Mathematics and Biology (the Pharma Vision)

I began this blog almost exactly three years ago. My goal was two-fold: first, to demonstrate thought leadership in an area in which I was then founding a company; and, second, to have a demonstrated track-record rather than a picture-perfect pitch-deck. This latter is clearly a sub-goal of the first.

In those early days, I began a series of articles on Mathematics and Biology. I began with a comparison of the two fields. From there I moved on to discussing the people and skills involved, essentially why mathematicians so rarely do biology. I then discussed the outlier which is bioinformatics. I had two further articles planned in the series, after which point I wanted to attempt a synthesis. The missing articles are on the Microbiome and Quantitative Systems Pharmacology (QSP). These will remain missing articles for now, time has moved on and my thoughts on all of these topics have progressed enormously.

A few weeks ago I published a futurecast about using virtual patient’s for pharma drug development. There was a key idea buried in that article which in essence is my current synthesis perspective on mathematics and biology. I want to highlight this idea here and flesh it out slightly.

What is the use of mathematics in biology?

Let’s start with some personal background and an anecdote. I worked in academic mathematical biology for roughly fifteen years. I worked in top groups across the scientific powerhouses of the northern hemisphere. That is, I was a long-term team member in Germany, France, and the USA. And I had extended research stays in Israel, Japan and Switzerland. My training in my native country, Ireland, rounds out my experience having given me exposure to the UK system.

In all of that time I have, I think, never seen math precede biological discovery.

There were a number of mathematical models which I studied in computational neuroscience which are taught as having led the discovery process. Every time I looked into such a case I discovered that the formal mathematical approach was subsequent to the biological discovery.

I am even aware of one case in which a journal editor significantly delayed an experimental paper so that he personally could first publish a theory paper predicting the discovery…. the bad side of academic-scientific behaviour.

What did I think I was doing all that time?

I used to explain to my family what I did as formalisation (yes a French-ism).

Mathematicians are very good at formalism. We construct equations, systems of equations, and then see if they make sense in explaining the world.

I thought, at the time, that this was a valid, and indeed valuable, scientific contribution because most medics and biologists are extremely bad (in my experience) at spotting the gaping holes in their pet theories. This phenomenon is not, of course, unique to people working in biology. We all become blind to reason when our favourite ideas are under attack. Formal analysis provides a means to escape this blindness by highlighting the inconsistencies.

As I found to my cost, formalism alone is not enough to build an academic career these days. There was a time when biologists happily allowed mathematicians to explain their results, in separate journals, and relied on the relative strengths of mathematically-minded colleagues to validate their hypotheses. This was fine until competition for scarce research resources got out of control. Nowadays, data is always published with an in-house ‘model’ first before theoreticians are allowed to make ‘better’ models of it. This has the obvious effect of putting the experimentalist in the driving seat when it comes to career positioning.

Leaving aside the career issues, the formalism approach to science is a bit like Popper’s falsification. It’s correct, but it is not so easy to advance science by falsification alone. Hypotheses need to be generated, proposed and validated. What is the value of a non-falsified hypothesis? In the high-dimensional world of a mathematical model the answer is not a lot.

And so formalism, while valid and intellectually interesting, is not enough.

Is there a higher-value contribution available to math?

As I mentioned in my futurecast article, I actually did have a project where the math came pretty close to leading the biological discovery.

During my PhD I sat half of my time in an experimental lab. There I would use my formalism approach to help to winnow experiments for the team. Over time, a relationship of trust was built up between us and they asked me to examine their favourite hypothesis.

They had some very basic evidence for this hypothesis. But even at the best of times this would not have been enough to convince the scientific community. To make things worse, they were on the wrong side of a debate which had been ‘won’ by some very powerful people in that field. Those power players had 30 years of reputation on saying the opposite to this particular hypothesis. So the team needed powerful proof or they needed to save time and work on other topics.

To cut a long story short, I built a model of their hypothesis. I embedded domain knowledge from across the spectrum of labs working on this particular field into the model. And I started looking for predictions, based on the model, which would completely shock the existing consensus view while remaining within the narrative of the model. In more mathematical terms, I first fitted the model then performed a sweep of the space of ‘experimental protocols’ to see if there were interesting outliers which could distinguish our model from the competing view.

This type of constraint-based search is essentially the limit of what can be attained by this purely formalistic approach. From my perspective, there are two reasons that this approach is not more widely accepted, (i) typical biologists lack the expertise necessary to interact with and develop these models themselves, (ii) quite a number of charlatans have devalued the approach by constructing complex mathematical models which don’t really do what they claim they do.

Can this be done at scale?

My model of cerebellar plasticity was nice and it helped to advance a scientific field. I think a colleague has even used it for neocortical plasticity with some success. But it required a lot of effort to construct and led to one single scientific question being answered well. The real question is, can this ever be done at a scale beyond which the returns outweight the input efforts?

I think so.

I have been running a series of experiments with pharma companies in recent years. I am essentially trying to understand where mathematical models can be used to best advantage in the pharma industry. An obvious confounder is that various interpersonal and career issues tend to muddy the waters when dealing with large (matrix-style !) organisations.

I call my approach: many small models. You could say that I have a natural affinity for design thinking in many of my actions. Small, by the way, is relative some of the mathematical models involved are extremely complex.

My take away:

Math will never replace bio in the development of drugs. These are biologically-driven companies. However, the work practice of a medicinal chemist – or other pharma worker – has changed enormously in the past twenty years. Gone is the reliance on personal memory, so too the paper-based citation indices. A computer is a tool, and workers today are comfortable relying upon it.

The goal of the mathematical modeller, then, should be to be able to provide a reasonable / semi-interesting answer most of the time. That’s why they need many models.

This is important because you need to provide a pull-factor so that people come to you looking for solutions.

It’s not enough to spend 6 months working on a specific system, just to answer one original question. Yes, there will always be specific high-value problems that need this level of detail.

But where the models will excel is in the early-stage filtering and suggesting of options. The first reflex of the biologist should become, “Hey, math team / software, what do you know about X? Can you narrow my search space a little?” And the answer should always be, “Yes.”

I see the basic output being constraint based optimisation of experimental protocols. The computer should set clear limits on the range of what is relevant. The experimentalist will have to do the rest.

Take home messages

This is a highly complex article written in too-technical language. Here is what I want the reader to take away.

Building complex mathematical models has value, but it is not the way to gain widespread acceptance in biology.

Building a system where you can always provide somewhat useful answers will generate a pull-factor. This means that you are no longer a solution looking for a problem. You are now a general problem solving machine that people know and seek-out.

The analogical solution in my work, in the medical field, is a Clinical Decision Support (CDS) solution. We no longer think that we can circumvent the doctor. We provide support – like autocomplete – and help them to make better decisions.

Ultimately where this will end up in pharma is as a decision support tool, coupled to an enterprise resource planning (ERP) backend, involved in planning the relevant experiments necessary to develop and validate new drugs.

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