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Introduction to Biomolecular Structure and Modeling Dhananjay Bhattacharyya Biophysics Division Saha Institute of Nuclear Physics Kolkata

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Biomolecular Structures These are determined experimentally by X-Ray Crystallography Nuclear Magnetic Resonance Spectroscopy Neutron Diffraction Study Raman Spectroscopy And also by theoretical methods

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2d sin =n

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Nucleic Acid Backbone is Connected to Either of Four Different Bases

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A G T C

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A-DNA B-DNA Z-DNA

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Proteins (polymers) are made up of Amino Acids (monomer units) There are Twenty different Amino Acids with different shape, size and electrostatic properties. These amino acids form covalent bonds to form a linear polypeptide chain.

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Alanine Phenylalanine Serine Cystine

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Glutamic Acid (Negatively charged) Arginine (Positively charged)

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Amino Acids are joined together by covalent bonds, called peptide bond, which is structurally very important

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helix: Hydrogen bonding between every i i+4 residues

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sheet: Hydrogen bonding between i j, i+1 j-1 (Antiparallel), or i j, i+1 j+1 (parallel)

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Coordinate System: External coordinates, such as (x,y,z), (r, , ), (r, ,z) Internal coordinates (BondLength, BondAngle, TorsionAngle)

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Bond Length Bond Angle Torsion Angle

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Internal External Coordinate

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Generated coordinates H C C C C H H

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Theoretical Modeling of Biomolecules: Quantum Mechanics based Methods Statistics based Methods Classical or Molecular Mechanics methods

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Peptide modeling initiated in India by G.N. Ramachandran (1950s) Postulates: Impenetrable spherical volumes for each atom Radius of the sphere depend on atom type No two atomic spheres can overlap if they are not covalently bonded

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Between HNOCPS H 2.0 (1.9)2.4 (2.2) 2.65(2.5) N 2.7 (2.6) 2.9 (2.8)3.2 (3.1)3.1 (3.0) O 2.7 (2.6)2.8 (2.7)3.2 (3.1)3.1 (2.9) C 3.0 (2.9)3.4 (3.2)3.3 (3.1) P 3.5 (3.3) S Normal and Extreme Limit (within parenthesis) distances (Å) used by Ramachandran co-workers

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Original Ramachandran Plot Fully Allowed Regions Partially Allowed Regions

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Ramachandran plot for 202 proteins at 1.5A or better resolution

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Variation of angle by 5 o allowed to fit observed phi-psi of protein structures.

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Schrodinger Equation: Quantum Mechanics Time dependent (3 Dimensional) Time independent

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DFT formalism with B3LYP Pseudoeigenvalue equation: where Potential due to exchange-correlation, is defined by with a, b and c as parameters obtained from fit with experimental data for sample compounds, E x are for electron exchange and E c are for correlation. Essentials of Computational Chemistry by C.J. Cramer (2002) John Wiley & Sons Ltd,

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Input data (atom coordinates, basis sets) Generate input guess density (overlap integrals) Construct the potential and Solve Kohn-Sham equation Generate output densities from Solutions to Kohn-Sham equations Are input and output density same? Analyze electronic population Repeat the cycle using the output density as the input density YESNO FLOW CHART DESCRIBING THE DFT METHODOLOGY

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G:C W:W C E = -26 kcal/mol A:U W:W C E = -14 G:U W:W C E = -15 A:G H:S T E = -10 A:G s:s T E = -6 A:U H:W T E = -13 A:A H:H T E = -10 G:A W:W C E = -15 G:A S:W T E = -11 A:A W:W T E = -12 A:U W:W T E = -13 A:A H:W T E = -11 2=>NH..O 1=>NH..N 1=>NH..O 1=>NH..N 2=>NH..O 2=>NH..N 1=>NH..N 1=>CH..O 1=>NH..O 1=>NH..N 2=>NH..N 1=>NH..O 1=>NH..N 2=>NH..N 1=>NH..O 1=>NH..N 1=>NH..O 1=>NH..N Strengths of different H-bonds from 33 non-canonical Base Pairs

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Considered Energy components, E NHO, E NHN, etc are additive. Additional stabilities, i may come from van der Waals, dipole- dipole etc interactions. Least Squares Fit indicates i, errors should be smallest for best Fit Type of H-bond E (kcal/mol) N-H…O-7.82 N-H…N-5.62 O-H…N-6.89 C-H…O-1.33 C-H…N-0.67 A. Roy, M. Bhattacharyya, S. Panigrahi, D. Bhattacharyya, (2008) J. Phys. Chem. B (in press)

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Netropsin like drugs bind in the B-DNA narrow and deep minor groove

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Actinomycin D like drugs make their place in between two stacked base pairs by distorting the DNA double helix

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DNA kinks by 90 o at the dyad location while binding to two subunits of Catabolite Activator Protein (CAP)

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TATA-box binding protein transforms the interfacing DNA region to A-DNA like structure

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DNA Smooth Curvature induced by Histone proteins in Chromatin (Nucleosome)

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Definition and Nomenclature of Base Pair Doublet Parameters

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Calculation of Base Pair parameters by NUPARM Local Step Parameters: Mean Local Helix Axis: Zm = Xm Ym, where Xm = Xaxis 1 + Xaxis 2 and Ym = Yaxis 1 + Yaxis 2 M is Base Pair Center to Center Vector Tilt : 2.0 * sin -1 ( -Zm Y1) Roll: 2.0 * sin -1 ( Zm X1) Twist:cos -1 (( X1 Zm) ( X2 Zm)) Shift (Dx) M Xm Slide(Dy)M Ym Rise(Dz) M Zm

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Partial list of DNA crystal structures available at bd : A C C G A C G T C G G T bd : A C C G G T A C C G G T bd : C G C G A A T T C G C G bd : G G C C A A T T G G bd : C G C A A A T A T G C G bd : C G C G A A T T C G C G bd : C C G C C G G C G G bd0017 9: C G C G C G G A G bd : G C G A A T T C G C G bd : G G C G A A T T C G C G bd : A C C G G C G C C A C A bd : C C A G T A C T G G Bd : C C G A A T G A G G

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Average Structural Parameters from Crystal Structures Base-Pair Step Size of Database TiltRollTwistRise G:G G:C C:G A:A A:T T:A A:C C:A A:G G:A

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DNA Bending: Experimental and Theory SequenceExperimental R L Theoretical bending (d/l) Random (AAANNNNNNN) n (AAAANNNNNN) n (AAAAANNNNN) n (AAAAAANNNN) n (AAAAAAAANN) n (AAAAAAAAAN) n

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Curved DNA models built from Crystal parameters (A 3 G 7 ) n (A 6 G 4 ) n (A 10 ) n

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Bond Angle Deformation Deformation from equilibrium value costs energy. Simplest form of energy penalty is: E k o

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Bonds are also stretchable but at a cost of energy Bond Breaking energy

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Ethane (three fold symmetry) Ethiline (two fold symmetry)

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Normal and Extreme Limiting (within parenthesis) distances (Å) used by Ramachandran co-workers Minimum Energy position: r ij o BetweenHNOCPS H2.0 (1.9)2.4 (2.2) 2.65 (2.5) N 2.7 (2.6) 2.9 (2.8)3.2 (3.1)3.1 (3.0) O 2.7 (2.6)2.8 (2.7)3.2 (3.1)3.1 (2.9) C 3.0 (2.9)3.4 (3.2)3.3 (3.1) P 3.5 (3.3) S Interaction between Instantaneous Atomic dipoles and Induced Atomic dipoles

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Force Field for Biomolecular Simulation

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E( x, y, z) E( x+1, y, z) E( x+2, y, z) ….. Search for Conformation with Lowest Energy

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Multivariable Optimization: NP-hard Problem Systematic Grid Search procedure: Impossible, large no. variables Guided Grid Search: Depends on Choice Approximate Method based on Taylor series Newton-Rhapson Method:

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Energy Landscape of typical bio-molecules Energy Positional Variables

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Always Accept Reject Accept Energy Uniformly generated Random numbers are used to accept if exp(- U/kT) > random no and reject otherwise Conformation 0: Calculate energy (E i ) Alter conformation randomly Calculate energy (E i+1 ) Calculate ρ = exp(-(E i+1 -E i )/kT) If ρ > random no accept the conformation Repeat the procedure

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Deterministic Method Molecular Dynamics Verlet Algorithm:

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Leapfrog-Verlet Algorithm t 0 -1/2 tt 0 +1/2 tt 0 +3/2 t t 0 +5/2 t t 0 +7/2 t t0t0 t 0 + t t 0 +2 tt 0 +3 t t 0 +4 t EEEE EEEE EEEE EEEE EEEE vvvv

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Time scale of Vibrational Motions TypeWave no (cm -1 )Period T p (λ/c) (fs) T p /π (fs) O-H, N-H stretch C-H Stretch O-C-O Asymm. Stretch C=C, C=N stretch C=O (carbonyl) stretch C=C stretch H-O-H bend C-N-H, H-N-H bend C-N stretch (amides) Water Libration (rocking) C=C-H bending

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Simple Pendulum Average Position of a simple pendulum Period of measurement of position : ~2.3 T Recommended period of measurement ~T /10

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Duration of Simulation Protein Folding requires 1 s to 1ms Ligand binding/dissociation requires 1 s No. of steps = 1ms / t = s/ s = Need of faster computer Engaging several computers in parallel Increasing t by Shake, Rattle or Lincs algorithms

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Softwares for Molecular Simulation Accelrys, MOE, SYBYL, TATA-BioSuite (Composite package, costly) CHARMM, AMBER (for Simulation, special Academic Price) GROMACS, NAMD (for Simulation, FREE) MOLDEN (for molecule Building, FREE) GAMESS (for QM calculation, FREE)

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Heating phase Equilibration

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Dickerson Dodecamer seq: d(CGCGAATTCGCG) 2

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CURVES calculated values

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S replaces O in backbone of substituted DNA. It yields two chiral conformers of DNA – PSR and PSS. S. Mukherjee and D. Bhattacharyya (2004) Biopolymers 73, 269–282

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PS-R PS-S Normal PO PS-R PS-S

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Students: Dr. Debashree Bandyopadhyay Dr. Shayantani Mukherjee Dr. Kakali Sen Mr. Sudipta Samanta Partially Supported by CSIR, DBT and CAMCS (SINP) Collaborators: Dr. Rabi Majudar Dr. Samita Basu Dr. Sangam Banerjee Dr. Abhijit Mitra (IIIT, Hyderabad) Dr. N. Pradhan (NIMHANS, Bangalore)

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