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Implementation of force distribution analysis for molecular dynamics simulations.

Stacklies W, Seifert C, Graeter F - BMC Bioinformatics (2011)

Bottom Line: We provide an additional R-package providing functions for advanced statistical analysis and presentation of the FDA data.Using FDA, we were able to explain the origin of mechanical robustness in immunoglobulin domains and silk fibers.FDA thus has the potential to be a valuable tool in the investigation and rational design of mechanical properties in proteins and nano-materials.

View Article: PubMed Central - HTML - PubMed

Affiliation: CAS-MPG Partner Institute and Key Laboratory for Computational Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, 320 Yueyang Road, Shanghai 200031, China.

ABSTRACT

Background: The way mechanical stress is distributed inside and propagated by proteins and other biopolymers largely defines their function. Yet, determining the network of interactions propagating internal strain remains a challenge for both, experiment and theory. Based on molecular dynamics simulations, we developed force distribution analysis (FDA), a method that allows visualizing strain propagation in macromolecules.

Results: To be immediately applicable to a wide range of systems, FDA was implemented as an extension to Gromacs, a commonly used package for molecular simulations. The FDA code comes with an easy-to-use command line interface and can directly be applied to every system built using Gromacs. We provide an additional R-package providing functions for advanced statistical analysis and presentation of the FDA data.

Conclusions: Using FDA, we were able to explain the origin of mechanical robustness in immunoglobulin domains and silk fibers. By elucidating propagation of internal strain upon ligand binding, we previously also successfully revealed the functionality of a stiff allosteric protein. FDA thus has the potential to be a valuable tool in the investigation and rational design of mechanical properties in proteins and nano-materials.

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The concept of pair-wise forces. (A) Conventional MD uses the sum of all forces, , acting on a certain atom to derive the atomic motion. (B) In contrast, FDA works with pair-wise forces Fij, which is the force calculated between each pair of atoms i, j during an MD simulation. (C) The total force Fiatomic acting on an atom quickly decays to zero under equilibrium conditions. Observation of quickly decaying signals is not possible due to high equilibrium fluctuations. The plot shows only the x component of the xyz force vector for a single hydrogen bond O atom in the titin I27 domain [4]. (D) In contrast, even in equilibrium, pair-wise forces will not average to zero. This allows to compare different (equilibrated) states of a system. The plot shows pair-wise forces between the O-H atoms for the same hydrogen bond as in Figure 1 C. (E) Approximations used to transform multi-body forces into a pair-wise representation. Only the force acting along the direction of atoms i, k for angles and i, l for dihedrals is considered. This is sufficient to detect even minor re-arrangements.
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Figure 1: The concept of pair-wise forces. (A) Conventional MD uses the sum of all forces, , acting on a certain atom to derive the atomic motion. (B) In contrast, FDA works with pair-wise forces Fij, which is the force calculated between each pair of atoms i, j during an MD simulation. (C) The total force Fiatomic acting on an atom quickly decays to zero under equilibrium conditions. Observation of quickly decaying signals is not possible due to high equilibrium fluctuations. The plot shows only the x component of the xyz force vector for a single hydrogen bond O atom in the titin I27 domain [4]. (D) In contrast, even in equilibrium, pair-wise forces will not average to zero. This allows to compare different (equilibrated) states of a system. The plot shows pair-wise forces between the O-H atoms for the same hydrogen bond as in Figure 1 C. (E) Approximations used to transform multi-body forces into a pair-wise representation. Only the force acting along the direction of atoms i, k for angles and i, l for dihedrals is considered. This is sufficient to detect even minor re-arrangements.

Mentions: FDA can be considered as a natural extension of any classical MD code. It allows to directly observe changes in atomic forces as a result of a perturbation. Examples for such perturbations are the application of an external force (pulling) or binding of a ligand. FDA makes use of pair-wise forces, i.e. the force an atom exerts on another atom. This is different from the total force acting on a certain atom, Figure 1A+B. By considering the direct force between each atom pair, the equilibrium force between these atoms can be different from zero, even for the theoretical case of a system without any motion. Atom-wise forces, i.e. the sum over all force vectors acting on an atom, instead average out to zero over time and are not of interest here. It is by observing pair-wise forces that we obtain the advantage to be able to detect signal propagation even through stiff materials where, by definition, forces propagate without causing major atomic displacement. A real world example is Newton's cradle. While coordinate changes and the corresponding ball-wise forces are non-zero only for the first and last ball, pair-wise forces are able to reveal the shock wave propagating through the stationary balls in-between as well.


Implementation of force distribution analysis for molecular dynamics simulations.

Stacklies W, Seifert C, Graeter F - BMC Bioinformatics (2011)

The concept of pair-wise forces. (A) Conventional MD uses the sum of all forces, , acting on a certain atom to derive the atomic motion. (B) In contrast, FDA works with pair-wise forces Fij, which is the force calculated between each pair of atoms i, j during an MD simulation. (C) The total force Fiatomic acting on an atom quickly decays to zero under equilibrium conditions. Observation of quickly decaying signals is not possible due to high equilibrium fluctuations. The plot shows only the x component of the xyz force vector for a single hydrogen bond O atom in the titin I27 domain [4]. (D) In contrast, even in equilibrium, pair-wise forces will not average to zero. This allows to compare different (equilibrated) states of a system. The plot shows pair-wise forces between the O-H atoms for the same hydrogen bond as in Figure 1 C. (E) Approximations used to transform multi-body forces into a pair-wise representation. Only the force acting along the direction of atoms i, k for angles and i, l for dihedrals is considered. This is sufficient to detect even minor re-arrangements.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3094238&req=5

Figure 1: The concept of pair-wise forces. (A) Conventional MD uses the sum of all forces, , acting on a certain atom to derive the atomic motion. (B) In contrast, FDA works with pair-wise forces Fij, which is the force calculated between each pair of atoms i, j during an MD simulation. (C) The total force Fiatomic acting on an atom quickly decays to zero under equilibrium conditions. Observation of quickly decaying signals is not possible due to high equilibrium fluctuations. The plot shows only the x component of the xyz force vector for a single hydrogen bond O atom in the titin I27 domain [4]. (D) In contrast, even in equilibrium, pair-wise forces will not average to zero. This allows to compare different (equilibrated) states of a system. The plot shows pair-wise forces between the O-H atoms for the same hydrogen bond as in Figure 1 C. (E) Approximations used to transform multi-body forces into a pair-wise representation. Only the force acting along the direction of atoms i, k for angles and i, l for dihedrals is considered. This is sufficient to detect even minor re-arrangements.
Mentions: FDA can be considered as a natural extension of any classical MD code. It allows to directly observe changes in atomic forces as a result of a perturbation. Examples for such perturbations are the application of an external force (pulling) or binding of a ligand. FDA makes use of pair-wise forces, i.e. the force an atom exerts on another atom. This is different from the total force acting on a certain atom, Figure 1A+B. By considering the direct force between each atom pair, the equilibrium force between these atoms can be different from zero, even for the theoretical case of a system without any motion. Atom-wise forces, i.e. the sum over all force vectors acting on an atom, instead average out to zero over time and are not of interest here. It is by observing pair-wise forces that we obtain the advantage to be able to detect signal propagation even through stiff materials where, by definition, forces propagate without causing major atomic displacement. A real world example is Newton's cradle. While coordinate changes and the corresponding ball-wise forces are non-zero only for the first and last ball, pair-wise forces are able to reveal the shock wave propagating through the stationary balls in-between as well.

Bottom Line: We provide an additional R-package providing functions for advanced statistical analysis and presentation of the FDA data.Using FDA, we were able to explain the origin of mechanical robustness in immunoglobulin domains and silk fibers.FDA thus has the potential to be a valuable tool in the investigation and rational design of mechanical properties in proteins and nano-materials.

View Article: PubMed Central - HTML - PubMed

Affiliation: CAS-MPG Partner Institute and Key Laboratory for Computational Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, 320 Yueyang Road, Shanghai 200031, China.

ABSTRACT

Background: The way mechanical stress is distributed inside and propagated by proteins and other biopolymers largely defines their function. Yet, determining the network of interactions propagating internal strain remains a challenge for both, experiment and theory. Based on molecular dynamics simulations, we developed force distribution analysis (FDA), a method that allows visualizing strain propagation in macromolecules.

Results: To be immediately applicable to a wide range of systems, FDA was implemented as an extension to Gromacs, a commonly used package for molecular simulations. The FDA code comes with an easy-to-use command line interface and can directly be applied to every system built using Gromacs. We provide an additional R-package providing functions for advanced statistical analysis and presentation of the FDA data.

Conclusions: Using FDA, we were able to explain the origin of mechanical robustness in immunoglobulin domains and silk fibers. By elucidating propagation of internal strain upon ligand binding, we previously also successfully revealed the functionality of a stiff allosteric protein. FDA thus has the potential to be a valuable tool in the investigation and rational design of mechanical properties in proteins and nano-materials.

Show MeSH
Related in: MedlinePlus