Adaptive sampling is a approach to sampling that uses heuristics to provide

efficiency Efficiency is the often measurable ability to avoid making mistakes or wasting materials, energy, efforts, money, and time while performing a task. In a more general sense, it is the ability to do things well, successfully, and without waste. ...

. The term ''adaptive sampling'' represents a general approach to the problem of sampling, rather than being a special method itself. Meaning it can be combined with suitable other approaches/methods. In some real world problems, sampling is implicitly/explicitly needed and used to obtain practical solutions. The sampling process will need resources and efficient usage of these resources is usually crucial. This is why there are multiple sampling methods instead of the brute-force approach. Let f(x) be a function that is to be sampled. For simplicity, let C(x,s) be the cost for sample x given the previous set of samples s (For simplicity, we can assume that C(x,s) is constant since sampling cost usually does not depend on the previous samples and the sampling input x to the function. In time-critical systems, where the cost for each sample is strongly related to computation time; usually there are other parameters to the function C like the current time...); and G(x, s) be the gain (anti-cost) from sampling the function at x, given the set of previous samples s. For example, it can be assumed that G(x, s)=0 if x has already been sampled. The sampling problem is then maximizing our cumulative gain minus cumulative cost. Which usually comes down to sampling the function n times until the next sample's estimated/deterministic cost C(x,s) is smaller than the gain G(x,s) of that sample. Adaptive sampling then assumes that given necessary knowledge about the problem, there is a theoretically optimal sequence s of samples that will maximize the information (gain) induced by that sample; and it is possible to estimate s using

heuristics A heuristic or heuristic technique (''problem solving'', '' mental shortcut'', ''rule of thumb'') is any approach to problem solving that employs a pragmatic method that is not fully optimized, perfected, or rationalized, but is nevertheless ...

. Adaptive sampling usually focuses on estimating the next optimal sample input x, given the previous set of samples. Thus, being adaptive to the current knowledge about the function.

Computational Molecular Biology

In computational

molecular biology Molecular biology is a branch of biology that seeks to understand the molecule, molecular basis of biological activity in and between Cell (biology), cells, including biomolecule, biomolecular synthesis, modification, mechanisms, and interactio ...

, adaptive sampling is used to efficiently simulate

protein folding Protein folding is the physical process by which a protein, after Protein biosynthesis, synthesis by a ribosome as a linear chain of Amino acid, amino acids, changes from an unstable random coil into a more ordered protein tertiary structure, t ...

when coupled with molecular dynamics simulations.

Background

Proteins spend a large portion – nearly 96% in some cases – of their folding time "waiting" in various

thermodynamic free energy In thermodynamics, the thermodynamic free energy is one of the state functions of a thermodynamic system. The change in the free energy is the maximum amount of work that the system can perform in a process at constant temperature, and its ...

minima. Consequently, a straightforward simulation of this process would spend a great deal of computation to this state, with the transitions between the states – the aspects of protein folding of greater scientific interest – taking place only rarely. Adaptive sampling exploits this property to simulate the protein's

phase space The phase space of a physical system is the set of all possible physical states of the system when described by a given parameterization. Each possible state corresponds uniquely to a point in the phase space. For mechanical systems, the p ...

in between these states. Using adaptive sampling, molecular simulations that previously would have taken decades can be performed in a matter of weeks.

Theory

If a protein folds through the metastable states A -> B -> C, researchers can calculate the length of the transition time between A and C by simulating the A -> B transition and the B -> C transition. The protein may fold through alternative routes which may overlap in part with the A -> B -> C pathway. Decomposing the problem in this manner is efficient because each step can be simulated in parallel.

Applications

Adaptive sampling is used by the

Folding@home Folding@home (FAH or F@h) is a distributed computing project aimed to help scientists develop new therapeutics for a variety of diseases by the means of simulating protein dynamics. This includes the process of protein folding and the movements ...

distributed computing project in combination with Markov state models.

Disadvantages

While adaptive sampling is useful for short simulations, longer trajectories may be more helpful for certain types of biochemical problems.

References

{{reflist , colwidth = 30em , refs = {{cite journal , author = Robert B Best , title = Atomistic molecular simulations of protein folding , journal = Current Opinion in Structural Biology , year = 2012 , type = review , volume = 22 , issue = 1 , pages = 52–61 , doi = 10.1016/j.sbi.2011.12.001 , pmid = 22257762 {{cite web , url=http://folding.stanford.edu/English/FAQ-Simulation , title=Folding@home Simulation FAQ , author1=TJ Lane , author2=Gregory Bowman , author3=Robert McGibbon , author4=Christian Schwantes , author5=Vijay Pande , author6=Bruce Borden , work=Folding@home , publisher=

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

, date=September 10, 2012 , access-date=September 10, 2012 , archive-url=https://web.archive.org/web/20120913150805/http://folding.stanford.edu/English/FAQ-Simulation , archive-date=2012-09-13 , url-status=dead {{cite journal , author1=G. Bowman , author2=V. Volez , author3=V. S. Pande , title = Taming the complexity of protein folding , journal = Current Opinion in Structural Biology , year = 2011 , volume = 21 , issue = 1 , pages = 4–11 , doi = 10.1016/j.sbi.2010.10.006 , pmc = 3042729 , pmid = 21081274 {{cite journal , author = David E. Shaw , author2=Martin M. Deneroff , author3=Ron O. Dror , author4=Jeffrey S. Kuskin , author5=Richard H. Larson , author6=John K. Salmon , author7=Cliff Young , author8=Brannon Batson , author9=Kevin J. Bowers , author10=Jack C. Chao , author11=Michael P. Eastwood , author12=Joseph Gagliardo , author13=J. P. Grossman , author14=C. Richard Ho , author15=Douglas J. Ierardi, Ist , title = Anton, A Special-Purpose Machine for Molecular Dynamics Simulation , journal = Communications of the ACM , volume = 51 , issue = 7 , pages = 91–97 , year = 2008 , doi = 10.1145/1364782.1364802 , doi-access=free {{cite journal , title = Biomolecular Simulation: A Computational Microscope for Molecular Biology , author1=Ron O. Dror , author2=Robert M. Dirks , author3=J.P. Grossman , author4=Huafeng Xu , author5=David E. Shaw , journal =

Annual Review of Biophysics The ''Annual Review of Biophysics'' is a peer-reviewed scientific journal published annually by Annual Reviews. It covers all aspects of biophysics with solicited review articles. Ken A. Dill has been its editor since 2013. As of 2023, ''Annual ...