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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.


Simulation of biased (2:1 well-depth), bond breaking chemical reaction, (13).(a) The potential energy (15) for the system. The parameters are given under simulation 2 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 B are near their equilibrium distance (2) and C is far from A. We see a successful AB + C → AC + B event happening very soon (red trace is close to the equilibrium distance, then becomes large; cyan trace is large, then becomes small). The trace exhibits the bias towards a stable AC bond, since the cyan trace is close to equilibrium longer than the red trace.
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f9: Simulation of biased (2:1 well-depth), bond breaking chemical reaction, (13).(a) The potential energy (15) for the system. The parameters are given under simulation 2 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 B are near their equilibrium distance (2) and C is far from A. We see a successful AB + C → AC + B event happening very soon (red trace is close to the equilibrium distance, then becomes large; cyan trace is large, then becomes small). The trace exhibits the bias towards a stable AC bond, since the cyan trace is close to equilibrium longer than the red trace.

Mentions: The parameters of the second simulation are chosen so that the reaction is biased in favor of AC. With the chosen parameters (DAC/DAB = 2), the AC bond is twice as stable as AB. Figure 9 shows the potential energy for this simulation (Fig. 9(a)), its corresponding level sets (Fig. 9(b)), and a realization of the simulation (Fig. 9(c)). In the energy surface plot and the level set plot, the asymmetry of the potential is evident. The realization shown in Fig. 9(c) starts with AB near its equilibrium length (2 Å) with C far from A. In this particular realization AC forms very quickly. Figure 9(c) shows the bias towards the more stable AC. The system spends most of its time with a stable AC molecule with a relatively small amount of time with a stable AB molecule. Thus, biased reactions can be captured in the framework. A movie of a part of the unbiased reaction simulation can be found in Supplementary Movie 2.


Programmable Potentials: Approximate N-body potentials from coarse-level logic
Simulation of biased (2:1 well-depth), bond breaking chemical reaction, (13).(a) The potential energy (15) for the system. The parameters are given under simulation 2 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 B are near their equilibrium distance (2) and C is far from A. We see a successful AB + C → AC + B event happening very soon (red trace is close to the equilibrium distance, then becomes large; cyan trace is large, then becomes small). The trace exhibits the bias towards a stable AC bond, since the cyan trace is close to equilibrium longer than the red trace.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f9: Simulation of biased (2:1 well-depth), bond breaking chemical reaction, (13).(a) The potential energy (15) for the system. The parameters are given under simulation 2 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 B are near their equilibrium distance (2) and C is far from A. We see a successful AB + C → AC + B event happening very soon (red trace is close to the equilibrium distance, then becomes large; cyan trace is large, then becomes small). The trace exhibits the bias towards a stable AC bond, since the cyan trace is close to equilibrium longer than the red trace.
Mentions: The parameters of the second simulation are chosen so that the reaction is biased in favor of AC. With the chosen parameters (DAC/DAB = 2), the AC bond is twice as stable as AB. Figure 9 shows the potential energy for this simulation (Fig. 9(a)), its corresponding level sets (Fig. 9(b)), and a realization of the simulation (Fig. 9(c)). In the energy surface plot and the level set plot, the asymmetry of the potential is evident. The realization shown in Fig. 9(c) starts with AB near its equilibrium length (2 Å) with C far from A. In this particular realization AC forms very quickly. Figure 9(c) shows the bias towards the more stable AC. The system spends most of its time with a stable AC molecule with a relatively small amount of time with a stable AB molecule. Thus, biased reactions can be captured in the framework. A movie of a part of the unbiased reaction simulation can be found in Supplementary Movie 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.