Reactions at Polymer Interfaces: Transitions from Chemical to Diffusion-Control and Mixed Order Kinetics

We study reactions between end-functionalized chains at a polymer-polymer interface. For small chemical reactivities (the typical case) the number of diblocks formed, $R_t$, obeys 2nd order chemically controlled kinetics, $R_t \sim t$, until interfacial saturation. For high reactivities (e.g. radicals) a transition occurs at short times to 2nd order diffusion-controlled kinetics, with $R_t \sim t/\ln t$ for unentangled chains while $t/\ln t$ and $t^{1/2}$ regimes occur for entangled chains. Long time kinetics are 1st order and controlled by diffusion of the more dilute species to the interface: $R_t \sim t^{1/4}$ for unentangled cases, while $R_t \sim t^{1/4}$ and $t^{1/8}$ regimes arise for entangled systems. The final 1st order regime is governed by center of gravity diffusion, $R_t \sim t^{1/2}$.Comment: 11 pages, 3 figures, uses poliface.sty, minor changes, to appear in Europhysics Letter

Exploration and stabilization of Ras1 mating zone: A mechanism with positive and negative feedbacks.

In mating fission yeast cells, sensing and response to extracellular pheromone concentrations occurs through an exploratory Cdc42 patch that stochastically samples the cell cortex before stabilizing towards a mating partner. Active Ras1 (Ras1-GTP), an upstream regulator of Cdc42, and Gap1, the GTPase-activating protein for Ras1, localize at the patch. We developed a reaction-diffusion model of Ras1 patch appearance and disappearance with a positive feedback by a Guanine nucleotide Exchange Factor (GEF) and Gap1 inhibition. The model is based on new estimates of Ras1-GDP, Ras1-GTP and Gap1 diffusion coefficients and rates of cytoplasmic exchange studied by FRAP. The model reproduces exploratory patch behavior and lack of Ras1 patch in cells lacking Gap1. Transition to a stable patch can occur by change of Gap1 rates constants or local increase of the positive feedback rate constants. The model predicts that the patch size and number of patches depend on the strength of positive and negative feedbacks. Measurements of Ras1 patch size and number in cells overexpressing the Ras1 GEF or Gap1 are consistent with the model

Spontaneous Cdc42 polarization independent of GDI-mediated extraction and actin-based trafficking.

The small Rho-family GTPase Cdc42 is critical for cell polarization and polarizes spontaneously in absence of upstream spatial cues. Spontaneous polarization is thought to require dynamic Cdc42 recycling through Guanine nucleotide Dissociation Inhibitor (GDI)-mediated membrane extraction and vesicle trafficking. Here, we describe a functional fluorescent Cdc42 allele in fission yeast, which demonstrates Cdc42 dynamics and polarization independent of these pathways. Furthermore, an engineered Cdc42 allele targeted to the membrane independently of these recycling pathways by an amphipathic helix is viable and polarizes spontaneously to multiple sites in fission and budding yeasts. We show that Cdc42 is highly mobile at the membrane and accumulates at sites of activity, where it displays slower mobility. By contrast, a near-immobile transmembrane domain-containing Cdc42 allele supports viability and polarized activity, but does not accumulate at sites of activity. We propose that Cdc42 activation, enhanced by positive feedback, leads to its local accumulation by capture of fast-diffusing inactive molecules

Local Pheromone Release from Dynamic Polarity Sites Underlies Cell-Cell Pairing during Yeast Mating.

Cell pairing is central for many processes, including immune defense, neuronal connection, hyphal fusion, and sexual reproduction. How does a cell orient toward a partner, especially when faced with multiple choices? Fission yeast Schizosaccharomyces pombe P and M cells, which respectively express P and M factor pheromones [1, 2], pair during the mating process induced by nitrogen starvation. Engagement of pheromone receptors Map3 and Mam2 [3, 4] with their cognate pheromone ligands leads to activation of the Gα protein Gpa1 to signal sexual differentiation [3, 5, 6]. Prior to cell pairing, the Cdc42 GTPase, a central regulator of cell polarization, forms dynamic zones of activity at the cell periphery at distinct locations over time [7]. Here we show that Cdc42-GTP polarization sites contain the M factor transporter Mam1, the general secretion machinery, which underlies P factor secretion, and Gpa1, suggesting that these are sub-cellular zones of pheromone secretion and signaling. Zone lifetimes scale with pheromone concentration. Computational simulations of pair formation through a fluctuating zone show that the combination of local pheromone release and sensing, short pheromone decay length, and pheromone-dependent zone stabilization leads to efficient pair formation. Consistently, pairing efficiency is reduced in the absence of the P factor protease. Similarly, zone stabilization at reduced pheromone levels, which occurs in the absence of the predicted GTPase-activating protein for Ras, leads to reduction in pairing efficiency. We propose that efficient cell pairing relies on fluctuating local signal emission and perception, which become locked into place through stimulation

Kinetic Regimes and Cross-Over Times in Many-Particle Reacting Systems

We study kinetics of single species reactions ("A+A -> 0") for general local reactivity Q and dynamical exponent z (rms displacement x_t ~ t^{1/z}.) For small molecules z=2, whilst z=4,8 for certain polymer systems. For dimensions d above the critical value d_c=z, kinetics are always mean field (MF). Below d_c, the density n_t initially follows MF decay, n_0 - n_t ~ n_0^2 Q t. A 2-body diffusion-controlled regime follows for strongly reactive systems (Q>Qstar ~ n_0^{(z-d)/d}) with n_0 - n_t ~ n_0^2 x_t^d. For Q<Qstar, MF kinetics persist, with n_t ~ 1/Qt. In all cases n_t ~ 1/x_t^d at the longest times. Our analysis avoids decoupling approximations by instead postulating weak physically motivated bounds on correlation functions.Comment: 10 pages, 1 figure, uses bulk2.sty, minor changes, submitted to Europhysics Letter

The Slowly Formed Guiselin Brush

We study polymer layers formed by irreversible adsorption from a polymer melt. Our theory describes an experiment which is a ``slow'' version of that proposed by Guiselin [Europhys. Lett., v. 17 (1992) p. 225] who considered instantaneously irreversibly adsorbing chains and predicted a universal density profile of the layer after swelling with solvent to produce the ``Guiselin brush.'' Here we ask what happens when adsorption is not instantaneous. The classic example is chemisorption. In this case the brush is formed slowly and the final structure depends on the experiment's duration, $t_{final}$. We find the swollen layer consists of an inner region of thickness $z^* \sim t_{final}^{-5/3}$ with approximately constant density and an outer region extending up to height $h \sim N^{5/6}$ which has the same density decay $\sim z^{-2/5}$ as for the Guiselin case.Comment: 7 pages, submitted to Europhysics Letter

The Ultrasensitivity of Living Polymers

Synthetic and biological living polymers are self-assembling chains whose chain length distributions (CLDs) are dynamic. We show these dynamics are ultrasensitive: even a small perturbation (e.g. temperature jump) non-linearly distorts the CLD, eliminating or massively augmenting short chains. The origin is fast relaxation of mass variables (mean chain length, monomer concentration) which perturbs CLD shape variables before these can relax via slow chain growth rate fluctuations. Viscosity relaxation predictions agree with experiments on the best-studied synthetic system, alpha-methylstyrene.Comment: 4 pages, submitted to Phys. Rev. Let

Irreversibility and Polymer Adsorption

Physisorption or chemisorption from dilute polymer solutions often entails irreversible polymer-surface bonding. We present a theory of the non-equilibrium layers which result. While the density profile and loop distribution are the same as for equilibrium layers, the final layer comprises a tightly bound inner part plus an outer part whose chains make only fN surface contacts where N is chain length. The contact fractions f follow a broad distribution, P(f) ~ f^{-4/5}, in rather close agreement with strong physisorption experiments [H. M. Schneider et al, Langmuir v.12, p.994 (1996)].Comment: 4 pages, submitted to Phys. Rev. Let

Condensation of actin filaments pushing against a barrier

We develop a model to describe the force generated by the polymerization of an array of parallel biofilaments. The filaments are assumed to be coupled only through mechanical contact with a movable barrier. We calculate the filament density distribution and the force-velocity relation with a mean-field approach combined with simulations. We identify two regimes: a non-condensed regime at low force in which filaments are spread out spatially, and a condensed regime at high force in which filaments accumulate near the barrier. We confirm a result previously known from other related studies, namely that the stall force is equal to N times the stall force of a single filament. In the model studied here, the approach to stalling is very slow, and the velocity is practically zero at forces significantly lower than the stall force.Comment: 21 pages, 6 figures: Combined figures, fixed typos, added extra material, altered symbolism to avoid confusion. Accepted by New Journal of Physic

Model of For3p-Mediated Actin Cable Assembly in Fission Yeast

Formin For3p nucleates actin cables at the tips of fission yeast cells for polarized cell growth. The results of prior experiments have suggested a possible mechanism for actin cable assembly that involves association of For3p near cell tips, For3p-mediated actin polymerization, retrograde flow of actin cables toward the cell center, For3p dissociation from cell tips, and cable disassembly. We used analytical and computational modeling to test the validity and implications of the proposed coupled For3p/actin mechanism. We compared the model to prior experiments quantitatively and generated predictions for the expected behavior of the actin cable system upon changes of parameter values. We found that the model generates stable steady states with realistic values of rate constants and actin and For3p concentrations. Comparison of our results to previous experiments monitoring the FRAP of For3p-3GFP and the response of actin cables to treatments with actin depolymerizing drugs provided further support for the model. We identified the set of parameter values that produces results in agreement with experimental observations. We discuss future experiments that will help test the model's predictions and eliminate other possible mechanisms. The results of the model suggest that flow of actin cables may establish actin and For3p concentration gradients in the cytoplasm that could be important in global cell patterning