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Signaling in cells is full of noise and, hence, described with stochastic biochemical models. Thus, an efficient computation algorithm for these fluctuating reactions is much needed. Apart from the very popular Monte Carlo simulation, methods based on probability distributions are frequently desired due to their analytical tractability and possible numerical advantages in diverse circumstances, among which the variational approach is the most notable. In this paper, new basis functions are proposed to better depict possibly complex distribution profiles, and an extra regularization scheme is supplied to the variational equation to remove occasional degeneracy-induced singularities during the evolution. The new extension is applied to four typical biochemical reaction models and restores the Gillespie results accurately but with greatly reduced simulation time. This modified variational approach is expected to work in a wide range of cell signaling networks., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Understanding how genetically encoded rules drive and guide complex neuronal growth processes is essential to comprehending the brain's architecture, and agent-based models (ABMs) offer a powerful simulation approach to further develop this understanding. However, accurately calibrating these models remains a challenge. Here, we present a novel application of Approximate Bayesian Computation (ABC) to address this issue. ABMs are based on parametrized stochastic rules that describe the time evolution of small components-the so-called agents-discretizing the system, leading to stochastic simulations that require appropriate treatment. Mathematically, the calibration defines a stochastic inverse problem. We propose to address it in a Bayesian setting using ABC. We facilitate the repeated comparison between data and simulations by quantifying the morphological information of single neurons with so-called morphometrics and resort to statistical distances to measure discrepancies between populations thereof. We conduct experiments on synthetic as well as experimental data. We find that ABC utilizing Sequential Monte Carlo sampling and the Wasserstein distance finds accurate posterior parameter distributions for representative ABMs. We further demonstrate that these ABMs capture specific features of pyramidal cells of the hippocampus (CA1). Overall, this work establishes a robust framework for calibrating agent-based neuronal growth models and opens the door for future investigations using Bayesian techniques for model building, verification, and adequacy assessment., (© 2024. The Author(s).)

We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of variations to derive optimality conditions for continuous time functions. We make no prior assumptions on the form of the mapping from measurements to state-estimate or on the distributions of the noise terms, making the framework more general than Kalman filtering/smoothing where this mapping is assumed to be linear and the noises Gaussian. The optimal solution that arises is interpreted as a continuous time spline, the structure and temporal dependency of which is determined by the system dynamics and the distributions of the process and measurement noise. Similar to Kalman smoothing, the optimal spline yields increased data accuracy at instants when measurements are taken, in addition to providing continuous time estimates outside the measurement instances. We demonstrate the utility and generality of our approach via illustrative examples that render both linear and nonlinear data filters depending on the particular system. Application of the proposed approach to a Monte Carlo simulation exhibits significant performance improvement in comparison to a common existing method., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Kearney, Fardad. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

The United States Environmental Protection Agency (USEPA) Four-step-Method (FSM) is a straightforward and extensively utilized tool for evaluating regional health risks, However, the complex and heterogeneous groundwater environment system causes great uncertainty in the assessment process. Triangular stochastic simulation (TSS) possesses certain advantages in solving uncertainty problems, but its inadequacy with discrete data reveals limitations in this aspect. To solve the above problems, this study proposes to construct trapezoidal fuzzy number-Monte Carlo stochastic simulation (TFN-MCSS) to compensate for the shortcomings of the first two methods. This method adopted trapezoidal fuzzy number (TFN) analysis to comprehensively consider the characteristics of a large dispersion of water quality monitoring data and the uncertainty of the human health risk assessment (HHRA) process. Concurrently, to overcome the subjectivity and uncertainty of artificially determining the interval of TFN in traditional methods, the slope was used to select the most probable interval value (TMPIV) of TFN combined with the α-truncated set technique (α-TST) and MCSS. Based on these, a TFN-MCSS was constructed and applied to groundwater HHRA in western Jilin Province. First, the groundwater chemical characteristic determination and water quality evaluation in western Jilin were performed to identify the main pollution indicators, and the health risk effects of pollutants in groundwater of different aquifers at different time periods on adults and children were evaluated using the TFN-MCSS. The uncertainty and sensitivity were analyzed, and the primary risk control indicators were identified and compared to FSM and TSS. The results reveal that TFN-MCSS was more sensitive to data and could reduce the uncertainty of assessment process. It indicated that over a 10-year period, the health risks associated with unconfined groundwater (UW) and confined water (CW) decreased by greater than 52 %. However, the highest total non-carcinogenic risk index (THI) was 1.3-fold higher than the safety threshold, and this posed a health risk., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier Inc. All rights reserved.)

The dynamics of locally interacting particles that are distributed in space give rise to a multitude of complex behaviours. However the simulation of reaction-diffusion processes which model such systems is highly computationally expensive, the cost increasing rapidly with the size of space. Here, we devise a graph neural network based approach that uses cheap Monte Carlo simulations of reaction-diffusion processes in a small space to cast predictions of the dynamics of the same processes in a much larger and complex space, including spaces modelled by networks with heterogeneous topology. By applying the method to two biological examples, we show that it leads to accurate results in a small fraction of the computation time of standard stochastic simulation methods. The scalability and accuracy of the method suggest it is a promising approach for studying reaction-diffusion processes in complex spatial domains such as those modelling biochemical reactions, population evolution and epidemic spreading., Competing Interests: Declaration of competing interest The authors declare no conflict of interests., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

Purpose: Through introducing stochastic quantities that can be connected to the dimensions of the microscopic structures exposed to radiations, microdosimetry is concerned with the substantive specifications of radiation quality that could help gain insight into radiation effects. Utilizing the μ -randomness method and Geant4-DNA code, we calculated microdosimetry quantities for nanometric structures in a spherical body of water irradiated with protons. To gain more insight into the effects of radiation on microscopic structures and validate the code parameters, we made a comparison between our results obtained within Geant4-DNA and results from other simulations., Materials and Methods: We calculated microdosimetric quantities through irradiating a spherical body of water of 6  μ m diameter with 0.5-100 MeV protons. Microdosimetric quantities were derived for cylinders with diameter × height values of 23 × 23, 50 × 100, and 300 × 300 Å × Å, which would resemble the typical sizes of sub-cellular organisms such as the DNA, nucleosome, and chromatin fiber. We exploited the concept of μ -randomness to introduce convex bodies of random positions and directions for calculating microdosimetric quantities. We used the Geant4-DNA Monte Carlo simulation toolkit for transporting protons and secondary particles and calculating the frequency- and dose-mean lineal and specific energies in cylindrical volumes. Specifically, for same-sized cylindrical volumes, microdosimetric parameters obtained by Nikjoo et al. using the KURBUC code were used for evaluation., Results: For the energy range investigated, the frequency-mean lineal energy, dose-mean lineal energy, frequency-mean specific energy, and dose-mean specific energy vary within [2.34,47.06] (keV/ μ m), [10.40,68.55] (keV/ μ m), [0.04,39.38] × 10 6  cGy, and [0.16,90.29] × 10 6  cGy, respectively. Regardless of the proton energy, our specific-energy results showed higher sensitivity to volume change, for smaller cylinder volumes rather than larger ones. Regardless of both proton energy and volume of the cylinder under study, we observed a generally better agreement between our frequency-mean, than dose-mean, specific energy results and the KURBUC results., Conclusion: Using Geant4-DNA to account for the stochastic nature of energy depositions due to physical interactions between radiation and matter, we calculated microdosimetry parameters concerning proton irradiation. By employing microdosimetry concepts in conjunction with simulation results of our previous work on radiation effects on the DNA, we pinpointed and quantified correlations between microdosimetry parameters and DNA damage. As such, for a volume with comparable mass and mean chord length to the DNA, we could observe the clear correspondence of the mean lineal and specific energy results with the double-strand-break yields of protons in Gy -1 .Gbp -1 .

An overarching theory of chromatography capable of modeling all analyte-stationary phase interactions would enable predictive design of pharmaceutically relevant separations. The stochastic theory of chromatography has been postulated as a suitable basis to achieve this goal. Here, we implement Dondi and Cavazzini's Monte Carlo framework that utilizes experimentally accessible single molecule kinetics and use it to correlate heterogenous adsorption statistics at the stationary phase to shifts in asymmetry. The contributions cannot be captured or modeled through ensemble chemometrics. Simulations reveal that peak asymmetry scales non-linearly with longer analyte-stationary phase interactions and migrates towards symmetry across the column length, even without column overloading., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020. Published by Elsevier B.V.)

Background: Solutions to stochastic Boolean models are usually estimated by Monte Carlo simulations, but as the state space of these models can be enormous, there is an inherent uncertainty about the accuracy of Monte Carlo estimates and whether simulations have reached all attractors. Moreover, these models have timescale parameters (transition rates) that the probability values of stationary solutions depend on in complex ways, raising the necessity of parameter sensitivity analysis. We address these two issues by an exact calculation method for this class of models., Results: We show that the stationary probability values of the attractors of stochastic (asynchronous) continuous time Boolean models can be exactly calculated. The calculation does not require Monte Carlo simulations, instead it uses graph theoretical and matrix calculation methods previously applied in the context of chemical kinetics. In this version of the asynchronous updating framework the states of a logical model define a continuous time Markov chain and for a given initial condition the stationary solution is fully defined by the right and left nullspace of the master equation's kinetic matrix. We use topological sorting of the state transition graph and the dependencies between the nullspaces and the kinetic matrix to derive the stationary solution without simulations. We apply this calculation to several published Boolean models to analyze the under-explored question of the effect of transition rates on the stationary solutions and show they can be sensitive to parameter changes. The analysis distinguishes processes robust or, alternatively, sensitive to parameter values, providing both methodological and biological insights., Conclusion: Up to an intermediate size (the biggest model analyzed is 23 nodes) stochastic Boolean models can be efficiently solved by an exact matrix method, without using Monte Carlo simulations. Sensitivity analysis with respect to the model's timescale parameters often reveals a small subset of all parameters that primarily determine the stationary probability of attractor states.

Purpose: Monte Carlo (MC) simulations are widely used for medical applications and nuclear reaction models are fundamental for the simulation of the particle interactions with patients in ion therapy. Therefore, it is of utmost importance to have reliable models in MC simulations for such interactions. Geant4 is one of the most used toolkits for MC simulation. However, its models showed severe limitations in reproducing the yields measured in the interaction of ion beams below 100 MeV/u with thin targets. For this reason, we interfaced two models, SMF ("Stochastic Mean Field") and BLOB ("Boltzmann-Langevin One Body"), dedicated to simulate such reactions, with Geant4., Methods: Both SMF and BLOB are semi-classical, one-body approaches to solve the Boltzmann-Langevin equation. They include an identical treatment of the mean-field propagation, on the basis of the same effective interaction, but they differ in the way fluctuations are included. Furthermore, we tested a correction to the excitation energy calculated for the light fragments emerging from the simulations and a simple coalescence model., Results: While both SMF and BLOB have been developed to simulate heavy ion interactions, they show very good results in reproducing the experimental yields of light fragments, up to alpha particles, obtained in the interaction of 12 C with a thin carbon target at 62 MeV/u., Conclusions: BLOB in particular gives promising results and this stresses the importance of integrating it into the Geant4 toolkit., (Copyright © 2019 Associazione Italiana di Fisica Medica. All rights reserved.)

Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random number input stream in a simulation procedure by a low-discrepancy number input stream, variance reductions of several orders have been observed in financial applications. Analysis of stochastic effects in well-mixed chemical reaction networks often relies on sample path simulation using Monte Carlo methods, even though these methods suffer from typical slow [Formula: see text] convergence rates as a function of the number of sample paths N. This paper investigates the combination of (randomised) quasi-Monte Carlo methods with an efficient sample path simulation procedure, namely [Formula: see text]-leaping. We show that this combination is often more effective than traditional Monte Carlo simulation in terms of the decay of statistical errors. The observed convergence rate behaviour is, however, non-trivial due to the discrete nature of the models of chemical reactions. We explain how this affects the performance of quasi-Monte Carlo methods by looking at a test problem in standard quadrature.

An adaptive enrichment design is a randomized trial that allows enrollment criteria to be modified at interim analyses, based on a preset decision rule. When there is prior uncertainty regarding treatment effect heterogeneity, these trial designs can provide improved power for detecting treatment effects in subpopulations. We present a simulated annealing approach to search over the space of decision rules and other parameters for an adaptive enrichment design. The goal is to minimize the expected number enrolled or expected duration, while preserving the appropriate power and Type I error rate. We also explore the benefits of parallel computation in the context of this goal. We find that optimized designs can be substantially more efficient than simpler designs using Pocock or O'Brien-Fleming boundaries.

Purpose: Advanced ion beam therapeutic techniques, such as hypofractionation, respiratory gating, or laser-based pulsed beams, have dose rate time structures which are substantially different from those found in conventional approaches. The biological impact of the time structure is mediated through the β parameter in the linear quadratic (LQ) model. The aim of this study was to assess the impact of changes in the value of the β parameter on the treatment outcomes, also accounting for noninstantaneous intrafraction dose delivery or fractionation and comparing the effects of using different primary ions., Methods: An original formulation of the microdosimetric kinetic model (MKM) is used (named MCt-MKM), in which a Monte Carlo (MC) approach was introduced to account for the stochastic spatio-temporal correlations characteristic of the irradiations and the cellular repair kinetics. A modified version of the kinetic equations, validated on experimental cell survival in vitro data, was also introduced. The model, trained on the HSG cells, was used to evaluate the relative biological effectiveness (RBE) for treatments with acute and protracted fractions. Exemplary cases of prostate cancer irradiated with different ion beams were evaluated to assess the impact of the temporal effects., Results: The LQ parameters for a range of cell lines (V79, HSG, and T1) and ion species (H, He, C, and Ne) were evaluated and compared with the experimental data available in the literature, with good results. Notably, in contrast to the original MKM formulation, the MCt-MKM explicitly predicts an ion and LET-dependent β compatible with observations. The data from a split-dose experiment were used to experimentally determine the value of the parameter related to the cellular repair kinetics. Concerning the clinical case considered, an RBE decrease was observed, depending on the dose, ion, and LET, exceeding up to 3% of the acute value in the case of a protraction in the delivery of 10 min. The intercomparison between different ions shows that the clinical optimality is strongly dependent on a complex interplay between the different physical and biological quantities considered., Conclusions: The present study provides a framework for exploiting the temporal effects of dose delivery. The results show the possibility of optimizing the treatment outcomes accounting for the correlation between the specific dose rate time structure and the spatial characteristic of the LET distribution, depending on the ion type used., (© 2017 American Association of Physicists in Medicine.)

We examine the performance of a strategy for Markov chain Monte Carlo (MCMC) developed by simulating a discrete approximation to a stochastic differential equation (SDE). We refer to the approach as diffusion MCMC. A variety of motivations for the approach are reviewed in the context of Bayesian analysis. In particular, implementation of diffusion MCMC is very simple to set-up, even in the presence of nonlinear models and non-conjugate priors. Also, it requires comparatively little problem-specific tuning. We implement the algorithm and assess its performance for both a test case and a glaciological application. Our results demonstrate that in some settings, diffusion MCMC is a faster alternative to a general Metropolis-Hastings algorithm.

Background: Mathematical models are used to gain an integrative understanding of biochemical processes and networks. Commonly the models are based on deterministic ordinary differential equations. When molecular counts are low, stochastic formalisms like Monte Carlo simulations are more appropriate and well established. However, compared to the wealth of computational methods used to fit and analyze deterministic models, there is only little available to quantify the exactness of the fit of stochastic models compared to experimental data or to analyze different aspects of the modeling results., Results: Here, we developed a method to fit stochastic simulations to experimental high-throughput data, meaning data that exhibits distributions. The method uses a comparison of the probability density functions that are computed based on Monte Carlo simulations and the experimental data. Multiple parameter values are iteratively evaluated using optimization routines. The method improves its performance by selecting parameters values after comparing the similitude between the deterministic stability of the system and the modes in the experimental data distribution. As a case study we fitted a model of the IRF7 gene expression circuit to time-course experimental data obtained by flow cytometry. IRF7 shows bimodal dynamics upon IFN stimulation. This dynamics occurs due to the switching between active and basal states of the IRF7 promoter. However, the exact molecular mechanisms responsible for the bimodality of IRF7 is not fully understood., Conclusions: Our results allow us to conclude that the activation of the IRF7 promoter by the combination of IRF7 and ISGF3 is sufficient to explain the observed bimodal dynamics.

Computational protein design depends on an energy function and an algorithm to search the sequence/conformation space. We compare three stochastic search algorithms: a heuristic, Monte Carlo (MC), and a Replica Exchange Monte Carlo method (REMC). The heuristic performs a steepest-descent minimization starting from thousands of random starting points. The methods are applied to nine test proteins from three structural families, with a fixed backbone structure, a molecular mechanics energy function, and with 1, 5, 10, 20, 30, or all amino acids allowed to mutate. Results are compared to an exact, "Cost Function Network" method that identifies the global minimum energy conformation (GMEC) in favorable cases. The designed sequences accurately reproduce experimental sequences in the hydrophobic core. The heuristic and REMC agree closely and reproduce the GMEC when it is known, with a few exceptions. Plain MC performs well for most cases, occasionally departing from the GMEC by 3-4 kcal/mol. With REMC, the diversity of the sequences sampled agrees with exact enumeration where the latter is possible: up to 2 kcal/mol above the GMEC. Beyond, room temperature replicas sample sequences up to 10 kcal/mol above the GMEC, providing thermal averages and a solution to the inverse protein folding problem. © 2016 Wiley Periodicals, Inc., (© 2016 Wiley Periodicals, Inc.)

The Authors present a new methodological approach in stochastic regime to determine the actual costs of an healthcare process. The paper specifically shows the application of the methodology for the determination of the cost of an Assisted reproductive technology (ART) treatment in Italy. The reason of this research comes from the fact that deterministic regime is inadequate to implement an accurate estimate of the cost of this particular treatment. In fact the durations of the different activities involved are unfixed and described by means of frequency distributions. Hence the need to determine in addition to the mean value of the cost, the interval within which it is intended to vary with a known confidence level. Consequently the cost obtained for each type of cycle investigated (in vitro fertilization and embryo transfer with or without intracytoplasmic sperm injection), shows tolerance intervals around the mean value sufficiently restricted as to make the data obtained statistically robust and therefore usable also as reference for any benchmark with other Countries. It should be noted that under a methodological point of view the approach was rigorous. In fact it was used both the technique of Activity Based Costing for determining the cost of individual activities of the process both the Monte Carlo simulation, with control of experimental error, for the construction of the tolerance intervals on the final result.

Preferential attachment is a stochastic process that has been proposed to explain certain topological features characteristic of complex networks from diverse domains. The systematic investigation of preferential attachment is an important area of research in network science, not only for the theoretical matter of verifying whether this hypothesized process is operative in real-world networks, but also for the practical insights that follow from knowledge of its functional form. Here we describe a maximum likelihood based estimation method for the measurement of preferential attachment in temporal complex networks. We call the method PAFit, and implement it in an R package of the same name. PAFit constitutes an advance over previous methods primarily because we based it on a nonparametric statistical framework that enables attachment kernel estimation free of any assumptions about its functional form. We show this results in PAFit outperforming the popular methods of Jeong and Newman in Monte Carlo simulations. What is more, we found that the application of PAFit to a publically available Flickr social network dataset yielded clear evidence for a deviation of the attachment kernel from the popularly assumed log-linear form. Independent of our main work, we provide a correction to a consequential error in Newman's original method which had evidently gone unnoticed since its publication over a decade ago.

Motivation: Fluorescence recovery after photobleaching (FRAP) is a functional live cell imaging technique that permits the exploration of protein dynamics in living cells. To extract kinetic parameters from FRAP data, a number of analytical models have been developed. Simplifications are inherent in these models, which may lead to inexhaustive or inaccurate exploitation of the experimental data. An appealing alternative is offered by the simulation of biological processes in realistic environments at a particle level. However, inference of kinetic parameters using simulation-based models is still limited., Results: We introduce and demonstrate a new method for the inference of kinetic parameter values from FRAP data. A small number of in silico FRAP experiments is used to construct a mapping from FRAP recovery curves to the parameters of the underlying protein kinetics. Parameter estimates from experimental data can then be computed by applying the mapping to the observed recovery curves. A bootstrap process is used to investigate identifiability of the physical parameters and determine confidence regions for their estimates. Our method circumvents the computational burden of seeking the best-fitting parameters via iterative simulation. After validation on synthetic data, the method is applied to the analysis of the nuclear proteins Cdt1, PCNA and GFPnls. Parameter estimation results from several experimental samples are in accordance with previous findings, but also allow us to discuss identifiability issues as well as cell-to-cell variability of the protein kinetics., Implementation: All methods were implemented in MATLAB R2011b. Monte Carlo simulations were run on the HPC cluster Brutus of ETH Zurich., Contact: lygeros@control.ee.ethz.ch or lygerou@med.upatras.gr, Supplementary Information: Supplementary data are available at Bioinformatics online., (© The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.)

Purpose: Accurate radiotherapy dose calculation algorithms are essential to any successful radiotherapy program, considering the high level of dose conformity and modulation in many of today's treatment plans. As technology continues to progress, such as is the case with novel MRI-guided radiotherapy systems, the necessity for dose calculation algorithms to accurately predict delivered dose in increasingly challenging scenarios is vital. To this end, a novel deterministic solution has been developed to the first order linear Boltzmann transport equation which accurately calculates x-ray based radiotherapy doses in the presence of magnetic fields., Methods: The deterministic formalism discussed here with the inclusion of magnetic fields is outlined mathematically using a discrete ordinates angular discretization in an attempt to leverage existing deterministic codes. It is compared against the EGSnrc Monte Carlo code, utilizing the emf_macros addition which calculates the effects of electromagnetic fields. This comparison is performed in an inhomogeneous phantom that was designed to present a challenging calculation for deterministic calculations in 0, 0.6, and 3 T magnetic fields oriented parallel and perpendicular to the radiation beam. The accuracy of the formalism discussed here against Monte Carlo was evaluated with a gamma comparison using a standard 2%/2 mm and a more stringent 1%/1 mm criterion for a standard reference 10 × 10 cm(2) field as well as a smaller 2 × 2 cm(2) field., Results: Greater than 99.8% (94.8%) of all points analyzed passed a 2%/2 mm (1%/1 mm) gamma criterion for all magnetic field strengths and orientations investigated. All dosimetric changes resulting from the inclusion of magnetic fields were accurately calculated using the deterministic formalism. However, despite the algorithm's high degree of accuracy, it is noticed that this formalism was not unconditionally stable using a discrete ordinate angular discretization., Conclusions: The feasibility of including magnetic field effects in a deterministic solution to the first order linear Boltzmann transport equation is shown. The results show a high degree of accuracy when compared against Monte Carlo calculations in all magnetic field strengths and orientations tested.

Single-molecule pulling experiments are widely used for studying the structure, dynamics, and function of single biological molecules via applying mechanical forces on them in a controlled way. Pulling at a constant speed or at a constant force builds up a mechanical force on a molecule or molecular complex leading to a molecular transition such as the dissociation of a molecular complex, unfolding of a protein, or unwrapping of a higher-order structure. We perform Brownian dynamics and Monte Carlo simulations of single-molecule pulling experiments. Through our simulations we demonstrate that the molecular transition rate based on the Kramers theory in the high-barrier limit becomes unsuitable as the applied force approaches the critical force at which the barrier disappears. We also demonstrate that use of molecular transition rate based on mean first passage time (MFPT) approach would be more relevant in describing molecular transition especially as the applied force approaches the critical force.

We have developed a Monte-Carlo photon-tracking and readout simulator called SCOUT to study the stochastic behavior of signals output from a simplified rectangular scintillation-camera design. SCOUT models the salient processes affecting signal generation, transport, and readout of a scintillation camera. In this work, we compare output signal statistics from SCOUT to experimental results for both a discrete and a monolithic camera. We also benchmark the speed of this simulation tool and compare it to existing simulation tools. We find this modeling tool to be relatively fast and predictive of experimental results. Depending on the modeled camera geometry, we found SCOUT to be 4 to 140 times faster than other modeling tools.

Nonlinear stochastic differential equation models with unobservable state variables are now widely used in analysis of PK/PD data. Unobservable state variables are usually estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable state variables, and a simulation-based M estimator is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations for discrete time and continuous time systems respectively, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

We discuss methods for optimally inferring the synaptic inputs to an electrotonically compact neuron, given intracellular voltage-clamp or current-clamp recordings from the postsynaptic cell. These methods are based on sequential Monte Carlo techniques ("particle filtering"). We demonstrate, on model data, that these methods can recover the time course of excitatory and inhibitory synaptic inputs accurately on a single trial. Depending on the observation noise level, no averaging over multiple trials may be required. However, excitatory inputs are consistently inferred more accurately than inhibitory inputs at physiological resting potentials, due to the stronger driving force associated with excitatory conductances. Once these synaptic input time courses are recovered, it becomes possible to fit (via tractable convex optimization techniques) models describing the relationship between the sensory stimulus and the observed synaptic input. We develop both parametric and nonparametric expectation-maximization (EM) algorithms that consist of alternating iterations between these synaptic recovery and model estimation steps. We employ a fast, robust convex optimization-based method to effectively initialize the filter; these fast methods may be of independent interest. The proposed methods could be applied to better understand the balance between excitation and inhibition in sensory processing in vivo.

Background: In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics. Stochasticity is ubiquitous in many areas of cell biology, for example in gene regulation, biochemical cascades and cell-cell interaction. However most discrete stochastic simulation techniques are slow. We apply Richardson extrapolation to the moments of three fixed-step methods, the Euler, midpoint and θ-trapezoidal τ-leap methods, to demonstrate the power of stochastic extrapolation. The extrapolation framework can increase the order of convergence of any fixed-step discrete stochastic solver and is very easy to implement; the only condition for its use is knowledge of the appropriate terms of the global error expansion of the solver in terms of its stepsize. In practical terms, a higher-order method with a larger stepsize can achieve the same level of accuracy as a lower-order method with a smaller one, potentially reducing the computational time of the system., Results: By obtaining a global error expansion for a general weak first-order method, we prove that extrapolation can increase the weak order of convergence for the moments of the Euler and the midpoint τ-leap methods, from one to two. This is supported by numerical simulations of several chemical systems of biological importance using the Euler, midpoint and θ-trapezoidal τ-leap methods. In almost all cases, extrapolation results in an improvement of accuracy. As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations., Conclusions: Extrapolation is a general framework for increasing the order of accuracy of any fixed-step stochastic solver. This enables the simulation of complicated systems in less time, allowing for more realistic biochemical problems to be solved.

In this paper, we study the feasibility of using the stochastic origin ensemble (SOE) algorithm for reconstructing images of secondary gammas emitted during proton radiotherapy from data measured with a three-stage Compton camera. The purpose of this study was to evaluate the quality of the images of the gamma rays emitted during proton irradiation produced using the SOE algorithm and to measure how well the images reproduce the distal falloff of the beam. For our evaluation, we performed a Monte Carlo simulation of an ideal three-stage Compton camera positioned above and orthogonal to a proton pencil beam irradiating a tissue phantom. Scattering of beam protons with nuclei in the phantom produces secondary gamma rays, which are detected by the Compton camera and used as input to the SOE algorithm. We studied the SOE reconstructed images as a function of the number of iterations, the voxel probability parameter, and the number of detected gammas used by the SOE algorithm. We quantitatively evaluated the capabilities of the SOE algorithm by calculating and comparing the normalized mean square error (NMSE) of SOE reconstructed images. We also studied the ability of the SOE reconstructed images to predict the distal falloff of the secondary gamma production in the irradiated tissue. Our results show that the images produced with the SOE algorithm converge in ~10,000 iterations, with little improvement to the image NMSE for iterations above this number. We found that the statistical noise of the images is inversely proportional to the ratio of the number of gammas detected to the SOE voxel probability parameter value. In our study, the SOE predicted distal falloff of the reconstructed images agrees with the Monte Carlo calculated distal falloff of the gamma emission profile in the phantom to within ±0.6 mm for the positions of maximum emission (100%) and 90%, 50% and 20% distal falloff of the gamma emission profile. We conclude that the SOE algorithm is an effective method for reconstructing images of a proton pencil beam from the data collected by an ideal Compton camera and that these images accurately model the distal falloff of secondary gamma emission during proton irradiation.

The white rot fungus Phanerochaete chrysosporium has been identified to be an environmentally useful microorganism for the degradation of various hazardous pollutants, mainly because of its ligninolytic enzyme system, particularly the lignin peroxidase (LiP) secreted by the fungus. In the present work, the behavior of the fungus in liquid medium due to variation in physico-chemical parameters, i.e., glucose concentration, nitrogen concentration, agitation, etc., was studied. Increment of the initial concentration of glucose in the medium increases the biomass growth and LiP activity, when cultured under controlled conditions. The biomass growth and LiP activity by the fungus was modeled following stochastic approach. The behavior of growth and enzyme activity of the fungus observed from the model were found to be in agreement with the experiments qualitatively.

Background: A prerequisite for the mechanistic simulation of a biochemical system is detailed knowledge of its kinetic parameters. Despite recent experimental advances, the estimation of unknown parameter values from observed data is still a bottleneck for obtaining accurate simulation results. Many methods exist for parameter estimation in deterministic biochemical systems; methods for discrete stochastic systems are less well developed. Given the probabilistic nature of stochastic biochemical models, a natural approach is to choose parameter values that maximize the probability of the observed data with respect to the unknown parameters, a.k.a. the maximum likelihood parameter estimates (MLEs). MLE computation for all but the simplest models requires the simulation of many system trajectories that are consistent with experimental data. For models with unknown parameters, this presents a computational challenge, as the generation of consistent trajectories can be an extremely rare occurrence., Results: We have developed Monte Carlo Expectation-Maximization with Modified Cross-Entropy Method (MCEM(2)): an accelerated method for calculating MLEs that combines advances in rare event simulation with a computationally efficient version of the Monte Carlo expectation-maximization (MCEM) algorithm. Our method requires no prior knowledge regarding parameter values, and it automatically provides a multivariate parameter uncertainty estimate. We applied the method to five stochastic systems of increasing complexity, progressing from an analytically tractable pure-birth model to a computationally demanding model of yeast-polarization. Our results demonstrate that MCEM(2) substantially accelerates MLE computation on all tested models when compared to a stand-alone version of MCEM. Additionally, we show how our method identifies parameter values for certain classes of models more accurately than two recently proposed computationally efficient methods., Conclusions: This work provides a novel, accelerated version of a likelihood-based parameter estimation method that can be readily applied to stochastic biochemical systems. In addition, our results suggest opportunities for added efficiency improvements that will further enhance our ability to mechanistically simulate biological processes.

We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from live-cell fluorescence microscopy in image-based systems biology. In addition, fluctuation time-courses from, e.g., fluorescence correlation spectroscopy (FCS) provide additional information about the system dynamics that can be used to more robustly infer parameters than when considering only mean concentrations. Estimating model parameters from a single experimental trajectory enables single-cell measurements and quantification of cell-cell variability. We propose a novel combination of an adaptive Monte Carlo sampler, called Gaussian Adaptation (GaA), and efficient exact stochastic simulation algorithms (SSA) that allows parameter identification from single stochastic trajectories. We benchmark the proposed method on a linear and a non-linear reaction network at steady state and during transient phases. In addition, we demonstrate that the present method also provides an ellipsoidal volume estimate of the viable part of parameter space and is able to estimate the physical volume of the compartment in which the observed reactions take place.

We present a method for mesoscopic, dynamic Monte Carlo simulations of pattern formation in excitable reaction-diffusion systems. Using a two-level parallelization approach, our simulations cover the whole range of the parameter space, from the noise-dominated low-particle number regime to the quasi-deterministic high-particle number limit. Three qualitatively different case studies are performed that stand exemplary for the wide variety of excitable systems. We present mesoscopic stochastic simulations of the Gray-Scott model, of a simplified model for intracellular Ca2+ oscillations and, for the first time, of the Oregonator model. We achieve simulations with up to 10(10) particles. The software and the model files are freely available and researchers can use the models to reproduce our results or adapt and refine them for further exploration.

Purpose: To test the stochastic model for DNA double-strand break (DSB) repair via non-homologous end joining (NHEJ) implemented in the Monte Carlo code PARTRAC (PARticle TRACks) against measured repair kinetics after nitrogen ion and (60)Co γ reference irradiation., Material and Methods: By combining Monte Carlo track structure calculations with multi-scale models of cellular DNA, yields of DSB are calculated for N ion and (60)Co γ-irradiation. The NHEJ model in PARTRAC is used to determine rejoining kinetics of the DNA ends and DNA fragment distributions after certain repair times. Model parameters are adapted to the measured rejoining kinetics for the different radiation types., Results: DSB rejoining kinetics after low- and high-linear energy transfer (LET) irradiation have been reproduced after refinements of the DNA repair model, in particular by considering an ongoing production of detectable DSB in the initial phase, e.g., by enzymatic processing of labile sites, and by assuming a limited availability of repair enzymes needed for processing complex lesions during the slow repair phase., Conclusions: The need for certain model refinements suggests mechanisms that may significantly contribute to the DSB rejoining kinetics during both initial and later phases of NHEJ.

Background: The lac operon genetic switch is considered as a paradigm of genetic regulation. This system has a positive feedback loop due to the LacY permease boosting its own production by the facilitated transport of inducer into the cell and the subsequent de-repression of the lac operon genes. Previously, we have investigated the effect of stochasticity in an artificial lac operon network at the single cell level by comparing corresponding deterministic and stochastic kinetic models., Results: This work focuses on the dynamics of cell populations by incorporating the above kinetic scheme into two Monte Carlo (MC) simulation frameworks. The first MC framework assumes stochastic reaction occurrence, accounts for stochastic DNA duplication, division and partitioning and tracks all daughter cells to obtain the statistics of the entire cell population. In order to better understand how stochastic effects shape cell population distributions, we develop a second framework that assumes deterministic reaction dynamics. By comparing the predictions of the two frameworks, we conclude that stochasticity can create or destroy bimodality, and may enhance phenotypic heterogeneity., Conclusions: Our results show how various sources of stochasticity act in synergy with the positive feedback architecture, thereby shaping the behavior at the cell population level. Further, the insights obtained from the present study allow us to construct simpler and less computationally intensive models that can closely approximate the dynamics of heterogeneous cell populations.

The resampling-based test, which often relies on permutation or bootstrap procedures, has been widely used for statistical hypothesis testing when the asymptotic distribution of the test statistic is unavailable or unreliable. It requires repeated calculations of the test statistic on a large number of simulated data sets for its significance level assessment, and thus it could become very computationally intensive. Here, we propose an efficient p-value evaluation procedure by adapting the stochastic approximation Markov chain Monte Carlo algorithm. The new procedure can be used easily for estimating the p-value for any resampling-based test. We show through numeric simulations that the proposed procedure can be 100-500 000 times as efficient (in term of computing time) as the standard resampling-based procedure when evaluating a test statistic with a small p-value (e.g. less than 10( - 6)). With its computational burden reduced by this proposed procedure, the versatile resampling-based test would become computationally feasible for a much wider range of applications. We demonstrate the application of the new method by applying it to a large-scale genetic association study of prostate cancer.

We consider Bayesian point and interval estimation for a risk ratio of two proportion parameters using two independent samples of binary data subject to misclassification. In order to obtain model identifiability, we apply a double sampling scheme. For the identifiable model, we propose a Bayesian method for statistical inference for a two proportion risk ratio. Specifically, we derive an easy-to-implement closed-form sampling algorithm to draw from the posterior distribution of interest. We demonstrate the efficiency of our algorithm for Bayesian inference via Monte Carlo simulation studies and using a real data example.

A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be easily truncated to include moments up to any desired order. The number of equations is dramatically reduced compared to the master equation. This formulation enables the simulation of complex reaction networks, involving a large number of reactive species much beyond the feasibility limit of any existing method. It provides an equation-based paradigm to the analysis of stochastic networks, complementing the commonly used Monte Carlo simulations.

Stochastic models, including the variability in extent and probability of microbial growth, are useful for estimating the risk of foodborne illness (i.e. Nauta, 2000). Risk assessment typically has to embrace all sources of variability. In this paper, a stochastic approach to evaluate growth of heat damaged Listeria monocytogenes cells influenced by different stresses (pH and presence of eugenol) was performed, using an individual-based approach of growth through OD measurements. Both the lag phase duration and the "work to be done" (h(0) parameter) were derived from the growth curves obtained. From results obtained histograms of the lag phase were generated and distributions were fitted. Histograms showed a shift to longer lag phases and an increase in variability with high stress levels. Using the distributions fitted, predictions of time to unacceptable growth (10(2) cfu/g) of L. monocytogenes were established by Monte Carlo simulation and they were compared with results from statistical methods. It was evidenced that both methods (Monte Carlo and regression analysis) gave a good indication of the probability of a certain level of growth other than the average. Tornado plots were obtained to establish a sensitivity analysis of the influence of the conditions tested (heat, pH, eugenol) applied to the microorganism and their combinations., (2009 Elsevier Ltd. All rights reserved.)

Purpose: To resolve the difficulty in counting merged DNA damage foci in high-LET (linear energy transfer) ion-induced patterns., Materials and Methods: The analysis of patterns of RIF (radiation-induced foci) produced by high-LET Fe and Ti ions were conducted by using a Monte Carlo model that combines the heavy ion track structure with characteristics of the human genome on the level of chromosomes. The foci patterns were also simulated in the maximum projection plane for flat nuclei., Results: The model predicts the spatial and genomic distributions of DNA DSB (double-strand breaks) in a cell nucleus for a particular dose of radiation. We used the model to do analyses for three irradiation scenarios: (i) The ions were oriented perpendicular to the flattened nuclei in a cell culture monolayer; (ii) the ions were parallel to that plane; and (iii) round nucleus. In the parallel scenario we found that the foci appeared to be merged due to their high density, while, in the perpendicular scenario, the foci appeared as one bright spot per hit. The statistics and spatial distribution of regions of densely arranged foci, termed DNA foci chains, were predicted numerically using this model. Another analysis was done to evaluate the number of ion hits per nucleus, which were visible from streaks of closely located foci., Conclusions: We showed that DSB clustering needs to be taken into account to determine the true DNA damage foci yield, which helps to determine the DSB yield. Using the model analysis, a researcher can refine the DSB yield per nucleus per particle. We showed that purely geometric artifacts, present in the experimental images, can be analytically resolved with the model, and that the quantisation of track hits and DSB yields can be provided to the experimentalists who use enumeration of radiation-induced foci in immunofluorescence experiment using proteins that detect DNA damage.

Deciphering and designing complex biomolecular networks in the cell are the goals of systems and synthetic biology, respectively. The effects of localization, spatial heterogeneity, and molecular fluctuations in biomolecular networks are not well understood. We present a theoretical approach based on physical principles to accurately simulate biomolecular networks using the Monte Carlo method. Incorporating this theory, a computational tool named Monte Carlo biomolecular simulator (MBS) was developed, enabling studies of biomolecular kinetics with both spatial and temporal resolutions. The accuracy of MBS was verified by comparison against the classical deterministic approaches. Furthermore, the effects of localization, spatial heterogeneity, and molecular fluctuations were studied in three simulated model systems, showing their impact on the overall reaction kinetics. This work demonstrates the unique insights that can be discovered by considering the subtle effects that can be created by the spatial and temporal kinetics of biomolecular reaction networks.

Monte Carlo methods have received much attention in the recent literature of phylogeny analysis. However, the conventional Markov chain Monte Carlo algorithms, such as the Metropolis-Hastings algorithm, tend to get trapped in a local mode in simulating from the posterior distribution of phylogenetic trees, rendering the inference ineffective. In this paper, we apply an advanced Monte Carlo algorithm, the stochastic approximation Monte Carlo algorithm, to Bayesian phylogeny analysis. Our method is compared with two popular Bayesian phylogeny software, BAMBE and MrBayes, on simulated and real datasets. The numerical results indicate that our method outperforms BAMBE and MrBayes. Among the three methods, SAMC produces the consensus trees which have the highest similarity to the true trees, and the model parameter estimates which have the smallest mean square errors, but costs the least CPU time.

Variation in organismal development is ubiquitous in nature but omitted from most age- and stage-structured population models. I give a general approach for formulating and analyzing its role in density-independent population models using the framework of integral projection models. The approach allows flexible assumptions, including correlated development times among multiple life stages. I give a new Monte Carlo numerical integration approach to calculate long-term growth rate, its sensitivities, stable age-stage distributions and reproductive value. This method requires only simulations of individual life schedules, rather than iteration of full population dynamics, and has practical and theoretical appeal because it ties easily implemented simulations to numerical solution of demographic equations. I show that stochastic development is demographically important using two examples. For a desert cactus, many stochastic development models, with independent or correlated stage durations, can generate the same stable stage distribution (SSD) as the real data, but stable age-within-stage distributions and sensitivities of growth rate to demographic rates differ greatly among stochastic development scenarios. For Mediterranean fruit flies, empirical variation in maturation time has a large impact on population growth. The systematic model formulation and analysis approach given here should make consideration of variable development models widely accessible and readily extendible.

The dynamics of many physical, chemical, and biological systems can be reduced to a succession of infrequent transitions in a network of discrete states representing low energy regions in configuration space. This enables accessing long-time dynamics and predicting macroscopic properties. Here we develop a new, perfectly general statistical mechanical/geometric formulation that expresses both state probabilities and all observables in the same Euclidean space, spanned by the eigenvectors of the symmetrized time evolution operator. Our formalism leads to simple expressions for nonequilibrium and equilibrium ensemble averages, variances, and time correlation functions of any observable and allows a rigorous decomposition of the dynamics into relaxation modes. Applying it to subglass segmental relaxation in atactic polystyrene up to times on the order of 10 micros, we probe the molecular mechanism of the gamma and delta processes and unequivocally identify the delta process with rotation of a single phenyl group around its stem.

Purpose: To study the energy deposition by low-energy electrons in submicron tissue-equivalent targets by comparing two widely used methodologies, namely, the continuous-slowing-down-approximation (CSDA) convolution integral and the Monte Carlo (MC) simulation., Methods: An MC track-structure code that simulates collision-by-collision the complete slowing down process is used to calculate the energy deposition in spherical volumes of unit density water medium. Comparisons are made with calculations based on the CSDA convolution integral using both empirical and MC-based range-energy analytic formulae., Results: We present self-irradiation absorbed fractions and S-factors for monoenergetic electrons of initial energies from 0.1-10 keV distributed uniformly in spheres of 5, 10, 50, 100, 500, and 1000 nm radius. The MC and CSDA results were found, in some cases, to differ by a factor of 2 or more; differences generally increase with decreasing sphere size. Contrary to high energies, the uncertainties associated with the straight-ahead approximation implicit in the CSDA calculations are of the same order as those related to straggling and delta-ray effects., Conclusion: The use of the CSDA methodology may be unsuitable for the sub-micron scale where a more realistic description of electron transport becomes important.

Ca(2+) dynamics underlying cardiac excitation-contraction coupling are essential for heart functions. In this study, we constructed microstructure-based models of Ca(2+) dynamics to simulate Ca(2+) influx through individual L-type Calcium channels (LCCs), an effective Ca(2+) diffusion within the cytoplasmic space and in the dyadic space, and the experimentally observed calcium-dependent inactivation (CDI) of the LCCs induced by local and global Ca(2+) sensing. The models consisted of LCCs with distal and proximal Ca(2+) (Calmodulin-Ca(2+) complex) binding sites. In one model, the intra-cellular space was organelle-free cytoplasmic space, and the other was with a dyadic space including sarcoplasmic reticulum membrane. The Ca(2+) dynamics and CDI of the LCCs in the model with and without the dyadic space were then simulated using the Monte Carlo method. We first showed that an appropriate set of parameter values of the models with effectively extra-slow Ca(2+) diffusion enabled the models to reproduce major features of the CDI process induced by the local and global sensing of Ca(2+) near LCCs as measured with single and two spatially separated LCCs by Imredy and Yue (Neuron. 1992;9:197-207). The effective slow Ca(2+) diffusion might be due to association and dissociation of Ca(2+) and Calmodulin (CaM). We then examined how the local and global CDIs were affected by the presence of the dyadic space. The results suggested that in microstructure modeling of Ca(2+) dynamics in cardiac myocytes, the effective Ca(2+) diffusion under CaM-Ca(2+) interaction, the nanodomain structure of LCCs for detailed CDI, and the geometry of subcellular space for modeling dyadic space should be considered.

Apoptosis, or genetically programmed cell death, is a crucial cellular process that maintains the balance between life and death in cells. The precise molecular mechanism of apoptosis signaling and the manner in which type 1 and type 2 pathways of the apoptosis signaling network are differentially activated under distinct apoptotic stimuli is poorly understood. Based on Monte Carlo stochastic simulations, we show that the type 1 pathway becomes activated under strong apoptotic stimuli, whereas the type 2 mitochondrial pathway dominates apoptotic signaling in response to a weak death signal. Our results also show signaling in the type 2 pathway is stochastic; the population average over many cells does not capture the cell-to-cell fluctuations in the time course (approximately 1-10 h) of downstream caspase-3 activation. On the contrary, the probability distribution of caspase-3 activation for the mitochondrial pathway shows a distinct bimodal behavior that can be used to characterize the stochastic signaling in type 2 apoptosis and other similar complex signaling processes. Interestingly, such stochastic fluctuations in apoptosis signaling occur even in the presence of large numbers of signaling molecules.

The time evolution of species concentrations in biochemical reaction networks is often modeled using the stochastic simulation algorithm (SSA) [Gillespie, J. Phys. Chem. 81, 2340 (1977)]. The computational cost of the original SSA scaled linearly with the number of reactions in the network. Gibson and Bruck developed a logarithmic scaling version of the SSA which uses a priority queue or binary tree for more efficient reaction selection [Gibson and Bruck, J. Phys. Chem. A 104, 1876 (2000)]. More generally, this problem is one of dynamic discrete random variate generation which finds many uses in kinetic Monte Carlo and discrete event simulation. We present here a constant-time algorithm, whose cost is independent of the number of reactions, enabled by a slightly more complex underlying data structure. While applicable to kinetic Monte Carlo simulations in general, we describe the algorithm in the context of biochemical simulations and demonstrate its competitive performance on small- and medium-size networks, as well as its superior constant-time performance on very large networks, which are becoming necessary to represent the increasing complexity of biochemical data for pathways that mediate cell function.

The issue of how the molecular organization of rod outer segments (ROS) discs affects the initial timing of the photoresponse in vertebrates has been recently raised by novel structural findings that raise doubts about the classical scenario of monomeric rhodopsin (R) and heterotrimeric transducin (G) freely diffusing in the membrane milieu. In this study, we investigate this issue by means of mesoscopic Monte Carlo (MMC) simulations of the stochastic encounters between one photoactivated R and one G, explicitly taking into account the molecular size and the diffusion coefficient of each species as well as crowding effects. Three different scenarios were compared with respect to their effects on timing, namely, (a) the classical framework, where both G and monomeric R are allowed to freely diffuse in the ROS disc membrane, (b) the ideal paracrystalline organization of R dimers considered as a structural unit, where ordered rows completely cover the disc membrane patch, and (c) the scenario suggested by recent AFM data, where R dimers organize in differently sized rafts with varying local concentrations. Our simulations suggest that a similar kinetic response could arise from very different microscopic scenarios, thus opening new interpretations to the controversial recent findings. Moreover, we show that if high-density R packing on ROS discs is characterized by a highly ordered structural organization rather than unspecific aggregation, an unexpected favorable effect on the temporal response of early phototransduction reactions can occur.

Using a continuum bead-spring Monte Carlo model, we study the anomalous diffusion dynamics of a self-avoiding tethered membrane by means of extensive computer simulations. We focus on the subdiffusive stochastic motion of the membrane's central node in the regime of flat membranes at temperatures above the membrane folding transition. While at times, larger than the characteristic membrane relaxation time tau(R) , the mean-square displacement of the center of mass of the sheet, , as well as that of its central node, , show the normal Rouse diffusive behavior with a diffusion coefficient D(N) scaling as D(N) proportional to N(-1) with respect to the number of segments N in the membrane, for short times t< or =tau(R) we observe a multiscale dynamics of the central node, proportional to t(alpha) , where the anomalous diffusion exponent alpha changes from alpha approximately 0.86 to approximately 0.27 , and then to alpha approximately 0.5 , before diffusion turns eventually to normal. By means of simple scaling arguments we show that our main result, alpha approximately equal to 0.27 , can be related to particular mechanisms of membrane dynamics which involve different groups of segments in the membrane sheet. A comparative study involving also linear polymers demonstrates that the diffusion coefficient of self-avoiding tethered membranes, containing N segments, is three times smaller than that of linear polymer chains with the same number of segments.

Monte Carlo methods have received much attention recently in the literature of phylogenetic tree construction. However, they often suffer from two difficulties, the curse of dimensionality and the local-trap problem. The former one is due to that the number of possible phylogenetic trees increases at a super-exponential rate as the number of taxa increases. The latter one is due to that the phylogenetic tree has often a rugged energy landscape. In this paper, we propose a new phylogenetic tree construction method, which attempts to alleviate these two difficulties simultaneously by making use of the sequential structure of phylogenetic trees in conjunction with stochastic approximation Monte Carlo (SAMC) simulations. The use of the sequential structure of the problem provides substantial help to reduce the curse of dimensionality in simulations, and SAMC effectively prevents the system from getting trapped in local energy minima. The new method is compared with a variety of existing Bayesian and non-Bayesian methods on simulated and real datasets. Numerical results are in favor of the new method in terms of quality of the resulting phylogenetic trees.