Computers in Chemistry Dr John Mitchell University of St Andrews 1. Why? • Working with experiment to test our theories. • Computer uses theory to calculate an answer that can be compared with experiment. • If prediction and experiment don’t agree, something has to give. Atoms in molecules are not spherical To Test Our Theories • The theory that lies beneath chemistry is ultimately quantum physics. • To turn this into a prediction of the rate of a chemical reaction or the frequency of a transition in an IR spectrum requires a lot of computation. To Test Our Theories • Computation’s ability to make accurate predictions of experimental measurements is a good test of the validity of a theory. • We only understand if we can predict. Crystal Structure Prediction • Given the structural diagram of an organic molecule, predict the 3D crystal structure. Br N S O O Slide after SL Price, Int. Sch. Crystallography, Erice, 2004 To Access Data that Experiment can’t • Computational chemistry also provides a way of obtaining information that would be very difficult, expensive or time-consuming to get experimentally. • Behaviour at very high temperature or pressure. • Details of structure of liquids at atomic scale. • Dynamics of proteins. Phase Changes of Iron in the Earth’s Core et al., Structure of Liquid Water and Water Clusters Computer simulations are an important source of evidence, since atomic scale details of an irregular structure are hard to obtain by experiment. Dynamic Motions of Proteins X-ray crystallography gives a single static structure Dynamic Motions of Proteins Simulation can show how the protein flexes 2. The Power to Compute Development of Computer Power University of Manchester SSEM, 1948 Development of Computer Power IBM Roadrunner, 2008 Computer Power: Moore’s Law Computer power doubles every two years: exponential growth Computer Power: Moore’s Law Logarithmic scale Computer Power: Moore’s Law This growth will, eventually, slow down as components reach atomic scale … we think! The Size of the Problem Scaling • Nonetheless, theoretical chemistry is expensive • Often cost scales as the fourth power of molecule size Scaling of the Expense of a Typical Quantum Chemical Calculation 700000 600000 500000 400000 Time (seconds) 300000 200000 100000 Atoms in Molecule 0 0 10 20 30 40 50 60 Typical scaling is ~N4. For the foreseeable future, there will be chemical problems at the limit of our computing power. 3. Philosophies of Computational Chemistry The Two Faces of Computational Chemistry Informatics Theoretical Chemistry Philosophy of Theoretical Chemistry “The problem is difficult, but by making suitable approximations we can solve it at reasonable cost based on our understanding of physics and chemistry.” Theoretical Chemistry • Calculations and simulations based on real physics. • Calculations are either quantum mechanical or use numbers derived from quantum mechanics. • Attempt to model or simulate reality. • Usually Low Throughput. What Kinds of Theoretical Chemistry can be Done? (1) Quantum Chemistry Prof. Eitan Geva What Kinds of Theoretical Chemistry can be Done? (1) Quantum Chemistry Using quantum mechanics to solve the structures and energetics of molecules; everything depends on the distribution of electrons. What Kinds of Theoretical Chemistry can be Done? (1) Quantum Chemistry Although quantum chemistry involves solving Schrödinger’s equation, it is not fully exact. There are some approximations involved. What Kinds of Theoretical Chemistry can be Done? (1) Quantum Chemistry Wavefunction Distribution of electrons within the molecule What Kinds of Theoretical Chemistry can be Done? (1) Quantum Chemistry Distribution of electrons Physical and chemical behaviour of the molecule What Kinds of Theoretical Chemistry can be Done? (1) Quantum Chemistry There are two main kinds of quantum chemistry: • Ab initio • Density Functional Theory What Kinds of Theoretical Chemistry can be Done? (1) Quantum Chemistry Ab initio “from first principles”. • Solve Schrödinger equation to get wavefunction. • In principle rigorous – we know what we calculate. • But the standard “Hartree-Fock” method contains significant approximations. • Expensive to adjust for these and get more accuracy. What Kinds of Theoretical Chemistry can be Done? (1) Quantum Chemistry Density Functional Theory • Makes use of the theorem that all properties of interest can be determined directly from the electron density. • True in principle, but the correct “functional” is unknown. • Less rigorous than ab initio, but usually more accurate for an equivalent cost (or cheaper for similar accuracy). What Kinds of Theoretical Chemistry can be Done? (2) Molecular Simulation What Kinds of Theoretical Chemistry can be Done? (2) Molecular Simulation There are various techniques for simulating molecules, the most significant is probably Molecular Dynamics. Molecular Dynamics makes a “balls-andsprings” model of the molecule in the computer, and follows its behaviour over time. What Kinds of Theoretical Chemistry can be Done? (2) Molecular Simulation Light-harvesting protein subunit. What Kinds of Theoretical Chemistry can be Done? (2) Molecular Simulation Time steps need to be very, very short (~10-15 seconds), so it takes a million steps to simulate one nanosecond of real time and a billion steps to simulate a microsecond. So it is hard to directly simulate relatively slow or rare events, such as protein folding. What Kinds of Theoretical Chemistry can be Done? (2) Molecular Simulation Also, a balls-and-springs model lacks the quantum mechanics needed to simulate a chemical reaction. Nonetheless, molecular dynamics is very important for understanding shape changes, interactions and energetics of large molecules. The Two Faces of Computational Chemistry Informatics Theoretical Chemistry Philosophy of Informatics “The problem is too difficult to solve at reasonable cost based on real physics and chemistry, so instead we will build a purely empirical model to predict the required molecular properties from chemical structure, using the available data.” Informatics • In general, informatics methods represent phenomena mathematically, but not in a physics-based way. • Inputs and output model are based on an empirically parameterised equation or more elaborate mathematical model. • Do not attempt to simulate reality. • Usually High Throughput. What is Cheminformatics? Calculating or predicting molecular properties without using a physics-based approach. Rather than modelling how the molecular world really works, cheminformatics is an empirical discipline, using available data to find correlations between chemical structure and properties. Cheminformatics techniques are often used in drug discovery and pharmaceutical research, and the requirements of the pharmaceutical industry have dominated the development of the subject. LOW THROUGHPUT Modelling in Chemistry PHYSICS-BASED ab initio Density Functional Theory Fluid Dynamics Car-Parrinello AM1, PM3 etc. Molecular Dynamics DPD ATOMISTIC Docking CoMFA EMPIRICAL 2-D QSAR/QSPR Machine Learning HIGH THROUGHPUT NON-ATOMISTIC Monte Carlo 4. How Best to Compute Solubility? Which would you Prefer ... or ? Which would you Prefer ... or ? Solubility in water (and other biological fluids) is highly desirable for pharmaceuticals! Solubility is an important issue in drug discovery and a major cause of failure of drug development projects This is expensive for the industry A good computational model for predicting the solubility of druglike molecules would be very valuable. Drug Disc.Today, 10 (4), 289 (2005) Our Methods … (A) Thermodynamic Cycle (Theoretical chemistry) Our Thermodynamic Cycle method … We want to construct a theoretical model that will predict solubility for druglike molecules … We expect our model to use real physics and chemistry and to give some insight … We don’t expect it to be fast by informatics standards, but it should be reasonably accurate … Can we use theoretical chemistry to calculate solubility via a thermodynamic cycle? Gsub comes from lattice energy minimisation based on the experimental crystal structure. Calculate Energy of Infinite Periodic Lattice Unit cell Calculate Energy of Infinite Periodic Lattice • • • • • • Take one molecule Solve its Schrödinger equation Calculate its interactions Allow unit cell to change Find best size, shape, packing Find energy of infinite lattice This is the same methodology as used in crystal structure prediction. Gsub comes from lattice energy minimisation based on the experimental crystal structure. Gsolv comes from a computational solvation model, RISM Model of Solvent-Solute Interaction Model is called RISM Calculate energy of interaction between solute and solvent Gsolv comes from model of solvent-solute interaction Theoretical Chemistry: Solubility Results Palmer et al., J. Chem. Theory Comput., 8, 3322-3337 (2012) Theoretical Chemistry: Solubility Results These results are OK, but we hope to do even better in the future Theoretical Chemistry: Solubility Results Our Methods … (B) Random Forest (informatics) Our Random Forest Model … We want to construct a model that will predict solubility for druglike molecules … We don’t expect our model either to use real physics and chemistry or to be easily interpretable … We do expect it to be fast and reasonably accurate … Random Forest A Machine Learning Method This is a decision tree. We use lots of them to make a forest! Random Forest This is a decision tree. Random Forest Generate more trees randomly. (1) By randomly sampling with replacement to make different “bootstrap samples” of the data for each tree. Random Forest Generate more trees randomly. (2) By randomly choosing the pool of questions to ask of the data for each node (junction) of each tree. Random Forest ● Machine Learning method introduced by Briemann and Cutler (2001) ● Development of Decision Trees (Recursive Partitioning): ● Dataset is partitioned into consecutively smaller subsets ● Each partition is based upon the value of one descriptor ● The descriptor used at each split is selected so as to optimise splitting ● Bootstrap sample of N objects chosen from the N available objects with replacement Random Forest Generate more trees randomly. Random Forest Generate more trees randomly. Random Forest Generate more trees randomly. Random Forest Generate more trees randomly. We use lots of them to make a forest! Random Forest for Solubility Prediction A Forest of Regression Trees Each leaf contains a group of molecules with similar solubility. Random Forest • The molecules whose solubility is to be predicted are run through every tree (~ flow chart) in the forest. • Each tree predicts a solubility for each molecule. • We average the predictions over hundreds of different trees. Random Forest Random Forest: Solubility Results RMSE(tr)=0.27 r2(tr)=0.98 Bias(tr)=0.005 RMSE(oob)=0.68 r2(oob)=0.90 Bias(oob)=0.01 RMSE(te)=0.69 r2(te)=0.89 Bias(te)=-0.04 DS Palmer et al., J. Chem. Inf. Model., 47, 150-158 (2007) RMSE(tr)=0.27 r2(tr)=0.98 Bias(tr)=0.005 RMSE(oob)=0.68 r2(oob)=0.90 Bias(oob)=0.01 RMSE(te)=0.69 r2(te)=0.89 Bias(te)=-0.04 These results are competitive with the best solubility prediction methods RMSE(tr)=0.27 r2(tr)=0.98 Bias(tr)=0.005 RMSE(oob)=0.68 r2(oob)=0.90 Bias(oob)=0.01 RMSE(te)=0.69 r2(te)=0.89 Bias(te)=-0.04 What Have we Learned? • For this particular problem, informatics does a bit better than pure theoretical chemistry. How to Utilise Informatics • Fast informatics models can be integrated into drug discovery to compute solubilities for molecules before deciding whether to synthesise them. • Saving much time and money on making useless compounds. Fits into drug discovery pipeline here Why Pursue Theory? • Theory promises to give a greater understanding of why some molecules are more soluble than others. • Advances in theory can be transferable to other contexts. • Theoretical models can be systematically improved.