Modeling robustness tradeoffs in yeast cell polarization induced by spatial gradients.
Cells localize (polarize) internal components to specific locations in response to external signals such as spatial gradients. For example, yeast cells form a mating projection toward the source of mating pheromone. There are specific challenges associated with cell polarization including amplification of shallow external gradients of ligand to produce steep internal gradients of protein components (e.g. localized distribution), response over a broad range of ligand concentrations, and tracking of moving signal sources. In this work, we investigated the tradeoffs among these performance objectives using a generic model that captures the basic spatial dynamics of polarization in yeast cells, which are small. We varied the positive feedback, cooperativity, and diffusion coefficients in the model to explore the nature of this tradeoff. Increasing the positive feedback gain resulted in better amplification, but also produced multiple steady-states and hysteresis that prevented the tracking of directional changes of the gradient. Feedforward/feedback coincidence detection in the positive feedback loop and multi-stage amplification both improved tracking with only a modest loss of amplification. Surprisingly, we found that introducing lateral surface diffusion increased the robustness of polarization and collapsed the multiple steady-states to a single steady-state at the cost of a reduction in polarization. Finally, in a more mechanistic model of yeast cell polarization, a surface diffusion coefficient between 0.01 and 0.001 µm(2)/s produced the best polarization performance, and this range is close to the measured value. The model also showed good gradient-sensitivity and dynamic range. This research is significant because it provides an in-depth analysis of the performance tradeoffs that confront biological systems that sense and respond to chemical spatial gradients, proposes strategies for balancing this tradeoff, highlights the critical role of lateral diffusion of proteins in the membrane on the robustness of polarization, and furnishes a framework for future spatial models of yeast cell polarization.
Department of Mathematics, Center for Mathematical and Computational Biology, Center for Complex Biological Systems, University of California Irvine, Irvine, California, United States of America.
Ching-Shan
CS
Chou
Qing
Q
Nie
Tau-Mu
TM
Yi
D016764:Cell Polarity; D004058:Diffusion; D025461:Feedback, Physiological; D008565:Membrane Proteins; D008954:Models, Biological; D015003:Yeasts / Q000166:cytology*
D008565:Membrane Proteins
J Cell Sci. 1999 Sep;112 ( Pt 17):2867-74
10444381
Biophys J. 2001 Sep;81(3):1314-23
11509347
Methods Enzymol. 2007;422:123-40
17628137
Syst Biol (Stevenage). 2004 Jun;1(1):54-61
17052115
Biophys J. 2004 Jan;86(1 Pt 1):10-22
14695245
Philos Trans R Soc Lond B Biol Sci. 2015 Apr 19;370(1666):
25750229
Cell. 1996 Feb 9;84(3):335-44
8608587
Proc Natl Acad Sci U S A. 2005 Nov 22;102(47):16927-32
16291809
Sci STKE. 2002 Sep 03;2002(148):re12
12209053
Science. 1995 Nov 17;270(5239):1210-3
7502048
Proc Natl Acad Sci U S A. 2004 Feb 17;101(7):1822-7
14766974
Curr Biol. 2003 Sep 16;13(18):1636-40
13678596
Annu Rev Physiol. 1987;49:163-75
3551795
J Cell Sci. 2000 Feb;113 ( Pt 3):365-75
10639324
Biophys J. 2002 Jan;82(1 Pt 1):50-63
11751295
PLoS Comput Biol. 2006 Nov 17;2(11):e154
17112312
J Biol Chem. 2003 Jun 6;278(23):20445-8
12672811
Cell. 2007 Apr 20;129(2):411-22
17448998
Biophys J. 2005 Oct;89(4):2806-23
16085764
Biophys J. 2004 Jan;86(1 Pt 1):589-98
14695303
Science. 2003 Feb 21;299(5610):1231-5
12560471
PLoS Comput Biol. 2007 Mar 16;3(3):e36
17367201
J Theor Biol. 2006 Jun 21;240(4):538-53
16343548
Mol Cell. 2000 Nov;6(5):1155-67
11106754
EMBO J. 2002 Apr 2;21(7):1565-76
11927541
Biophys J. 2007 Feb 1;92(3):744-68
17098793
Science. 2005 Oct 21;310(5747):496-8
16239477
Bull Math Biol. 2006 Jul;68(5):1169-211
16794915