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

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

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

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

Non-Equilibrium in Adsorbed Polymer Layers

High molecular weight polymer solutions have a powerful tendency to deposit adsorbed layers when exposed to even mildly attractive surfaces. The equilibrium properties of these dense interfacial layers have been extensively studied theoretically. A large body of experimental evidence, however, indicates that non-equilibrium effects are dominant whenever monomer-surface sticking energies are somewhat larger than kT, a common case. Polymer relaxation kinetics within the layer are then severely retarded, leading to non-equilibrium layers whose structure and dynamics depend on adsorption kinetics and layer ageing. Here we review experimental and theoretical work exploring these non-equilibrium effects, with emphasis on recent developments. The discussion addresses the structure and dynamics in non-equilibrium polymer layers adsorbed from dilute polymer solutions and from polymer melts and more concentrated solutions. Two distinct classes of behaviour arise, depending on whether physisorption or chemisorption is involved. A given adsorbed chain belonging to the layer has a certain fraction of its monomers bound to the surface, f, and the remainder belonging to loops making bulk excursions. A natural classification scheme for layers adsorbed from solution is the distribution of single chain f values, P(f), which may hold the key to quantifying the degree of irreversibility in adsorbed polymer layers. Here we calculate P(f) for equilibrium layers; we find its form is very different to the theoretical P(f) for non-equilibrium layers which are predicted to have infinitely many statistical classes of chain. Experimental measurements of P(f) are compared to these theoretical predictions.Comment: 29 pages, Submitted to J. Phys.: Condens. Matte

Possible origins of macroscopic left-right asymmetry in organisms

I consider the microscopic mechanisms by which a particular left-right (L/R) asymmetry is generated at the organism level from the microscopic handedness of cytoskeletal molecules. In light of a fundamental symmetry principle, the typical pattern-formation mechanisms of diffusion plus regulation cannot implement the "right-hand rule"; at the microscopic level, the cell's cytoskeleton of chiral filaments seems always to be involved, usually in collective states driven by polymerization forces or molecular motors. It seems particularly easy for handedness to emerge in a shear or rotation in the background of an effectively two-dimensional system, such as the cell membrane or a layer of cells, as this requires no pre-existing axis apart from the layer normal. I detail a scenario involving actin/myosin layers in snails and in C. elegans, and also one about the microtubule layer in plant cells. I also survey the other examples that I am aware of, such as the emergence of handedness such as the emergence of handedness in neurons, in eukaryote cell motility, and in non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue. Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec

Irreversible Adsorption from Dilute Polymer Solutions

We study irreversible polymer adsorption from dilute solutions theoretically. Universal features of the resultant non-equilibrium layers are predicted. Two cases are considered, distinguished by the value of the local monomer-surface sticking rate Q: chemisorption (very small Q) and physisorption (large Q). Early stages of layer formation entail single chain adsorption. While single chain physisorption times tau_ads are typically microsecs, for chemisorbing chains of N units we find experimentally accessible times tau_ads = Q^{-1} N^{3/5}, ranging from secs to hrs. We establish 3 chemisorption universality classes, determined by a critical contact exponent: zipping, accelerated zipping and homogeneous collapse. For dilute solutions, the mechanism is accelerated zipping: zipping propagates outwards from the first attachment, accelerated by occasional formation of large loops which nucleate further zipping. This leads to a transient distribution omega(s) \sim s^{-7/5} of loop lengths s up to a size s_max \approx (Q t)^{5/3} after time t. By tau_ads the entire chain is adsorbed. The outcome of the single chain adsorption episode is a monolayer of fully collapsed chains. Having only a few vacant sites to adsorb onto, late arriving chains form a diffuse outer layer. In a simple picture we find for both chemisorption and physisorption a final loop distribution Omega(s) \sim s^{-11/5} and density profile c(z) \sim z^{-4/3} whose forms are the same as for equilibrium layers. In contrast to equilibrium layers, however, the statistical properties of a given chain depend on its adsorption time; the outer layer contains many classes of chain, each characterized by different fraction of adsorbed monomers f. Consistent with strong physisorption experiments, we find the f values follow a distribution P(f) \sim f^{-4/5}.Comment: 18 pages, submitted to Eur. Phys. J. E, expanded discussion sectio