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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.


DNA transcription.The red trace (TF) corresponds to the distance between the RNA pol and the promoter region. r5,9 (cyan), r6,12 (gold), r7,15 (black), and r8,18 (blue) correspond to the sites on the complementary A-U, C-G, T-A, and G-C pairs from the base strand and the free nucleotides. At the start, the RNA pol and the free nucleotides diffuse around in space. Around 900 ps, the RNA pol binds to the promoter region (TF trace ≈ 0). The free nucleotides then bind in the the order of the designed logic. U binds to A (r5,9 ≈ 0) around 1100 ps; G binds with C (r6,12 ≈ 0) between 1800 and 1900 ps; A binds to T (r7,15 ≈ 0) around 2400 ps; and finally C binds to G (r8,18 ≈ 0) around 2700 ps. Once this final free nucleotide has bounded with its complement, the complementary chain is finished formed and unbinds as does the RNA pol. The RNA pol can rebind to the promoter region, but the complementary strand cannot rebind to the original DNA strand.
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f11: DNA transcription.The red trace (TF) corresponds to the distance between the RNA pol and the promoter region. r5,9 (cyan), r6,12 (gold), r7,15 (black), and r8,18 (blue) correspond to the sites on the complementary A-U, C-G, T-A, and G-C pairs from the base strand and the free nucleotides. At the start, the RNA pol and the free nucleotides diffuse around in space. Around 900 ps, the RNA pol binds to the promoter region (TF trace ≈ 0). The free nucleotides then bind in the the order of the designed logic. U binds to A (r5,9 ≈ 0) around 1100 ps; G binds with C (r6,12 ≈ 0) between 1800 and 1900 ps; A binds to T (r7,15 ≈ 0) around 2400 ps; and finally C binds to G (r8,18 ≈ 0) around 2700 ps. Once this final free nucleotide has bounded with its complement, the complementary chain is finished formed and unbinds as does the RNA pol. The RNA pol can rebind to the promoter region, but the complementary strand cannot rebind to the original DNA strand.

Mentions: Figure 11 shows a trace of the pairwise distances between atoms for a typical simulation using this potential in LAMMPS (parameters in Supplementary Information Table IV). We use the same qualitative approximation of the force as was used in the inhibitor molecule example. For simplicity, all the potentials are taken to be Morse potentials. The red trace (TF) corresponds to the distance between the RNA pol and the promoter region. The variables r5,9 (cyan), r6,12 (gold), r7,15 (black), and r8,18 (blue) correspond to the sites on the complementary A-U, C-G, T-A, and G-C pairs from the base strand and the free nucleotides. At the start, the RNA pol and the free nucleotides diffuse around in space. Around 900 ps, the RNA pol binds to the promoter region (TF trace ≈0). The free nucleotides then bind in the the order of the designed logic. U binds to A (r5,9 ≈ 0) around 1100 ps; G binds with C (r6,12 ≈ 0) between 1800 and 1900 ps; A binds to T (r7,15 ≈ 0) around 2400 ps; and finally C binds to G (r8,18 ≈ 0) around 2700 ps. Once this final free nucleotide has bounded with its complement, the complementary chain has finished forming and unbinds as does the RNA pol. The RNA pol can rebind to the promoter region, but the complementary RNA strand cannot rebind to the original DNA strand. This is exactly the behavior designed into the potential. Supplementary Movie 3 in the Supplementary Information shows one simulation of the DNA transcription.


Programmable Potentials: Approximate N-body potentials from coarse-level logic
DNA transcription.The red trace (TF) corresponds to the distance between the RNA pol and the promoter region. r5,9 (cyan), r6,12 (gold), r7,15 (black), and r8,18 (blue) correspond to the sites on the complementary A-U, C-G, T-A, and G-C pairs from the base strand and the free nucleotides. At the start, the RNA pol and the free nucleotides diffuse around in space. Around 900 ps, the RNA pol binds to the promoter region (TF trace ≈ 0). The free nucleotides then bind in the the order of the designed logic. U binds to A (r5,9 ≈ 0) around 1100 ps; G binds with C (r6,12 ≈ 0) between 1800 and 1900 ps; A binds to T (r7,15 ≈ 0) around 2400 ps; and finally C binds to G (r8,18 ≈ 0) around 2700 ps. Once this final free nucleotide has bounded with its complement, the complementary chain is finished formed and unbinds as does the RNA pol. The RNA pol can rebind to the promoter region, but the complementary strand cannot rebind to the original DNA strand.
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Related In: Results  -  Collection

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f11: DNA transcription.The red trace (TF) corresponds to the distance between the RNA pol and the promoter region. r5,9 (cyan), r6,12 (gold), r7,15 (black), and r8,18 (blue) correspond to the sites on the complementary A-U, C-G, T-A, and G-C pairs from the base strand and the free nucleotides. At the start, the RNA pol and the free nucleotides diffuse around in space. Around 900 ps, the RNA pol binds to the promoter region (TF trace ≈ 0). The free nucleotides then bind in the the order of the designed logic. U binds to A (r5,9 ≈ 0) around 1100 ps; G binds with C (r6,12 ≈ 0) between 1800 and 1900 ps; A binds to T (r7,15 ≈ 0) around 2400 ps; and finally C binds to G (r8,18 ≈ 0) around 2700 ps. Once this final free nucleotide has bounded with its complement, the complementary chain is finished formed and unbinds as does the RNA pol. The RNA pol can rebind to the promoter region, but the complementary strand cannot rebind to the original DNA strand.
Mentions: Figure 11 shows a trace of the pairwise distances between atoms for a typical simulation using this potential in LAMMPS (parameters in Supplementary Information Table IV). We use the same qualitative approximation of the force as was used in the inhibitor molecule example. For simplicity, all the potentials are taken to be Morse potentials. The red trace (TF) corresponds to the distance between the RNA pol and the promoter region. The variables r5,9 (cyan), r6,12 (gold), r7,15 (black), and r8,18 (blue) correspond to the sites on the complementary A-U, C-G, T-A, and G-C pairs from the base strand and the free nucleotides. At the start, the RNA pol and the free nucleotides diffuse around in space. Around 900 ps, the RNA pol binds to the promoter region (TF trace ≈0). The free nucleotides then bind in the the order of the designed logic. U binds to A (r5,9 ≈ 0) around 1100 ps; G binds with C (r6,12 ≈ 0) between 1800 and 1900 ps; A binds to T (r7,15 ≈ 0) around 2400 ps; and finally C binds to G (r8,18 ≈ 0) around 2700 ps. Once this final free nucleotide has bounded with its complement, the complementary chain has finished forming and unbinds as does the RNA pol. The RNA pol can rebind to the promoter region, but the complementary RNA strand cannot rebind to the original DNA strand. This is exactly the behavior designed into the potential. Supplementary Movie 3 in the Supplementary Information shows one simulation of the DNA transcription.

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.