Physics of Living Systems

Point of View: Are theoretical results ‘Results’?

Raymond E Goldstein

University of Cambridge, United Kingdom

Jul 23, 2018

https://doi.org/10.7554/eLife.40018

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5 figures

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Figure 1

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Experimental setup to study diffusion of the green alga Chlamydomonas.

(a) A light sheet is used to gather the algae, which are swimming in a petri dish, into a narrow strip of cells along the $y$ -axis. (b) After the light is turned off, the cells swim randomly and spread out. The concentration profile, $C (x, t)$ , is then measured along a thin strip parallel to the $x$ -axis; $t$ is time.

Figure 2

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Experimental results on diffusion in a population of the green alga Chlamydomonas.

(a) Concentration profiles, $C (x, t)$ , normalized to unity, at the following times: 1 second (red), 3 seconds (green), 7 seconds (blue) and 30 seconds (black). (b) The variance, $⟨ x^{2} ⟩$ , of the data shown in (a) as a function of time; the dashed magenta line is a linear fit to the data. (c) The peak height, $C (0, t)$ , of the data shown in (a) as a function of time.

Figure 3

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A random walk in one dimension.

(a) A cell at site $m$ moves with probability $1 / 2$ to the left or right. (b) Diagram illustrating the counting that underlies the evolution equation (Equation 1).

Figure 4

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Flux and the diffusion equation.

(a) Concentration profiles, $C (x, t)$ , at times $t = 3$ s and $t = 3.2$ s . (b) The flux of cells past a given point, $J$ (black; left axis), and the concentration gradient, $\partial C / \partial x$ (yellow; right axis), versus position, $x$ . (c) Flux, $J$ , versus concentration gradient, $\partial C / \partial x$ , for all the values of $x$ and $t$ shown in Figure 2a. The dashed magenta line has a slope $D = 0.1$ mm²/s.

Flux and the diffusion equation.

(a) Concentration profiles, $C (x, t)$ , at times $t = 3$ s and $t = 3.2$ s . (b) The flux of cells past a given point, $J$ (black; left axis), and the concentration gradient, $\partial C / \partial x$ (yellow; right axis), versus position, $x$ . (c) Flux, $J$ , versus concentration gradient, $\partial C / \partial x$ , for all the values of $x$ and $t$ shown in Figure 2a. The dashed magenta line has a slope $D = 0.1$ mm²/s.

Figure 5

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Rescaling the data.

(a) The peak amplitude, $C (0, t)$ , from Figure 2c plotted as a function time, $t$ , on a log-log scale; the dashed magenta line has a slope of $- 1 / 2$ , which shows that $C (0, t) \sim t^{- 1 / 2}$ . (b) When the data in Figure 2a are rescaled (see main text) and replotted, they collapse to a universal curve; the dashed magenta curve is the function $\exp (- ξ^{2} / 2)$ .

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Raymond E Goldstein

(2018)

Point of View: Are theoretical results ‘Results’?

eLife 7:e40018.

https://doi.org/10.7554/eLife.40018

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