Modeling the interference between shear and longitudinal waves under high intensity focused ultrasound propagation in bone.

Magnetic resonance-guided high intensity focused ultrasound (MR-HIFU) is a noninvasive thermal technique that enables rapid heating of a specific area in the human body. Its clinical relevance has been proven for the treatments of soft tissue tumors, like uterine fibroids, and for the treatments of solid tumors in bone. In MR-HIFU treatment, MR-thermometry is used to monitor the temperature evolution in soft tissue. However, this technique is currently unavailable for bone tissue. Computer models can play a key role in the accurate prediction and monitoring of temperature. Here, we present a computer ray tracing model that calculates the heat production density in the focal region. This model accounts for both the propagation of shear waves and the interference between longitudinal and shear waves. The model was first compared with a finite element approach which solves the Helmholtz equation in soft tissue and the frequency-domain wave equation in bone. To obtain the temperature evolution in the focal region, the heat equation was solved using the heat production density generated by the raytracer as a heat source. Then, we investigated the role of the interaction between shear and longitudinal waves in terms of dissipated power and temperature output. The results of our model were in agreement with the results obtained by solving the Helmholtz equation and the frequency-domain wave equation, both in soft tissue and bone. Our results suggest that it is imperative to include both shear waves and their interference with longitudinal waves in the model when simulating high intensity focused ultrasound propagation in solids. In fact, when modeling HIFU treatments, omitting the interference between shear and longitudinal waves leads to an over-estimation of the temperature increase in the tissues.

Visible Blue Light Therapy: Molecular Mechanisms and Therapeutic Opportunities.

BACKGROUND: Visible light is absorbed by photoacceptors in pigmented and non-pigmented mammalian cells, activating signaling cascades and downstream mechanisms that lead to the modulation of cellular processes. Most studies have investigated the molecular mechanisms and therapeutic applications of UV and the red to near infrared regions of the visible spectrum. Considerably less effort has been dedicated to the blue, UV-free part of the spectrum. OBJECTIVE: In this review, we discuss the current advances in the understanding of the molecular photoacceptors, signaling mechanisms, and corresponding therapeutic opportunities of blue light photoreception in non-visual mammalian cells in the context of inflammatory skin conditions. METHODS: The literature was scanned for peer-reviewed articles focusing on the molecular mechanisms, cellular effects, and therapeutic applications of blue light. RESULTS: At a molecular level, blue light is absorbed by flavins, porphyrins, nitrosated proteins, and opsins; inducing the generation of ROS, nitric oxide release, and the activation of G protein coupled signaling. Limited and contrasting results have been reported on the cellular effects of blue light induced signaling. Some investigations describe a regulation of proliferation and differentiation or a modulation of inflammatory parameters; others show growth inhibition and apoptosis. Regardless of the elusive underlying mechanism, clinical studies show that blue light is beneficial in the treatment of inflammatory skin conditions. CONCLUSION: To strengthen the use of blue light for therapeutic purposes, further in depth studies are clearly needed with regard to its underlying molecular and cellular mechanisms, and their translation into clinical applications.

Coarse-grained simulations of poly(propylene imine) dendrimers in solution.

The behavior of poly(propylene imine) (PPI) dendrimers in concentrated solutions has been investigated using molecular dynamics simulations containing up to a thousand PPI dendrimers of generation 4 or 5 in explicit water. To deal with large system sizes and time scales required to study the solutions over a wide range of dendrimer concentrations, a previously published coarse-grained model was applied. Simulation results on the radius of gyration, structure factor, intermolecular spacing, dendrimer interpenetration, and water penetration are compared with available experimental data, providing a clear concentration dependent molecular picture of PPI dendrimers. It is shown that with increasing concentration the dendrimer volume diminishes accompanied by a reduction of internalized water, ultimately resulting in solvent filled cavities between stacked dendrimers. Concurrently dendrimer interpenetration increases only slightly, leaving each dendrimer a separate entity also at high concentrations. Moreover, we compare apparent structure factors, as calculated in experimental studies relying on the decoupling approximation and the constant atomic form factor assumption, with directly computed structure factors. We demonstrate that these already diverge at rather low concentrations, not because of small changes in form factor, but rather because the decoupling approximation fails as monomer positions of separate dendrimers become correlated at concentrations well below the overlap concentration.

Parameter uncertainty in biochemical models described by ordinary differential equations.

Improved mechanistic understanding of biochemical networks is one of the driving ambitions of Systems Biology. Computational modeling allows the integration of various sources of experimental data in order to put this conceptual understanding to the test in a quantitative manner. The aim of computational modeling is to obtain both predictive as well as explanatory models for complex phenomena, hereby providing useful approximations of reality with varying levels of detail. As the complexity required to describe different system increases, so does the need for determining how well such predictions can be made. Despite efforts to make tools for uncertainty analysis available to the field, these methods have not yet found widespread use in the field of Systems Biology. Additionally, the suitability of the different methods strongly depends on the problem and system under investigation. This review provides an introduction to some of the techniques available as well as gives an overview of the state-of-the-art methods for parameter uncertainty analysis.

Combined in vivo and in silico investigations of activation of glycolysis in contracting skeletal muscle.

The hypothesis was tested that the variation of in vivo glycolytic flux with contraction frequency in skeletal muscle can be qualitatively and quantitatively explained by calcium-calmodulin activation of phosphofructokinase (PFK-1). Ischemic rat tibialis anterior muscle was electrically stimulated at frequencies between 0 and 80 Hz to covary the ATP turnover rate and calcium concentration in the tissue. Estimates of in vivo glycolytic rates and cellular free energetic states were derived from dynamic changes in intramuscular pH and phosphocreatine content, respectively, determined by phosphorus magnetic resonance spectroscopy ((31)P-MRS). Computational modeling was applied to relate these empirical observations to understanding of the biochemistry of muscle glycolysis. Hereto, the kinetic model of PFK activity in a previously reported mathematical model of the glycolytic pathway (Vinnakota KC, Rusk J, Palmer L, Shankland E, Kushmerick MJ. J Physiol 588: 1961-1983, 2010) was adapted to contain a calcium-calmodulin binding sensitivity. The two main results were introduction of regulation of PFK-1 activity by binding of a calcium-calmodulin complex in combination with activation by increased concentrations of AMP and ADP was essential to qualitatively and quantitatively explain the experimental observations. Secondly, the model predicted that shutdown of glycolytic ATP production flux in muscle postexercise may lag behind deactivation of PFK-1 (timescales: 5-10 s vs. 100-200 ms, respectively) as a result of accumulation of glycolytic intermediates downstream of PFK during contractions.

A Bayesian approach to targeted experiment design.

MOTIVATION: Systems biology employs mathematical modelling to further our understanding of biochemical pathways. Since the amount of experimental data on which the models are parameterized is often limited, these models exhibit large uncertainty in both parameters and predictions. Statistical methods can be used to select experiments that will reduce such uncertainty in an optimal manner. However, existing methods for optimal experiment design (OED) rely on assumptions that are inappropriate when data are scarce considering model complexity. RESULTS: We have developed a novel method to perform OED for models that cope with large parameter uncertainty. We employ a Bayesian approach involving importance sampling of the posterior predictive distribution to predict the efficacy of a new measurement at reducing the uncertainty of a selected prediction. We demonstrate the method by applying it to a case where we show that specific combinations of experiments result in more precise predictions. AVAILABILITY AND IMPLEMENTATION: Source code is available at: http://bmi.bmt.tue.nl/sysbio/software/pua.html.

An integrated strategy for prediction uncertainty analysis.

MOTIVATION: To further our understanding of the mechanisms underlying biochemical pathways mathematical modelling is used. Since many parameter values are unknown they need to be estimated using experimental observations. The complexity of models necessary to describe biological pathways in combination with the limited amount of quantitative data results in large parameter uncertainty which propagates into model predictions. Therefore prediction uncertainty analysis is an important topic that needs to be addressed in Systems Biology modelling. RESULTS: We propose a strategy for model prediction uncertainty analysis by integrating profile likelihood analysis with Bayesian estimation. Our method is illustrated with an application to a model of the JAK-STAT signalling pathway. The analysis identified predictions on unobserved variables that could be made with a high level of confidence, despite that some parameters were non-identifiable. AVAILABILITY AND IMPLEMENTATION: Source code is available at: http://bmi.bmt.tue.nl/sysbio/software/pua.html.

Unchanged muscle fiber conduction velocity relates to mild acidosis during exhaustive bicycling.

Muscle fiber conduction velocity (MFCV) has often been shown to decrease during standardized fatiguing isometric contractions. However, several studies have indicated that the MFCV may remain constant during fatiguing dynamic exercise. It was investigated if these observations can be related to the absence of a large decrease in pH and if MFCV can be considered as a good indicator of acidosis, also during dynamic bicycle exercise. High-density surface electromyography (HDsEMG) was combined with read-outs of muscle energetics recorded by in vivo (31)P magnetic resonance spectroscopy (MRS). Measurements were performed during serial exhausting bouts of bicycle exercise at three different workloads. The HDsEMG recordings revealed a small and incoherent variation of MFCV during all high-intensity exercise bouts. (31)P MRS spectra revealed a moderate decrease in pH at the end of exercise (~0.3 units down to 6.8) and a rapid ancillary drop to pH 6.5 during recovery 30 s post-exercise. This additional degree of acidification caused a significant decrease in MFCV during cycling immediately after the rest period. From the data a significant correlation between MFCV and [H(+)] ([H(+)] = 10(-pH)) was calculated (p < 0.001, Pearson's R = -0.87). Our results confirmed the previous observations of MFCV remaining constant during fatiguing dynamic exercise. A constant MFCV is in line with a low degree of acidification, considering the presence of a correlation between pH and MFCV after further increasing acidification.

Single-variable reaction systems: deterministic and stochastic models.

Biochemical reaction networks are often described by deterministic models based on macroscopic rate equations. However, for small numbers of molecules, intrinsic noise can play a significant role and stochastic methods may thus be required. In this work, we analyze the differences and similarities between a class of macroscopic deterministic models and corresponding mesoscopic stochastic models. We derive expressions that provide a clear and intuitive view upon the behavior of the stochastic model. In particular, these expressions show the dependence of both the dynamics and the stationary distribution of the stochastic model on the number of molecules in the system. As expected, most properties of the stochastic model correspond well with those in the deterministic model if the number of molecules is large enough. However, for some properties, both models are inconsistent, even if the number of molecules in the stochastic model tends to infinity. Throughout this paper, we use a bistable autophosphorylation cycle as a running example. For such a bistable system, we give an explicit proof that the rate of convergence to the stationary distribution (or the second eigenvalue of the transition matrix) depends exponentially on the number of molecules.

Computing the stochastic dynamics of phosphorylation networks.

Cells of all organisms share the ability to respond to various extracellular signals. Depending on the cell type and the organism, these signals may include hormones secreted by other cells or changes in nutrient concentrations. The signals are processed by an intricate network of protein-protein interactions, including phosphorylation and de-phosphorylation events. As some signaling proteins are only present in low concentrations, random fluctuations may affect the dynamics of the network. The mathematical modeling of networks with significant random fluctuations requires the use of stochastic methods. The stochastic dynamics of a chemical reaction system are described by the Chemical Master Equation. Often the numerical evaluation of this equation is problematic. The first problem is that many systems have an infinite number of possible states; leaving simulations of individual trajectories as the only alternative. To circumvent this problem, we focus on a class of systems that have a finite state space. More specifically, we focus on networks of phosphorylation cycles without taking into account the synthesis and degradation of proteins. The second problem is that memory requirements cause a practical limit to the size of systems that can be evaluated. In this paper, we discuss how these limitations can be overcome using parallel computation and methods dealing efficiently with the available memory. These methods were implemented in a parallel C++ program. We discuss two networks for which the stochastic dynamics were evaluated using this program: a single phosphorylation cycle and an oscillating MAP-kinase cascade.

Speckle-initialized dynamic segmentation of the prostate.

Echography is a commonly used modality for prostate imaging. Prostate segmentation is the first step in analyzing echographic prostate images. Because of the nature of these images, traditional local image processing operators are inadequate for finding the prostate boundary. Most automated segmentations described in literature require user interaction for contour initializing or editing. Also shape templates are applied as prior knowledge. In this paper, an automatic segmentation method is presented, based on prostate specific image granulation and image intensity. First, a granulation detector is used to extract granulation. Subsequently, the Hessian is adopted to evaluate granulation shape and intensity for the extraction of the prostate-specific dot pattern. This dot pattern is used to construct the contour initialization. A smooth contour model (discrete dynamic contour; DDC) is evolved from this initialization to the final contour. The guiding vector field for the DDC deformation is the gradient vector flow field calculated from an edge map of the original image. The scale of the relevant edges (large compared to granulation) is estimated from the prostate-specific dot pattern. Comparison of automated segmentations with clinical expert manual segmentations reveals a mean sensitivity and accuracy of 0.90 and 0.93, respectively.

Vesicle deformation by draining: geometrical and topological shape changes.

A variety of factors, including changes in temperature or osmotic pressure, can trigger morphological transitions of vesicles. Upon osmotic upshift, water diffuses across the membrane in response to the osmotic difference, resulting in a decreased vesicle volume to membrane area ratio and, consequently, a different shape. In this paper, we study the vesicle deformations on osmotic deflation using coarse grained molecular dynamics simulations. Simple deflation of a spontaneously formed spherical vesicle results in oblate ellipsoid and discous vesicles. However, when the hydration of the lipids in the outer membrane leaflet is increased, which can be the result of a changed pH or ion concentration, prolate ellipsoid, pear-shaped and budded vesicles are formed. Under certain conditions the deflation even results in vesicle fission. The simulations also show that vesicles formed by a bilayer to vesicle transition are, although spontaneously formed, not immediately stress-free. Instead, the membrane is stretched during the final stage of the transition and only reaches equilibrium once the excess interior water has diffused across the membrane. This suggests the presence of residual membrane stress immediately after vesicle closure in experimental vesicle formation and is especially important for MD simulations of vesicles where the time scale to reach equilibrium is out of reach.

Computing algebraic functions with biochemical reaction networks.

In biological organisms, networks of chemical reactions control the processing of information in a cell. A general approach to study the behavior of these networks is to analyze common modules. Instead of this analytical approach to study signaling networks, we construct functional motifs from the bottom up. We formulate conceptual networks of biochemical reactions that implement elementary algebraic operations over the domain and range of positive real numbers. We discuss how the steady state behavior relates to algebraic functions, and study the stability of the networks' fixed points. The primitive networks are then combined in feed-forward networks, allowing us to compute a diverse range of algebraic functions, such as polynomials. With this systematic approach, we explore the range of mathematical functions that can be constructed with these networks.

Computational modelling identifies the impact of subtle anatomical variations between amphibian and mammalian skeletal muscle on spatiotemporal calcium dynamics.

The physical sites of calcium entry and exit in the skeletal muscle cell are distinct and highly organised in space. It was investigated whether the highly structured spatial organisation of sites of Ca(2+) release, uptake and action in skeletal muscle cells substantially impacts the dynamics of cytosolic Ca(2+) handling and thereby the physiology of the cell. Hereto, the spatiotemporal dynamics of the free calcium distribution in a fast-twitch (FT) muscle sarcomere was studied using a reaction-diffusion computational model for two genotypes with known anatomical differences. A computational model of a murine FT muscle sarcomere is developed, de novo including a closed calcium mass balance to simulate spatiotemporal high stimulation frequency calcium dynamics at 35 degrees C. Literature data on high-frequency calcium dye measurements were used as a first step towards model validation. The murine and amphibian sarcomere models were phenotypically distinct to capture known differences in positions of troponin C, actin-myosin overlap and calcium release within the sarcomere between frog and mouse. The models predicted large calcium gradients throughout the myoplasm as well as differences in calcium concentrations near the mitochondria of frog and mouse. Furthermore, the predicted Ca(2+) concentration was high at positions where Ca(2+) has a regulatory function, close to the mitochondria and troponin C.

Modeling glucose and water dynamics in human skin.

BACKGROUND: Glucose is heterogeneously distributed in the different physiological compartments in the human skin. Therefore, for the development of a noninvasive measurement method, both a good quantification of the different compartments of human skin and an understanding of glucose transport processes are important. METHODS: The composition of human skin was quantified by histology research. Based on this information a mathematical model was developed to simulate glucose dynamics in human skin. RESULTS: The model predicts dynamically glucose concentrations in the different layers of the skin as a result of changes in blood glucose concentration. The model was validated with published time course data of blood and interstitial fluid glucose during a clamp study with three different set points for blood glucose, and model outcomes were compared to measurements for the lag time and gradient. According to the model, glucose in the interstitial fluid of the dermis best matches the amplitude and dynamics of blood glucose. CONCLUSIONS: The new data obtained from quantitative histology appeared crucial for the model. The proposed model was successfully validated. This result was obtained without tuning or fitting of any parameter. It was shown how the model can be used to set standards for measurements and to define the best measurement depth for noninvasive glucose monitoring.

Lipid-based mechanisms for vesicle fission.

Shape transformations and topological changes of lipid vesicles, such as fusion, budding, and fission, have important chemical physical and biological significance. In this paper, we study the fission process of lipid vesicles. Two distinct routes are considered that are both based on an asymmetry of the lipid distribution within the membrane. This asymmetry consists of a nonuniform distribution of two types of lipids. In the first mechanism, the two types of lipids are equally distributed over both leaflets of the membrane. Phase separation of the lipids within both leaflets, however, results in the formation of rafts, which form buds that can split off. In the second mechanism, the asymmetry consists of a difference in composition between the two monolayers of the membrane. This difference in composition yields a spontaneous curvature, reshaping the vesicle into a dumbbell such that it can split. Both pathways are studied with molecular dynamics simulations using a coarse-grained lipid model. For each of the pathways, the conditions required to obtain complete fission are investigated, and it is shown that for the second pathway, much smaller differences between the lipids are needed to obtain fission than for the first pathway. Furthermore, the lipid composition of the resulting split vesicles is shown to be completely different for both pathways, and essential differences between the fission pathway and the pathway of the inverse process, i.e., fusion, are shown to exist.

Vesicle shapes from molecular dynamics simulations.

Lipid bilayer membranes are known to form various structures such as large sheets or vesicles. When the two leaflets of the bilayer have an equal composition, the membrane preferentially forms a flat sheet or a spherical vesicle. However, a difference in the composition of the two leaflets may result in a curved bilayer or in a wide variety of vesicle shapes. Vesicles with different shapes have already been shown in experiments and diverse vesicle shapes have been predicted theoretically from energy minimization of continuous curves. Here we present a molecular dynamics study of the effect of small changes in the phospholipid headgroups on the spontaneous curvature of the bilayer and on the resulting vesicle shape transformations. Small asymmetries in the bilayers already result in high spontaneous curvature and large vesicle deformations. Vesicle shapes that are formed include ellipsoids, discoids, pear-shaped vesicles, cup-shaped vesicles, as well as budded vesicles. Comparison of these vesicles with theoretically derived vesicle shapes shows both resemblances and differences.

Computational model of excitable cell indicates ATP free energy dynamics in response to calcium oscillations are undampened by cytosolic ATP buffers.

Mitochondria in excitable cells are recurrently exposed to pulsatile calcium gradients that activate cell function. Rapid calcium uptake by the mitochondria has previously been shown to cause uncoupling of oxidative phosphorylation. To test (i) if periodic nerve firing may cause oscillation of the cytosolic thermodynamic potential of ATP hydrolysis and (ii) if cytosolic adenylate (AK) and creatine kinase (CK) ATP buffering reactions dampen such oscillations, a lumped kinetic model of an excitable cell capturing major aspects of the physiology has been developed. Activation of ATP metabolism by low-frequency calcium pulses caused large oscillation of the cytosolic, but not mitochondrial ATP/ADP, ratio. This outcome was independent of net ATP synthesis or hydrolysis during mitochondrial calcium uptake. The AK/CK ATP buffering reactions dampened the amplitude and rate of cytosolic ATP/ADP changes on a timescale of seconds, but not milliseconds. These model predictions suggest that alternative sources of capacitance in neurons and striated muscles should be considered to protect ATP-free energy-driven cell functions.

Coarse-grained transmembrane proteins: hydrophobic matching, aggregation, and their effect on fusion.

Molecular transport between organelles is predominantly governed by vesicle fission and fusion. Unlike experimental vesicles, the fused vesicles in molecular dynamics simulations do not become spherical readily, because the lipid and water distribution is inappropriate for the fused state and spontaneous amendment is slow. Here, we study the hypothesis that enhanced transport across the membrane of water, lipids, or both is required to produce spherical vesicles. This is done by adding several kinds of model proteins to fusing vesicles. The results show that equilibration of both water and lipid content is a requirement for spherical vesicles. In addition, the effect of these transmembrane proteins is studied in bilayers and vesicles, including investigations into hydrophobic matching and aggregation. Our simulations show that the level of aggregation does not only depend on hydrophobic mismatch, but also on protein shape. Additionally, one of the proteins promotes fusion by inducing pore formation. Incorporation of these proteins allows even flat membranes to fuse spontaneously. Moreover, we encountered a novel spontaneous vesicle enlargement mechanism we call the engulfing lobe, which may explain how lipids added to a vesicle solution are quickly incorporated into the inner monolayer.

A detailed look at vesicle fusion.

Many different hypotheses on the molecular mechanisms of vesicle fusion exist. Because these mechanisms cannot be readily asserted experimentally, we address the problem by a coarse-grained molecular dynamics simulations study and compare the results with the results of other techniques. The simulations performed include the fusion of small and large vesicles and exocytosis, i.e., the fusion of small vesicles with flat bilayers. We demonstrate that the stalk, the initial contact between two fusing vesicles, is initiated by lipid tails that extend spontaneously. The stalk is revealed to be composed of the contacting monolayers only, yet without hydrophobic voids. Anisotropic and radial expansion of the stalk have been theorized; we show that stalk evolution can proceed via both pathways starting from similar setups and that water triggers the transition from elongated stalk to hemifusion diaphragm.