Author: Jessica Mackin // Editor: Erin Pallott

Feature photo by Snufkin (CC0 1.0)

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The introduction and development of technology has vastly changed our day-to-day lives. We have limitless information to hand in a mobile phone. Saving, loading, and running data from a laptop is simple and convenient. The development of technology in life sciences has led to great change in how we approach our subject area.

Research conducted by PGRs in FBMH is often collaborative and interdisciplinary in nature, frequently bringing together mathematics and life science. One such example is the use of mathematical models to understand complex biological systems.

Cells, organs, and bodies are extremely complex; you cannot have an action without a reaction. For example, a genetic mutation leading to under or over-expression of a protein, the reaction of pharmaceutical and recreational drugs on the body, or environmental triggers of disease. How can you process all this dynamic information, the intricacies, reactions, and outcomes? Simply put, you cannot, unless you break it down into smaller, simpler, and more manageable information. This is, in essence, what mathematical models enable us to do.

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As a biologist, we tend to avoid complex mathematics as some of us really do not like numbers, the thought of using and understanding complex mathematics can be daunting. However, the use of predictive models enables us to understand our system better and generate testable hypotheses that can advance our research.

Using a superficial overview, models use biology in its simplest form with a series of equations such as protein X interacting with protein Y (X + Y → XY). From this, a mathematician can generate a series of ordinary differential equations (ODEs) which describe the rates, interactions, and relationships of your species (proteins) over time. Using software such as MATLAB and Python, you can solve these ODEs to generate a predictive model on how your species interact over time.

Once you have a basic model, you can then start to perturb the system. For example, you have a mutation in protein X’s binding domain to Y, X has become either more or less stable at the RNA or protein level, and you add protein Z, a modulator of X.

By investigating the model, you can see how subtle changes in parameters impact the system, meaning you can generate experimentally testable hypotheses. At this point, your model would need refinement. You would run experiments to gain real input parameters such as the rate of protein synthesis, decay, association, and dissociation. With these values, you would run the model again to generate more hypotheses and repeat this process until you develop a model that is more realistic and accurate to the system you are investigating.

Outside of the lab environment, mathematical models (predictive and statistical) have real world implications and capabilities. A perfect example of this is the COVID-19 pandemic and the involvement of the scientific advisory group for emergencies that included researchers at the University of Manchester. There were several predictive and statistical mathematical models developed to study properties of the virus such as transmission, severity of disease and fatality rate, which were an integral part to making COVID-19 policies.

Computational models and simulations are being used in the biomedical industry and most recently, there has been a rise in the discussion and development of in silico clinical trials. This is relates to the 3Rs strategy (reduce, replace and refine), the need to find more cost-effective methods to generate hits and, to some extent, an outcome of COVID-19 which caused suspension or termination of clinical trials in hospitals. Unlike the simplistic model described above, a model to predict the effect of a drug in a human is far more complex, requiring thousands of input parameters and equations. You would need to develop model subsets to include things such as a pharmacokinetics, pharmacodynamics, clinical simulation, and individualised patient predictive modelling.

In short, it is a lot, why bother?

Most compounds in the drug discovery phase do not pass pre-clinical testing due to adverse effects during in vitro or in vivo studies, meaning a lot of time and money invested goes towards drugs that never make it to patients. Although models, at this stage, cannot fully recapitulate a human, it can offer some insight into how a compound may react. For example, if you know patients have an underlying genetic cause of disease, you will want to know how a mutation in key residues impacts drug efficacy or what are the knock-on effects to alternate genes related to the pathway you are targeting.

Years ago, the idea of an in silico clinical trial may have seemed impossible and arguably still is. However, in the current moment, we do not know the full extent of modelling and the advances it can make.  

Overall, models are not perfect and are often wrong. This is something my supervisors have often told me. If they are often wrong, why use them in biology? The answer being, they are predictive, not definitive. They give you questions to find answers to and proving why they are wrong is what makes it interesting.

If you had the answer to everything, then it wouldn’t be research.

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