A chemical reaction mixture consists of one or more reactants (most often two) that combine to make a product. In addition, a catalyst may be added, or other reagents acting as acid, base or other such activating agent, and a solvent to create a homogeneous mixture of a predetermined concentration. Then the mixture may be heated or cooled, stirred in a variety of ways and at different speeds in a choice of vessels. As you can see, the permutations of the different options can be vast. Even with high-throughput technology, a full exploration of a chemical reaction is a massive undertaking that is rarely achieved in practice. It is hugely beneficial to the chemist or process engineer to employ a systematic approach to understanding the significance of each reaction variable as quickly as possible with the aim of maximising the result (typically measured by yield, ideally in as short a time as possible). The two basic approaches are summarised here.
The One Factor at a Time (OFAT) method is an experimental approach where one variable is changed sequentially while keeping other variables constant to determine the effects on the outcome of interest (Czitrom, 1999). This is a tempting approach if only one experiment is conducted at a time, seeking gains on the previous experiment. It will take a long time to optimise the variables and risks getting trapped at a 'local maxima': a phenomenon where, for example, the yield of the reaction may be best within certain limited parameters, but a fuller exploration of the reaction variables could return even greater yields (Murray et al., 2016).
Design of Experiments (DoE) is an approach to selecting which experiments to perform in order to achieve the best outcome in the fewest attempts. The experimental plan usually consists of minimising and maximising each reaction variable and also obtaining intermediate datapoints to verify the relationship between variables (temperature, pressure, catalyst, catalyst loading, etc.) and outcome (yield, rate constant, etc.) (Tye, 2004). Below are illustrated examples of how two variables may effect the outcome of a reaction. The first example on the left is how pressure and temperature might influence the yield of a reaction. The maximum achievable temperature and pressure is ideal, with one variable more influential than the other. The annotated datapoints are a one-dimensional DoE approach more consistent with OFAT, with one variable increased until the yield was satisfactory without knowing the full potential of the system.
The second example (above right) shows a non-uniform response to two variables. Although x1 has a strong influence when x2 is low, increasing x2 is beneficial and x1 has minimal influence when x2 is high. This might occur if x1 is catalyst concentration and x2 is temperature and the response being measured is yield: at high temperature the reaction is fast and complete before the chosen reaction duration even with low catalyst loading (time is not being varied here). The five data points give a good spread of information, but reaction duration should also be investigated as well as any other variables that effect the yield.
In the pharmaceutical sector, DoE is helpful in streamlining drug development processes, from the synthesis of active pharmaceutical ingredients (Nishimura and Saitoh, 2016) to the formulation of the final medicine (Hwang and Noack, 2011). DoE is invaluable for identifying critical process parameters, optimising product formulations, and ensuring robust and reproducible processes, thereby enhancing efficiency, quality, and compliance with regulatory standards (Politis et al., 2017). Where many variables are relevant, a statistical analysis is needed to optimise the result and this is where DoE methods are much more efficient than the One Factor at a Time (OFAT) method.
The DoE methodology works best when combined with high throughput technologies. A large number of experiments can be performed simultaneously. The principles of Green Chemistry and Safe and Sustainable by Design can be incorporated into high throughout screening experiments by operating at small scales to reduce waste, and including safer substances in the screening process to evaluate their effectiveness.
One-factor-at-a-time versus designed experiments: Czitrom, V., The American Statistician 1999, 53, 126-131.
The application of design of experiments (DoE) reaction optimisation and solvent selection in the development of new synthetic chemistry: Murray, P.M., Bellany, F., Benhamou, L., Bučar, D.-K., Tabor A.B. and Sheppard, T.D., Org. Biomol. Chem. 2016, 14, 2373-2384.
Application of statistical ‘design of experiments’ methods in drug discovery: Tye, H., Drug Discovery Today 2004, 9, 485-491.
Introducing telescoping process to synthesis of a key intermediate of drug discoveries using design of experiment: Nishimura, K. and Saitoh, T., Chemical and Pharmaceutical Bulletin 2016, 64, 1043-1046.
Application of design of experiments to pharmaceutical formulation development: Hwang, R. and Noack, R.M., Int. J. Experiment. Design Process Optimisation 2011, 2, 58-65.
Design of experiments (DoE) in pharmaceutical development: Politis, S.N., Colombo, P., Colombo, G. and Rekkas, D.M., Drug Development and Industrial Pharmacy 2017, 43, 889-901.