Limits...
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.


Simple signaling molecule mechanism, , modeled by three rods.When C is not present, A and B form a complex. When C is present, A and B dissociate and diffuse apart. Molecule C is free to diffuse away from molecule A. This behavior is captured with the following rules. When atom 5 is far from atom 2, the potential between atoms 2 and 3 is on. When atom 5 is close to atom 2, the potential between atoms 2 and 3 is turned off allowing molecules A and B dissociate and diffuse apart. Atom 5 can diffuse away from atom 2.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5037383&req=5

f2: Simple signaling molecule mechanism, , modeled by three rods.When C is not present, A and B form a complex. When C is present, A and B dissociate and diffuse apart. Molecule C is free to diffuse away from molecule A. This behavior is captured with the following rules. When atom 5 is far from atom 2, the potential between atoms 2 and 3 is on. When atom 5 is close to atom 2, the potential between atoms 2 and 3 is turned off allowing molecules A and B dissociate and diffuse apart. Atom 5 can diffuse away from atom 2.

Mentions: There are a number of examples in biology where chemical reactions occurring within a cell are initiated by some signal or stimulus, followed by an ordered sequence of biochemical reactions. Often the term signal transduction is used to refer to such processes. One such example is the epidermal growth factor (EGF) signaling910. Motivated by this example, we construct a hypothetical system to demonstrate how the proposed formulation can be used to construct a Hamiltonian potential for it. Assume a system of three species, A, B and C, has an evolution dictated by the chemical equation The sequence in which these reactions happen define logical “interaction rules” used to design the potential. Specifically, these rules are (1) when molecules A and B are close, and C is far, then A and B bond; and (2) If C approaches the AB complex, then A and B dissociate. This mechanism is visualized in Fig. 2.


Programmable Potentials: Approximate N-body potentials from coarse-level logic
Simple signaling molecule mechanism, , modeled by three rods.When C is not present, A and B form a complex. When C is present, A and B dissociate and diffuse apart. Molecule C is free to diffuse away from molecule A. This behavior is captured with the following rules. When atom 5 is far from atom 2, the potential between atoms 2 and 3 is on. When atom 5 is close to atom 2, the potential between atoms 2 and 3 is turned off allowing molecules A and B dissociate and diffuse apart. Atom 5 can diffuse away from atom 2.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Simple signaling molecule mechanism, , modeled by three rods.When C is not present, A and B form a complex. When C is present, A and B dissociate and diffuse apart. Molecule C is free to diffuse away from molecule A. This behavior is captured with the following rules. When atom 5 is far from atom 2, the potential between atoms 2 and 3 is on. When atom 5 is close to atom 2, the potential between atoms 2 and 3 is turned off allowing molecules A and B dissociate and diffuse apart. Atom 5 can diffuse away from atom 2.
Mentions: There are a number of examples in biology where chemical reactions occurring within a cell are initiated by some signal or stimulus, followed by an ordered sequence of biochemical reactions. Often the term signal transduction is used to refer to such processes. One such example is the epidermal growth factor (EGF) signaling910. Motivated by this example, we construct a hypothetical system to demonstrate how the proposed formulation can be used to construct a Hamiltonian potential for it. Assume a system of three species, A, B and C, has an evolution dictated by the chemical equation The sequence in which these reactions happen define logical “interaction rules” used to design the potential. Specifically, these rules are (1) when molecules A and B are close, and C is far, then A and B bond; and (2) If C approaches the AB complex, then A and B dissociate. This mechanism is visualized in Fig. 2.

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.