1. Elastic models of conformational transitions in macromolecules
Moon K. Kim, Gregory S. Chirikjian, Robert L. Jernigan
Presented by: Amit Jain
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2. Outline Introduction Problem Statement Related Work Elastic Model
Approach
Results
Conclusion
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3. Introduction What are Macromolecules ?
Carbohydrates
Proteins
Nucleic Acids
Why are conformational transitions important ?
Understanding functional relationship
Macromolecules are molecules with large molecular sizes as compared to normal molecules. Normally usage is restricted to polymers. Here we are interested in biological macromolecules like proteins
Functional relationships like catalysts, etc. in which the transitionary conformation is useful
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4. Problem Statement Input: Two conformation x, χ
Output: List of realistic displacements δ
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5. Related Work Interpolation Molecular Dynamics Coarse models
Linear interpolation in cartesian space
Linear interpolation in bond lengths and bond angles
Molecular Dynamics
Coarse models
Simple
Unrealistic bond lengths and bond angles
Solves the unrealistic bond lengths and angles
Can still get impossible paths
Linear interpolation by Vonrhein
Impossible paths because: the bond lengths and angles are supposed to be fixed in interpolation but they can be different in the conformations themselves. 2: since interpolation is local it might create high energy molecules
Molecular Dynamics: propogate the dynamics and wait for it to reach the destination conformation. Computationally very expensive
Coarse Models: model only the backbone and a simplified energy function in order to aproximate the whole thing. Good for global motion prediction.
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6. Outline Introduction Problem Statement Related Work Elastic Model
Approach
Results
Conclusion
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7. Elastic Model Key Enabler Model
Discrete model for small conformational changes about an equilibrium position for macromolecules
Model
Alpha carbons
Inter carbon force interactions
Alpha carbons: x,y,z
Origin at COM, axis along moment of inertia.
Force interactions are springs = kx, where k is 1 when distance smaller than some threshold.
Explain the concept of springs having forces stored in change from equilibrium positions
Sparcity and reality maintained in motion by keeping a constant number of neighbors starting from closest to farthest.
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8. Elastic Model
Potential Energy function
Can be reduced to
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9. Elastic Model Substituting, We get,
Energy is crucial for an elastic model, stable configurations have low energy
Spring energy functions are of this form
Significance of this change is that this provides a cheap way of calculating energy about a stable configuration, useful for carrying out coarse grained NMA. This is an important analysis tool in calculating analytical motions of macromolecules.
Values of k are such that the same expression comes about …
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10. Elastic Model Analytical equation for motion
where M is diagonal matrix
If masses are equal then eigenvectors of K are the normal modes,
Normal mode analysis is a common way to evaluate potential protein motions
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11. Approach Interpolate conformation
Find the displacement(δ) which minimizes cost
Increment alpha
Calculate new
Use new conformation to find new displacement
Cost means:my potential energy if target (l_i,j) is a stable state
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12. Approach Cost can be simplified to, Hence, minimizing for δ
Info: Solution to the displacement is not unique,
And so a linear momentum constraint is added
Masses are assumed to be same. So only, \sum_i \delta_i = 0
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13. Approach Issue: Solution:
Position and orientation of final conformation does not match
Solution:
Superposition
RMS Superposition
Incremental Rotation
Does not match because: we are going around dealing only with the inter molecule distance as constraints.
We want them to match because we would like to verify that the process has happened correctly in an automated way.
RMS superposition: compares the two conformations and gives a one shot rotation answer
Incremental Rotation: calculates the rotation for each intermediate conformation. By minimizing the rotational error.
Incremental is more efficient but need to generate all intermediate conformations
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14. Outline Introduction Problem Statement Related Work Elastic Model
Approach
Results
Conclusion
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15. Results
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16. Results
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17. Results: Comparison with NMA
Consistent with NMA analysis
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18. Conclusion Elastic network model has been introduced Benefits
Efficient and realistic simulation of macromolecules transitions
Faster NMA analysis (Coarse grained)
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19. Questions
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20. Thank You
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