21 April 2015

Postdoc position: numerical simulations for biophysics

A post-doctoral fellowship is available at the MSC laboratory of the Paris Diderot University (Paris, France), in the framework of our ANR project.

Title: Modelling the many-body interactions between protein inclusions in cell membranes
Gross salary: ~ 2500 €/month (varies with seniority).
Duration: ~ 12 months.
Summary of the research topic: The MSC laboratory is a research unit at the very heart of Paris working on three main axes: non-linear physics, soft-matter and interface between physics, biology and medicine. The subject proposed here is part of a wider research effort, pursued in collaboration with three other laboratories from the Paris area, in the framework of a project financed by the ANR (French grant agency). In particular, the successful candidate will work in close collaboration with an experimental group in the Laboratory of Solid State Physics (LPS, Orsay).

Integral proteins, such as gramicidin, experience membrane-mediated interactions due to the pinching action they exert on the membrane. In our theoretical group at MSC, we have developed a detailed, state-of-the art, elastic model describing the energy cost of such membrane thickness deformations, and two numerical codes, in C and Haskell, to calculate the interaction energy between two inclusions coupled to the membrane thickness. Preliminary fitting of the experimental data obtained from X-ray scattering in protein doped lamellar phases [2] shows a very promising agreement with the model.

A numerical study of the many-body interactions is now necessary, however, in order to fully validate our model. The candidate is expected to extend our codes in order to account for an arbitrary number of inclusions and perform Monte Carlo simulations of the fluid protein phase, in order to fit the data for various protein densities. The outcome of this study should be a clearer image of lipid membranes as two-dimensional complex fluids, as well as of the way they influence the inclusions, in particular biological molecules.

We are looking for a candidate with a good background in theoretical physics and a profound taste for numerical simulations, preferably in the areas of soft matter or continuum elasticity. He/she should hold a PhD in physics, materials science or a related topic. The numerical code solves an elliptic linear partial differential equation by means of a multipolar expansion, using standard mathematical libraries for special functions evaluation, quadratures or Fast Fourier Transforms, and the solution of systems of linear equations. Good programming skills in C and experience with Monte Carlo simulations are required. Knowledge of functional (Haskell) and literate (noweb) programming are a plus. Previous experience with biological systems or liquid state theory would be a significant asset. A good level of oral and written expression in English is mandatory. Knowledge of French is not required.


References:
[1] Repulsion between inorganic particles inserted within surfactant bilayers, Doru Constantin, Brigitte Pansu, Marianne Impéror, Patrick Davidson, and François Ribot, Physical Review Letters 101, 098101 (2008).
[2] Membrane-Mediated Repulsion between Gramicidin Pores, Doru Constantin, Biochimica et Biophysica Acta - Biomembranes 1788, 1782-1789 (2009).
[3] The interaction of hybrid nanoparticles inserted within surfactant bilayers , Doru Constantin, The Journal of Chemical Physics 133, 144901 (2010).
[4] Bilayer Elasticity at the Nanoscale: The Need for New Terms, Anne-Florence Bitbol, Doru Constantin, and Jean-Baptiste Fournier, PLOS One 7, e48306 (2012).
[5] Dynamics of the force exchanged between membrane inclusions, J.-B. Fournier, Physical Review Letters 112, 128101 (2014).

13 April 2015

Temporary positions in science

A very interesting article in Nature on the future of postdoc positions. Well worth reading, although the solutions proposed (increasing the proportion of permanent research staff, in one way or another) are completely impractical. The comments are even more interesting than the article itself.

7 April 2015

Posting on arXiv

Since I'm on vacation these days, I decided to finally submit my published research papers to arXiv. A previous attempt was about as pleasant as a visit to the dentist, but somewhat longer (and unsuccessful). This time around I tried to submit other papers, and things went more or less smoothly, as soon as I learned to follow some guidelines (for documents produced using LaTeX):
  • Make sure that all .eps figures are of reasonable size: no files above 6MB and no more that 10MB for the whole submission. I downsized some very large files by first converting them to .pdf and cropping to remove white margins (using Acrobat) then opened the .pdf files in Photoshop and saved a copy in .eps format (without preview and using jpeg compression).
  • Check that the figures are correctly invoked in the .tex file (the name should be case-sensitive, something that is not required on Windows systems). File names should not contain special characters (more details).
  • Run LaTeX locally until the compilation is error-free.
  • Create a .zip archive with the .tex file, the .eps figures and the .bbl file (the compiling process on arXiv does not include Bibtex) and, if necessary, with supplementary material in .ps format.
  • Hope that the compilation works without errors, otherwise wade through about three screens of output, fix things and reload files. The supplementary files are simply appended to the final .pdf; this is an easy way to include additional material or tricky parts that fail to compile on the arXiv server. This is how I managed to add to one paper a page-wide table in landscape orientation, which had resisted all other methods.
The final result is here.
 
For Word documents the process should be much easier, since one can directly submit the .pdf version. I only tried this for one paper, currently on hold because it has line numbers in the margin. This restriction is not mentioned anywhere on the arXiv site (neither is the size limit, by the way.)

Overall, the entire procedure was easier than I thought. Still, the system is far from user-friendly (metadata retrieval using the DOI would be nice), the interface is firmly stuck in the 90s, some limitations seem a bit arbitrary and the help could be more detailed.

4 April 2015

How to read an equation

The mere formal expression of an equation is not very useful, unless complemented by a more or less intuitive understanding. Different people may have different intuitions of a given formula or different mental images of one physical systems (more on that later).

The interesting part is that putting together two such different intuitions of a relation can yield non-trivial results with almost no algebraic manipulation, as I'll show below. What is the meaning of the following formula ?
\[\frac{1}{\sqrt{2\pi} \sigma} \int_{-\infty}^{\infty} \text{d}x \exp (i q x) \exp \left (- \frac{x^2}{2 \sigma ^2} \right ) \tag{1}\]

  • It can be seen as the Fourier transform of a Gaussian (or normal) distribution with zero mean and standard deviation \(\sigma\): \( \displaystyle \underbrace{\int_{-\infty}^{\infty} \text{d}x \exp (i q x)}_{\cal{F}(\cdot)} \frac{1}{\sqrt{2\pi} \sigma} \exp \left (- \frac{x^2}{2 \sigma ^2} \right ) = \cal{F} \left ( \cal{N} (0,\sigma) \right )  \tag{1a} \) 
  • ... or as the expectation of a phase factor over said Gaussian distribution: \( \displaystyle \underbrace{\int_{-\infty}^{\infty} \text{d}x \frac{1}{\sqrt{2\pi} \sigma} \exp \left (- \frac{x^2}{2 \sigma ^2} \right )}_{\left \langle \cdot \right \rangle} \exp (i q x) = \left \langle \exp (i q x) \right \rangle \tag{1b} \)
Equating the rhs expressions in the two equations above (which are simply two different readings of (1)!) and recalling that the Fourier transform of a Gaussian is itself a Gaussian yields the very useful identity:
\[\left \langle \exp (i q x) \right \rangle = \cal{N} \left (0,\frac{1}{\sigma} \right ) \tag{2} \]employed, for instance, in proving the Siegert relation.

Note that both sides of (2) are now functions of \(q\), since we have already integrated over \(x\).

Fundamental physics

The other day at the gym I realized I am a force of nature. The weak force, to be specific. It could have been worse, though: gravity was on a treadmill not far away.

1 March 2015

Top nine trending physicists

A colleague asked a few days ago who where the most popular physicists on the Internet. I tried to find an answer using Google Trends, and the answer is below:


As expected, only astrophysicists and particle physicists are represented.
 
I hope the ranking is correct (it is difficult to extract the raw data for more than five topics at a time). Who do you think should complete the top ten?

Here is the time trend (for only four among the nine):




21 February 2015

Pitfalls of logic: modus tollens

From Slate:
 
Does it mean that if you are alone you do understand the warnings?

11 February 2015

29 January 2015

Zero-lens microscopy

Visible light is good for seeing details down to a fraction of a micron. Below this limit, one uses X-rays, with a wavelength of the order of one Ångström. The problem is that there are no high-quality lenses for X-rays, and so, instead of direct images, one has to settle for scattering or diffraction patterns, much more difficult to interpret (but sometimes more useful).

If the magnifying glass is a one-lens optical instrument and the microscope is (schematically) a two-lens device, then an X-ray scattering setup does zero-lens microscopy!