In this work novel computational methods will be developed to efficiently explore chemical space in the search for compounds with desirable properties. To improve the efficiency of exploration two methods will be used: reducing the cost of evaluating a point in chemical space, or reducing the number of points which require evaluating to find the desired compound. The first chapter of this work will introduce the topics relevant to this work, place them in the wider context of drug design and outline the theory used to generate the results presented in subsequent chapters.

The first result of this thesis, discussed in chapter 2, is for the application of free energy methods to the problem of computational fluorine scanning. The application made in this work will allow for all fluorinated analogues of a compound to be tested five times faster than existing computational methods and with comparable predictive accuracy.

In chapters 3 and 4 we will consider the application of numerical methods to ligand-protein binding problems in order to optimize the charge/steric parameters of the ligand and maximize binding affinity of these ligands to a given protein target. In these two optimization-based chapters we will use free energy methods to calculate gradients of the binding free energy with respect to the parameters which describe the ligand, thus allowing optimal sets of parameters to be found efficiently. In chapter 3 we search for optimized sets of charge parameters from which design ideas can be generated and tested; 73% of the design ideas were found to beneficially improve binding affinity. In chapter 4 we find optimized sets of steric parameters from which beneficial growth vectors for methyl groups can be predicted. These predictions correlate with existing free energy methods with a Spearman's rank order correlation of 0.59. The advantage of the optimization methods presented in these chapters are: 1) the methods can generate ideas for mutations which improve ligand binding free energy and 2) these methods require less computational time to explore the same volume of chemical space than existing free energy methods.

Finally, chapter 5 will discuss a collaborative open source work to find new malaria therapeutics. Ligand based machine learning methods will be applied to generate and evaluate the potency of hundreds of thousands of compounds in a manner far faster than is possible with free energy methods. Based on the computational predictions, compounds are selected and evaluated experimentally with one compound tested and verified to be active with a pIC50 of 6.2 in good agreement with the computational prediction of 6.42 +- 0.75.