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A Molecular Dynamic Modeling of Hemoglobin-Hemoglobin Interactions
1Tao
Wu,
1Department
Abstract
2Ye
Yang,
2Sheldon
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
Cohen, and
3Hongya
Ge
of Computer Science, 2Departments of Mathematical Sciences, 3Departments of Electrical & Computer Engineering,
New Jersey Institute of Technology, Newark, New Jersey, 07102, USA
Approach
In this poster, we present a study of hemoglobin-hemoglobin interaction with
Wang,
1Barry
Hemoglobin (HBB) Mutation
• Build a spring test problem. Use this known-parameter system to
verify the multi-scale method.
• Perform molecular dynamics (MD) simulations of hemoglobinhemoglobin interaction systems.
HBB sequence in normal adult hemoglobin (HbA):
HBB sequence in mutant adult hemoglobin (HbS):
Nucleotide: CTG ACT CCT GAG GAG AAG TCT
Amino Acid: Leu Thr Pro Glu Glu Lys Ser
|
|
|
3
6
9
Nucleotide: CTG ACT CCT GTG GAG AAG TCT
Amino Acid: Leu Thr Pro Val Glu Lys Ser
|
|
|
3
6
9
DT
DT
Coarse Temporal Scale
Relaxation
Fine Temporal Scale
Hemoglobin Protein Structure
Dt
• Based on MD simulation results, derive the strategy of multi-scale
methods and corresponding coarse grained models.
recover the principal direction of this system, namely the model direction.
This model direction will be matched with the eigenvector derived from
Dt
Spring Test Problem
Dt
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 interatomic and inter-molecular potentials are replaced by nonlinear springs. We
Dimensionality Reduction: Singular Value Decomposition and Principal
Components Analysis
Red: Fine Temporal Scale
Blue: Coarse Temporal Scale
DT
Consider an m × n matrix A. The singular value decomposition (SVD)
of A is then depicted as: A = USVT
Hemoglobin-Hemoglobin Interactions
employ the same method to get the most significant modes and their
frequencies of this complex dynamical system. More complex physical
Principal Component Analysis
phenomena can then be further studied by these coarse grained models.
(PCA): approximating a highdimensional data set with a
lower-dimensional linear
Introduction
subspace.
Snapshot with water molecules visible
Molecular dynamics (MD) simulations are widely used. However,
Simulation with NAMD
conformational changes and molecular interactions usually occur over
microseconds or even seconds and are consequently too computationally
Snapshot with water molecule display suppressed
Red: Fine Temporal Scale Solution
Blue: Coarse Temporal Scale Solution
Sickle Hemoglobin Polymerization
expensive for MD simulation available today. Therefore multi-scale or
Fine Scale Solution vs. Coarse Temporal Scale Solution
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
REFERENCES
present a multi-scale method to analyze such complex systems.
• Tao Wu, X. Sheldon Wang, Hongya Ge and Barry Cohen. Multi-scale and
Molecular Dynamics Simulation
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.
Multi-scale Method
Sickle Cell Anaemia
Red: MD simulation data
Blue: Recovered data with six
principal components
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
Scale
Accuracy
Fine Scale
Time step 10-15 sec
Coarse Scale
Time step 10-12 sec
High (Atomic Level)
Low (Molecular Level)
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
Computing
Cost
Simulation
Time Scale
Expensive
Inexpensive
~months of parallel computing
~days of parallel computing
Nanosecond
~10-9 s
Millisecond
~10-6 s
Red: Normal red blood cell
This work is supported in part by the National Science Foundation, Grand
CMMI-0503652 and CBET-0503649.
Blue: Sickled red blood cell
Macroscopic cell behaviors within capillary vessels.
Simulation data vs. Recovered data
Special thanks for the support of the Open Science Grid Project, which
provided computing resources.