The Golden Bird (with panel zoom)/n/t/t/t - Classics Illustrated Junior

Second, Cesari et al. In particular, the force field was trained to reproduce NMR data for nucleosides and dinucleoside monophosphates. The number of parameters used in the fit was significantly smaller than the number of available experimental data points to avoid overfitting. The corrections were then validated on tetranucleotides, resulting also in this case in an improved agreement with NMR experimental data.

Notably, both the training and the validation were performed using as reference solution NMR data, which is expected to describe structural dynamics of flexible motifs better than an individual crystallographic structure. Possible problems in these torsions might be related to the occurrence of intercalated structures in simulations of tetranucleotides see section 4.

Their modifications were tested on selected tetraloops, tetranucleotides, and RNA duplexes, with promising results, albeit with only limited sampling of the tetranucleotide simulations. A particularly interesting aspect of all of these works is that all dihedral potentials were fitted simultaneously, at variance with the usual procedure where one dihedral angle at a time is modified. None of these new modifications has yet been tested extensively, and so all of these force fields should be considered experimental and only used with this caveat in mind. This divergence necessitated the development of separate Cornell et al.

We therefore do not recommend its use in RNA simulations. This force field is also not recommended for use with RNA. Reparameterizations of the remaining dihedrals achieved some additional improvements for DNA, and OL15 probably represents the upper limit of what can be achieved by reparameterizing uncoupled dihedrals for DNA.

Despite these improvements, the force field is far from flawless. The fact that state-of-the-art force fields for RNA and DNA require different dihedral parameters is a further confirmation that these parameters are nonphysical and only used to compensate errors arising from other missing interactions. Further tuning of the force field would require modification of the nonbonded terms and consideration of better solvent models.

As a first attempt in this direction, Chen and Garcia modified the balance between stacking, H-bonding, and solvation. This involved i rescaling the vdW parameters of the nucleobases, and ii adjustment of vdW combination rules for base-water interactions nonbonded fix, NBfix. The modified force field offered partial improvements in simulations of RNA tetraloops, albeit of a lesser magnitude , than was originally suggested, and some side effects have been later reported see section 4.

Another work considering alternative vdW parameters was published by Bergonzo et al. The simulations showed a slightly better description of tetranucleotides than reported by Bergonzo et al. However, the latter modification seems to have only marginal effects on the simulations, which become apparent after detailed scrutiny of the published data. However, none of these modifications were tested on a broad range of RNA structures, and their general applicability remains to be determined. In summary, most attempts to modify the vdW terms have required simultaneous modification of the vdW combination rules.

It is therefore not clear whether RNA simulations can be improved by tuning the vdW term alone without using additional tricks such as NBfix, which effectively increase the number of parameters that can be tuned.

In addition, none of the reported attempts seems to have yielded a real breakthrough in the quality of RNA simulations. In addition to attempts to improve the general parameterization of the RNA force field, simulations of specific systems can be improved by structure-specific force-field modifications. The HBfix method not to be confused with the NBfix-type modifications discussed above adds a local spherical auxiliary potential supporting native hydrogen bonds. HBfix only indirectly promotes forward folding corresponding to k on in experiments but directly increases the lifetime of folded structures i.

Note that when utilizing structure-specific potentials, one is typically limited by the functions that are implemented in the simulation codes; in practice, HBfix is constructed as a linear combination of two standard restraints. For this reason, HBfix has been so far implemented in a way that does not account for the directionality of the H-bonds. For instance, the typical number of hydrogen bonds stabilized in an 8-mer including a GAGA tetraloop in the HBfix approach would be 9.

Obviously, the use of structure-specific force-field adjustments may seem unsatisfactory. However, pragmatic use of such biases is legitimate, and, due to the persistent performance problems of the general force fields, their use may become increasingly common, or even inevitable. We suggest that the best approach is to first try to achieve the best possible performance with the general force field.

Once one has then reached the point at which further tuning is unproductive, the native state s can be supported with gentle structure-specific biases rather than continuing with cumbersome force-field refinements that may cause many undesired side effects. In addition, in principle, the HBfix type of potential could be generalized in an interaction-specific manner. It is not clear whether these contrasting reports reflect the use of somewhat different force-field implementations including a possible difference between periodic boundary and solvent sphere computations; see section 4.

The robustness of this refinement is not yet fully clear; in our opinion, it has reduced but not eliminated the tendency toward fraying. As we noted in several other places of this review e. However, there is always a potential risk that such structural changes may not be fully realistic. We reiterate that the CHARMM force-field developers are currently leading the efforts to derive polarizable force fields for nucleic acids. A very important issue closely related to the development of new force fields is their validation.

In general, as we discussed, classical force fields contain nonphysical terms that might predict correct relative stabilities of multiple conformers as a consequence of error cancellation. This makes it very difficult to validate the force field from an ab initio perspective, by using for example QM benchmarks. When possible, this comparison should be made in situations where the MD trajectory is ergodic see section 3.

This analysis is computationally demanding when testing several force-field variants due to the fact that a full simulation has to be performed every time a force-field term is changed. An efficient alternative comes from reweighting the already available simulations to take into account changes in the force field. This procedure is analogous to the free-energy perturbation method see section 3. Reweighting has been used, for instance, in ref to predict the effect of small perturbations applied on the dihedral angles on tetranucleotides and tetraloops, and in refs and to test full dihedral reparameterizations on tetranucleotides.

Unfortunately, this procedure, known as exponential averaging, is only effective when the fluctuations of the difference between the two potential energy functions are small. Effective sample size will be large only when the ensembles generated by the two force fields are significantly overlapping. If some structure that is stabilized by the force field U 1 is never visited by the force field U 0 , its effect on the ensemble averages cannot be estimated without running a new simulation using the force field U 1.

In addition, reweighting might be highly inefficient when charges are perturbed, because, due its long-range nature, electrostatic energy can be heavily affected by very small changes in the charges. MD simulations allow the equations of motion to be solved and the evolution of the system to be followed in real time.

This is achieved using a model empirical potential, the force field, which mimics the real interatomic forces acting on the simulated molecular system. Aside from the approximations inherent in the force field, which are discussed in sections 3. The time scales over which the conformational transformations of RNA occur are very heterogeneous. Slower processes such as ligand-induced riboswitch folding , occur on scales of seconds to minutes or beyond. Such comprehensive simulations are clearly beyond the reach of current computers.

From a theoretical point of view, MD simulations can be seen as Markov chains see section 3. When used to compute ensemble averages such as populations of individual substates, MD simulations will suffer, as any method based on Markov chains, from a statistical error due to the finite length of the simulation. The former effect can be decreased by making a simulation longer, and the latter by discarding the initial equilibration part see, e.

However, whenever an MD simulation remains stuck in a given conformation, one should try to understand whether this specific conformation corresponds to the global minimum of the free energy of the system or it is just a kinetically trapped local minimum. Rigorously speaking, the only way to answer this question is to run a simulation capable to explore the whole conformational space.

In practice, one might try simulations starting from different conformations and see if results are independent of the starting point. Using state-of-the-art hardware and software, the only RNA systems for which a fully converged exploration of the conformational space can be achieved with plain molecular dynamics are probably nucleosides or dinucleotides.

However, using highly optimized hardware 73 or with the enhanced sampling techniques discussed in this section, tetranucleotides or even tetraloops see sections 4.

Shock Absorption Material for Wheelchair Caster

Probably, neither plain MD nor enhanced sampling methods can completely sample the conformational space of larger systems. In these cases, one might only be able to sample different conformations that are in the vicinity of the initial structure. Still, in some cases, it is possible to obtain relative populations of relevant substates that can be compared to experiments.

In other words, whereas full convergence might be impossible to reach, one might be in the situation where multiple transitions between the locally available substates are seen and local exploration is virtually converged. In addition, series of smartly designed simulations initiated in different parts of the conformational space and characterizing properties of different types of conformations present on the free-energy landscape may provide unique insights complementing the available experimental data even without simulating large-scale transitions.

In general, RNA tends to have multiple metastable states, and its folding landscape is very rugged. In other words, the metastable states may persist over diverse time scales and may include different backbone conformations, diverse patterns of directly bound ions, differences in base-pair geometries, or even entirely different folds.

The definition of metastability depends on the observed time scale and the capability of experiments to detect the ruggedness of the folding landscape. When reconformations are faster than the temporal resolution of the experiments, or in a bulk experiment where a macroscopic number of copies of the same molecule is present in a buffer, an experiment would probe some averaged ensemble property.

• RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview.
• Joe Nick Patoski : The Wittliff Collections.
• Works of Andrew Marvell.
• Missa Solemnis, No. 5: Benedictus.

MD is a fundamental method for studying the ruggedness of the RNA conformational landscape. In principle, MD simulations are not limited by experimentally detectable properties and temporal resolutions, which is important because many dynamic processes not resolvable by experiments may be critically important for the biochemical and biological functions of RNAs. To tackle this issue, several groups have worked over the last few decades to develop methods that allow properties that emerge over long time scales to be investigated using relatively short simulations see, e.

Scheme representing some of the methods discussed in this section. A In Markov state models, extensive simulations usually sets of simulations are analyzed, and the observed states are clustered. A kinetic matrix is then constructed that provides the probability of observing transitions between pairs of clusters section 3. B In replica exchange simulations, numerous replicas of the system are simulated in parallel using different parameters e.

From time to time, exchanges are attempted with a Monte Carlo procedure. Sampling in the reference unmodified replica is enhanced by the method section 3. C In metadynamics, a bias potential is added to compensate the underlying free-energy barriers along a preselected collective variable CV. If the chosen CV is capable of discriminating the transition state, the transition probability is enhanced section 3. It is important to mention that enhanced sampling techniques would be almost wholly unnecessary if they could be replaced by straightforward MD simulations with sufficiently long time scales.

Even more striking has been the effort made by the D. Shaw group, which has developed a dedicated machine for MD 73 that allows access to the millisecond time scale when simulating small proteins and DNA. Despite this remarkable progress, biologically relevant time scales are currently out of reach and will likely remain so for decades. A wide array of methods have been developed over the years for obtaining information about biomolecular systems that emerges over long time scales from short simulations. In general, they have been tested more extensively on proteins than nucleic acids, and fewer studies still have focused on RNA.

These methods are also difficult to classify because many of them combine elements of previous methods that were developed on the basis of diverse principles. The conceptually simplest way to obtain long time scale information is to combine multiple short trajectories section 3. Techniques of this class, such as Markov state models MSM , mostly provide recipes for initializing the simulations in a way that maximizes the sampling of important events e. MSM methods can also be exceptionally useful for analyzing MD simulation results from huge amounts of simulation data, and visualizing them in a humanly comprehensible way.

Indeed, meaningfully analyzing raw MD trajectories is often insurmountably complex due to the vast amount of data they contain. Alternatively, one could use enhanced sampling methods to accelerate events. The methods of this kind that have been most widely used for exploring the conformational space of RNA molecules are based on the principle of annealing and replica-exchange section 3. In this approach, a set of simulations replicas at different temperatures are performed in parallel, and exchanges among the replicas allow free-energy barriers to be crossed by coupling the cold replicas with the more ergodic hot ones.

Other approaches are based on the principle of importance sampling, where an artificially modified ensemble is explored section 3. In general, importance sampling techniques aim to derive properties of a particular ensemble probability distribution of structures of interest from samples generated from a different biased distribution. In these methods, a biasing force or a bias potential is used to accelerate sampling in a reduced low-dimensional space consisting of slow degrees of freedom or collective variables CVs.

The CVs should reflect the essence of the studied processes, resembling reaction coordinates in simple chemical reactions. These methods thus assume that the studied process can be described with sufficient realism using just a few degrees of freedom, which can be seen as a coarse graining of the full coordinate space, that is, a low-dimensional projection. The remaining dynamics that is orthogonal to the space defined by the CVs is assumed to be unimportant to the studied process. CVs can be very complex functions of the Cartesian coordinates of the system.

Enhanced sampling methods aim to flatten the Boltzmann distribution in the CV space by imposing a bias that allows sampling of the whole CV space. The effect of this external potential is reweighted a posteriori using procedures similar to that discussed in section 3. Enhanced sampling methods are based on the idea of guiding the system in some way through unrealistically fast trajectories so as to observe the desired events.

This idea can be taken to its logical extreme by considering a case in which the path consists of a transformation in which the chemical identity of the simulated molecules is changed, as it is done in alchemical methods section 3. These alchemical transitions may involve the use of chemically unrealistic intermediate states in which, for example, atoms present in the initial system are simply removed because the free energy is a state function and the free-energy difference between two states is path-independent.

Finally, it is possible to remove solvent degrees of freedom to accelerate sampling section 3. Whereas this procedure introduces some unavoidable approximations that might be critical in RNA systems, it is particularly attractive as it allows free energies to be computed from single conformations, bypassing the need to simulate reactive trajectories. The following sections discuss these methods and their strengths and limitations in more detail, with a particular focus on those that have been applied to RNA systems. In recent years, the availability of massively parallel computing resources has increased exponentially.

Modern supercomputing clusters make it possible to run hundreds of parallel simulations. However, advanced analysis techniques must be used to combine the data generated by multiple, out-of-equilibrium, short simulations, and extract relevant information from them. The framework of Markov state models MSMs is perfectly suited for this task. Each microstate consists of a number of structures that can be considered sufficiently similar to be indistinguishable equivalent in kinetic terms.

Note that the T matrix is often used in its transposed form, and then the meaning of indexes i and j is interchanged.

1. Believe Me, Goldilocks Rocks! (The Other Side of the Story).
2. A New Health Food Plan : For the Whole Family;
3. Spider #62 November 1938 (The Spider)!
4. .
5. ?
6. 79 best FUN - Junior Classics images on Pinterest | Comics, Cartoons and Comic Book.
7. La poule de Marcel (Les petites histoires de philomène t. 1) (French Edition)!

The resulting discrete MSM aims to approximate the continuous dynamics of the simulated system by a discrete process. Using a MSM, one can evolve either the individual stochastic trajectories time series of microstates, i. The MSM approximation can be extremely accurate; that is, it can provide the same time-development picture as the MD simulations. The interpretation of the eigenvalues and eigenvectors of the transition matrix of an MSM is the following: MSM can be fruitfully applied to help extracting human-interpretable information from a single long MD trajectory, which repeatedly and spontaneously samples the rare event under investigation.

If the simulation samples the process sufficiently well, the MSM can be used to create a coarse-grained model of the process, providing the much-needed insights into the otherwise overwhelming amount of raw simulation data. Alternatively, MSMs can be used to merge together separate MD trajectories, by discretizing the ensemble spanned by all trajectories, and counting the transitions occurring in any of the trajectories.

This enables one to rigorously combine the information coming from multiple trajectories in a single quantitative model. The first step in the construction of a MSM is the discretization of the phase space into microstates. This can be done employing different clustering methods as well as different metrics. This allows the subsequent clustering to be done in a lower dimensionality, in the space of the leading TICA components, by projecting the simulation trajectories onto the largest TICA components.

TICA can be viewed as a method analogous to principal component analysis PCA , which has been conventionally used to process MD trajectories in the past. PCA identifies linear combinations of the input degrees of freedom with the highest variance, while TICA finds those with the highest autocorrelation times, that is, corresponding to the slowest processes occurring in the simulations.

TICA can be performed starting from a description based on the Cartesian coordinates of all of the solute atoms, or using a description defined on some internal coordinates, as, for instance, dihedral angles or pairwise distances between relevant atoms. As with other dimensionality reduction methods, one must always be aware that some important pieces of information might be discarded, distorting the description of fast time-scale processes.

Because of the remarkable results it has achieved, TICA has been recommended as a standard tool for coordinate transformation and dimensionality reduction of MD trajectories data. Discretization of the phase space into a finite number of microstates is the main source of systematic error in a MSM. This step breaks the Markovianity of the system, that is, the assumption that the transition probabilities only depend on the current state of the system.

Thus, modeling the system as a Markov chain causes deviations from the true dynamics. It has been shown that these deviations can be reduced in two ways: In practice, when dealing with real finite-length simulations, both factors affect the quality of the computation. The lag time depends intrinsically on the Markovianity of the system and the desired temporal resolution.

Too short of a lag time will make the model non-Markovian. As a rule of thumb, the interconversions among structures within each individual microstates must be fast as compared to the lag time. The number of microstates should be large enough to avoid losing resolution due to coarse graining of the phase space but small enough for there to be a reasonable number of transitions between them i.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

For simulations of medium-sized biomolecules with contemporary methods, one typically uses MSMs with at least 10 2 —10 4 microstates. Several methods exist to overcome this problem by exploiting the kinetic information provided by an MSM to construct an even coarser representation of the system, lumping the MSM microstates into a few metastable macrostates. A commonly used approach is Perron-cluster cluster analysis PCCA , a method that exploits the sign structure of the eigenvectors of the transition matrix to define the optimal metastable partition of the MSM microstates.

These macrostates are not directly observable but are measured by looking at the microstate, which at every step is extracted from a distribution probability that depends on the hidden macrostate. Thus, one assumes that an additional hidden variable can be used to label the states, and its time series is inferred by the time series of the observed variables. The HMM defines states without neat boundaries, and a given conformation has probabilities to be simultaneously participating in multiple macrostates. A key strength of the MSM approach is the observation that it is not necessary to assume global equilibration in the ensemble of trajectories provided that the MD is in local equilibrium within each microstate.

This is what makes MSMs powerful tools for accessing long-time-scale kinetics. In fact, by choosing smart initialization points for the simulations, one can obtain an ensemble of relatively short trajectories, each of them sampling transitions relevant to different steps of a complex and slow configurational change.

By combining these trajectories in a MSM, it is, in principle, possible to reconstruct even processes that occur on a time scale longer than the span of any of the individual trajectories. The largest implied time scale can be of the same order of magnitude of the aggregate duration of all MD trajectories used to build the MSM. There are various ways of selecting the starting points for MD simulations to be used in the construction of a MSM. If available, prior knowledge about the system can be used to initialize simulations in different positions along interesting conformational changes for example, if experimental structures of multiple conformations are available.

If this step is repeated recursively on each new simulation, it will produce a cascade of MD trajectories, sampling increasingly larger regions of the available phase space. By changing the criteria for identifying candidate starting points for new trajectories, it is possible to drive the system along the path of the conformational change of interest. Another powerful approach is to extract the initial structures from an ensemble of configurations obtained with some different enhanced sampling technique.

As with all methods designed to reduce the computational cost of MD simulations, a MSM may provide wrong results when used in a way that is inconsistent with its basic approximations and assumptions. It is therefore important to test the validity of the Markovian approximation before drawing any conclusions from a MSM. It is useful to point out that the common practice of showing the time scales in logarithmic scale may give a false impression of convergence due to the negative convexity of the logarithm function. It is important to note that the convergence of the implied time scales is a necessary but not sufficient condition for Markovianity.

When convergence is reached, the slowest implied time scale should correspond to the slowest transition mode in the studied system. Its comparison with previous knowledge of the system can provide some hint on whether the full free-energy landscape has been sufficiently sampled or not. A too short implied time scale as compared to experiment could indicate that important parts of the free-energy landscape are entirely missing in the simulation data set, and the MSM characterizes only a local segment of the folding landscape.

This could happen when simulations are too short or not initialized to cover sufficiently the relevant portions of the phase space. For example, in studies of the folding landscape, series of simulations may be initiated seeded from some unfolding pathway, obtained by forced unfolding or high-temperature simulation initiated from the folded state.

This may work well for molecules with fast folding via a funnel mechanism. Note, however, that as in all of the algorithms based on statistical sampling, there is no way to infer information about conformations that were never sampled in the simulated trajectory.

Bucks County

Thus, these tests are not a panacea. As mentioned in the previous paragraph, in case of kinetic partitioning, even sophisticated convergence tests would not reveal the lack of convergence because the free-energy basins corresponding to the misfolded states are entirely inaccessible to the simulations. Thus, the investigators must always perform a rational overall appraisal of the studied process and not rely merely on the numbers provided by the computational procedures.

Another important source of uncertainty in the predictions of a MSM is the statistical error due to finite sampling. The results of these studies with all of their limitations are discussed in section 4. The results of these studies are discussed in section 4. MSMs were used to characterize kinetic properties of very short RNA oligonucleotides, dinucleotides composed of combinations of adenine and cytidine as well as tri- and tetranucleotides composed of adenines. The coordinates used were the dihedral angles of the studied systems and the G-vectors introduced in ref , which take into account the formation and direction of stacking interactions.

Thus, agreement with experiments was only obtained after manually removing the intercalated structures from the trajectory. MSM modeling has also been used to analyze conformational substates of conformationally restricted single-stranded three-nucleotide loops of DNA quadruplexes; 76 such approaches should be readily applicable also to various single-stranded RNA segments with restrained positions of the strand termini. Schematic representation of four-state hidden Markov model for adenine trinucleotide. Shading indicates the distribution of the simulation data projected on the plane defined by the two leading TICA components.

Another study investigated the process of pairing and fraying of a terminal base pair of an RNA duplex with methods closely related to MSM. Interestingly, they identified a rate-determining trapped state, in which the base is stacked but the backbone assumes a non-native conformation.

MSM methodologies have developed rapidly over the past few years, and many procedures that were favored in the past have been surpassed by better alternatives. Being already successfully applied to the study of many protein systems, they are now starting to cut their space also in the world of RNA. The most widely used enhanced sampling method in biomolecular simulations is probably the parallel tempering PT method, which is also known as temperature-replica-exchange MD T-REMD.

This is because the time required to cross a free-energy barrier depends exponentially on the height of the enthalpic part of the barrier divided by the temperature of the system. However, the temperature also affects the equilibrium populations of different conformations. Therefore, running MD simulations at a high temperature would yield faster conformational transitions but might also result in extensive sampling of structures whose population is negligible at lower temperatures e.

High temperature simulations have sometimes been used qualitatively to enhance sampling of RNA systems see, e. However, high temperature simulations alone cannot be used to directly estimate the values of experimental observables at physiological temperatures, and this approach is considered rather obsolete these days. The idea of annealing is, after the transition, to slowly decrease the simulation temperature so as to gradually shift the system to explore a relevant region of its conformational space. The main problem of simulated annealing is that the results can heavily depend on the schedule used to reduce the temperature.

In particular, final conformations might retain properties of the initial high temperature part of the simulation if the cooling is too fast. An important step forward was introduction of the simulated tempering approach. The goal of the method is to perform a random walk across the temperature space, leading to multiple heating and cooling cycles.

Once a set of temperatures is chosen from a given range, a weight is assigned to each temperature state that determines the probability of visiting that state i. If the weights are not chosen properly, the random walk in the temperature space will be confined to a subspace to some degree rather than fully exploring the entire space. Schemes for automatically adjusting these weights have been proposed. From time to time, an exchange of coordinates between two replicas in the temperature ladder is attempted and either accepted or rejected using a MC procedure based on the potential energies of the simulated systems.

Because the number of simulations at each temperature is fixed i. T-REMD was originally introduced in studies on spin glasses and was subsequently used by the biomolecular research community in conjunction with Monte Carlo methods and then with MD. One important choice when setting up a T-REMD study is the temperature range spanned by the replicas.

The range typically goes from the reference temperature to a temperature high enough for enthalpic barriers to be easily crossed usually between and K. These high temperatures are far from the physiological conditions because they are well above the boiling point of water under simulated conditions. However, one should note that the water models used in MD simulations typically have higher boiling points than that of real water. Additionally, most T-REMD simulations are performed at constant volume and so are not subject to this issue. While this is not usually a problem, it should be accounted for properly whenever conformational changes are correlated with changes in the effective volume of the solute, as done by Garcia et al.

It should therefore be optimized to enable the observation of the greatest possible number of conformational changes. T-REMD is certainly a robust tool for overcoming enthalpic barriers. However, folding barriers often contain significant entropic contributions, and then the effect of high temperatures to enhance sampling is limited. Paradoxically, the addition of more high temperature replicas could even make the algorithm less computationally efficient because the additional cost of the extra replicas might not be fully compensated by more effective sampling and corresponding shorter folding time.

Moreover, the number of states that should be explored increases significantly with temperature, so the dimensionality of the generalized ensemble i.

Joe Nick Patoski

For these reasons, evaluations of the computational efficiency of a T-REMD procedure could yield very different answers depending on the specific system investigated. The goal of replica exchange methods is to maximize the number of statistically independent visits at low temperatures. To do this, it is important to maximize the number of successful exchanges and reduce the time a replica needs to visit a high temperature and return.

Put another way, one must minimize the time the replica needs to traverse the temperature ladder. This time depends on the average exchange acceptance across the replicas, the number of replicas, and the stride of the replica exchange attempt. In practice, the exchange stride in explicit-solvent T-REMD is typically set to a fraction of a picosecond. Recent algorithms have achieved performance improvements by using a procedure that mimics the limit of exchanging at every MD step the so-called infinite swapping limit.

When setting up a T-REMD simulation, it is also important to properly fix the temperature distribution so that the potential energy distributions of neighboring replicas overlap. This is often done so as to obtain a high and, possibly, uniform acceptance across the replica ladder. Analytical derivations in simple systems have shown that for a uniform acceptance ratio, the difference between adjacent temperatures should be chosen inversely proportional to the square root of the systems heat capacity and should increase with the temperature.

This makes T-REMD very computationally demanding in large systems such as explicitly solvated biomolecules. It must be also noted that the assumption that specific heat is temperature independent, which leads to a geometric progression of temperatures, is not always realistic. This approximation is less appropriate for systems simulated in an implicit solvent see section 3.

Many approaches have been developed to optimize the distribution of replicas to maintain a uniform acceptance, to reduce round-trip times, or to adjust the replicas to specific heat capacity see, e. After a T-REMD simulation has been performed, unbiased populations of different substates can be obtained from the reference low-temperature replica. Interestingly, there have been some attempts to reconstruct kinetics from T-REMD simulations by making some a priori assumptions on the dependence of the transition rates on the temperature, including one on an RNA system simulated using a native-centric potential.

While a standard blocking analysis could be used to analyze the populations in the reference replica of a T-REMD simulation, the resulting errors might be significantly underestimated because of the correlations hidden in the replica swaps. In an extreme case, one might encounter a large number of apparent transitions that are only a signature of the swaps and do not correspond to a true exploration of the conformational space. Several works see, e. Demultiplexed trajectories can also be used in more rigorous error estimations based on an autocorrelation function.

Twenty-four histograms from a T-REMD simulation after ns black and ns red per replica are shown. In the first part of the simulation black data , it is evident that different trajectories sample different parts of the space, suggesting the simulation not to be converged. At the end of the simulation the red data , all of the substates are almost equivalently sampled by all of the replicas. A common practical problem with all replica exchange methods is that the minimum number of replicas required to achieve reasonable acceptance might be impractically large.

A possible solution is to use the simulated tempering scheme discussed above, where a single simulation is performed and the temperature is changed over time. This approach could thus be interpreted as a CV-based method like those discussed in section 3. The WT ensemble approach thus can be directly combined with T-REMD in a hybrid approach where multiple replicas are still employed but the number of replicas is significantly reduced, thanks to the increased fluctuations of the potential energy.

Alternatively, one could increase the acceptance rate by using short nonequilibrium simulations provided that the acceptance rate is properly computed. Therefore, there is no theoretical guarantee that these methods will accelerate sampling, although they have done so in empirical cases examined to date. The replica exchange protocol can be generalized to methods where ergodicity is not obtained by increasing temperature but by scaling portions of the force field or adding penalty potentials disfavoring specific structures e.

These methods are generally known as Hamiltonian replica exchange H-REMD methods because the different replicas use different Hamiltonian functions. Here, instead of changing the temperature, one scales down portions of the potential energy of the system.

This variant of REST has been used to accelerate the dynamics of an RNA tetraloop without affecting those of the corresponding stem, allowing different conformations of the capping nucleotides to be captured in a very short time. By constructing a ladder of such replicas that are increasingly biased, one can exploit the REMD strategy to obtain an unbiased ensemble in the reference replica.

It is worth mentioning that alternative procedures to reconstruct unbiased distributions from aMD simulations have been proposed that do not require the use of replicas but instead make some assumption on the distribution of the potential energy. In the case of tetranucleotides, this replica exchange framework proved more efficient than using the Hamiltonian or the temperature separately, although it required a very large number of replicas. The idea of accelerating a portion of the system e.

For instance, in ref , the capping nucleotides of an RNA stem-loop were accelerated by coupling each region to a different thermostat. Historically, the idea of accelerating only a portion of the system was first proposed as an enhanced sampling method per se. In the locally enhanced sampling LES technique, multiple copies of a system are simulated. The replicated atoms are subjected to a force that is scaled down by a factor corresponding to the number of copies. There is a clear parallel between the copies in a LES simulation and the biased replicas in the solute tempering approach: A strong point of the LES approach is that the use of multiple copies enables an intrinsically parallel and thus fast exploration of the conformational space for the region of interest.

However, when used in explicit solvent, all solvent molecules are typically shared among the copies and effectively keep the copies highly correlated. Therefore, it has been suggested that LES is best used with implicit solvent simulations see section 3. Thus, while it significantly improves the speed of conformational sampling, it cannot be used to estimate populations that can be directly compared to experiments.

This is probably the main reason why LES has not been used in recent works. Another class of enhanced sampling methods is based on umbrella sampling US. In its original formulation, US works by adding a bias potential that is a function of the selected CVs and that can bring the system as an umbrella through the transition state. Like a catalyst, this bias potential should ideally decrease the energy of the transition state to increase the transition rate.

In contrast to the above-mentioned annealing methods, the important sampling techniques are generally able to address entropically driven processes such as folding events by using properly chosen CVs. In addition, they allow high free-energy barriers on a priori known CVs to be crossed in a short time. On the other hand, the sampling is enhanced only in these few selected CVs, so that the probability of overcoming barriers is increased only in these few dimensions, while all perpendicular degrees of freedom are sampled as in efficiently as in the plain unbiased simulations.

The entropically rich unfolded state that typically occupies a large part of the multidimensional configuration space will be thus sampled less efficiently than the conformationally well-defined folded state. Another main obstacle of this approach is that it is usually difficult to know a priori the position of the transition state in the CV space and its stability. For this reason, US is almost invariably used by performing multiple simulations where the CV is restrained to explore the vicinity of a series of given values along the CV joining the initial and final states, or by defining a path along which the free-energy profile is calculated.

Note that, in practice, the US simulations are usually seeded using some form of a short pulling simulation, which generates series of starting configurations for the individual US windows between the initial and final states. The effect of this procedure can be nontrivial as discussed later in this section. The name PMF derives from the fact that its negative gradient determines the mean force acting on the system in the given point of the CV space. The words PMF and free-energy profile are largely interchangeable when discussing the dependence of the free energy on a CV. This equation relates the populations of different structures with the free-energy landscapes.

Note that the relative free energies of two sub states from the free-energy landscapes can be obtained by integrating the corresponding populations over the respective parts of the landscape that correspond to the sub states. Alternatively, WHAM can be formulated to provide the full unbiased distribution, allowing one to compute populations of specific states even though these states are not identified by the biased CVs alone. US with multiple restraints is probably the method of this class that has been most widely applied to RNA systems see, e.

For instance, the unfolding of a small hairpin has been studied by biasing its end-to-end distance. Overlaps are required for the self-consistent procedure used by WHAM method to converge to a unique solution. This limitation might be to some extent lifted by using an umbrella integration method. As with all other methods based on importance sampling, the accuracy of US depends on the convergence with respect to the simulated time. Evaluating this convergence is not trivial. Statistical errors on the reported free-energy landscapes or in the corresponding populations are sometimes computed by bootstrapping, which could significantly underestimate the error due to sample correlation.

A more robust approach is to use blocking analysis or, equivalently, to use block bootstrapping, or at least to compare two independent US simulation sets. Care is also necessary when using this approach: This assumption makes it impossible to determine whether neighboring simulations overlap in the full conformational space rather than only in the CV space; overlap is very difficult to test without observing transitions, and its absence can lead to severe error underestimation.

The error was estimated using a standard blocking analysis that in principle accounted for the time correlation between samples. At first sight, the calculations appeared to be adequately converged, as is commonly claimed in the literature describing such computations. However, two independent US simulations initialized in two different ways yielded completely different PMF profiles, both of which were incompatible with the statistical error calculated for the other simulation, indicating a drastic but hidden lack of convergence.

The difference between the two simulations stemmed from the use of different initial structures: The selected CV was not sufficient to sample transitions between docked and undocked state likely due to the presence of other kinetically relevant CVs, so-called hidden variables, that were not biased.

The calculated free energy thus depended strongly on the chosen computational protocol.

CONTAINER LIST

Note that many published papers do not provide such error analyses, and in many cases their authors are even unaware of the danger of a hidden lack of convergence. Common statistical methods to analyze convergence are usually not sufficient to identify such problems. Potential of mean force PMF as a function of the distance between the centers of mass of the kissing-loops in an adenine riboswitch. Results for Holo with ligand and Apo without ligand forms are shown as obtained from two independent US simulations using different protocols to obtain the initial structures forward, Fwd, where the loops are initially in contact; and backward, Bwd, where the loops are initially separated.

Fwd and Bwd profiles are aligned at the maximum distance. The result is strongly dependent on the initialization procedure, indicating that it cannot be quantitatively trusted, even though errors computed with standard block analysis shown as error bars would suggest so. Reprinted from ref ; http: Copyright BioMed Central Ltd.

A much more robust approach to US is to include it in an REMD scheme where swaps in the conformations of neighboring replicas are periodically attempted and either accepted or rejected on the basis of an MC scheme. The advantage of this formulation is that demultiplexed trajectories can be constructed see section 3. In contrast to classical US, which might lead to large differences between PMFs for association and dissociations pathways as highlighted in the preceding paragraph see, e. Example of a free-energy landscape i. Results are obtained using an asynchronous replica exchange US procedure where these three CVs are biased.

White dots represent lowest free-energy pathways connecting different pucker conformations. Local minima and saddle points are shown as blue and red spheres, respectively. Alternative approaches to WHAM that retain the dynamics information have been proposed see, e. The advantage of these approaches is that they are less sensitive to the initial structures. If one considers a limiting case in which the restraints used in US are infinitely strong i.

This allows one to explicitly account for the nonequilibrium work using the Jarzynski equality. A common problem of all of the unidirectional approaches is that there is an intrinsic bias in the final result. Whereas this might not be a problem when qualitative results are desired e. This is also true when Jarzynski-based methods are employed with a finite number of simulations, although the bias decreases as the number of simulations increases.

In the simplest formulation of this approach, forward and backward calculations might be compared. The result might be trusted only if it is independent of the steering direction. It is also possible to rigorously combine forward and backward calculations using a maximum likelihood approach. This illustrates the richness of the possibilities that one can consider when choosing CVs. Another notable idea derived from the original US method is that of constructing a potential adaptively during the simulation.

It is important to note that this is not usually done by restraining the simulation to a given region in the CV space as is common in multiple-restraint US. Several methods of this type have been proposed. One of the most popular adaptively biased methods is metadynamics, where a history-dependent procedure is used to disfavor already visited states.

In other words, the free-energy landscape and thus also the probability histograms of the biased simulation is flattened in the CV space. Unbiased free-energy surface as defined in the low-dimensional CV space can then be estimated by inverting the bias potential. In a more recent well-tempered variant of this approach WT-metadynamics , the penalty potential grows more slowly as the simulation progresses, eventually reaching a quasi-equilibrium state.

WT-metadynamics reduces fluctuations in estimation of the free-energy differences between the metastable states of the system. Moreover, in WT-metadynamics, one can easily tune the parameters of the simulation to obtain a controllable partial flattening of the free-energy landscape, avoiding the exploration of unnecessary high-energy states. Another important parameter controlling flattening of the free-energy landscape is the shape of the Gaussian functions used as a bias. Nonetheless, a method for setting their width automatically was also developed.

Nevertheless, even simulations that did not achieve statistical convergence have provided useful insights into the studied systems. For instance, WT-metadynamics results complemented those obtained with other methods indicating that the native structure of a TL was not correctly predicted by the tested force fields see sections 4. The main advantage of methods based on construction of an adaptive bias potential when compared to multiple restraint US is that they only converge when explicit conformational transitions are observed, and so their reliability is significantly easier to assess.

In other words, when multiple recrossing events are reported in metadynamics simulations, the result is statistically trustable. Simple tests can be performed to verify whether important CVs are missing. Note that a basic hysteresis in metadynamics typically leads to some overestimation of the barriers. However, use of entirely inappropriate CVs that create an overlap of different metastable states in the low-dimensional CV projection typically causes barriers to be severely underestimated.

In this case, finding more appropriate CVs that lift the overlap of the metastable states reveals the true free-energy barriers; the barriers in the mentioned work were estimated using a reweighting procedure see section 3. The Texas Monthly correspondence are mostly from fans and critics of Patoski's work in the magazine. Also contained in the Texas Monthly correspondence are interoffice memos, letters from other publications soliciting Patoski's work, correspondence regarding editing, general fan letters, and several personal letters.

The promotional material series is predominately made up of photographic and printed material sent to Patoski from music, television and film production companies, record companies, and talent agencies. Other promotional materials in this series include catalogs, newsletters, festival advertisements, press releases and ephemera all relating to the music industry.

This series of subject files and artist files, made up of newspaper clippings, notes, interviews, photographs and ephemera, illustrates Patoski's many areas of interest and his research methods. Patoski wrote about and published pieces relating to many of the topics and people in the subject and artist files. Of particular note is the large amount on material on Joe "King" Carrasco and his band, who Patoski managed in the s.

This series consists of bank records and a photograph from Joe Nick Patoski's music management business, Artist Development, Inc. Patoski managed these groups while he was also working full-time at Texas Monthly. This series contains a small group of documents pertaining to Patoski's personal financial, legal, and medical matters, as well as art works on paper, and an array of artifacts.

The photographs in this series are more personal in nature than those in previous series. Many images of Patoski throughout his life are contained in this series. This series is a collection of miscellaneous clippings and notes. They are divided into different categories. They are writing related, travel related, health and medical related, or arts related. The majority of phonographs in this series are from Patoski's personal collection, but some were sent to him as promotional material.

The audio cassettes are mostly non-professional recordings of music, and a few are of interviews with musicians. A relatively large portion of the audio cassettes are of the band Joe "King" Carrasco, which Patoski managed during the s. Music Catalogs by title. Music Newsletters by title.



Music Festivals by festival. Music Press Releases by subject. Television and Film by label. Clippings of Patoski's work, Music by label, , n. Promotional Material, — , n. Music by label, — , cont. Music Catalogs by title, Music Newsletters by title, Music Festivals by festival, , n. Music Press Releases by subject, , n. Music Ephemera, , n. Television and Film by label, , n. Promotional Material, , n. Research Material, , n. Subject Files, , n. Into the Edwards Aquifer. Artist Files, , n. Art on Paper, n. Sound Recordings, , n. Women Love Uncle Bud".

Blues," "Curley Haired Baby". Wilson - "Mean Old World," "U. Audio Cassettes, , n. Songs of Los Angeles Premies. Please contact the archivist for details. One box containing an assortment of personal and professional related material in no discernible including: Lady Be Good C6th. Sounds In the Night. Fruit Loop Captain Original. The Service Station Song. Asylum — American Explorer Series Elektra Nonesuch — American Series Lowest Common Denominator No.

Assorted personal and professional materials dated around Oct. Posters, photographs, notes, drafts, correspondence, and ephemera related to the research and writing career of Joe Nick Patoski, dating from s Broken Spoke poster featuring pencil drawing of James White in front of dancehall, signed to Joe Nick, n. Malone, 2-color Hatch poster co-sponsored by UT Press, 12x Light in Architecture and Art: The Work of Dan Flavin: March 19, , at Las Manitas 2color block print poster, 11x17 2 copies.

The Jan Reid Rescue Concert: Wooden plaque memento from The Nightcaps to Joe Nick: Photographs, notes, drafts, correspondence, and ephemera related to the research and writing career of Joe Nick Patoski, dating from General correspondence; invitations, newsletters, birthday cards, letters, postcards, faxes, accession reports, printed e-mail. Posters, SXSW material, magazines, photographs, notes, clippings, certificates, drafts, story ideas, correspondence, invites, brochures, material in reference to the Young Authors Conference, receipts, and ephemera related to the research and writing career of Joe Nick Patoski, dating from - Clayton and Joe W.

Performing Songwriter - Vol. Singer Magazine - No. Time Out New York - March , - located in box no. Posters, photographs, notes, newspaper clippings, certificates, drafts, story ideas, correspondence, invitations, brochures, receipts, and ephemera related to the research and writing career of Joe Nick Patoski. Posters, photographs, notes, newspaper clippings, research material, correspondence, invitations, compact discs, brochures, and ephemera related to the research and writing career of Joe Nick Patoski.

Butt Grocery Company, Texas mountains, untitled manuscript,. Notes, research material, correspondence, invitations, compact discs, brochures, and ephemera related to SxSW and the writing career of Joe Nick Patoski.