Elastic models of conformational transitions in macromolecules

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Elastic models of conformational transitions in
macromolecules

• Moon K. Kim, Gregory S. Chirikjian, Robert L.
  Jernigan
• Presented by Amit Jain

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Outline

• Introduction
• Problem Statement
• Related Work
• Elastic Model
• Approach
• Results
• Conclusion

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Introduction

• What are Macromolecules ?
• Carbohydrates
• Proteins
• Nucleic Acids
• Why are conformational transitions important ?
• Understanding functional relationship

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Problem Statement

• Input Two conformation x, ?
• Output List of realistic displacements d

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Related Work

• Interpolation
• 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

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Outline

• Introduction
• Problem Statement
• Related Work
• Elastic Model
• Approach
• Results
• Conclusion

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Elastic Model

• Key Enabler
• Discrete model for small conformational changes
  about an equilibrium position for macromolecules
• Model
• Alpha carbons
• Inter carbon force interactions

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Elastic Model

• Potential Energy function
• Can be reduced to

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Elastic Model

• Substituting,
• We get,

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Elastic Model

• Analytical equation for motion
• where M is diagonal matrix

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Approach

• Interpolate conformation
• Find the displacement(d) which minimizes cost
• Increment alpha
• Calculate new
• Use new conformation to find new displacement

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Approach

• Cost can be simplified to,
• Hence, minimizing for d

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Approach

• Issue
• Position and orientation of final conformation
  does not match
• Solution
• Superposition
• RMS Superposition
• Incremental Rotation

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Outline

• Introduction
• Problem Statement
• Related Work
• Elastic Model
• Approach
• Results
• Conclusion

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Results
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Results
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Results Comparison with NMA

• Consistent with NMA analysis

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Conclusion

• Elastic network model has been introduced
• Benefits
• Efficient and realistic simulation of
  macromolecules transitions
• Faster NMA analysis (Coarse grained)

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Questions
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Thank You