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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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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 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
Protein structure Low sequence similarity 11% (difficult prediction) model template predicted experimental High structure similarity conserved in evolution
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.
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)
d+ d- Target SpecificCompoundClassification: Support Vector Machines H1 drugs Maximize margin between H1 and H2 hypersurfaces ↓ Lagrangian formulation L = i – ½ikxi•xk H2 not drugs
Nonlinear support VectorMachines L = i – ½ikxi•xk L = i-½ikK(xi,xk) K(xi,xk)= (xi) • (xj) nonlinear Kernel
Bionanotechnology • Modelling dynamics, aggregation, and diffusion of macromolecules • reduced models for internal dynamics • electrostatic properties • design of antibiotics targeting RNA • targeting bacterial ribosome assembly
Reduced dynamics models P and Cα anharmonic network model (~10’000) Ribosome, 235’000 atoms
Ribosome: reduced dynamics and principal component analysis
Electrostatics: Poisson-Boltzmann equation } solvent } molecule ions
Ribosome assembly map Electrostatics ↓ RNA-proteins binding affinities ↓ Assembly map (binding sequence)
Antibiotics binding to Ribosome Antibiotic Ribosome subunit RNA
Antibiotics binding: Brownian dynamics Antibiotic - driving force - stochastic force
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
Potential energy surface for proton transfer Ab initio or DFT calculations ↓ AVB or modified Shepard interpolation ↓ analytical potential approximation
Molecular dynamics of proton transfer in porphycene
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
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
