The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved. P. A. M. Dirac
The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.
Rationalisierung einer unueblichen (strained) Struktur des Allyls
Elektronen Strukturen von Molekuelen Spektroskopie ( fingerprints ) Nukleare Bewegungen Katalyse Wie und warum laufen chem. Reaktionen ab? Proteindynamik
Nukleare Bewegungen ( ) ( ) ( ) [ ] t x p e x e x D x t t x p x G x G, ) ( ), ( β β = ( ) ( ) ( ) x E x x V m i i i r r r h Ψ = Ψ + Δ 2 2 Loesung von Differentialgleichungen unterschiedlicher Komplexitaet Newton Smoluchowski Schroedinger
System Experimental Techniques Theory/Modelling He-HN 2 + Ne-HF (Ne) n -HN 2 + Clusters MbCO MbNO Insulin Vibrational Spectroscopy Vibrational Spectroscopy X-ray, NMR, FTIR, femtosecondtime resolved IR X-ray, NMR, thermodynamic measurements Ab initio calculations with bound states Vibrational adiabatic correction Morphing potentials Morphing Potentials Diffusion Monte Carlo Molecular Dynamics, Reactive MD, Accurate Electrostatics, Umbrella Sampling, Smoluchowski equation Molecular Dynamics, Free energy simulations HIV-I X-ray, binding affinity measurements Molecular Dynamics, Scoring
Verstaendnis der Ligand Diffusion in Proteinen (z. B. Myoglobin)
Verteilung der fluessigen Phase abhaengig von der Dichte der stationaeren Phase. Experimentelles Problem: keine direkte Strukturbestimmung moeglich
G(q) is possibly rough: Smoluchowski equation difficult to solve No extensions to several dimensions Use of Hierarchical Discrete Approximation: 1 Introduce a hierarchy of grids Local rates (subgrid) and overall rates from these 1 Banushkina and Meuwly, JCTC, 2, 218 (2005)
Smoluchowski equation Computational Chemistry Discretization into a master equation with transition probabilities l DA approximation for transition probabilities (one possibility) 1 Banushkina and Meuwly, JCTC, 2, 218 (2005)
Mean first passage time between n and n+1 Transition probability between n and n+1 Time propagation of the probability distribution Analytical expression for mean first passage time based on time propagation 1 Banushkina and Meuwly, JCTC, 2, 218 (2005)
Calculated binding free energy: -11.9 kcal/mol (Expt: 7.2 kcal/mol) Dimerization mainly due to nonpolar (van der Waals, nonpolar desolvation) interactions. Stabilizing effect of H-bonds is counterbalanced by desolvation energy upon dimerization. Most stabilizing residues: Phe24, Phe25, Tyr26 (B chain)
All backbone Simulation Chain A Helix chain B Experiment A chain and helix of B chain very stable Motion of C-ter exposes N-ter of A chain (function) Results in agreement with expt data (preliminary X-ray, Raman, NMR) V. Zoete, M. Meuwly, M. Karplus JMB, 342, 913 (2004)
Q( N, V, T ) 1 1 = 3N 3N E( p, q) d pd q exp 3N N! h kt Alle thermodynamischen Observablen (Experiment!) koennen aus Q oder Ableitungen von Q gewonnen werden. Problem: hochdimensionales Integral! Loesung : Monte Carlo Sampling F( N, V, T ) = kt ln Q( N, V, T ) p F = V T, N S F = T V, N μ = F N V, T Zentral bei der Berechnung von Bindungsstaerken fuer pharmakologisch aktive Liganden an Proteine.
Zusammenfassung Computational Chemistry Viele fundamentale Gleichungen/Zusammenhaenge, welche fuer die Chemie von Bedeutung sind, sind bekannt. Problem ist die Vielteilchen-Natur der Prozesse Fuer die Chemie ist immer ein reales System von Bedeutung. Modellbildung ist essentiell. Dazu ist ein detailliertes Verstaendnis des Prozesses entscheidend. Ziele der CompChem beinhalten das atomare Verstaendnis von chemisch und biologisch wichtigen Prozessen Katalyse (Reaktionen/Reaktivitaeten) Struktur und Spektroskopie (Analyse) Reaktionsdynamik Zwischenmolekulare Wechselwirkungen Vereinfachte Modelle basierend auf genauen Rechnungen Ursachen von Selektivitaet ( warum genau dieser Ligand?)