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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.


Simulation of an unbiased (1:1 well-depth), bond breaking chemical reaction, (13).(a) The potential energy (15) for the system. The parameters are given under simulation 1 in Supplementary Table II. (b) The level set plot of the potential energy. (c) A typical trajectory of the simulation. The cyan trace denotes the distance between molecules A and C (), whereas the red trace corresponds to the distance between molecules A and B (). Initially, A and C are near their equilibrium length (2) and B is far from A. We see a successful AC + B → AB + C event happening very soon (red trace is close to the equilibrium distance, then becomes large; cyan trace is large, then becomes small).
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f8: Simulation of an unbiased (1:1 well-depth), bond breaking chemical reaction, (13).(a) The potential energy (15) for the system. The parameters are given under simulation 1 in Supplementary Table II. (b) The level set plot of the potential energy. (c) A typical trajectory of the simulation. The cyan trace denotes the distance between molecules A and C (), whereas the red trace corresponds to the distance between molecules A and B (). Initially, A and C are near their equilibrium length (2) and B is far from A. We see a successful AC + B → AB + C event happening very soon (red trace is close to the equilibrium distance, then becomes large; cyan trace is large, then becomes small).

Mentions: The force derived from (15) is used in LAMMPS25 to simulate the system for an unbiased and a biased potential (parameters in Supplementary Information Table II). The parameters of the first simulation are chosen so that the AB and AC are symmetric (DAC/DAB = 1). In this case, the chemical reaction is unbiased and if averaged over all realizations of the noise, it is expected that the amount of time AB is formed is equal to the amount of time AC is formed. Figure 8 shows the potential energy for this simulation (Fig. 8(a)), the corresponding level sets (Fig. 8(b)), and a typical realization of the simulation (Fig. 8(c)). In the energy surface plot and the level set plot, the symmetry of the potential is evident. The realization shown in Fig. 8(c) starts with AB near its equilibrium length (2 Å) with C far from A. The realization shows the approximately equal times that AB and AC are formed. The deviation is due to this being a particular realization rather than an average over an ensemble of realizations and the finite nature of the simulation.


Programmable Potentials: Approximate N-body potentials from coarse-level logic
Simulation of an unbiased (1:1 well-depth), bond breaking chemical reaction, (13).(a) The potential energy (15) for the system. The parameters are given under simulation 1 in Supplementary Table II. (b) The level set plot of the potential energy. (c) A typical trajectory of the simulation. The cyan trace denotes the distance between molecules A and C (), whereas the red trace corresponds to the distance between molecules A and B (). Initially, A and C are near their equilibrium length (2) and B is far from A. We see a successful AC + B → AB + C event happening very soon (red trace is close to the equilibrium distance, then becomes large; cyan trace is large, then becomes small).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f8: Simulation of an unbiased (1:1 well-depth), bond breaking chemical reaction, (13).(a) The potential energy (15) for the system. The parameters are given under simulation 1 in Supplementary Table II. (b) The level set plot of the potential energy. (c) A typical trajectory of the simulation. The cyan trace denotes the distance between molecules A and C (), whereas the red trace corresponds to the distance between molecules A and B (). Initially, A and C are near their equilibrium length (2) and B is far from A. We see a successful AC + B → AB + C event happening very soon (red trace is close to the equilibrium distance, then becomes large; cyan trace is large, then becomes small).
Mentions: The force derived from (15) is used in LAMMPS25 to simulate the system for an unbiased and a biased potential (parameters in Supplementary Information Table II). The parameters of the first simulation are chosen so that the AB and AC are symmetric (DAC/DAB = 1). In this case, the chemical reaction is unbiased and if averaged over all realizations of the noise, it is expected that the amount of time AB is formed is equal to the amount of time AC is formed. Figure 8 shows the potential energy for this simulation (Fig. 8(a)), the corresponding level sets (Fig. 8(b)), and a typical realization of the simulation (Fig. 8(c)). In the energy surface plot and the level set plot, the symmetry of the potential is evident. The realization shown in Fig. 8(c) starts with AB near its equilibrium length (2 Å) with C far from A. The realization shows the approximately equal times that AB and AC are formed. The deviation is due to this being a particular realization rather than an average over an ensemble of realizations and the finite nature of the simulation.

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.