of this functional specificity, we determined the solution structure of MIH from the Kuruma prawn Marsupenaeus japonicus and compared the solution structure of MIH with a homology-modeled structure of M. japonicus CHH. The solution structure of MIH consisted of five alpha-helices and no beta-structures, constituting a novel structural motif. The homology-modeled structure of M. japonicus CHH was very similar to the solution structure of MIH with the exception of the absence of the N-terminal alpha-helix and the C-terminal tail, which were sterically close to each other. The surface properties of MIH around this region were quite different from those of CHH. These results strongly suggest that this region is a functionally important site for conferring molt-inhibiting activity.     

Optimizing tensor contraction expressions for hybrid CPU-GPU execution

Tensor contractions are generalized multidimensional matrix multiplication operations that widely occur in quantum chemistry. Efficient execution of tensor contractions on Graphics Processing Units (GPUs) requires several challenges to be addressed, including index permutation and small dimension-sizes reducing thread block utilization. Moreover, to apply the same optimizations to various expressions, we need a code generation tool. In this paper, we present our approach to automatically generate CUDA code to execute tensor contractions on GPUs, including management of data movement between CPU and GPU. To evaluate our tool, GPU-enabled code is generated for the most expensive contractions in CCSD(T), a key coupled cluster method, and incorporated into NWChem, a popular computational chemistry suite. For this method, we demonstrate speedup over a factor of 8.4 using one GPU as compared to one CPU core and over 2.6 when utilizing the entire system using hybrid CPU+GPU solution with 2 GPUs and 5 cores (instead of 7 cores per node). We further investigate tensor contraction code on a new series of GPUs, the Fermi GPUs, and provide several effective optimization algorithms. For the same computation of CCSD(T), on a cluster with Fermi GPUs, we achieve a speedup of 3.4 over a cluster with T10 GPUs. With a single Fermi GPU on each node, we achieve a speedup of 43 over the sequential CPU version.     

Genomic organization,chromosomal localization,and alternative splicing of the human phosphodiesterase 8B gene

We have characterized the gene for human phosphodiesterase 8B, PDE8B, and cloned the full-length cDNA for human PDE8B (PDE8B1) and two splice variants (PDE8B2 and PDE8B3). The PDE8B gene is mapped to the long arm of chromosome 5 (5q13) and is composed of 22 exons spanning over approximately 200kb. The donor and acceptor splice site sequences match the consensus sequences for the exon-intron boundaries of most eukaryotic genes. PDE8B1 encodes an 885 amino acid enzyme, containing an N-terminal REC domain, a PAS domain, and a C-terminal catalytic domain. PDE8B2 and PDE8B3 both have deletion in the PAS domain and encode 838 and 788 amino acid proteins, respectively. RT-PCR analysis revealed that while PDE8B1 is the most abundant variant in thyroid gland, PDE8B3, but not PDE8B1, is the most abundant form in brain. These findings suggest that selective usage of exons produces three different PDE8B variants that exhibit a tissue-specific expression pattern.     

Phosphodiesterase types 3 and 4 regulate the phasic contraction of neonatal rat bladder smooth myocytes via distinct mechanisms

Activation of the cyclic AMP (cAMP) pathway reduces bladder contractility. However, the role of phosphodiesterase (PDE) families in regulating this function is poorly understood. Here, we compared the contractile function of the cAMP hydrolyzing PDEs in neonatal rat bladder smooth myocytes. RT-PCR and Western blotting analysis revealed that several isoforms of PDE1–4 were expressed in neonatal rat bladder. While 8-methoxymethyl-3-isobutyl-1-methylxanthine (a PDE1 inhibitor) and BAY-60-7550 (a PDE2 inhibitor) had no effect on the carbachol-enhanced phasic contractions of bladder strips, cilostamide (Cil, a PDE3 inhibitor) and Ro-20-1724 (Ro, a PDE4 inhibitor) significantly reduced these contractions. This inhibitory effect of Ro was blunted by the PKA inhibitor H-89, while the inhibitory effect of Cil was strongly attenuated by the PKG inhibitor KT 5823. Application of Ro in single bladder smooth myocytes resulted in an increase in Ca^2 + spark frequency but a decrease both in Ca^2 + transients and in sarcoplasmic reticulum (SR) Ca^2 + content. In contrast, Cil had no effect on these events. Furthermore, Ro-induced inhibition of the phasic contractions was significantly blocked by ryanodine and iberiotoxin. Taken together, PDE3 and PDE4 are the main PDE isoforms in maintaining the phasic contractions of bladder smooth myocytes, with PDE4 being functionally more active than PDE3. However, their roles are mediated through different mechanisms.     

Transient kinetics of thermodynamic buffering

The transient response of mitochondrial ATP production towards perturbations was studied by analyzing the trajectories leading from arbitrary initial conditions of the adenine nucleotide pool to the final steady state. These trajectories were calculated from differential equations based on linear relations between flows and thermodynamic forces of the adenylate kinase system including oxidative phosphorylation. The motion of the system along the trajectories consists of two phases: (1) a rapid phase leading from initial states to a common relaxation curve; and (2) a slow phase leading along the relaxation curve to the final steady state. The first phase corresponds to a motion close to the loci of constant adenylic energy charge. In line with this observation is the finding that the energy charge is a constant of motion of the adenylate kinase reaction. The second phase corresponds to a motion along a relaxation curve characterized by minimal Lyapunov exponents in the concentration space of the adenine nucleotides. Thus, both phases of the transient kinetics can be approximated in terms of thermodynamic functions to a high degree of precision. Incubations with isolated rat liver mitochondria were in excellent agreement with the theoretical predictions. In summary, these studies show that the adenylate kinase system not only optimizes the efficiency of oxidative phosphorylation through thermodynamic buffering but, in addition, also deeply influences the transient response of the whole system.     

Constrained Unfolding of a Helical Peptide: Implicit versus Explicit Solvents

Steered Molecular Dynamics (SMD) has been seen to provide the potential of mean force (PMF) along a peptide unfolding pathway effectively but at significant computational cost, particularly in all-atom solvents. Adaptive steered molecular dynamics (ASMD) has been seen to provide a significant computational advantage by limiting the spread of the trajectories in a staged approach. The contraction of the trajectories at the end of each stage can be performed by taking a structure whose nonequilibrium work is closest to the Jarzynski average (in naive ASMD) or by relaxing the trajectories under a no-work condition (in full-relaxation ASMD—namely, FR-ASMD). Both approaches have been used to determine the energetics and hydrogen-bonding structure along the pathway for unfolding of a benchmark peptide initially constrained as an α-helix in a water environment. The energetics are quite different to those in vacuum, but are found to be similar between implicit and explicit solvents. Surprisingly, the hydrogen-bonding pathways are also similar in the implicit and explicit solvents despite the fact that the solvent contact plays an important role in opening the helix.     

The more‐individuals hypothesis revisited: the role of community abundance in species richness regulation and the productivity–diversity relationship

Species richness increases with energy availability, yet there is little consensus as to the exact processes driving this species–energy relationship. The most straightforward explanation is the more‐individuals hypothesis (MIH). It states that higher energy availability promotes a higher total number of individuals in a community, which consequently increases species richness by allowing for a greater number of species with viable populations. Empirical support for the MIH is mixed, partially due to the lack of proper formalisation of the MIH and consequent confusion as to its exact predictions. Here, we review the evidence of the MIH and evaluate the reliability of various predictions that have been tested. There is only limited evidence that spatial variation in species richness is driven by variation in the total number of individuals. There are also problems with measures of energy availability, with scale‐dependence, and with the direction of causality, as the total number of individuals may sometimes itself be driven by the number of species. However, even in such a case the total number of individuals may be involved in diversity regulation. We propose a formal theory that encompasses these processes, clarifying how the different factors affecting diversity dynamics can be disentangled.     

Pulsed magnetohydrodynamic blood flow in a rigid vessel under physiological pressure gradient

Blood flow in a steady magnetic field has been of great interest over recent years. Many researchers have examined the effects of magnetic fields on velocity profiles and arterial pressure, and major studies have focused on steady or sinusoidal flows. In this paper, we present a solution for pulsed magnetohydrodynamic blood flow with a somewhat realistic physiological pressure wave obtained using a Windkessel lumped model. A pressure gradient is derived along a rigid vessel placed at the output of a compliant module which receives the ventricle outflow. Then, velocity profile and flow rate expressions are derived in the rigid vessel in the presence of a steady transverse magnetic field. As expected, results showed flow retardation and flattening. The adaptability of our solution approach allowed a comparison with previously addressed flow cases and calculations presented a good coherence with those well established solutions.     

Ultrasound hemolysis

An ultrasound unit for hemolysis for an analytic device is presented which permits hemolysis without the need of a specific insonification chamber which is an unwanted discontinuity along the probe path. This is possible by direct insonification of a flexible tube which contains the flowing blood. The influence of ultrasound power, insonification time and coupling conditions on the result of hemolysis is investigated.