A statistical mechanical model for beta-hairpin kinetics.

Protein chains coil into alpha-helices and beta-sheet structures. Knowing the timescales and mechanism of formation of these basic structural elements is essential for understanding how proteins fold. For the past 40 years, alpha-helix formation has been extensively investigated in synthetic and natural peptides, including by nanosecond kinetic studies. In contrast, the mechanism of formation of beta structures has not been studied experimentally. The minimal beta-structure element is the beta-hairpin, which is also the basic component of antiparallel beta-sheets. Here we use a nanosecond laser temperature-jump apparatus to study the kinetics of folding a beta-hairpin consisting of 16 amino-acid residues. Folding of the hairpin occurs in 6 micros at room temperature, which is about 30 times slower than the rate of alpha-helix formation. We have developed a simple statistical mechanical model that provides a structural explanation for this result. Our analysis also shows that folding of a beta-hairpin captures much of the basic physics of protein folding, including stabilization by hydrogen bonding and hydrophobic interactions, two-state behaviour, and a funnel-like, partially rugged energy landscape.

In a simple nonequilibrium statistical mechanics model (two coupled nonlinear stochastic reaction-diffusion equations), self-sustained oscillations appear as a symmetry-breaking effect for the associated probability density. Correlation and response functions are approximately calculated above and below the transition point. Renormalization-group theory yields the leading-order scaling of order parameter, relaxation time, correction to the collective frequency, and correlation length.

A purely static characterisation of “atomic” versus “ionized” states is given in terms of the spectral properties of the pair reduced density matrix. These spectral properties can be analyzed in a simple model (a “short range electron” with classical “hard core protons”). In the model the Mott effect occurs at high density as a consequence of the reduction of particle fluctuations.

Local signals in the energy landscape of collapsed helical proteins

The behavior of the inter-ionic potential of condensed liquid cesium in a wide temperature range

Historically, the development of equations of state for fluids has almost invariably followed the lead of the van der Waals (vdW) equation which includes an attraction term and a repulsion term. In this paper, using a simple statistical mechanics model, we introduce a parameter σ as both the power and a coefficient of the packing fraction y which locates at the numerator of the vdW attraction term. Then nine equations of state are constructed to solve the critical conditions and the main thermodynamic properties of pure substances at liquid-vapor equilibrium. As a result, the correct critical compressibility factors of Nitrogen, Argon, Carbon dioxide, Ethene, Methane, Oxygen, Propene, Water and Hydrogen, are obtained with an optimal choice of parameter σ. Good predictions of these equations to the liquid-vapor equilibrium properties below critical temperature are reported and compared with experimental data.

Following a review of the problem of stilbene isomerism an account is given of recent picosecond tinescale experiments on this system.Transient absorption methods are used to expose vibrational relaxation details for molecules in solution and streak camera measurements of fluorescence decay are presented to demonstrate the irreversibility of the Si (trans) decay.A simple statistical mechanical model is presented to describe the effect of viscosity on the twisting dynamics of trans-stilbene.A summary of recent experiments involving stilbene in the gas phase is presented.The isolated molecules twist very rapidly (15 ps at 265 nm excitation) and display characteristics typical of systems with a potential barrier.Finally the solution and gas phase processes are contrasted. INTRODUCTORY REVIEWIt is well known that substituted ethylenes can undergo cis-trans isomerism following optical excitation.A large literature already exists on this topic and the particular case of stilbenes (1,2-diphenylethylenes) was recently reviewed by Saltiel and coworkers (1).Phenyl substituted ethylenes received considerable attention from photochenists because their optical spectra are in the near ultraviolet, readily accessible to traditional light sources.The groundwork for understanding the photoisomerisn process in solutions was laid on the basis of conventional (pre-laser) experiments (1,2) but the intrinsic molecular steps involved are now known from vapor phase studies to be subnanosecond (3,4).The basic model for the isomerism is that a twisted, less conjugated form of tilbene is formed following optical excitation (5) .This twisted form may then undergo relaxation processes that result in both cis and trans structures (6).The solvent slows down the isomerization and at sufficiently low temperature or high viscosity the rate is found to be even slower than the natural radiative processes (7).The fluorescent properties of the system therefore can be used to monitor the isonerization.Saltiel and coworkers (8,9) have shown that the principal ultraviolet photochemistry of stilbeme arises from the singlet excited surface.The triplet state can be involved when sensitizers are present (9,10), and the ground state pathway requires moderately high temperatures (1,2).There is also evidence that isomerization is not the exclusive photoprocess since small yields of rearranged species have been reported (11).

Several key problems previously analyzed by simulated annealing are well described by a simple two-state statistical mechanical model, equivalent to the one-dimensional Ising model, in conjunction with an Arrhenius type rate equation. With this model we develop an analytic solution for the optimal cooling strategy which computationally is much faster than the previously developed adaptive algorithm. In the long time limit the analytic solution reduces to the one cooling schedule which is sure to reach the ground state. Our model predictions are in good agreement with earlier numerical simulation results for optimal cooling schedules as well as for stationary and dynamic properties of system energy, heat capacity, and relaxation time.

An extremely simple univariate statistical model called ‘IndOzy’ was developed to predict El Niño‐Southern Oscillation (ENSO) events. The model uses five delayed‐time inputs of the Niño 3.4 sea surface temperature anomaly (SSTA) index to predict up to 12 months in advance. The prediction skill of the model was assessed using both short‐ and long‐term indices and compared with other operational dynamical and statistical models. Using ENSO‐CLIPER(climatology and persistence) as benchmark, only a few statistical models including IndOzy are considered skillful for short‐range prediction. All models, however, do not differ significantly from the benchmark model at seasonal Lead‐3–6. None of the models show any skill, even against a no‐skill random forecast, for seasonal Lead‐7. When using the Niño 3.4 SSTA index from 1856 to 2005, the ultra simple IndOzy shows a useful prediction up to 4 months lead, and is slightly less skillful than the best dynamical model LDEO5. That such a simple model such as IndOzy, which can be run in a few seconds on a standard office computer, can perform comparably with respect to the far more complicated models raises some philosophical questions about modelling extremely complicated systems such as ENSO. It seems evident that much of the complexity of many models does little to improve the accuracy of prediction. If larger and more complex models do not perform significantly better than an almost trivially simple model, then perhaps future models that use even larger data sets, and much greater computer power may not lead to significant improvements in both dynamical and statistical models. Investigating why simple models perform so well may help to point the way to improved models. For example, analysing dynamical models by successively stripping away their complexity can focus in on the most important parameters for a good prediction. Copyright © 2007 Royal Meteorological Society

In many cases, transcriptional regulation involves the binding of transcription factors at sites on the DNA that are not immediately adjacent to the promoter of interest. This action at a distance is often mediated by the formation of DNA loops: Binding at two or more sites on the DNA results in the formation of a loop, which can bring the transcription factor into the immediate neighborhood of the relevant promoter. These processes are important in settings ranging from the historic bacterial examples (bacterial metabolism and the lytic-lysogeny decision in bacteriophage), to the modern concept of gene regulation to regulatory processes central to pattern formation during development of multicellular organisms. Though there have been a variety of insights into the combinatorial aspects of transcriptional control, the mechanism of DNA looping as an agent of combinatorial control in both prokaryotes and eukaryotes remains unclear. We use single-molecule techniques to dissect DNA looping in the lac operon. In particular, we measure the propensity for DNA looping by the Lac repressor as a function of the concentration of repressor protein and as a function of the distance between repressor binding sites. As with earlier single-molecule studies, we find (at least) two distinct looped states and demonstrate that the presence of these two states depends both upon the concentration of repressor protein and the distance between the two repressor binding sites. We find that loops form even at interoperator spacings considerably shorter than the DNA persistence length, without the intervention of any other proteins to prebend the DNA. The concentration measurements also permit us to use a simple statistical mechanical model of DNA loop formation to determine the free energy of DNA looping, or equivalently, the for looping.

Machine learning (ML) often provides applicable high-performance models to facilitate decision-makers in various fields. However, this high performance is achieved at the expense of the interpretability of these models, which has been criticized by practitioners and has become a significant hindrance in their application. Therefore, in highly sensitive decisions, black boxes of ML models are not recommended. We proposed a novel methodology that uses complex supervised ML models and transforms them into simple, interpretable, transparent statistical models. This methodology is like stacking ensemble ML in which the best ML models are used as a base learner to compute relative feature weights. The index of these weights is further used as a single covariate in the simple logistic regression model to estimate the likelihood of an event. We tested this methodology on the primary dataset related to cardiovascular diseases (CVDs), the leading cause of mortalities in recent times. Therefore, early risk assessment is an important dimension that can potentially reduce the burden of CVDs and their related mortality through accurate but interpretable risk prediction models. We developed an artificial neural network and support vector machines based on ML models and transformed them into a simple statistical model and heart risk scores. These simplified models were found transparent, reliable, valid, interpretable, and approximate in predictions. The findings of this study suggest that complex supervised ML models can be efficiently transformed into simple statistical models that can also be validated.

Statistical seasonal prediction models for the Arctic sea ice concentration (SIC) were developed for the late summer (August-October) when the downward trend is dramatic. The absorbed solar radiation (ASR) at the top of the atmosphere in June has a significant seasonal leading role on the SIC. Based on the lagged ASR-SIC relationship, two simple statistical models were established: the Markovian stochastic and the linear regression models. Crossvalidated hindcasts of SIC from 1979 to 2014 by the two models were compared with each other and observation. The hindcasts showed general agreement between the models as they share a common predictor, ASR in June and the observed SIC was well reproduced, especially over the relatively thin-ice regions (of one- or multi-year sea ice). The robust predictability confirms the functional role of ASR in the prediction of SIC. In particular, the SIC prediction in October was quite promising probably due to the pronounced icealbedo feedback. The temporal correlation coefficients between the predicted SIC and the observed SIC were 0.79 and 0.82 by the Markovian and regression models, respectively. Small differences were observed between the two models; the regression model performed slightly better in August and September in terms of temporal correlation coefficients. Meanwhile, the prediction skills of the Markovian model in October were higher in the north of Chukchi, the East Siberian, and the Laptev Seas. A strong non-linear relationship between ASR in June and SIC in October in these areas would have increased the predictability of the Markovian model.

<div class="htmlview paragraph">The failure time of automobile and its components is typical random variable. In studying reliability automobile and its components some simple theoretical statistical models, such as Normal distribution, Lognormal distribution and Weibull's distribution, index distribution etc., are used to describe automobile reliability. These distributions can not often represent actual datum well, then more complex theoretical statistical model is needed. If using complex statistical theoretical model the more parameters must be determined. Methods of moment, Maximum likelihood method can not estimate the parameters of complex statistical models yet. With graph method though the type of random variable distribution can be recognized, the precision of estimated parameters is not high. Meanwhile there is not an objectively criterion to judge statistical model reasonability.</div> <div class="htmlview paragraph">Based on the adaptability of Weibull's distribution, multiple-mixed Weibull's distribution suits to describe the complex statistical distribution of random variable. To estimate the parameters of multiple Weibull's distribution correctly, optimization model for estimating parameters of multiple-mixed Weibull's distribution is presented, according to the principle of least-square.</div> <div class="htmlview paragraph">In order to obtain the optimal estimation, the Levebberg-Marquardt method with line-search and Gauss-Newton method are alternatively used. A safeguarded mixed quadratic and cubic polynomial interpolation and extrapolation are chosen as algorithm of line-search. The example shows that multiple Weibull's distribution has quite good adaptability in describing the complex statistical distribution of random variable. The model and algorithm of optimization for estimating multiple Weibull's distribution parameters have steady convergence.</div>

We use a combination of variable-temperature high-resolution synchrotron X-ray powder diffraction measurements and Monte Carlo simulations to characterise the evolution of two different types of ferroic multipolar order in a series of cyano elpasolite molecular perovskites. We show that ferroquadrupolar order in [C3N2H5]2Rb[Co(CN)6] is a first-order process that is well described by a 4-state Potts model on the simple cubic lattice. Likewise, ferrooctupolar order in [NMe4]2B[Co(CN)6] (B = K, Rb, Cs) also emerges via a first-order transition that now corresponds to a 6-state Potts model. Hence, for these particular cases, the dominant symmetry breaking mechanisms are well understood in terms of simple statistical mechanical models. By varying composition, we find that the effective coupling between multipolar degrees of freedom—and hence the temperature at which ferromultipolar order emerges—can be tuned in a chemically sensible manner.

PM10 is one of the aerosol particles that can endanger human health. This research conducted by forcasteing for PM10 concentration. Forecasting is an activity of estimating or predicting events in the future, therefore it is necessary to do analysis simple statistical model to know goog results. In this case, several forecasting models are used for the daily PM10 concentration in Kototabang, that is Liniear, Quadratic, and Exponential Trend Model. As the results of this research, monthly forecasting using Linear Trend Model has the highest correlation value in October (-60) with MAD value 0.254, MSE 0.0651, RMSE 0.255, and MAPE 1848.8. Monthly forecasting using the Quadratic Trend Model has the highest correlation value in February (+0.52) with MAD value 0.013, MSE 0.0002, RMSE 0.015, and MAPE 103.934. then, for monthly forecasting using the Exponential Trend Model has the highest value in October (+0.61) with MAD value 0.124, MSE 0.0154, RMSE 0.124, and MAPE 893.484. the output of the forecasting model obtained the best model for forecasting the daily PM10 concentration in Kototabang i.e by using a simple statistical model, linear trend model.