Messages diffuse faster than messengers

doi:10.1073/pnas.0509576103

Messages diffuse faster than messengers

*Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139;
^‡Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, 1428 Buenos Aires, Argentina;
^§Department of Physiology, University of Pennsylvania, B400 Richards Buildings, 3700 Hamilton Walk, Philadelphia, PA 19104-6085; and
^¶Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM 87545

Edited by Joseph Schlessinger, Yale University School of Medicine, New Haven, CT, and approved January 24, 2006 (received for review November 3, 2005)

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Fig. 1.
Simulated diffusion of particles in the presence of traps. (A) One-dimensional simulation of the spread of tagged and untagged particles, denoted by superscripts t and u, respectively, in an experiment in which a bolus of tagged particles (such as radioactive calcium) is released at t = 0, raising the concentration of free particles by 20% in the leftmost 1.1 μm. The four curves are P_f^u − P_feq (dashed), P_f^t (dotted), P_f^u + P_f^t − P_feq (thick solid), and P_b^t + P_f^t (thin solid) at t = 0.1 s. MP is the measurement point from which the signals shown in B were obtained. (B) Time course of particle concentrations at MP. The dotted line denotes the total tagged-particle concentration, P_b^t + P_f^t, and the solid line denotes total free particle concentration above background, P_f^t + P_f^u − P_feq. (C) Two three-dimensional simulations in a 5-μm sphere. First, a FRAP-like simulation is shown in which all particles in a sphere of radius 1.1 μm were untagged at t = 0, whereas the particles in the rest of the 5-μm sphere remained tagged. The plot shows the recovery of tagged particles, P_f^t + P_b ^t at t = 0.1 s (solid line, left scale). A “particle deficit experiment” is also shown in which the free particle concentration was reduced to P _f = 0.8P_feq in the 1.1-μm sphere at t = 0. The plot shows the free particle recovery at t = 0.1 s (dotted line, right scale). Note that the concentration is almost fully recovered in the particle deficit case but not in the FRAP-like case. (D) Percent recovery as a function of time for the FRAP-like (solid line) and particle deficit (dashed line) simulation (see Methods).
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Fig. 2.
Effective diffusion coefficients. (A) (〈 x ² 〉 − 〈 x₀ ² 〉)/(2d)vst (where d is the space dimension: d = 1 in the tagged-particle bolus simulation discussed in Fig. 1 A, and d = 3 in the FRAP and particle deficit experiments discussed in Fig. 1 C). The four lines shown are for P_f^u + P_f^t (dashed) and P_f^t (dashed–dotted) in the tagged particle bolus simulation, P_f^u in the particle-deficit simulation (dotted), and P_f^t in the FRAP simulation (solid). The slopes of these lines give the effective diffusion coefficients. (B) D^t/D^u as a function of S _eq/K _D. The dotted line corresponds to S _eq/S _T = 0.9, the dashed line corresponds to S _eq/S _T = 0.3, and the solid line corresponds to S _eq/S _T = 0.1. For large S _eq/K _D, the ratio approaches its asymptotic value: S _eq/S _T. The black dot corresponds to the parameters used in all simulations in this report.