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Programmable Potentials: Approximate N-body potentials from coarse-level logic

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ABSTRACT

This paper gives a systematic method for constructing an N-body potential, approximating the true potential, that accurately captures meso-scale behavior of the chemical or biological system using pairwise potentials coming from experimental data or ab initio methods. The meso-scale behavior is translated into logic rules for the dynamics. Each pairwise potential has an associated logic function that is constructed using the logic rules, a class of elementary logic functions, and AND, OR, and NOT gates. The effect of each logic function is to turn its associated potential on and off. The N-body potential is constructed as linear combination of the pairwise potentials, where the “coefficients” of the potentials are smoothed versions of the associated logic functions. These potentials allow a potentially low-dimensional description of complex processes while still accurately capturing the relevant physics at the meso-scale. We present the proposed formalism to construct coarse-grained potential models for three examples: an inhibitor molecular system, bond breaking in chemical reactions, and DNA transcription from biology. The method can potentially be used in reverse for design of molecular processes by specifying properties of molecules that can carry them out.

No MeSH data available.


Behavior of the hα,n function fromEquation (6).(a) α controls the transition point. (b) n controls the sharpness of the transition.
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f3: Behavior of the hα,n function fromEquation (6).(a) α controls the transition point. (b) n controls the sharpness of the transition.

Mentions: for some choices of parameters α1, α2, n1, and n2. The parameters α and n control how well hα,n approximates a proximity function (see Fig. 3). In particular, hα,n(0) = 1 for any 0 < α < ∞ and positive n. Furthermore, and it is strictly monotonically decreasing. On the other hand, for a fixed 0 < α < ∞, the transition from 1 to 0 becomes sharper as n increases (Fig. 3(b)). To match a specific indicator function χ[0,R), choose α = R. With this choice of α, the function satisfies hR,n(R) = 1/2 for all n ≥ 1;


Programmable Potentials: Approximate N-body potentials from coarse-level logic
Behavior of the hα,n function fromEquation (6).(a) α controls the transition point. (b) n controls the sharpness of the transition.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037383&req=5

f3: Behavior of the hα,n function fromEquation (6).(a) α controls the transition point. (b) n controls the sharpness of the transition.
Mentions: for some choices of parameters α1, α2, n1, and n2. The parameters α and n control how well hα,n approximates a proximity function (see Fig. 3). In particular, hα,n(0) = 1 for any 0 < α < ∞ and positive n. Furthermore, and it is strictly monotonically decreasing. On the other hand, for a fixed 0 < α < ∞, the transition from 1 to 0 becomes sharper as n increases (Fig. 3(b)). To match a specific indicator function χ[0,R), choose α = R. With this choice of α, the function satisfies hR,n(R) = 1/2 for all n ≥ 1;

View Article: PubMed Central - PubMed

ABSTRACT

This paper gives a systematic method for constructing an N-body potential, approximating the true potential, that accurately captures meso-scale behavior of the chemical or biological system using pairwise potentials coming from experimental data or ab initio methods. The meso-scale behavior is translated into logic rules for the dynamics. Each pairwise potential has an associated logic function that is constructed using the logic rules, a class of elementary logic functions, and AND, OR, and NOT gates. The effect of each logic function is to turn its associated potential on and off. The N-body potential is constructed as linear combination of the pairwise potentials, where the &ldquo;coefficients&rdquo; of the potentials are smoothed versions of the associated logic functions. These potentials allow a potentially low-dimensional description of complex processes while still accurately capturing the relevant physics at the meso-scale. We present the proposed formalism to construct coarse-grained potential models for three examples: an inhibitor molecular system, bond breaking in chemical reactions, and DNA transcription from biology. The method can potentially be used in reverse for design of molecular processes by specifying properties of molecules that can carry them out.

No MeSH data available.