Monte Carlo Estimation for Nonlinear Non-Gaussian State Space Models

We develop a proposal or importance density for state spacemodels with a nonlinear non-Gaussian observation vector y p(y¦)and an unobserved linear Gaussian signal vector p(). The proposaldensity is obtained from the Laplace approximation of the smoothingdensity p(¦y). We present efficient algorithms to calculatethe mode of p(¦y) and to sample from the proposal density.The samples can be used for importance sampling and Markov chainMonte Carlo methods. The new results allow the application ofthese methods to state space models where the observation densityp(y¦) is not log-concave. Additional results are presentedthat lead to computationally efficient implementations. We illustratethe methods for the stochastic volatility model with leverage.     

Biofilm model calibration and microbial diversity study using Monte Carlo simulations

Mathematical models are useful tools for studying and exploring biological conversion processes as well as microbial competition in biological treatment processes. A single‐species biofilm model was used to describe biofilm reactor operation at three different hydraulic retention times (HRT). The single‐species biofilm model was calibrated with sparse experimental data using the Monte Carlo filtering method. This calibrated single‐species biofilm model was then extended to a multi‐species model considering 10 different heterotrophic bacteria. The aim was to study microbial diversity in bulk phase biomass and biofilm, as well as the competition between suspended and attached biomass. At steady state and independently of the HRT, Monte Carlo simulations resulted only in one unique dominating bacterial species for suspended and attached biomass. The dominating bacterial species was determined by the highest specific substrate affinity (ratio of µ/K_S). At a short HRT of 20 min, the structure of the microbial community in the bulk liquid was determined by biomass detached from the biofilm. At a long HRT of 8 h, both biofilm detachment and microbial growth in the bulk liquid influenced the microbial community distribution. Biotechnol. Bioeng. 2013; 110: 1323–1332. © 2012 Wiley Periodicals, Inc.     

Alpha-helix folding by Monte Carlo simulated annealing in isolated C-peptide of ribonuclease A

Conformation of the C-peptide fragment of RNase A is calculated by Monte Carlo simulated annealing. We adopt the total potential energy as given by the sum of generic interatomic energies whose parameters are determined separately for each amino acid without referring to the empirical structure of the C-peptide. The simulation is carried out in a completely unrestricted way without imposing any weight towards given final destinations. Starting from completely random initial conformations and minimizing the total potential energy with respect to main-chain dihedral angles and side-chain torsion angles, we have obtained partial alpha-helix structure with a high probability (approximately 40%). The energetically most favourable structure exhibits a 2.5-turn alpha-helix at the location identical with that of the 3-turn alpha-helix in the native enzyme molecule. Classification of conformations obtained in the simulation into clusters of similar structure shows that our simulation indeed predicts the alpha-helix structure for the isolated C-peptide with specific charged residues. The results of simulation with various amino acid substitutions are also found to be consistent with the experimental implication for the importance of intramolecular ionic interactions for alpha-helix stability for this peptide.     

Helix-forming tendencies of nonpolar amino acids predicted by Monte Carlo simulated annealing

Monte Carlo simulated annealing is applied to the study of the α-helix-forming tendencies of seven nonpolar amino acids, Ala, Leu, Met, Phe, Ile, Val, and Gly. Homooligomers of 10 amino acids are used and the helix tendency is calculated by folding α-helicies from completely random initial conformations. The results of the simulation imply that Met, Ala, and Leu are helix formers and that Val, Ile, and Gly are helix breakers, while Phe comes in between the two groups. The differences between helix formers and breakers turned out to be large in agreement with the recent experiments with short peptides. It is argued from the energy distributions of the obtained conformations that the helix tendency is small for the helix breakers because of steric hindrance of side chains. Homoglycine is shown to favor a random coil conformation. The β-strand tendencies of the same homooligomers are also considered, and they are shown to agree with the frequencies of amino acids in β-sheet from the protein data base. © 1994 Wiley-Liss, Inc.     

Dependence on the dielectric model and pH in a synthetic helical peptide studied by Monte Carlo simulated annealing

Monte Carlo simulated annealing is applied to the tertiary structure prediction of a 17-residue synthetic peptide, which is known by experiment to exhibit high helical content at low pH. Two dielectric models are considered: sigmoidal distance-dependent dielectric function and a constant dielectric function (? = 2). Starting from completely random initial conformations, our simulations for both dielectric models at low pH gave many helical conformations. The obtained low-energy conformations are compared with the nuclear Overhauser effect spectroscopy cross-peak data for both main chain and side chains, and it is shown that the results for the sigmoidal dielectric function are in remarkable agreement with the experimental data. The results predict the existence of two disjoint helices around residues 5–9 and 11–16, while nmr experiments imply significant α-helix content between residues 5 and 14. Simulations with high pH, on the other hand, hardly gave a helical conformation, which is also in accord with the experiment. These findings indicate that when side chains are charged, electrostatic interactions due to these charges play a major role in the helix stability. Our results are compared with the previous 500 ps molecular dynamics simulations of the same peptide. It is argued that simulated annealing is superior to molecular dynamics in two respects: (1) direct folding of α-helix from completely random initial conformations is possible for the former, whereas only unfolding of an α-helix can be studied by the latter; (2) while both methods predict high helix content for low pH, the results for high pH agree with experiment (low helix content) only for the former method. © 1994 John Wiley & Sons, Inc.     

A prediction of tertiary structures of peptide by the Monte Carlo simulated annealing method

The Monte Carlo simulated annealing method has been applied to the prediction of three-dimensional structures of enkephalin. The low-energy conformations obtained were classified into a few groups of similar structures, which indicates that our method is effective. New low-energy structures were identified together with previously proposed structures.     

Biogeochemistry of a gypsum-encrusted microbial ecosystem

Gypsum crusts containing multicolored stratified microbial populations grow in the evaporation ponds of a commercial saltern in Eilat, Israel. These crusts contain two prominent cyanobacterial layers, a bright purple layer of anoxygenic phototrophs, and a lower black layer with active sulphate reduction. We explored the diel dynamics of oxygen and sulphide within the crust using specially constructed microelectrodes, and further explored the crust biogeochemistry by measuring rates of sulphate reduction, stable sulphur isotope composition, and oxygen exchange rates across the crust–brine interface. We explored crusts from ponds with two different salinities, and found that the crust in the highest salinity was the less active. Overall, these crusts exhibited much lower rates of oxygen production than typical organic‐rich microbial mats. However, this was mainly due to much lower cell densities within the crusts. Surprisingly, on a per cell‐volume basis, rates of photosynthesis were similar to organic‐rich microbial mats. Due to relatively low rates of oxygen production and deep photic zones extending from 1.5 to 3 cm depth, a large percentage of the oxygen produced during the day accumulated into the crusts. Indeed, only between 16% to 34% of the O₂ produced in the crust escaped, and the remainder was internally recycled, used mainly in O₂ respiration. We view these crusts as potential homologs to ancient salt‐encrusted microbial ecosystems, and we compared them to the 3.45 billion‐year‐old quartz barite deposits from North Pole, Australia, which originally precipitated gypsum.     

Parameter sensitivity of a model of viral epidemics simulated with Monte Carlo techniques. II. Durations and peaks

This is the second of a series of papers concerning sensitivity analyses of stochastic micropopulation models. A model of epidemic spread of viral infection is used in the series to illustrate the principles and performance of the sensitivity analysis system. For these studies the analysis system now known as SENSEN was redesigned; it can be used with any specialization of the SUMMERS simulation shell. Previous applications of SENSEN and its predecessors studied the sensitivity simultaneously to at most six input parameters. The applicability of SENSEN when twelve input parameters are selected is illustrated by sensitivity analyses of epidemic durations. A time-related output, day of the epidemic at which the peak number of cases are present, is also studied.     

Electrostatic interaction between RNA and protein capsid in cowpea chlorotic mottle virus simulated by a coarse-grain RNA model and a Monte Carlo approach

Although many viruses have been crystallized and the protein capsid structures have been determined by x-ray crystallography, the nucleic acids often cannot be resolved. This is especially true for RNA viruses. The lack of information about the conformation of DNA/RNA greatly hinders our understanding of the assembly mechanism of various viruses. Here we combine a coarse-grain model and a Monte Carlo method to simulate the distribution of viral RNA inside the capsid of cowpea chlorotic mottle virus. Our results show that there is very strong interaction between the N-terminal residues of the capsid proteins, which are highly positive charged, and the viral RNA. Without these residues, the binding energy disfavors the binding of RNA by the capsid. The RNA forms a shell close to the capsid with the highest densities associated with the capsid dimers. These high-density regions are connected to each other in the shape of a continuous net of triangles. The overall icosahedral shape of the net overlaps with the capsid subunit icosahedral organization. Medium density of RNA is found under the pentamers of the capsid. These findings are consistent with experimental observations.     

Inversion of terrestrial ecosystem model parameter values against eddy covariance measurements by Monte Carlo sampling

Effective measures to counter the rising levels of carbon dioxide in the Earth's atmosphere require that we better understand the functioning of the global carbon cycle. Uncertainties about, in particular, the terrestrial carbon cycle's response to climate change remain high. We use a well‐known stochastic inversion technique originally developed in nuclear physics, the Metropolis algorithm, to determine the full probability density functions (PDFs) of parameters of a terrestrial ecosystem model. By thus assimilating half‐hourly eddy covariance measurements of CO₂ and water fluxes, we can substantially reduce the uncertainty of approximately five model parameters, depending on prior uncertainties. Further analysis of the posterior PDF shows that almost all parameters are nearly Gaussian distributed, and reveals some distinct groups of parameters that are constrained together. We show that after assimilating only 7 days of measurements, uncertainties for net carbon uptake over 2 years for the forest site can be substantially reduced, with the median estimate in excellent agreement with measurements.     

Monte Carlo simulations of individual variability and their effects on simulated heat stress using thermoregulatory modeling

This paper addresses a variable-dependence (VD) MC method developed based on a previous attempt (VI-MC method) (J. Therm. Biol. 29 (2004), 515) to be incorporated in a thermoregulatory model. Simulated individuals with anthropometrics by VI- and VD-MC methods for US Army population were compared using principal component analysis and Fisher's exact tests. The results indicated that VD-MC data represented overall body size as the primary component and body shape as the secondary component that were more realistic and similar to the measured US Army data (p>0.05) rather than VI-MC data (p<0.05). Such differences consequently affected individual thermoregulatory responses to simulated heat stress. The VD-MC method provides a more realistic representation of individual variability and thus underpins more realistic predictions of individual thermoregulatory responses.     

肠道微生态与肥胖

人的肠道是一个丰富的微生态系统,含有100万亿多的微生物,种类多达500-1000个,这些微生物的基因总数是人体基因组所含基因总数的100倍。肠道微生物丛的组成种类和数量与宿主的肥胖有关,无菌小鼠含有的脂肪量比正常饲养小鼠低42％,如果将微生物丛植入到无菌小鼠体内后,导致脂肪总量增加57％。提示肠道微生物丛可以明显的促进小鼠对热能的摄人,促使脂肪的沉积,触动全身性炎症反应。因此,对肥胖的治疗可以采用益生菌和益生元来调节肠道微生物丛的状态以期获得治疗效果。本研究述及肠道微生丛对宿主肥胖及其代谢机制的研究进展。     

益生元与肠道微生态

益生元是一种非消化的成分,通过选择性的刺激肠道中一种或少数种益生菌的增长和/或活性而对宿主有利.具有抵抗致病菌侵入的天然功能.目前广泛研究的有果糖和半乳糖,体内与体外试验均表明不被正常人酶类所消化,在大肠中容易发酵,粪便内未能检出这种糖的成分.通过大肠细菌对益生元的发酵产生的短链脂肪酸是刺激双歧杆菌和乳杆菌增长的重要因素.应用现代技术获得了人肠道微生物细菌群的组成与种类的多样性.本文综述有关益生元的研究状况,强调益生元选择性刺激的机制和对人生理功能的影响.     

A general Monte Carlo/simulated annealing algorithm for resonance assignment in NMR of uniformly labeled biopolymers

We describe a general computational approach to site-specific resonance assignments in multidimensional NMR studies of uniformly ¹⁵N,¹³C-labeled biopolymers, based on a simple Monte Carlo/simulated annealing (MCSA) algorithm contained in the program MCASSIGN2. Input to MCASSIGN2 includes lists of multidimensional signals in the NMR spectra with their possible residue-type assignments (which need not be unique), the biopolymer sequence, and a table that describes the connections that relate one signal list to another. As output, MCASSIGN2 produces a high-scoring sequential assignment of the multidimensional signals, using a score function that rewards good connections (i.e., agreement between relevant sets of chemical shifts in different signal lists) and penalizes bad connections, unassigned signals, and assignment gaps. Examination of a set of high-scoring assignments from a large number of independent runs allows one to determine whether a unique assignment exists for the entire sequence or parts thereof. We demonstrate the MCSA algorithm using two-dimensional (2D) and three-dimensional (3D) solid state NMR spectra of several model protein samples (α-spectrin SH3 domain and protein G/B1 microcrystals, HET-s_218–289 fibrils), obtained with magic-angle spinning and standard polarization transfer techniques. The MCSA algorithm and MCASSIGN2 program can accommodate arbitrary combinations of NMR spectra with arbitrary dimensionality, and can therefore be applied in many areas of solid state and solution NMR.     

Biochar and woodchip amendments alter restoration outcomes,microbial processes,and soil moisture in a simulated semi‐arid ecosystem

Amendments, such as woodchips or biochar, may improve success of arid and semi‐arid wildland revegetation limited by unpredictable and insufficient rainfall as well as low soil water holding capacity. In an 116‐day greenhouse experiment simulating a nearby savannah, response to four amendment treatments (no treatment, incorporated biochar, incorporated woodchips, and surface woodchips) was tested across two field soils (Chiricahua and Hathaway) and four simulated precipitation treatments (100, 80, 60, and 40% of average) in a replicated design. Soil type, amendment treatments, and simulated precipitation all had significant (p < 0.01) effects on aboveground biomass. The surface woodchip treatment averaged the highest biomass production of the amendment treatments (489 kg/ha) and the incorporated woodchips had the lowest (298 kg/ha). Aboveground biomass decreased with decreasing precipitation (533, 468, 350, and 216 kg/ha, respectively). Biochar amended soils averaged 5–10% higher volumetric water content than the woodchip amendments and controls through a 28‐day dry down. Microbial nitrogen and phosphorus acquiring activities were higher in Hathaway soils while carbon activities were higher in Chiricahua soils. The surface woodchip treatment resulted in a different species composition than the other amendment and control treatments (p < 0.01). None of the amendment treatments ameliorated low precipitation conditions for plants. Contrary to expectations, carbon and phosphorus exoenzyme activities were highest in the lower precipitation treatments (60 and 40%) and nitrogen exoenzyme activities remained high in Hathaway soils regardless of precipitation. Surface application of woodchips increased vegetation as well as carbon and phosphorus exoenzyme activities while incorporating woodchips suppressed vegetation.     

A multibody, whole-residue potential for protein structures, with testing by Monte Carlo simulated annealing

A new multibody, whole-residue potential for protein tertiary structure is described. The potential is based on the local environment surrounding each main-chain alpha carbon (CA), defined as the set of all residues whose CA coordinates lie within a spherical volume of set radius in 3-dimensional (3D) space surrounding that position. It is shown that the relative positions of the CAs in these local environments belong to a set of preferred templates. The templates are derived by cluster analysis of the presently available database of over 3000 protein chains (750,000 residues) having not more than 30% sequence similarity. For each template is derived also a set of residue propensities for each topological position in the template. Using lookup tables of these derived templates, it is then possible to calculate an energy for any conformation of a given protein sequence. The application of the potential to ab initio protein tertiary structure prediction is evaluated by performing Monte Carlo simulated annealing on test protein sequences.