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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The bilayer-vesicle transition is entropy driven.

Self-assembled bilayer membranes have a remarkable inclination to form closed shells or vesicles. This bilayer-vesicle transition has been shown experimentally and by various kinds of computer simulation techniques. Here we study this transition using coarse-grained molecular dynamics. The advantage of this simulation technique is that it allows for a detailed analysis of the transition, such as changes of the internal energy. Generally it is assumed that the bilayer-vesicle transition is driven by minimization of the edge energy. However, our simulations, which include solvent particles, show an increase in the potential energy of the system during the transition, implicating that the transition is not energy but entropy driven.

Molecular dynamics study of the influence of wall-gas interactions on heat flow in nanochannels.

Especially at the nanometer scale interfaces play an important role. The effect of the wettability on the solid-liquid interface has already been studied with molecular dynamics. In this paper we study the dependence of wetting on the solid-gas interface for different density gases and investigate the influence of wetting on the heat transport properties over such an interface using molecular dynamics. Subsequently we show how the flow profile of a gas flowing along a surface also depends on this wettability. These simulations show that wettability increases the conductivity of a solid to a stationary gas and decreases the flow velocity near the interface for a gas flow. These two effects influence the cooling of a solid achieved by a cold gas flowing along its surface in opposite ways. However, we show that a higher wettability has a positive net effect on the cooling, explaining experimental results that showed an increased heat cooling effect of hydrophilic over hydrophobic microchannels.

Hybrid method coupling molecular dynamics and Monte Carlo simulations to study the properties of gases in microchannels and nanochannels.

We combine molecular dynamics (MD) and Monte Carlo (MC) simulations to study the properties of gas molecules confined between two hard walls of a microchannel or nanochannel. The coupling between MD and MC simulations is introduced by performing MD near the boundaries for accuracy and MC in the bulk because of the low computational cost. We characterize the influence of different densities and molecule sizes on the equilibrium properties of the gas in the microchannel. The effect of the particle size on the simulation results is very small in the case of a dilute gas and increases with the density. The hybrid MD-MC simulation method is validated by comparing the results for density and temperature profiles with those of pure MD and pure MC simulations. These results compare well for pure MD and pure MC, as well as hybrid MD-MC, both in the bulk and near the boundaries, when hard-sphere interactions are used. When Lennard-Jones potentials are used to accurately model the interactions between the gas and wall molecules instead, the results of pure MD simulations differ significantly from the pure MC simulations near the boundaries, but the results of the hybrid method compare well with the pure MD results near the wall, and with the pure MC and pure MD results in the middle of the channel. The hybrid method also very accurately simulates the interface between the MD and MC simulation domains. Comparisons between MD, MC, and hybrid MD-MC computational costs are outlined. The speedup when using 50% of the domain for MD simulations and 50% for MC simulations is very small compared to pure MD simulations times, but this speedup increases drastically for more realistic situations where the region near the wall is small compared to the bulk region.

Transient behavior in single-file systems.

We have used Monte Carlo methods and analytical techniques to investigate the influence of the characteristics, such as pipe length, diffusion, adsorption, desorption, and reaction rates on the transient properties of single-file systems. The transient or the relaxation regime is the period in which the system is evolving to equilibrium. We have studied the system when all the sites are reactive and also when only some of them are reactive. Comparisons between mean-field predictions, cluster approximation predictions, and Monte Carlo simulations for the relaxation time of the system are shown. We outline the cases where the mean-field analysis gives good results compared to dynamic Monte Carlo results. For some specific cases we can analytically derive the relaxation time. Occupancy profiles for different distributions of the sites both for the mean field and simulations are compared. Different results for slow and fast reaction systems and different distributions of reactive sites are discussed.

Steady-state properties of single-file systems with conversion.

We have used Monte Carlo methods and analytical techniques to investigate the influence of the characteristic parameters, such as pipe length, diffusion, adsorption, desorption, and reaction rate constants on the steady-state properties of single-file systems with a reaction. We looked at cases when all the sites are reactive and when only some of them are reactive. Comparisons between mean-field predictions and Monte Carlo simulations for the occupancy profiles and reactivity are made. Substantial differences between mean-field and the simulations are found when rates of diffusion are high. Mean-field results only include single-file behavior by changing the diffusion rate constant, but it effectively allows passing of particles. Reactivity converges to a limit value if more reactive sites are added: sites in the middle of the system have little or no effect on the kinetics. Occupancy profiles show approximately exponential behavior from the ends to the middle of the system.

Infinitely fast diffusion in single-file systems.

We have used dynamic Monte Carlo(DMC) methods and analytical techniques to analyze single-file systems for which diffusion is infinitely fast. We have simplified the master equation removing the fast reactions, and we have introduced a DMC algorithm for infinitely fast diffusion. The DMC method for fast diffusion give similar results as the standard DMC with high diffusion rates. We have investigated the influence of characteristic parameters, such as pipe length, adsorption, desorption, and conversion rate constants on the steady-state properties of single-file systems with a reaction, looking at cases when all the sites are reactive and when only some of them are reactive. We find that the effect of fast diffusion on single-file properties of the system is absent even when diffusion is infinitely fast. Diffusion is not important in these systems. Smaller systems are less reactive and the occupancy profiles for infinitely long systems show an exponential behavior.

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.