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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.


Flow chart of procedure.Using experimentally observed data and quantum calculations (red), we extract coarse-grain behavior (orange) namely: interactions rules and pairwise interaction potentials. This information is used to obtain an N-body potential (blue) for the system by employing the proposed formalism (green).
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f1: Flow chart of procedure.Using experimentally observed data and quantum calculations (red), we extract coarse-grain behavior (orange) namely: interactions rules and pairwise interaction potentials. This information is used to obtain an N-body potential (blue) for the system by employing the proposed formalism (green).

Mentions: This article begins with a motivating example which is used as an impetus for our modeling framework. In the Methodology section, we define the major components of the framework — logic functions, permissible logical operations, and the translation to the associated encoding functions — and specify how they combine with the pairwise potentials to define the approximate potential. The procedure is depicted in Fig. 1.


Programmable Potentials: Approximate N-body potentials from coarse-level logic
Flow chart of procedure.Using experimentally observed data and quantum calculations (red), we extract coarse-grain behavior (orange) namely: interactions rules and pairwise interaction potentials. This information is used to obtain an N-body potential (blue) for the system by employing the proposed formalism (green).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: Flow chart of procedure.Using experimentally observed data and quantum calculations (red), we extract coarse-grain behavior (orange) namely: interactions rules and pairwise interaction potentials. This information is used to obtain an N-body potential (blue) for the system by employing the proposed formalism (green).
Mentions: This article begins with a motivating example which is used as an impetus for our modeling framework. In the Methodology section, we define the major components of the framework — logic functions, permissible logical operations, and the translation to the associated encoding functions — and specify how they combine with the pairwise potentials to define the approximate potential. The procedure is depicted in Fig. 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 “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.