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Explore current research topics at ICM, including bioinformatics, bionanotechnology, and quantum molecular dynamics. Unravel the challenges and innovations in protein structure prediction, ligand classification, and antibiotic design. Witness the intersection of mathematics and biology in understanding biomolecules. Join us on a journey into the intricate world of biomolecular modeling.
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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
