Abstract

1. A Molecular Dynamic Modeling of Hemoglobin-Hemoglobin Interactions1Tao Wu, 2Ye Yang, 2Sheldon Wang, 1Barry Cohen, and 3Hongya Ge1Department of Computer Science, 2Departments of Mathematical Sciences, 3Departments of Electrical & Computer Engineering, New Jersey Institute of Technology, Newark, New Jersey, 07102, USA Abstract 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. Approach Hemoglobin (HBB) Mutation HBB sequence in normal adult hemoglobin (HbA): Nucleotide: CTG ACT CCT GAG GAG AAG TCT Amino 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 TCT Amino Acid: Leu Thr Pro Val Glu Lys Ser | | | 3 6 9 • 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. DT DT Coarse Temporal Scale Relaxation Fine Temporal Scale Hemoglobin Protein Structure Dt Dt Spring Test Problem Dt Dimensionality Reduction:Singular Value Decomposition and Principal Components Analysis Red: Fine Temporal Scale Blue: Coarse Temporal Scale DT Consider an m × nmatrix A. The singular value decomposition (SVD) of A is then depicted as: A = USVT Hemoglobin-Hemoglobin Interactions Principal Component Analysis (PCA): approximating a high-dimensional data set with a lower-dimensional linear subspace. 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. Snapshot with water molecules visible Snapshot with water molecule display suppressed Simulation with NAMD Red: Fine Temporal Scale Solution Blue: Coarse Temporal Scale Solution Sickle Hemoglobin Polymerization Fine Scale Solution vs. Coarse Temporal Scale Solution • 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. 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 data Blue: Recovered data with six principal components Sickle Cell Anaemia 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. Red: Normal red blood cell Blue: Sickled red blood cell Simulation data vs. Recovered data Macroscopic cell behaviors within capillary vessels.