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

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.


Inhibitor molecule example.When the inhibitor molecule, C, is not present (panel (a)), a bond between receptor A’s site 2 and site 3 on the active molecule B can form. When the inhibitor molecule is present, it can either take up the receptor site through a (2, 5) bond (panel (b)) or bind to site 3 on B with site 6 (panel (c)). Either of these cases prevents to active molecule B from binding with its receptor site on A.
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f4: Inhibitor molecule example.When the inhibitor molecule, C, is not present (panel (a)), a bond between receptor A’s site 2 and site 3 on the active molecule B can form. When the inhibitor molecule is present, it can either take up the receptor site through a (2, 5) bond (panel (b)) or bind to site 3 on B with site 6 (panel (c)). Either of these cases prevents to active molecule B from binding with its receptor site on A.

Mentions: This example can be thought of as a simple model for the action of an inhibitor molecule in a plane. Consider the three interacting molecules in Fig. 4. The configuration space for this example is , where is written as . The set of interacting atom pairs is . For this example, the multiplicity function is identically 1. Thus we have the pairwise potentials Φ(2,3), Φ(2,5), and Φ(3,6). It is assumed that these potentials are formed using a Morse potential (see (12)). Molecule C is an inhibitor molecule and prevents the formation of the AB complex. Without C, we have A + B → AB. With C present, the there are two possibilities: (i) or (ii) .


Programmable Potentials: Approximate N-body potentials from coarse-level logic
Inhibitor molecule example.When the inhibitor molecule, C, is not present (panel (a)), a bond between receptor A’s site 2 and site 3 on the active molecule B can form. When the inhibitor molecule is present, it can either take up the receptor site through a (2, 5) bond (panel (b)) or bind to site 3 on B with site 6 (panel (c)). Either of these cases prevents to active molecule B from binding with its receptor site on A.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: Inhibitor molecule example.When the inhibitor molecule, C, is not present (panel (a)), a bond between receptor A’s site 2 and site 3 on the active molecule B can form. When the inhibitor molecule is present, it can either take up the receptor site through a (2, 5) bond (panel (b)) or bind to site 3 on B with site 6 (panel (c)). Either of these cases prevents to active molecule B from binding with its receptor site on A.
Mentions: This example can be thought of as a simple model for the action of an inhibitor molecule in a plane. Consider the three interacting molecules in Fig. 4. The configuration space for this example is , where is written as . The set of interacting atom pairs is . For this example, the multiplicity function is identically 1. Thus we have the pairwise potentials Φ(2,3), Φ(2,5), and Φ(3,6). It is assumed that these potentials are formed using a Morse potential (see (12)). Molecule C is an inhibitor molecule and prevents the formation of the AB complex. Without C, we have A + B → AB. With C present, the there are two possibilities: (i) or (ii) .

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.