Monthly Archives: October 2013

Don’t be stupid: get vaccinated

There’s a lot of stuff in the media about vaccines right now, particularly here in Southern Alberta where we’re going through a measles epidemic because we have an unusual number of people in our region who don’t get vaccinated. It’s also flu shot time.

Look, it’s simple: Getting vaccinated protects you from getting sick. It also protects people around you from getting sick because, once you have been vaccinated, you can’t participate in spreading the disease around. Vaccines are among the safest and most effective methods we have for fighting illness. I know a lot of people think that measles and the flu aren’t serious diseases, but they are. The mortality rate from measles in the developed world is between 1 and 3 per 1000 cases. I don’t know about you, but I definitely would not want to bet my life against those odds, particularly when the alternative, the vaccine, involves little more than a little inconvenience. Flu mortality varies wildly with age and strain, but it’s a serious risk, too. And of course there are lots of complications that are less dramatic than death, but still very serious. Similar comments could be made about any of the diseases for which we get vaccinated.

But, you say, what about the risk of vaccine side-effects? If you’re allergic to some of the vaccine ingredients (which include things like eggs), then of course you might have a reaction. The people who administer vaccines know about these things, they ask about them, and then they make sure you stay around for a while after getting the vaccine, just in case. In some cases, they can provide an alternative formulation that excludes a particular allergen. Most of the other side-effects of vaccines are mild (muscle soreness, low-grade fever), and much less disruptive of your daily activities than the diseases they protect you against. The sensational side-effects you hear about from time to time are mostly urban legends. The health care provider administering the vaccine ought to be able to tell you about any realistic side-effects if you’re concerned.

There’s a nice Ph.D. Comics video about vaccination that has just been posted. (Ph.D. Comics does some serious stuff, and they’re really good at explaining things in language we can all understand, regardless of education.) If you need further convincing, watch it, and get vaccinated.

The big five-oh, Part 2

When I arrived in Lethbridge in the summer of 1995, my first job was to write an NSERC research grant proposal. This proposal used delay systems, a theme I had first explored in detail while I was a postdoc at McGill, as a connecting theme. It’s interesting to go back to this first proposal, because some of the ideas are recognizable in my current research program, but others were dropped long ago. It included a proposal to develop a detailed model of the lac operon, something I never quite got around to doing, but which is clearly related to my current research interests in gene expression. There was a proposal to work on the equivalence between various types of differential equations, including master equations, which I’m still working on. There were also some ideas for stochastic optimizers, which led to some work on the structures of ion clusters,1 but which I didn’t pursue for long.

So what did I busy myself with? My very first paper in Lethbridge was on competitive inhibition oscillations,2 a phenomenon I had first discovered in the final stages of my Ph.D. This line of thought eventually led to the discovery of sustained stochastic oscillations in this system many years later.3

I’m not going to go through all the work I’ve done since those early years, so maybe I’ll just mention a few major themes that emerged over time, and take the opportunity to formulate a bit of advice to young scientists.

I continued to be interested in model reduction, a topic I continue to work on to this day. After leaving Toronto, I had thought that I would stop working on these problems. I wasn’t sure that I had all that much more to say about the theory of slow invariant manifolds. But colleagues in the field encouraged me to keep working on these problems, and from time to time I had some new idea that I thought would contribute something to the field. I am no longer under any illusion that I’m going to stop working on these problems anytime soon. What is the lesson to young scientists here? If you work on a sufficiently interesting set of problems during your Ph.D., this work is likely to follow you throughout your career, and that’s not a bad thing.

While I was finishing my Ph.D., I remember having a talk with Ray Kapral in which I said, with the certainty that only a young, inexperienced scientist can muster, that the problems involved in modelling chemical systems with ordinary differential equations were sufficient to keep me occupied, and that I would never (I actually remember using this word) work on partial differential equation or stochastic models. By 2002, I was studying reaction-diffusion (partial differential equation) models with my then postdoc, Jichang Wang. By 2004, I was working on stochastic models with Rui Zhu, also a postdoc at the time. In fact, most of my research effort is currently directed to stochastic systems. It was silly of me to say I would never work in one modelling framework or another. What I had the wisdom to do as I matured was to pick the correct modelling paradigm at the appropriate moment to tackle the problems I wanted to solve.

One of the things that, I think, has kept my research program relevant and vital over the years is that we’ve done a lot of different things: in addition to the topics mentioned above, there were projects on dynamical systems with stochastic switching, on stochastic modelling of gene expression, on photosynthesis, and on graph-theoretical approaches to bifurcation theory, to name just a few. Most of these topics connect to each other in some way, or at least they do in my head.

Looking back on my first 50 papers, much as it’s fun to think about the research, it’s the people that stand out. I’ve worked with many fine supervisors, colleagues, postdocs and students. I have learned something from each and every one of them. In fact, if I have one piece of advice for young scientists, it’s to find good people to work with, and to pay attention to what they do and how they do it. You can’t necessarily do things exactly the same way as someone else does, but you ought to be able to derive some general lessons you can use to guide your own research career and interactions with other scientists.

Be brave in choosing research topics. Work hard. Find good people to work with. I can’t guarantee that doing these things will lead to success, but not doing them will, at best, lead to mediocrity.

1Richard A. Beekman, Marc R. Roussel and P. J. Wilson (1999) Equilibrium configurations of systems of trapped ions. Phys. Rev. A 59, 503–511. Taunia L.L. Closson and Marc R. Roussel (2009) The flattening phase transition in systems of trapped ions. Can. J. Chem. 87, 1425–1435.
2Lan G. Ngo and Marc R. Roussel (1997) A new class of biochemical oscillator models based on competitive binding. Eur. J. Biochem. 245, 182–190.
3Kevin L. Davis and Marc R. Roussel (2006) Optimal observability of sustained stochastic competitive inhibition oscillations at organellar volumes. FEBS J. 273, 84–95.

The big five-oh, Part 1

No, I haven’t turned 50 yet. However, my 50th refereed paper has now appeared in print. This therefore seems like an appropriate time to look back on some of the research I have done since I started out as a graduate student at the University of Toronto. (I had two prior papers from my undergraduate work, but these were both in areas of science I didn’t pursue.) My intention here isn’t to write a scholarly review paper, so you won’t find a detailed set of citations here. My full list of publications is, in any event, available on my web site.

My M.Sc. and Ph.D. theses were both on the application of invariant manifold theory to steady-state kinetics. I was introduced to these problems by my supervisor at the University of Toronto, Simon J. Fraser. Simon is a great person to work for. He is supportive, and full of ideas, but he also lets you pursue your own ideas. I had a great time working for him, and learned an awful lot of nonlinear dynamics from him.

One way to think of the evolution of a chemical system is as a motion in a phase space, typically a space whose axes are the concentrations of the various chemical species involved, but sometimes including other relevant variables like temperature. The  phase space of a chemical system is typically very high-dimensional. The reactions that transform one species into another occur on many different time scales. The net result is that we can picture the motion in phase space as involving a hierarchy of collapse processes onto surfaces of lower and lower dimension, the fastest processes being responsible for the first collapse events, followed by slower and slower processes.1 These surfaces are invariant manifolds of the differential equations, and we developed methods to compute them. Given the equation of a low-dimensional manifold, we obtain a reduced model of the motion in phase space, i.e. one involving the few variables necessary to describe motion on this manifold.

Invariant manifold theory has been a fertile area of research for me over the years. I continue to publish in this area from time to time. In fact, one of my current M.Sc. students, Blessing Okeke, is working on a set of problems in this area. Expect more work on these problems in the future!

Toward the end of my time in Toronto, my supervisor, Simon J. Fraser, allowed me to spend some time working with Carmay Lim who, at the time, was cross-appointed to several departments at the University of Toronto, and worked out of the Medical Sciences Building. This was a very productive time, and I learned a lot from Carmay, particularly about doing research efficiently.

We worked on a set of applied problems on the lignification of wood using an interesting piece of hardware called a cellular automata machine. This was a special-purpose computer built to efficiently simulate two-dimensional cellular automata. The machine was programmed in Forth, a programming language most of you have probably never heard of, with some bits written in assembly language for extra efficiency. For a geek like me, programming this machine was great fun. I think we did some useful work, too, as our work on lignification kinetics still gets cited from time to time.

I had been to the 1992 SIAM Conference on Applications of Dynamical Systems in Snowbird which, I think, was just the second of what would become a long-lived series of conferences. There, I had discovered that there was a lot of interest in delay-differential equations (DDEs), as the tools necessary to analyze these equations were being sharpened. I had thought about the possibility of applying DDEs to chemical modelling, and decided to apply to work with Michael Mackey at McGill University, who was an expert on the application of DDEs in biological modelling. McGill was a great environment, and I learned a lot from Michael and his students. The most significant outcome of my time in Montreal was a paper published in the Journal of Physical Chemistry on the use of DDEs in chemical modelling.2

I pursued this style of modelling in a handful of papers. Eventually, I got interested in the use of delays to simplify models that can’t be described by differential equations, namely stochastic systems.3 This is another one of those ideas that I have kept following down through the years.

In my next blog post, I will reflect on some of the work I have done since arriving in Lethbridge.

1Marc R. Roussel and Simon J. Fraser (1991) On the geometry of transient relaxation. J. Chem. Phys. 94, 7106–7113.
2Marc R. Roussel (1996) The use of delay-differential equations in chemical kinetics. J. Phys. Chem. 100, 8323–8330.
3Marc R. Roussel and Rui Zhu (2006) Validation of an algorithm for delay stochastic simulation of transcription and translation in prokaryotic gene expression. Phys. Biol. 3, 274–284.