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ICM University of Warsaw

Mathematical modelling of biomolecules. Current research topics at ICM. Bioinformatics K. Ginalski, D. Plewczynski et al Bionanotechnology M. Dlugosz, J. Trylska et al Quantum molecular dynamics M. Hallay-Suszek, P. Grochowski. ICM University of Warsaw. 2I1B. 2ILA. 1BFG.

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ICM University of Warsaw

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  1. Mathematical modelling of biomolecules. Current research topics at ICM • Bioinformatics • K. Ginalski, D. Plewczynski et al • Bionanotechnology • M. Dlugosz, J. Trylska et al • Quantum molecular dynamics • M. Hallay-Suszek, P. Grochowski ICM University of Warsaw

  2. 2I1B 2ILA 1BFG Bioinformatics: Template-based protein structure prediction ~30.000.000 protein sequences ~45.000 protein structures (PDB) ~1000 unique folds (SCOP) Template selection ↓ Sequence-to-structure alignment ↓ Replacements, insertions and deletions ↓ Refinement

  3. Protein structure Low sequence similarity 11% (difficult prediction) model template predicted experimental High structure similarity conserved in evolution

  4. consensus model 3D-Jury model Template-based protein structure prediction collected models Critical Assessment of Techniques for Protein Structure Prediction (CASP5, CASP6) targets: sequences of proteins about to be solved exp.

  5. Bioinformatics: Target SpecificCompound Classification Set of ligands (small compounds) verified by experiments to be active for a specific target (protein) Learning Model distinguishing if a ligand is a drug of this taget based on 2D/3D data. 2D/3D structure of a new ligand Classification: new drug or not. (~70% recall value)

  6. d+ d- Target SpecificCompoundClassification: Support Vector Machines H1 drugs Maximize margin between H1 and H2 hypersurfaces ↓ Lagrangian formulation L = i – ½ikxi•xk H2 not drugs

  7. Nonlinear support VectorMachines  L = i – ½ikxi•xk L = i-½ikK(xi,xk) K(xi,xk)= (xi) • (xj) nonlinear Kernel

  8. Bionanotechnology • Modelling dynamics, aggregation, and diffusion of macromolecules • reduced models for internal dynamics • electrostatic properties • design of antibiotics targeting RNA • targeting bacterial ribosome assembly

  9. Reduced dynamics models P and Cα anharmonic network model (~10’000) Ribosome, 235’000 atoms

  10. Ribosome: reduced dynamics and principal component analysis

  11. Electrostatics: Poisson-Boltzmann equation } solvent } molecule ions

  12. Ribosome assembly map Electrostatics ↓ RNA-proteins binding affinities ↓ Assembly map (binding sequence)

  13. Antibiotics binding to Ribosome Antibiotic Ribosome subunit RNA

  14. Antibiotics binding: Brownian dynamics Antibiotic - driving force - stochastic force

  15. Microscopic molecular dynamics Small molecules (porphyrin, porphycene) Born-Oppenheimer approximation in the ground or an excited electronic state Dynamics: transfer of protons (including quantum effects) and structure oscillations Comparison: experimental spectroscopic data

  16. Potential energy surface for proton transfer Ab initio or DFT calculations ↓ AVB or modified Shepard interpolation ↓ analytical potential approximation

  17. Molecular dynamics of proton transfer in porphycene

  18. Including quantum effects in dynamics of atomic nuclei Multidimensional (all-atom) Gaussian wave packet (→ zero point energy, energy barrier lowering) Quantum dynamics of protons (→ full delocalization, correlation and exchange) Lagrangian formulation of mixed classical-quantum equations of motion

  19. Quantum proton dynamics

  20. d+ d- • Bioinformatics • K. Ginalski, D. Plewczynski et al. • Bionanotechnology • M. Dlugosz, J. Trylska et al. • Quantum molecular dynamics • M. Hallay-Suszek, P. Grochowski Thank you

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