Archive for July, 2018

ECMTB 2018 in Lisbon, part 2

July 27, 2018

In the mini-workshops at the conference related to chemical reaction network theory the most striking new result to be announced was by Balazs Boros. His preprint on this is arXiv:1710.04732. In fact it is necessary to say in what sense this is new but I will postpone that point and first discuss the mathematics. This result is very easy to formulate and I will try to make the discussion here as self-contained as possible. We start with a chemical reaction network consisting of reactions and complexes (the expressions on the left and right hand sides of the reactions like X+Y). This network can be represented by a directed graph where the nodes are the complexes and the edges are the reactions, oriented from the complex on the LHS to that on the RHS. The network is called weakly reversible if whenever we can get from node X to node Y by following directed edges we can get from Y to X. If we assume mass action kinetics and choose a positive reaction rate for each reaction we get a system of ODE describing the evolution of the concentrations of the substances belonging to the network in a standard way. Because of the interpretation we are interested in positive solutions, i.e. solutions for which all concentrations are positive. The theorem proved by Boros says: if the network is weakly reversible then the corresponding ODE system with mass action kinetics has at least one positive steady state. Actually he proves that the stronger (and more natural) statement holds that there is a solution in each positive stoichiometric compatibility class. Evidently the hypotheses only involve the graph of the network and require no details of the form of the complexes or the values of the reaction constants. Thus it is a remarkably strong result. In contrast to the statement of the theorem the proof is not at all easy. It involves reducing the desired statement to an application of the Brouwer fixed point theorem. Returning to the question of the novelty of the result, it was announced in a preprint of Deng et al. in 2011 (arXiv:1111.2386). It has never been published and it seems that the proof proposed by the authors is far from complete. Furthermore, the authors do not seem to be willing and able to repair the argument. Thus this result has been blocked for seven years. For anyone else it is an ungrateful task to provide a proof since a positive reaction from the authors of the original paper is doubtful. Furthermore other people not familiar with the background may also fail to give due credit to the author of the new paper. I think that with this work Balazs has done a great service to the reaction network community and we who belong to this community should take every opportunity to express our gratitude for this.

There was a nice talk by Ilona Kosiuk on her work with Peter Szmolyan on NF\kappaB. She expressed doubts about the derivation of the three-dimensional system mentioned in a previous post from the four-dimensional system. The work she explained in some detail concerned the four-dimensional system and uses GSPT to investigate the existence of periodic solutions of that system.

I feel that I got a lot more out of this conference than that I did out of that in Nottingham two years ago. I found more points of contact with my own research. This fact perhaps has less to do with the conference itself than it does with me. It is simply that I have penetrated a lot more deeply into mathematical biology during the last two years.


ECMTB 2018 in Lisbon

July 24, 2018

I am attending a meeting of the ESMTB in Lisbon. I am happy that the temperatures are very moderate, much more moderate than those at home in Mainz. The highest temperatures I encountered so far were due to body heat, for the following reason. The first two sessions on reaction networks were in rooms much too small for the number of participants with people sitting on extra chairs brought in from outside, windowsills and the floor, as available. This caused a rise in temperature despite the open windows. In any case, the size of those audiences is a good sign for the field.

The first plenary talk, by Samuel Kou, was about something called Google Flu Trends. The idea of this initiative, which started in 2008, was to predict the development of epidemics such as influenza by using data on the number of Google searches for phrases related to cases of flu. The idea is that between the time someone goes to the doctor because they are suffering from an infectious disease and the time data finally come together on a national level there can be a lag of about two weeks, even in countries like the US with a highly developed reporting system. Thus the hope was that using data on Google searches could enable predictions two weeks earlier than other methods. The first test of this system looked very successful and obtained a lot of positive media coverage. After about a year the predictions started to be very wrong (perhaps due to the swine flu prevalent at that time being atypical). After modifications were made to the method the predictions were even further off and in the opposite direction. Then there was a lot of negative media coverage. Google did not make the raw data available in order to allow experts to look into what had gone wrong. However a paper published in Nature revealed some things. The number of search terms used was optimized and showed a clear local maximum. The search terms were not made public but one striking jump in the distribution was revealed to be a search term related to the Oscar ceremony. It was later suggested that what the analysis was predicting was not the incidence of flu but the beginning of winter. The mathematics used in the analysis was made public and was extremely elementary, although that by itself is not necessarily a bad thing. The group which Kou belonged to was able to make a low-grade reconstruction of the raw data using the freely available Google services called Google Trends and Google Correlate. They could then apply sophisticated statistical techniques to this data, creating a model called ARGO which performed a lot better than Google Flu Trends. Later Google stopped publishing their own analyses and made at least part of their data available to external researchers.

Another plenary talk, by Eörs Szathmáry, was about relationships between learning processes in the brain and evolution. I only understood a limited amount of the content but I nevertheless enjoyed the presentation, which combined a wide variety of different ideas. One specific point I did pick up concerns the Darwin finches. The speaker explained that the molecular (genetic) basis of the different beak shapes of these birds is now understood. This evolution takes place in a three-parameter space and it was indicated how this kind of space can be established. A similar process has been modelled in the case of RNA by Uri Alon. In the talk there was a nice partially implicit joke. One of the speaker’s main collaborators in this work is called Watson and he hinted at the idea of himself as Sherlock Holmes. Apart from the content I found the delivery of the talk very accomplished. I found it good in a way I cannot make precise.