Is mathematics invading human cells? Impressions from a collaboration with diabetes doctors

Along with space exploration and military and civilian nuclear power design, medical devices belong to the mathematically most sophisticated areas of modern technology. There are, for example, many mathematicians that have either contributed or could have contributed to magnetic spin resonance imaging (MRI), and there is hardly a single mathematician who masters all the math involved in that technology. The same goes for electron tomography, multi-beam confocal laser microscopy and many other advanced devices. Medicine has become a mathematical discipline. The ominous military-industrial complex has grown into an eminent mathematical sick-and-health industry.

But mathematics is encapsulated in the apparatus. Whether it is about a specific diagnosis or treatment, most patients will probably, at least when you come from mathematical physics, be surprised at how little medical science seems to really know and understand about the individual diseases. It is quite normal that a doctor must simply experiment -or just stick to an established symptom diagnosis and symptom treatment. Without a detailed identification of the real causes of the individual patient’s ailment, often a successful treatment, defined as cure, is unattainable.

Physics can also be complicated and in many cases without established answers. But in physics there is after all only a very short list of “First Principles”, one must stick to. There we have relatively well-defined interfaces between certain knowledge, reasoned or vague presumption and ignorance. And in most cases, our ignorance in physics can be condensed in some mathematical equations (which we, however, may not immediately fully understand). This is not the case so in medicine.

The strong medical pull. From pure mathematical research, we know the feeling of being pulled forward by an overarching issue: the relationship between local and global properties, between the smooth and the continuous, between analytic and algebraic methods, the Four Color Problem, the Poincaré Conjecture, the Riemann Hypothesis, the Clay Millennium Problems. Of course, we would never admit such personal ambitions in public. But for me there is no doubt about the role that major well-stated problems play and have played in the design of the career paths of many mathematicians, at least indirectly and in daydreams: with many doubts and a persistent feeling of self-deception and of fighting against mountains -or windmills.

Working as a mathematician with diabetes doctors is different. A bristling cascade of medical issues pulls the research forward: For nearly 90 years we have known that lack of secretion of the hormone insulin is one of the many serious issues in both diabetes type 1 (juvenile) and type 2 (obesity and age driven). For a large group of these patients, actually insulin is produced in pancreatic β-cells and stored in thousands of mini bags, vesicles, in the cell’s interior. But the cells do not respond correctly to external stimuli with the actual secretion, called regulated exocytosis. That manifests itself in elevated blood sugar, which can be tasted and measured by urine sample. That has now been done for nearly four thousand years. 2 We call it a symptom diagnosis because the diagnosis says nothing about the wide range of causes which may underlie the lack of uptake of glucose in the muscles.

Previously, failure of insulin secretion automatically led to weakening the muscles, inflammation of the extremities, loss of vision and the body’s final decay. Since the discovery of insulin, this tragic development can be countered by artificial supply of insulin by injection several times a day. We call it a symptom treatment because it is not even attempted to cure the patient or to make an effort to restore the body’s own insulin secretion. Some claim that the relative success of the overall symptom diagnosis and symptomatic treatment of diabetes has blocked patient-centered, individualized diagnosis and treatment.

In any case collaboration with diabetes doctors is a powerful experience for a mathematician of continually being pulled forward by well-defined medical problems. Here it is simply to detect the functioning and system behavior of the regulated exocytosis in healthy β-cells and to identify everything that can stand in the way in the case of weakened β-cells, see Fig. 1. The purpose is clear: mathematician, please come and help find the way to an earlier and more specific diagnosis and a cure or alleviation of the specific failure!

The technological push. The technological push is not completely unfamiliar in mathematics, we may think: readily available electronic journals, large user-friendly collections of mathematical preprints and reviews, efficient numerical software packages, homemade LaTeX editing can put us under pressure as mathematicians. But it’s nothing compared to the immense technological pressure cell research is subject to: with each new generation of equipment, oce

This content is AI-processed based on open access ArXiv data.