Modeling technique of prosthetic heart valves

This paper demonstrates a modeling technique of prosthetic heart valves. In the modeling, a pumping cycle is divided into four phases, in which the state of the valve and flow is different. The pressure-flow relation across the valve is formulated separately in each phase. This technique is developed to build a mathematical model used in the real time estimation of the hemodynamic state under artificial heart pumping. The model built by this technique is simple enough for saving the computational time in the real time estimation. The model is described by the first-order ordinary differential equation with 12 parameters. These parameters can be uniquely determined beforehand from in-vitro experimental data. It is shown that the model can adapt, with sufficient accuracy, to a change in the practical pumping condition and the viscosity of the fluid in their practical range, and is also demonstrated that the estimated backflow volume by model agrees closely with the actual one.     

Multistability property in cardiac ionic models of mammalian and human ventricular cells

The underlying mechanisms of irregular cardiac rhythms are still poorly understood. Many experimental and modeling studies are aimed at identifying factors which cause cardiac arrhythmias. However, a lack of understanding of heart rhythm dynamical properties makes it difficult to uncover precise mechanisms of electrical instabilities, and hence to predict the onset of heart rhythm disorders. We review and compare the existing methods of studying cardiac dynamics, including restitution protocol (S1-S2), dynamic restitution protocol and multistability test protocol (S1-CI-S2). We focus on cardiac cell dynamics to elucidate regularities of heart rhythm. We demonstrate the advantages of our newly proposed systematic approach of analysis of cardiac cell dynamics using mammalian Luo Rudy 1991 and human ventricular Ten Tusscher 2006 single cell models under healthy and diseased conditions such as altered K⁺ or Ca²⁺ related currents. We investigate the role of ionic properties and the shape of an action potential on the nonlinear dynamics of electrical processes in periodically stimulated cardiac cells. We show the existence of multistability property for human ventricular cells. Moreover, the multistability is proposed to be an intrinsic property of cardiac cells, and is also suggested to be one of the mechanisms which could underlie the sudden triggering of life-threatening ventricular arrhythmias in the human heart.     

Free energies for coarse-grained proteins by integrating multibody statistical contact potentials with entropies from elastic network models

We propose a novel method of calculation of free energy for coarse grained models of proteins by combining our newly developed multibody potentials with entropies computed from elastic network models of proteins. Multi-body potentials have been of much interest recently because they take into account three dimensional interactions related to residue packing and capture the cooperativity of these interactions in protein structures. Combining four-body non-sequential, four-body sequential and pairwise short range potentials with optimized weights for each term, our coarse-grained potential improved recognition of native structure among misfolded decoys, outperforming all other contact potentials for CASP8 decoy sets and performance comparable to the fully atomic empirical DFIRE potentials. By combing statistical contact potentials with entropies from elastic network models of the same structures we can compute free energy changes and improve coarse-grained modeling of protein structure and dynamics. The consideration of protein flexibility and dynamics should improve protein structure prediction and refinement of computational models. This work is the first to combine coarse-grained multibody potentials with an entropic model that takes into account contributions of the entire structure, investigating native-like decoy selection.     

A Multiscale Red Blood Cell Model with Accurate Mechanics, Rheology, and Dynamics

Red blood cells (RBCs) have highly deformable viscoelastic membranes exhibiting complex rheological response and rich hydrodynamic behavior governed by special elastic and bending properties and by the external/internal fluid and membrane viscosities. We present a multiscale RBC model that is able to predict RBC mechanics, rheology, and dynamics in agreement with experiments. Based on an analytic theory, the modeled membrane properties can be uniquely related to the experimentally established RBC macroscopic properties without any adjustment of parameters. The RBC linear and nonlinear elastic deformations match those obtained in optical-tweezers experiments. The rheological properties of the membrane are compared with those obtained in optical magnetic twisting cytometry, membrane thermal fluctuations, and creep followed by cell recovery. The dynamics of RBCs in shear and Poiseuille flows is tested against experiments and theoretical predictions, and the applicability of the latter is discussed. Our findings clearly indicate that a purely elastic model for the membrane cannot accurately represent the RBC's rheological properties and its dynamics, and therefore accurate modeling of a viscoelastic membrane is necessary.     

Dynamics of the primary cilium in shear flow

In this work, the equilibrium shape and dynamics of a primary cilium under flow are investigated by using both theoretical modeling and experiment. The cilium is modeled as an elastic beam that may undergo large deflection due to the hydrodynamic load. Equilibrium results show that the anchoring effects of the basal body on the cilium axoneme behave as a nonlinear rotational spring. Details of the rotational spring are elucidated by coupling the elastic beam with an elastic shell. We further study the dynamics of cilium under shear flow with the cilium base angle determined from the nonlinear rotational spring, and obtain good agreement in cilium bending and relaxing dynamics when comparing between modeling and experimental results. These results potentially shed light on the physics underlying the mechanosensitive ion channel transport through the ciliary membrane.     

Simultaneous Determination of Protein Structure and Dynamics Using Cryo-Electron Microscopy

Cryo-electron microscopy is rapidly emerging as a powerful technique to determine the structures of complex macromolecular systems elusive to other techniques. Because many of these systems are highly dynamical, characterizing their movements is also a crucial step to unravel their biological functions. To achieve this goal, we report an integrative modeling approach to simultaneously determine structure and dynamics of macromolecular systems from cryo-electron microscopy density maps. By quantifying the level of noise in the data and dealing with their ensemble-averaged nature, this approach enables the integration of multiple sources of information to model ensembles of structures and infer their populations. We illustrate the method by characterizing structure and dynamics of the integral membrane receptor STRA6, thus providing insights into the mechanisms by which it interacts with retinol binding protein and translocates retinol across the membrane.     

Mechanism of Cohesin Loading onto Chromosomes: A Conformational Dynamics Study

The structure-function relationship of cohesin, an essential chromosome maintenance protein, is investigated by analyzing its collective dynamics and conformational flexibility, enhancing our understanding of the sister chromatid cohesion process. A three-dimensional model of cohesin has been constructed by homology modeling using both crystallographic and electron microscopy image data. The harmonic dynamics of the cohesin structure are calculated with a coarse-grained elastic network model. The model shows that the bending motion of the cohesin ring is able to adopt a head-to-tail conformation, in agreement with experimental data. Low-frequency conformational changes are observed to deform the highly conserved glycine residues at the interface of the cohesin heterodimer. Normal mode analysis further reveals that, near large globular structures such as nucleosome and accessory proteins docked to cohesin, the mobility of the coiled-coil regions is notably affected. Moreover, fully solvated molecular dynamics calculations, performed specifically on the hinge region, indicate that hinge opening starts from one side of the dimerization interface, and is coordinated by highly conserved glycine residues.     

On the Mechanics of Cardiac Function of Drosophila Embryo

The heart is a vital organ that provides essential circulation throughout the body. Malfunction of cardiac pumping, thus, leads to serious and most of the times, to fatal diseases. Mechanics of cardiac pumping is a complex process, and many experimental and theoretical approaches have been undertaken to understand this process. We have taken advantage of the simplicity of the embryonic heart of an invertebrate, Drosophila melanogaster, to understand the fundamental mechanics of the beating heart. We applied a live imaging technique to the beating embryonic heart combined with analytical imaging tools to study the dynamic mechanics of the pumping. Furthermore, we have identified one mutant line that exhibits aberrant pumping mechanics. The Drosophila embryonic heart consists of only 104 cardiac cells forming a simple straight tube that can be easily accessed for real-time imaging. Therefore, combined with the wealth of available genetic tools, the embryonic Drosophila heart may serve as a powerful model system for studies of human heart diseases, such as arrhythmia and congenital heart diseases. We, furthermore, believe our mechanistic data provides important information that is useful for our further understanding of the design of biological structure and function and for engineering the pumps for medical uses.     

Myxococcus xanthus Gliding Motors Are Elastically Coupled to the Substrate as Predicted by the Focal Adhesion Model of Gliding Motility

Myxococcus xanthus is a model organism for studying bacterial social behaviors due to its ability to form complex multi-cellular structures. Knowledge of M. xanthus surface gliding motility and the mechanisms that coordinated it are critically important to our understanding of collective cell behaviors. Although the mechanism of gliding motility is still under investigation, recent experiments suggest that there are two possible mechanisms underlying force production for cell motility: the focal adhesion mechanism and the helical rotor mechanism, which differ in the biophysics of the cell–substrate interactions. Whereas the focal adhesion model predicts an elastic coupling, the helical rotor model predicts a viscous coupling. Using a combination of computational modeling, imaging, and force microscopy, we find evidence for elastic coupling in support of the focal adhesion model. Using a biophysical model of the M. xanthus cell, we investigated how the mechanical interactions between cells are affected by interactions with the substrate. Comparison of modeling results with experimental data for cell-cell collision events pointed to a strong, elastic attachment between the cell and substrate. These results are robust to variations in the mechanical and geometrical parameters of the model. We then directly measured the motor-substrate coupling by monitoring the motion of optically trapped beads and find that motor velocity decreases exponentially with opposing load. At high loads, motor velocity approaches zero velocity asymptotically and motors remain bound to beads indicating a strong, elastic attachment.     

Valve-related modes of pump failure in collecting lymphatics: numerical and experimental investigation

Lymph is transported along collecting lymphatic vessels by intrinsic and extrinsic pumping. The walls have muscle of a type intermediate between blood-vascular smooth muscle and myocardium; a contracting segment between two valves (a lymphangion) constitutes a pump. This intrinsic mechanism is investigated ex vivo in isolated, spontaneously contracting, perfused segments subjected to controlled external pressures. The reaction to varying afterload is probed by slowly ramping up the outlet pressure until pumping fails. Often the failure occurs when the contraction raises intra-lymphangion pressure insufficiently to overcome the outlet pressure, open the outlet valve and cause ejection, but many segments fail by other means, the mechanisms of which are not clear. We here elucidate those mechanisms by resort to a numerical model. Experimental observations are paired with comparable findings from computer simulations, using a lumped-parameter model that incorporates previously measured valve properties, plus new measurements of active contractile and passive elastic properties, and the dependence of contraction frequency on transmural pressure, all taken from isobaric twitch contraction experiments in the same vessel. Surprisingly, the model predicts seven different possible modes of pump failure, each defined by a different sequence of valve events, with their occurrence depending on the parameter values and boundary conditions. Some, but not all, modes were found experimentally. Further model investigation reveals routes by which a vessel exhibiting one mode of failure might under altered circumstances exhibit another.     

Stochastic computer model of cellular microtubule dynamics

A computer model of the system of microtubules has been developed to study the mechanisms of action of various factors on this system. The model describes the process of polymerization/depolymerization of microtubules as a set of chemical reactions with certain rate constants using a stochastic approach. Microtubules are visualized in the program field, which makes the model visual. The program imitates the dynamics and structure of the system of cellular microtubules with great, reliability. The parameters generated by the model correlate with the corresponding parameters of microtubules in living cells. We are going to develop this approach to modeling microtubules and similar structures to bring them into a better accord with living systems and to study the influence of various factors on these systems.     

Patient-specific modeling of dyssynchronous heart failure: A case study

The development and clinical use of patient-specific models of the heart is now a feasible goal. Models have the potential to aid in diagnosis and support decision-making in clinical cardiology. Several groups are now working on developing multi-scale models of the heart for understanding therapeutic mechanisms and better predicting clinical outcomes of interventions such as cardiac resynchronization therapy. Here we describe the methodology for generating a patient-specific model of the failing heart with a myocardial infarct and left ventricular bundle branch block. We discuss some of the remaining challenges in developing reliable patient-specific models of cardiac electromechanical activity, and identify some of the main areas for focusing future research efforts. Key challenges include: efficiently generating accurate patient-specific geometric meshes and mapping regional myofiber architecture to them; modeling electrical activation patterns based on cellular alterations in human heart failure, and estimating regional tissue conductivities based on clinically available electrocardiographic recordings; estimating unloaded ventricular reference geometry and material properties for biomechanical simulations; and parameterizing systemic models of circulatory dynamics from available hemodynamic measurements.     

Evidence for the existence of a functional helical myocardial band

Characterization of local and global contractile activities in the myocardium is essential for a better understanding of cardiac form and function. The spatial distribution of regions that contribute the most to cardiac function plays an important role in defining the pumping parameters of the myocardium like ejection fraction and dynamic aspects such as twisting and untwisting. In general, myocardium shortening, tangent to the wall, and ventricular wall thickening are important parameters that characterize the regional contribution within the myocardium to the global function of the heart. We have calculated these parameters using myocardium displacement fields, which were captured through the displacement-encoding with stimulated echoes (DENSE) MRI technique in three volunteers. High spatial resolution of the acquired data revealed transmural changes of thickening and tangential shortening with high fidelity in beating hearts. By filtering myocardium regions that showed a tangential shortening index of <0.23, we were able to identify the complete or a portion of a macrostructure composed of connected regions in the form of a helical bundle within the left ventricle mass. In this study, we present a representative case that shows the complete morphology of a helical myocardial band as well as two other cases that present ascending and descending portions of the helical myocardial band. Our observation of a helical functional band based on dynamics is in agreement with diffusion tensor MRI observations and gross dissection studies in the arrested heart.     

On the Conservation of the Slow Conformational Dynamics within the Amino Acid Kinase Family: NAGK the Paradigm

N-Acetyl-L-Glutamate Kinase (NAGK) is the structural paradigm for examining the catalytic mechanisms and dynamics of amino acid kinase family members. Given that the slow conformational dynamics of the NAGK (at the microseconds time scale or slower) may be rate-limiting, it is of importance to assess the mechanisms of the most cooperative modes of motion intrinsically accessible to this enzyme. Here, we present the results from normal mode analysis using an elastic network model representation, which shows that the conformational mechanisms for substrate binding by NAGK strongly correlate with the intrinsic dynamics of the enzyme in the unbound form. We further analyzed the potential mechanisms of allosteric signalling within NAGK using a Markov model for network communication. Comparative analysis of the dynamics of family members strongly suggests that the low-frequency modes of motion and the associated intramolecular couplings that establish signal transduction are highly conserved among family members, in support of the paradigm sequence→structure→dynamics→function.     

Structural model of the Ca V 1.2 pore

Understanding the structure and functional mechanisms of voltage-gated calcium channels remains a major task in membrane biophysics. In the absence of three dimensional structures, homology modeling techniques are the method of choice, to address questions concerning the structure of these channels. We have developed models of the open Ca(V)1.2 pore, based on the crystal structure of the mammalian voltage-gated potassium channel K(V)1.2 and a model of the bacterial sodium channel NaChBac. Our models are developed to be consistent with experimental data and modeling criteria. The models highlight major differences between voltage-gated potassium and calcium channels in the P segments, as well as the inner pore helices. Molecular dynamics simulations support the hypothesis of a clockwise domain arrangement and experimental observations of asymmetric calcium channel behavior. In the accompanying paper these models were used to study structural effects of a channelopathy mutation.     

Network Scale Modeling of Lymph Transport and Its Effective Pumping Parameters

The lymphatic system is an open-ended network of vessels that run in parallel to the blood circulation system. These vessels are present in almost all of the tissues of the body to remove excess fluid. Similar to blood vessels, lymphatic vessels are found in branched arrangements. Due to the complexity of experiments on lymphatic networks and the difficulty to control the important functional parameters in these setups, computational modeling becomes an effective and essential means of understanding lymphatic network pumping dynamics. Here we aimed to determine the effect of pumping coordination in branched network structures on the regulation of lymph flow. Lymphatic vessel networks were created by building upon our previous lumped-parameter model of lymphangions in series. In our network model, each vessel is itself divided into multiple lymphangions by lymphatic valves that help maintain forward flow. Vessel junctions are modeled by equating the pressures and balancing mass flows. Our results demonstrated that a 1.5 s rest-period between contractions optimizes the flow rate. A time delay between contractions of lymphangions at the junction of branches provided an advantage over synchronous pumping, but additional time delays within individual vessels only increased the flow rate for adverse pressure differences greater than 10.5 cmH₂O. Additionally, we quantified the pumping capability of the system under increasing levels of steady transmural pressure and outflow pressure for different network sizes. We observed that peak flow rates normally occurred under transmural pressures between 2 to 4 cmH₂O (for multiple pressure differences and network sizes). Networks with 10 lymphangions per vessel had the highest pumping capability under a wide range of adverse pressure differences. For favorable pressure differences, pumping was more efficient with fewer lymphangions. These findings are valuable for translating experimental measurements from the single lymphangion level to tissue and organ scales.     

Four-scale description of membrane sculpting by BAR domains

BAR domains are proteins that sense and sculpt curved membranes in cells, furnishing a relatively well-studied example of mechanisms employed in cellular morphogenesis. We report a computational study of membrane bending by BAR domains at four levels of resolution, described by 1), all-atom molecular dynamics; 2), residue-based coarse-graining (resolving single amino acids and lipid molecules); 3), shape-based coarse-graining (resolving overall protein and membrane shapes); and 4), a continuum elastic membrane model. Membrane sculpting performed by BAR domains collectively is observed in agreement with experiments. Different arrangements of BAR domains on the membrane surface are found to lead to distinct membrane curvatures and bending dynamics.     

Computer modeling of nonlinear heart rate dynamics during train extracardial impulsation in the sinoatrial node

A computer model of excitation conduction in the heart has been employed to study the nonlinear heart rate dynamics under stress loads. The modeling was aimed to test the hypothesis explaining changes in the heart rate dynamics during nociceptive stress loads by the occurrence of train extracardial impulsation arriving at the sinoatrial node. The computer simulation shows that, with a particular set of parameters, the model imitates the dynamics of RR intervals observed in experiments. The present model provides a unified theoretical basis for further simulation of various types of ventricular disturbances under external extreme loads.