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The adaptive biasing force method: everything you always wanted to know but were afraid to ask.

Comer J, Gumbart JC, Hénin J, Lelièvre T, Pohorille A, Chipot C - J Phys Chem B (2014)

Bottom Line: The method has also been successfully applied to many challenging problems in chemistry and biology.In this contribution, the method is presented in a comprehensive, self-contained fashion, discussing with a critical eye its properties, applicability, and inherent limitations, as well as introducing novel extensions.On the basis of the discussions in this paper, a number of good practices for improving the efficiency and reliability of the computed free-energy differences are proposed.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche CNRS n°7565, Université de Lorraine , B.P. 70239, 54506 Vandoeuvre-lès-Nancy cedex, France.

ABSTRACT
In the host of numerical schemes devised to calculate free energy differences by way of geometric transformations, the adaptive biasing force algorithm has emerged as a promising route to map complex free-energy landscapes. It relies upon the simple concept that as a simulation progresses, a continuously updated biasing force is added to the equations of motion, such that in the long-time limit it yields a Hamiltonian devoid of an average force acting along the transition coordinate of interest. This means that sampling proceeds uniformly on a flat free-energy surface, thus providing reliable free-energy estimates. Much of the appeal of the algorithm to the practitioner is in its physically intuitive underlying ideas and the absence of any requirements for prior knowledge about free-energy landscapes. Since its inception in 2001, the adaptive biasing force scheme has been the subject of considerable attention, from in-depth mathematical analysis of convergence properties to novel developments and extensions. The method has also been successfully applied to many challenging problems in chemistry and biology. In this contribution, the method is presented in a comprehensive, self-contained fashion, discussing with a critical eye its properties, applicability, and inherent limitations, as well as introducing novel extensions. Through free-energy calculations of prototypical molecular systems, many methodological aspects are examined, from stratification strategies to overcoming the so-called hidden barriers in orthogonal space, relevant not only to the adaptive biasing force algorithm but also to other importance-sampling schemes. On the basis of the discussions in this paper, a number of good practices for improving the efficiency and reliability of the computed free-energy differences are proposed.

No MeSH data available.


Related in: MedlinePlus

Common free-energy landscapefeaturing parallel valleys, collinearto the transition coordinate, ξ. These valleys are separatedby substantial free-energy barriers in the direction ζ, orthogonalto ξ. ζ can be interpreted as a slow degree of freedomcoupled to ξ and hampering progression along the latter direction.Excessively stratified reaction pathways preclude spontaneous crossingof high barriers, typically ΔA1.Wider windows should allow diffusion toward values of ξ, wherethe barrier separating valleys in the direction ζ is smaller,typically ΔA2.
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fig8: Common free-energy landscapefeaturing parallel valleys, collinearto the transition coordinate, ξ. These valleys are separatedby substantial free-energy barriers in the direction ζ, orthogonalto ξ. ζ can be interpreted as a slow degree of freedomcoupled to ξ and hampering progression along the latter direction.Excessively stratified reaction pathways preclude spontaneous crossingof high barriers, typically ΔA1.Wider windows should allow diffusion toward values of ξ, wherethe barrier separating valleys in the direction ζ is smaller,typically ΔA2.

Mentions: Potential difficulties in applying the adaptive biasing force algorithmare intimately related to the choice of transition coordinate. A basic,yet seldom verified assumption that underlies this choice is the separationbetween time scales of motions along the transition coordinate andorthogonal degrees of freedom (see section TransitionCoordinates and Rare Events). For complex, rugged free-energylandscapes, notably those formed by parallel valleys separated byconsiderable barriers in the direction orthogonal to the transitioncoordinate (Figure 8),88 assuming time scale separation may turn out to be unwarranted. Becausethe adaptive biasing force algorithm exerts no direct action in theorthogonal space, it will not improve sampling at constant ξ.Returning to the foundational expression for the adaptive biasingforce method, eq 8, which relates the gradientof the free energy to an ensemble average at constant value of thetransition coordinate, the inability to cross hidden barriers in theorthogonal space is tantamount to incomplete ensemble averages and,hence, poor estimates of free-energy changes.


The adaptive biasing force method: everything you always wanted to know but were afraid to ask.

Comer J, Gumbart JC, Hénin J, Lelièvre T, Pohorille A, Chipot C - J Phys Chem B (2014)

Common free-energy landscapefeaturing parallel valleys, collinearto the transition coordinate, ξ. These valleys are separatedby substantial free-energy barriers in the direction ζ, orthogonalto ξ. ζ can be interpreted as a slow degree of freedomcoupled to ξ and hampering progression along the latter direction.Excessively stratified reaction pathways preclude spontaneous crossingof high barriers, typically ΔA1.Wider windows should allow diffusion toward values of ξ, wherethe barrier separating valleys in the direction ζ is smaller,typically ΔA2.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4306294&req=5

fig8: Common free-energy landscapefeaturing parallel valleys, collinearto the transition coordinate, ξ. These valleys are separatedby substantial free-energy barriers in the direction ζ, orthogonalto ξ. ζ can be interpreted as a slow degree of freedomcoupled to ξ and hampering progression along the latter direction.Excessively stratified reaction pathways preclude spontaneous crossingof high barriers, typically ΔA1.Wider windows should allow diffusion toward values of ξ, wherethe barrier separating valleys in the direction ζ is smaller,typically ΔA2.
Mentions: Potential difficulties in applying the adaptive biasing force algorithmare intimately related to the choice of transition coordinate. A basic,yet seldom verified assumption that underlies this choice is the separationbetween time scales of motions along the transition coordinate andorthogonal degrees of freedom (see section TransitionCoordinates and Rare Events). For complex, rugged free-energylandscapes, notably those formed by parallel valleys separated byconsiderable barriers in the direction orthogonal to the transitioncoordinate (Figure 8),88 assuming time scale separation may turn out to be unwarranted. Becausethe adaptive biasing force algorithm exerts no direct action in theorthogonal space, it will not improve sampling at constant ξ.Returning to the foundational expression for the adaptive biasingforce method, eq 8, which relates the gradientof the free energy to an ensemble average at constant value of thetransition coordinate, the inability to cross hidden barriers in theorthogonal space is tantamount to incomplete ensemble averages and,hence, poor estimates of free-energy changes.

Bottom Line: The method has also been successfully applied to many challenging problems in chemistry and biology.In this contribution, the method is presented in a comprehensive, self-contained fashion, discussing with a critical eye its properties, applicability, and inherent limitations, as well as introducing novel extensions.On the basis of the discussions in this paper, a number of good practices for improving the efficiency and reliability of the computed free-energy differences are proposed.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche CNRS n°7565, Université de Lorraine , B.P. 70239, 54506 Vandoeuvre-lès-Nancy cedex, France.

ABSTRACT
In the host of numerical schemes devised to calculate free energy differences by way of geometric transformations, the adaptive biasing force algorithm has emerged as a promising route to map complex free-energy landscapes. It relies upon the simple concept that as a simulation progresses, a continuously updated biasing force is added to the equations of motion, such that in the long-time limit it yields a Hamiltonian devoid of an average force acting along the transition coordinate of interest. This means that sampling proceeds uniformly on a flat free-energy surface, thus providing reliable free-energy estimates. Much of the appeal of the algorithm to the practitioner is in its physically intuitive underlying ideas and the absence of any requirements for prior knowledge about free-energy landscapes. Since its inception in 2001, the adaptive biasing force scheme has been the subject of considerable attention, from in-depth mathematical analysis of convergence properties to novel developments and extensions. The method has also been successfully applied to many challenging problems in chemistry and biology. In this contribution, the method is presented in a comprehensive, self-contained fashion, discussing with a critical eye its properties, applicability, and inherent limitations, as well as introducing novel extensions. Through free-energy calculations of prototypical molecular systems, many methodological aspects are examined, from stratification strategies to overcoming the so-called hidden barriers in orthogonal space, relevant not only to the adaptive biasing force algorithm but also to other importance-sampling schemes. On the basis of the discussions in this paper, a number of good practices for improving the efficiency and reliability of the computed free-energy differences are proposed.

No MeSH data available.


Related in: MedlinePlus