Condensation in nongeneric trees

We study nongeneric planar trees and prove the existence of a Gibbs measure on infinite trees obtained as a weak limit of the finite volume measures. It is shown that in the infinite volume limit there arises exactly one vertex of infinite degree and the rest of the tree is distributed like a subcritical Galton-Watson tree with mean offspring probability $m<1$. We calculate the rate of divergence of the degree of the highest order vertex of finite trees in the thermodynamic limit and show it goes like $(1-m)N$ where $N$ is the size of the tree. These trees have infinite spectral dimension with probability one but the spectral dimension calculated from the ensemble average of the generating function for return probabilities is given by $2\beta -2$ if the weight $w_n$ of a vertex of degree $n$ is asymptotic to $n^{-\beta}$.Comment: 57 pages, 14 figures. Minor change

The association of spirometric small airways obstruction with respiratory symptoms, cardiometabolic diseases, and quality of life : results from the Burden of Obstructive Lung Disease (BOLD) study

Funding Information: NHLI; Wellcome Trust grant (085790/Z/08/Z). Publisher Copyright: © 2023, The Author(s).Background: Spirometric small airways obstruction (SAO) is common in the general population. Whether spirometric SAO is associated with respiratory symptoms, cardiometabolic diseases, and quality of life (QoL) is unknown. Methods: Using data from the Burden of Obstructive Lung Disease study (N = 21,594), we defined spirometric SAO as the mean forced expiratory flow rate between 25 and 75% of the FVC (FEF25-75) less than the lower limit of normal (LLN) or the forced expiratory volume in 3 s to FVC ratio (FEV3/FVC) less than the LLN. We analysed data on respiratory symptoms, cardiometabolic diseases, and QoL collected using standardised questionnaires. We assessed the associations with spirometric SAO using multivariable regression models, and pooled site estimates using random effects meta-analysis. We conducted identical analyses for isolated spirometric SAO (i.e. with FEV1/FVC ≥ LLN). Results: Almost a fifth of the participants had spirometric SAO (19% for FEF25-75; 17% for FEV3/FVC). Using FEF25-75, spirometric SAO was associated with dyspnoea (OR = 2.16, 95% CI 1.77–2.70), chronic cough (OR = 2.56, 95% CI 2.08–3.15), chronic phlegm (OR = 2.29, 95% CI 1.77–4.05), wheeze (OR = 2.87, 95% CI 2.50–3.40) and cardiovascular disease (OR = 1.30, 95% CI 1.11–1.52), but not hypertension or diabetes. Spirometric SAO was associated with worse physical and mental QoL. These associations were similar for FEV3/FVC. Isolated spirometric SAO (10% for FEF25-75; 6% for FEV3/FVC), was also associated with respiratory symptoms and cardiovascular disease. Conclusion: Spirometric SAO is associated with respiratory symptoms, cardiovascular disease, and QoL. Consideration should be given to the measurement of FEF25-75 and FEV3/FVC, in addition to traditional spirometry parameters.Peer reviewe

Self-healing microtubules

The walls of microtubules can self-repair bending-induced damage

Microtubule networks for plant cell division

During cytokinesis the cytoplasm of a cell is divided to form two daughter cells. In animal cells, the existing plasma membrane is first constricted and then abscised to generate two individual plasma membranes. Plant cells on the other hand divide by forming an interior dividing wall, the so-called cell plate, which is constructed by localized deposition of membrane and cell wall material. Construction starts in the centre of the cell at the locus of the mitotic spindle and continues radially towards the existing plasma membrane. Finally the membrane of the cell plate and plasma membrane fuse to form two individual plasma membranes. Two microtubule-based cytoskeletal networks, the phragmoplast and the pre-prophase band (PPB), jointly control cytokinesis in plants. The bipolar microtubule array of the phragmoplast regulates cell plate deposition towards a cortical position that is templated by the ring-shaped microtubule array of the PPB. In contrast to most animal cells, plants do not use centrosomes as foci of microtubule growth initiation. Instead, plant microtubule networks are striking examples of self-organizing systems that emerge from physically constrained interactions of dispersed microtubules. Here we will discuss how microtubule-based activities including growth, shrinkage, severing, sliding, nucleation and bundling interrelate to jointly generate the required ordered structures. Evidence mounts that adapter proteins sense the local geometry of microtubules to locally modulate the activity of proteins involved in microtubule growth regulation and severing. Many of the proteins and mechanisms involved have roles in other microtubule assemblies as well, bestowing broader relevance to insights gained from plants

Diffusible crosslinkers generate directed forces in microtubule networks

Cytoskeletal remodeling is essential to eukaryotic cell division and morphogenesis. The mechanical forces driving the restructuring are attributed to the action of molecular motors and the dynamics of cytoskeletal filaments, which both consume chemical energy. By contrast, non-enzymatic filament crosslinkers are regarded as mere friction-generating entities. Here, we experimentally demonstrate that diffusible microtubule crosslinkers of the Ase1/PRC1/Map65 family generate directed microtubule sliding when confined between partially overlapping microtubules. The Ase1-generated forces, directly measured by optical tweezers to be in the piconewton-range, were sufficient to antagonize motor-protein driven microtubule sliding. Force generation is quantitatively explained by the entropic expansion of confined Ase1 molecules diffusing within the microtubule overlaps. The thermal motion of crosslinkers is thus harnessed to generate mechanical work analogous to compressed gas propelling a piston in a cylinder. As confinement of diffusible proteins is ubiquitous in cells, the associated entropic forces are likely of importance for cellular mechanics beyond cytoskeletal networks

Microtubule-associated protein65 is essential for maintenance of Phragmoplast bipolarity and formation of the cell plate in Physcomitrella patens

The phragmoplast, a plant-specific apparatus that mediates cytokinesis, mainly consists of microtubules (MTs) arranged in a bipolar fashion, such that their plus ends interdigitate at the equator. Membrane vesicles are thought to move along the MTs toward the equator and fuse to form the cell plate. Although several genes required for phragmoplast MT organization have been identified, the mechanisms that maintain the bipolarity of phragmoplasts remain poorly understood. Here, we show that engaging phragmoplast MTs in a bipolar fashion in protonemal cells of the moss Physcomitrella patens requires the conserved MT cross-linking protein MICROTUBULE-ASSOCIATED PROTEIN65 (MAP65). Simultaneous knockdown of the three MAP65s expressed in those cells severely compromised MT interdigitation at the phragmoplast equator after anaphase onset, resulting in the collapse of the phragmoplast in telophase. Cytokinetic vesicles initially localized to the anaphase midzone as normal but failed to further accumulate in the next several minutes, although the bipolarity of the MT array was preserved. Our data indicate that the presence of bipolar MT arrays is insufficient for vesicle accumulation at the equator and further suggest that MAP65-mediated MT interdigitation is a prerequisite for maintenance of bipolarity of the phragmoplast and accumulation and/or fusion of cell plate–destined vesicles at the equatorial plan

Adaptive braking by Ase1 prevents overlapping microtubules from sliding completely apart.

Short regions of overlap between ends of antiparallel microtubules are central elements within bipolar microtubule arrays. Although their formation requires motors1, recent in vitro studies demonstrated that stable overlaps cannot be generated by molecular motors alone. Motors either slide microtubules along each other until complete separation2, 3, 4 or, in the presence of opposing motors, generate oscillatory movements5, 6, 7. Here, we show that Ase1, a member of the conserved MAP65/PRC1 family of microtubule-bundling proteins, enables the formation of stable antiparallel overlaps through adaptive braking of Kinesin-14-driven microtubule–microtubule sliding. As overlapping microtubules start to slide apart, Ase1 molecules become compacted in the shrinking overlap and the sliding velocity gradually decreases in a dose-dependent manner. Compaction is driven by moving microtubule ends that act as barriers to Ase1 diffusion. Quantitative modelling showed that the molecular off-rate of Ase1 is sufficiently low to enable persistent overlap stabilization over tens of minutes. The finding of adaptive braking demonstrates that sliding can be slowed down locally to stabilize overlaps at the centre of bipolar arrays, whereas sliding proceeds elsewhere to enable network self-organization

Microtubule-Driven Multimerization Recruits ase1p onto Overlapping Microtubules

Microtubule (MT) crosslinking proteins of the ase1p/PRC1/Map65 family play a major role in the construction of MT networks such as the mitotic spindle. Most homologs in this family have been shown to localize with a remarkable specificity to sets of MTs that overlap with an antiparallel relative orientation []. Regulatory proteins bind to ase1p/PRC1/Map65 and appear to use the localization to set up precise spatial signals []. Here, we present evidence for a mechanism of localized protein multimerization underlying the specific targeting of ase1p, the fision yeast homolog. In controlled in vitro experiments, dimers of ase1-GFP diffused along the surface of single MTs and, at concentrations above a certain threshold, assembled into static multimeric structures. We observed that this threshold was significantly lower on overlapping MTs. We also observed diffusion and multimerization of ase1-GFP on MTs inside living cells, suggesting that a multimerization-driven localization mechanism is relevant in vivo. The domains responsible for MT binding and multimerization were identified via a series of ase1p truncations. Our findings show that cells use a finely tuned cooperative localization mechanism that exploits differences in the geometry and concentration of ase1p binding sites along single and overlapping MT