A comparison of model linear chain molecules with constrained and flexible bond lengths under planar Couette and extensional flows

We compare directly under flow two commonly used coarse grained models of linear polymers, namely the flexible finitely extensible nonlinear elastic (FENE) chain, and the freely jointed tangent sphere chain, otherwise known as the freely jointed chain. The comparison is based on viscometric, structural and dynamical properties. We use non-equilibrium molecular dynamics to simulate steady-state systems under planar Couette flow and planar extensional flow. Computed properties include shear and elongational viscosities, normal stresses, radius of gyration and end-to-end distances, order parameters, alignment angles and spin angular velocities. In all computed properties we observe very little difference between the two molecular models. Therefore, the choice of either model is suitable, though there is a computational advantage in the use of the FENE model.     

Effects of chain unsaturation on the equation of state for lipid monolayers at the air-water interface.

An equation of state for lipid monolayers at the air-water interface is presented, which takes into account the effects of the conformation and the number and position of double bonds of the hydrocarbon chains. The total Hamiltonian of the monolayer is assumed to consist of three terms. Two of them are calculated exactly within the limitations of the formulation. These are the two-dimensional entropy of mixing of the lipid and water molecules at the surface and the conformational entropy of the chains using a model available from the literature. These two terms give rise to positive surface pressure. The third term, which includes all energies that are not amenable to calculation, was obtained as the difference between the sum of the two calculated terms and experimental data and is found to represent an approximately area-independent tension. The effects of chain unsaturation on the equation of state were modeled in the present theory in two ways; the chain bend caused by cis double bonds increases the minimal molecular area, and the double bond linkage on a chain decreases the degrees of freedom of the chain. Calculations revealed that the former is highly significant whereas the latter is negligible. The deduced equation of state reproduces experimental data with appropriate values for three parameters, which represent the collapse area, the overlap of adjacent chains, and the combined effects of the intra- and intermolecular interactions other than the surface mixing entropy and the chain conformational energy.     

Simulation of upper airway occlusion without and with mandibular advancement in obstructive sleep apnea using fluid-structure interaction

Obstructive Sleep Apnea (OSA) is a common sleep disorder characterized by repetitive collapse of the upper airway (UA). One treatment option is a mandibular advancement splint (MAS) which protrudes the lower jaw, stabilizing the airway. However not all patients respond to MAS therapy and individual effects are not well understood. Simulations of airway behavior may represent a non-invasive means to understand OSA and individual treatment responses. Our aims were (1) to analyze UA occlusion and flow dynamics in OSA using the fluid structure interaction (FSI) method, and (2) to observe changes with MAS. Magnetic resonance imaging (MRI) scans were obtained at baseline and with MAS in a known treatment responder. Computational models of the patients' UA geometry were reconstructed for both conditions. The FSI model demonstrated full collapse of the UA (maximum 5.83 mm) pre-treatment (without MAS). The UA collapse was located at the oropharynx with low oropharyngeal pressure (−51.18 Pa to −39.08 Pa) induced by velopharyngeal jet flow (maximum 10.0 m/s). By comparison, simulation results from the UA with MAS, showed smaller deformation (maximum 2.03 mm), matching the known clinical response. Our FSI modeling method was validated by physical experiment on a 1:1 flexible UA model fabricated using 3D steriolithography. This is the first study of airflow dynamics in a deformable UA structure and inspiratory flow. These results expand on previous UA models using computational fluid dynamics (CFD), and lay a platform for application of computational models to study biomechanical properties of the UA in the pathogenesis and treatment of OSA.     

Protein structural variation in computational models and crystallographic data

Normal mode analysis offers an efficient way of modeling the conformational flexibility of protein structures. We use anisotropic displacement parameters from crystallography to test the quality of prediction of both the magnitude and directionality of conformational flexibility. Normal modes from four simple elastic network model potentials and from the CHARMM force field are calculated for a data set of 83 diverse, ultrahigh-resolution crystal structures. While all five potentials provide good predictions of the magnitude of flexibility, all-atom potentials have a clear edge at prediction of directionality, and the CHARMM potential has the highest prediction quality. The low-frequency modes from different potentials are similar, but those computed from the CHARMM potential show the greatest difference from the elastic network models. The comprehensive evaluation demonstrates the costs and benefits of using normal mode potentials of varying complexity.     

Discrimination of near-native protein structures from misfolded models by empirical free energy functions

Free energy potentials, combining molecular mechanics with empirical solvation and entropic terms, are used to discriminate native and near-native protein conformations from slightly misfolded decoys. Since the functional forms of these potentials vary within the field, it is of interest to determine the contributions of individual free energy terms and their combinations to the discriminative power of the potential. This is achieved in terms of quantitative measures of discrimination that include the correlation coefficient between RMSD and free energy, and a new measure labeled the minimum discriminatory slope (MDS). In terms of these criteria, the internal energy is shown to be a good discriminator on its own, which implies that even well-constructed decoys are substantially more strained than the native protein structure. The discrimination improves if, in addition to the internal energy, the free energy expression includes the electrostatic energy, calculated by assuming non-ionized side chains, and an empirical solvation term, with the classical atomic solvation parameter model providing slightly better discrimination than a structure-based atomic contact potential. Finally, the inclusion of a term representing the side chain entropy change, and calculated by an established empirical scale, is so inaccurate that it makes the discrimination worse. It is shown that both the correlation coefficient and the MDS value (or its dimensionless form) are needed for an objective assessment of a potential, and that together they provide much more information on the origins of discrimination than simple inspection of the RMSD-free energy plots.     

Computer Modelling of Elastic Properties of LaF3 Using Free Energy Minimisation Techniques

An effective use of computer simultion methods in the study of solids depends on the derivation of reliable potential models. Hence, the empirically derived interionic potentials of LaF₃ were tested by free energy minimisation techniques, within the quasi-harmonic approximation. This was achieved by calculating the temperature variation of elastic constants derived directly from the shell model potentials. These changes agree reasonably well with those calculated from an experimental lattice expansion, below 800 K. However, the departure from linearity and experimental results occur in the range 800–1100 K, which is below the transition temperature to the state of high ionic conductivity. This shows how far the fitted shell model potentials can reliably predict the elastic behaviour of LaF₃.     

Direct visualizations of air flow in the human upper airway using in-vitro models

A better understanding of airflow characteristics in the upper airway(UA) is crucial in investigating obstructive sleep apnea(OSA), particle sedimentation, drug delivery, and many biomedical problems. Direct visualization of air flow patterns in in-vitro models with realistic anatomical structures is a big challenge. In this study, we constructed unique half-side transparent physical models of normal UA based on realistic anatomical structures. A smoke-wire method was developed to visualize the air flow in UA models directly. The results revealed that the airflow through the pharynx was laminar but not turbulent under normal inspiration, which suggested that compared with turbulent models, a laminar model should be more suitable in numerical simulations. The flow predicted numerically using the laminar model was consistent with the observations in the physical models. The comparison of the velocity fields predicted numerically using the half-side and complete models confirmed that it was reasonable to investigate the flow behaviors in UA using the half-side model. Using the laminar model, we simulated the flow and evaluated the effects of UA narrowing caused by rostral fluid shift on pharyngeal resistance. The results suggested that fluid shift could play an important role in the formation of hypopnea or OSA during sleep.     

Using the Unfolded State as the Reference State Improves the Performance of Statistical Potentials

Distance-dependent statistical potentials are an important class of energy functions extensively used in modeling protein structures and energetics. These potentials are obtained by statistically analyzing the proximity of atoms in all combinatorial amino-acid pairs in proteins with known structures. In model evaluation, the statistical potential is usually subtracted by the value of a reference state for better selectivity. An ideal reference state should include the general chemical properties of polypeptide chains so that only the unique factors stabilizing the native structures are retained after calibrating on reference state. However, reference states available as of this writing rarely model specific chemical constraints of peptide bonds and therefore poorly reflect the behavior of polypeptide chains. In this work, we proposed a statistical potential based on unfolded state ensemble (SPOUSE), where the reference state is summarized from the unfolded state ensembles of proteins produced according to the statistical coil model. Due to its better representation of the features of polypeptides, SPOUSE outperforms three of the most widely used distance-dependent potentials not only in native conformation identification, but also in the selection of close-to-native models and correlation coefficients between energy and model error. Furthermore, SPOUSE shows promising possibility of further improvement by integration with the orientation-dependent side-chain potentials.     

Monte carlo simulations of protein-like heteropolymers.

Properties of a simple model of polypeptide chains were studied by the means of the Monte Carlo method. The chains were built on the (310) hybrid lattice. The residues interacted with long-range potential. There were two kinds of residues: hydrophobic and hydrophilic forming a typical helical pattern -HHPPHPP-. Short range potential was used to prefer helical conformations of the chain. It was found that at low temperatures the model chain formes dense and partially ordered structures (non-unique). The presence of the local potential led to an increase of helicity. The effect of the interplay between the two potentials was studied. After the collapse of the chain further annealing caused rearrangement of helical structures. Dynamic properties of the chain at low temperature depended strongly on the local chain ordering.     

Intrinsic atomic-level forces in polymer networks exhibiting non-gaussian effects: relationship with the limited chain extensibility

Intrinsic atomic-level forces for networks exhibiting non-Gaussian effects were evaluated during the integration of the equations of motion using the Verlet algorithm. The forces acting on the junction points of the cross-linking chains and the elastomeric chains of unimodal and bimodal network arrangements showed no apparent change as a consequence of the network variation. The forces acting on the short chains in a bimodal network cross-linked using sulfur atoms and relatively long polyquinone chains had much higher values than those in a unimodal network arrangement. Nevertheless, the intrinsic forces acting on the polyquinone atoms decreased dramatically as a result of the formation of bimodal networks. The presence of relatively long polyquinone chains in bimodal networks caused the short sulfur chains to stretch to their maximum extensibility and they can no longer increase their end-to-end separation by simple rotations about their skeletal bonds. Limited chain extensibility of the short chains resulting from the deformation of the bond angles and bond lengths led to much higher potential energies, as determined using the dynamic quenching technique. This resulted in the non-Gaussian effects known for bimodal networks and their subsequent anomalous mechanical properties. The dynamical behavior of the nuclei bending and torsional angles was also investigated for the unimodal and bimodal networks.     

Mutational and structural-based analyses of the osmolyte effect on protein stability

It is known that several naturally occurring substances known as osmolytes increase the conformational stability of proteins. Bolen and co-worker proposed the osmophobic theory, which asserts the osmolyte effect occurs because of an unfavorable interaction of osmolytes mainly with the protein backbone, based on the results on the transfer Gibbs energy of amino acids (Deltag) [Bolen and Baskakov (2001) J. Mol. Biol. 310, 955-963]. In this paper, we report the effect of sarcosine on the conformational stability (DeltaG) of RNase Sa (96 residues and one disulfide bond) and four mutant proteins. The thermal denaturation curves for RNase Sa in sarcosine fitted a two-state model on nonlinear least-squares analysis. All the RNase Sa proteins were stabilized by sarcosine. For example, the increase in stability of the wild-type protein in 4 M sarcosine due to the osmolyte effect (Delta(o)DeltaG) is 3.2 kcal/mol. Mutational analysis of the osmolyte effect indicated that the changed Delta(o)DeltaG values upon mutation (Delta(m)Delta(o)DeltaG), as estimated from the Deltag values, are similar to the experimental values. Structural-based analysis of the osmolyte effect was also performed using model denatured structures: (a) a fully extended model (single chain) with no disulfide bond, (b) two-part, unfolded models (two chains) with a disulfide bond constructed through molecular dynamic (MD) simulation, and (c) a two-part, folded model (two chains). The two-part, unfolded models were expected to be more suitable as denatured structures. The Delta(o)DeltaG values calculated using the two-part, unfolded models were more consistent with experimental values than those calculated using the fully extended and two-part, folded models. This suggests that MD simulation is useful for testing denatured structures. These results indicate that the osmophobic theory can explain the osmolyte effect on protein stability.     

Scaling behaviour of different polymer models in dissipative particle dynamics of unentangled melts

We present a dissipative particle dynamics (DPD) study of scaling behaviour for three polymer models. The scaling behaviour is explored for the conformational and dynamic properties of unentangled polymer melts. DPD employs a bead–spring model together with an aggressive coarse-graining to represent polymers at the mesoscale. The first model studied utilises a simple soft repulsion potential for the bead–bead interactions together with a harmonic spring potential to connect beads into a polymer chain. The second model differs from the first model by replacing the harmonic spring with a finitely extensible nonlinear elastic spring. The third model uses realistic coarse-grain potentials for the bead–bead, spring and bending interactions based on the iterative Boltzmann inversion procedure and it corresponds to a mesoscopic model of polyethylene. We systematically vary the chain length and spring constant (in the case of the first and second models), and simulate the conformational properties such as the end-to-end distance or radius of gyration, and dynamic properties such as the centre-of-mass self-diffusion coefficient or viscosity. The scaling of the conformational and dynamic properties with chain length (scaling laws) is compared with the Rouse theory, which is considered as a standard theory for unentangled polymer melts. The comparison shows that simulated scaling laws typically agree with the Rouse scaling laws for the DPD polymer models with more than 10 DPD beads. For the shorter DPD polymers, deviations from the Rouse theory exist and become significant for the dynamic properties, especially for the viscosity of the polymer melts.     

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.     

Propagation of action potentials between parallel chains of cardiac muscle cells in PSpice simulation

Propagation of action potentials between parallel chains of cardiac muscle cells was simulated using the PSpice program. Excitation was transmitted from cell to cell along a strand of three or four cells not connected by low-resistance tunnels (gap-junction connexons) in parallel with one or two similar strands. Thus, two models were used: a 2 x 3 model (two parallel chains of three cells each) and a 3 x 4 model (three parallel chains of four cells each). The entire surface membrane of each cell fired nearly simultaneously, and nearly all the propagation time was spent at the cell junctions, thus giving a staircase-shaped propagation profile. The junctional delay time between contiguous cells in a chain was about 0.2-0.5 ms. A significant negative cleft potential develops in the narrow junctional clefts, whose magnitude depends on several factors, including the radial cleft resistance (Rjc). The cleft potential (Vjc) depolarizes the postjunctional membrane to threshold by a patch-clamp action. Therefore, one mechanism for the transfer of excitation from one cell to the next is by the electric field (EF) that is generated in the junctional cleft when the prejunctional membrane fires. Propagation velocity increased with elevation of Rjc. With electrical stimulation of the first cell of the first strand (cell A1), propagation rapidly spread down that chain and then jumped to the second strand (B chain), followed by jumping to the third strand (C chain) when present. The rapidity by which the parallel chains became activated depended on the longitudinal resistance of the narrow extracellular cleft between the parallel strands (Rol2). The higher the Rol2 resistance, the faster the propagation (lower propagation time) over the cardiac muscle sheet (2-dimensional). The transverse resistance of the cleft had no effect. When the first cell of the second strand (cell B1) was stimulated, propagation spread down the B chain and jumped to the other two strands (A and C) nearly simultaneously. When cell C1 was stimulated, propagation traveled down the C chain and jumped to the B chain, followed by excitation of the A chain. Thus, there was transverse propagation of excitation as longitudinal propagation was occurring. Therefore, transmission of excitation by the EF mechanism can occur between myocardial cells lying closely parallel to one another without the requirement of a specialized junction.     

Functional imaging using computational fluid dynamics to predict treatment success of mandibular advancement devices in sleep-disordered breathing

Mandibular advancement devices (MADs) have emerged as a popular alternative for the treatment of sleep-disordered breathing. These devices bring the mandibula forward in order to increase upper airway (UA) volume and prevent total UA collapse during sleep. However, the precise mechanism of action appears to be quite complex and is not yet completely understood; this might explain interindividual variation in treatment success. We examined whether an UA model, that combines imaging techniques and computational fluid dynamics (CFD), allows for a prediction of the treatment outcome with MADs. Ten patients that were treated with a custom-made mandibular advancement device (MAD), underwent split-night polysomnography. The morning after the sleep study, a low radiation dose CT scan was scheduled with and without the MAD. The CT examinations allowed for a comparison between the change in UA volume and the anatomical characteristics through the conversion to three-dimensional computer models. Furthermore, the change in UA resistance could be calculated through flow simulations with CFD. Boundary conditions for the model such as mass flow rate and pressure distributions were obtained during the split-night polysomnography. Therefore, the flow modeling was based on a patient specific geometry and patient specific boundary conditions. The results indicated that a decrease in UA resistance and an increase in UA volume correlate with both a clinical and an objective improvement. The results of this pilot study suggest that the outcome of MAD treatment can be predicted using the described UA model.     

Algorithmic generation of freely jointed hard sphere chains and properties of their inertial tensors

A statistical algorithm, capable of generating a large number of freely jointed hard sphere chains, is presented. This is the first of a series of algorithms being developed to model unfolded proteins by different modes of hard sphere chains. The aim of these studies is to systematically investigate the effects of different factors, such as atomic radii, bond angles, torsion angles, chain length, etc., on the conformation of unfolded proteins and other random polymers. As continuous models, various types of hard sphere chains enable one to isolate the aforementioned factors one at a time for investigation and thus are advantageous over discrete lattice models. In particular, the freely jointed hard sphere chain model allows one to evaluate the excluded volume effect. As a first step in this endeavor, the average determinant D(N, r) and the average trace T(N, r) of the inertial tensor A of the random chains were calculated at various sphere radii r and chain lengths N. It is found that both the average determinant D(N, r) and the average trace T(N, r) scale linearly with chain length N after logarithmic transformation. However, the critical exponent of D(N, r) increases with r faster than that of T(N, r) as a result of the non-commutativity between the det operator and the average operator < >. The significance of the algorithm and the results obtained on understanding random polypeptide chains are discussed.     

Simulation of deformable models with the Poisson equation

In this paper, we present a new methodology for the deformation of soft objects by drawing an analogy between the Poisson equation and elastic deformation from the viewpoint of energy propagation. The potential energy stored due to a deformation caused by an external force is calculated and treated as the source injected into the Poisson system, as described by the law of conservation of energy. An improved Poisson model is developed for propagating the energy generated by the external force in a natural manner. An autonomous cellular neural network (CNN) model is established by using the analogy between the Poisson equation and CNN to solve the Poisson model for the real-time requirement of soft object deformation. A method is presented to derive the internal forces from the potential energy distribution. The proposed methodology models non-linear materials with the non-linear Poisson equation and thus non-linear CNN, rather than geometric non-linearity. It not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply modifying constitutive coefficients. A haptic virtual reality system has been developed for deformation simulation with force feedback. Examples are presented to demonstrate the efficiency of the proposed methodology.     

Simulation of deformable models with the Poisson equation

In this paper, we present a new methodology for the deformation of soft objects by drawing an analogy between the Poisson equation and elastic deformation from the viewpoint of energy propagation. The potential energy stored due to a deformation caused by an external force is calculated and treated as the source injected into the Poisson system, as described by the law of conservation of energy. An improved Poisson model is developed for propagating the energy generated by the external force in a natural manner. An autonomous cellular neural network (CNN) model is established by using the analogy between the Poisson equation and CNN to solve the Poisson model for the real-time requirement of soft object deformation. A method is presented to derive the internal forces from the potential energy distribution. The proposed methodology models non-linear materials with the non-linear Poisson equation and thus non-linear CNN, rather than geometric non-linearity. It not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply modifying constitutive coefficients. A haptic virtual reality system has been developed for deformation simulation with force feedback. Examples are presented to demonstrate the efficiency of the proposed methodology.