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A Molecular Dynamic Modeling of Hemoglobin-Hemoglobin Interactions 1Tao Wu, 2Ye Yang, 2Sheldon Wang, 1Barry Cohen, and 3Hongya Ge
1Department of Computer Science, 2Departments of Mathematical Sciences, 3Departments of Electrical & Computer Engineering,
New Jersey Institute of Technology, Newark, New Jersey, 07102, USAAbstract
In this poster, we present a study of hemoglobin-hemoglobin interaction with
model reduction methods. We begin with a simple spring-mass system with
given parameters (mass and stiffness). With this known system, we compare
the mode superposition method with Singular Value Decomposition (SVD)
based Principal Component Analysis (PCA). Through PCA we are able to
recover the principal direction of this system, namely the model direction.
This model direction will be matched with the eigenvector derived from
mode superposition analysis. The same technique will be implemented in a
much more complicated hemoglobin-hemoglobin molecule interaction
model, in which thousands of atoms in hemoglobin molecules are coupled
with tens of thousands of T3 water molecule models. In this model, complex
inter-atomic and inter-molecular potentials are replaced by nonlinear
springs. We employ the same method to get the most significant modes and
their frequencies of this complex dynamical system. More complex physical
phenomena can then be further studied by these coarse grained models.
Introduction
Molecular dynamics (MD) simulations are widely used. However,
conformational changes and molecular interactions usually occur over
microseconds or even seconds and are consequently too computationally
expensive for MD simulation available today. Therefore multi-scale or
coarse-grained methods have been applied.
The protein-protein interaction can be simplified as a complex spring-mass
network system. If the protein molecule is treated as a rigid body, which
means that during the interaction the overall shape changes little and is not
the dominant mode of the whole system, the system can be simplified into
two rigid bodies connected by some complex springs. In this poster, we
present a multi-scale method to analyze such complex systems.
Spring Test Problem
Dimensionality Reduction: Singular Value Decomposition and Principal Components Analysis
Consider an m × n matrix A. The singular value decomposition (SVD)
of A is then depicted as: A = UVT
Principal Component Analysis
(PCA): approximating a high-
dimensional data set with a
lower-dimensional linear
subspace.
Hemoglobin-Hemoglobin Interactions
Simulation with NAMD
Snapshot with water molecules visible Snapshot with water molecule display suppressed
REFERENCES
• Tao Wu, X. Sheldon Wang, Hongya Ge and Barry Cohen. Multi-scale and
multi-physics modeling of sickle-cell disease Part I Molecular Dynamics
Simulation, IMECE2008-66418.
• J. Israelachvili. Intermolecular and Surface Forces. Academic, 1992.
• Tamar Schlick. Molecular Modeling and Simulation: An Interdisciplinary
Guide. Springer Verlag, 2002.
• James C. Phillips, Rosemary Braun, Wei Wang, James Gumbart, Emad
Tajkhorshid, Elizabeth Villa, Christophe Chipot, Robert D. Skeel,
Laxmikant Kale, and Klaus Schulten. Scalable molecular dynamics with
namd. Journal of Computational Chemistry, 26:1781–1802, 2005.
Acknowledgments
This work is supported in part by the National Science Foundation, Grand CMMI-0503652 and CBET-0503649.
Special thanks for the support of the Open Science Grid Project, which provided computing resources.
Molecular Dynamics Simulation Multi-scale Method
Scale Fine Scale
Time step 10-15 sec Coarse Scale
Time step 10-12 sec
Accuracy High (Atomic Level) Low (Molecular Level)
Computing Cost
Expensive ~months of parallel computing
Inexpensive~days of parallel computing
Simulation Time Scale
Nanosecond
~10-9 s
Millisecond
~10-6 s
Approach
• Build a spring test problem. Use this known-parameter system to verify the multi-scale method.
• Perform molecular dynamics (MD) simulations of hemoglobin-hemoglobin interaction systems.
• Based on MD simulation results, derive the strategy of multi-scale methods and corresponding coarse grained models.
The most conformational changes occur onβsheet. Each of the hemoglobin changes little and could treat as rigid body. This result shows that it is possible to build a coarse grained model to analyze the low frequency mode of this system.
Red: MD simulation dataBlue: Recovered data with six principal components
Simulation data vs. Recovered data
Fine Scale Solution vs. Coarse Temporal Scale Solution
Sickle Cell Anaemia
Macroscopic cell behaviors within capillary vessels.
Red: Normal red blood cell Blue: Sickled red blood cell
Red: Fine Temporal Scale SolutionBlue: Coarse Temporal Scale Solution
Hemoglobin (HBB) MutationHBB sequence in normal adult hemoglobin (HbA):
Nucleotide: CTG ACT CCT GAG GAG AAG TCTAmino Acid: Leu Thr Pro Glu Glu Lys Ser | | | 3 6 9
HBB sequence in mutant adult hemoglobin (HbS):
Nucleotide: CTG ACT CCT GTG GAG AAG TCTAmino Acid: Leu Thr Pro Val Glu Lys Ser | | | 3 6 9
Hemoglobin Protein Structure
Sickle Hemoglobin Polymerization
Red: Fine Temporal ScaleBlue: Coarse Temporal Scale
t
T
RelaxationCoarse Temporal Scale
t
TT
t
Fine Temporal Scale