Forcing Adsorption of a Tethered Polymer by Pulling

We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fixed angle away from the point of tethering. Using the kernel method, we derive the full generating function for this model in two and three dimensions and obtain the respective phase diagrams. We observe adsorbed and desorbed phases with a thermodynamic phase transition in between. In the absence of a pulling force this model has a second-order thermal desorption transition which merely gets shifted by the presence of a lateral pulling force. On the other hand, if the pulling force contains a non-zero vertical component this transition becomes first-order. Strikingly, we find that if the angle between the pulling force and the surface is beneath a critical value, a sufficiently strong force will induce polymer adsorption, no matter how large the temperature of the system. Our findings are similar in two and three dimensions, an additional feature in three dimensions being the occurrence of a reentrance transition at constant pulling force for small temperature, which has been observed previously for this model in the presence of pure vertical pulling. Interestingly, the reentrance phenomenon vanishes under certain pulling angles, with details depending on how the three-dimensional polymer is modeled

A simple model of a vesicle drop in a confined geometry

We present the exact solution of a two-dimensional directed walk model of a drop, or half vesicle, confined between two walls, and attached to one wall. This model is also a generalisation of a polymer model of steric stabilisation recently investigated. We explore the competition between a sticky potential on the two walls and the effect of a pressure-like term in the system. We show that a negative pressure ensures the drop/polymer is unaffected by confinement when the walls are a macroscopic distance apart

A self-interacting partially directed walk subject to a force

We consider a directed walk model of a homopolymer (in two dimensions) which is self-interacting and can undergo a collapse transition, subject to an applied tensile force. We review and interpret all the results already in the literature concerning the case where this force is in the preferred direction of the walk. We consider the force extension curves at different temperatures as well as the critical-force temperature curve. We demonstrate that this model can be analysed rigorously for all key quantities of interest even when there may not be explicit expressions for these quantities available. We show which of the techniques available can be extended to the full model, where the force has components in the preferred direction and the direction perpendicular to this. Whilst the solution of the generating function is available, its analysis is far more complicated and not all the rigorous techniques are available. However, many results can be extracted including the location of the critical point which gives the general critical-force temperature curve. Lastly, we generalise the model to a three-dimensional analogue and show that several key properties can be analysed if the force is restricted to the plane of preferred directions.Comment: 35 pages, 14 figure

Knotting probabilities after a local strand passage in unknotted self-avoiding polygons

We investigate the knotting probability after a local strand passage is performed in an unknotted self-avoiding polygon on the simple cubic lattice. We assume that two polygon segments have already been brought close together for the purpose of performing a strand passage, and model this using Theta-SAPs, polygons that contain the pattern Theta at a fixed location. It is proved that the number of n-edge Theta-SAPs grows exponentially (with n) at the same rate as the total number of n-edge unknotted self-avoiding polygons, and that the same holds for subsets of n-edge Theta-SAPs that yield a specific after-strand-passage knot-type. Thus the probability of a given after-strand-passage knot-type does not grow (or decay) exponentially with n, and we conjecture that instead it approaches a knot-type dependent amplitude ratio lying strictly between 0 and 1. This is supported by critical exponent estimates obtained from a new maximum likelihood method for Theta-SAPs that are generated by a composite (aka multiple) Markov Chain Monte Carlo BFACF algorithm. We also give strong numerical evidence that the after-strand-passage knotting probability depends on the local structure around the strand passage site. Considering both the local structure and the crossing-sign at the strand passage site, we observe that the more "compact" the local structure, the less likely the after-strand-passage polygon is to be knotted. This trend is consistent with results from other strand-passage models, however, we are the first to note the influence of the crossing-sign information. Two measures of "compactness" are used: the size of a smallest polygon that contains the structure and the structure's "opening" angle. The opening angle definition is consistent with one that is measurable from single molecule DNA experiments.Comment: 31 pages, 12 figures, submitted to Journal of Physics

Fresh look at randomly branched polymers

We develop a new, dynamical field theory of isotropic randomly branched polymers, and we use this model in conjunction with the renormalization group (RG) to study several prominent problems in the physics of these polymers. Our model provides an alternative vantage point to understand the swollen phase via dimensional reduction. We reveal a hidden Becchi-Rouet-Stora (BRS) symmetry of the model that describes the collapse ($\theta$-)transition to compact polymer-conformations, and calculate the critical exponents to 2-loop order. It turns out that the long-standing 1-loop results for these exponents are not entirely correct. A runaway of the RG flow indicates that the so-called $\theta^\prime$-transition could be a fluctuation induced first order transition.Comment: 4 page

A cross-sectional study of 2550 amateur cyclists shows lack of knowledge regarding relevant sports nutrition guidelines

Background: Amateur cyclists use a wide variety of supplements and nutritional substances to increase performance in addition to their training.Objectives: The intended nutritional supplement use, carbohydrate (CHO) use and hydration practices of amateur cyclists before, during and after endurance cycling were analysed. Evidence of ignorance regarding the use of sports supplements and CHO, as well as the disregard of hydration strategy was hypothesised.Methods: Amateur cyclists, of all age and sex groups, were requested to complete an online survey anonymously on the 2013 Momentum 94.7 Cycle Challenge website, a few days before the event.Results: Responses were received from 2 550 out of 30 640 race entrants (8%); representing a distribution of 75% males, 25% females, with the majority between 25 to 45 years old. Nutritional supplements were used by 59% of respondents, with 77% dose adherence, and 29% with supplement ingredient knowledge. Half of the respondents (48%) planned to carbo-load two-three days before the event, while only five percent used professional advice to scientifically calculate their carbo-loading requirements. CHO were consumed by 81% during the event. Hydration preferences during the race were sports drinks (59%) and water (22%); and after the race 45% preferred a sports drink and 40% water. Ingredients, taste, colour, and temperature were criteria used to choose a sports drink. Only 18% of respondents knew to use both colour of urine and thirstiness to determine post-race fluid requirements.Conclusion: The authors concluded that amateur cyclists had insufficient knowledge regarding nutritional supplement ingredients and usage, CHO requirements and carbo-loading practices, and hydration strategies before, during and after the event.Keywords: ergogenic aids, nutritional supplements, carbohydrate us

MicroRNA Expression Patterns in Human Anterior Cingulate and Motor Cortex: A Study of Dementia with Lewy Bodies Cases and Controls

Overview MicroRNAs (miRNAs) have been implicated in neurodegenerative diseases including Parkinson’s disease and Alzheimer’s disease (AD). Here, we evaluated the expression of miRNAs in anterior cingulate (AC; Brodmann area [BA] 24) and primary motor (MO; BA 4) cortical tissue from aged human brains in the University of Kentucky AD Center autopsy cohort, with a focus on dementia with Lewy bodies (DLB). Methods RNA was isolated from gray matter of brain samples with pathology-defined DLB, AD, AD+DLB, and low-pathology controls, with n=52 cases initially included (n=23 with DLB), all with low (\u3c4hrs) postmortem intervals. RNA was profiled using Exiqon miRNA microarrays. Quantitative PCR for post-hoc replication was performed on separate cases (n=6 controls) and included RNA isolated from gray matter of MO, AC, primary somatosensory (BA 3), and dorsolateral prefrontal (BA 9) cortical regions. Results The miRNA expression patterns differed substantially according to anatomic location: of the relatively highly-expressed miRNAs, 150/481 (31%) showed expression that was different between AC versus MO (at p\u3c0.05 following correction for multiple comparisons), most (79%) with higher expression in MO. A subset of these results were confirmed in qPCR validation focusing on miR-7, miR-153, miR-133b, miR-137, and miR-34a. No significant variation in miRNA expression was detected in association with either neuropathology or sex after correction for multiple comparisons. Conclusion A subset of miRNAs (some previously associated with α-synucleinopathy and/or directly targeting α-synuclein mRNA) were differentially expressed in AC and MO, which may help explain why these brain regions show differences in vulnerability to Lewy body pathology

Knot localization in adsorbing polymer rings

We study by Monte Carlo simulations a model of knotted polymer ring adsorbing onto an impenetrable, attractive wall. The polymer is described by a self-avoiding polygon (SAP) on the cubic lattice. We find that the adsorption transition temperature, the crossover exponent $\phi$ and the metric exponent $\nu$, are the same as in the model where the topology of the ring is unrestricted. By measuring the average length of the knotted portion of the ring we are able to show that adsorbed knots are localized. This knot localization transition is triggered by the adsorption transition but is accompanied by a less sharp variation of the exponent related to the degree of localization. Indeed, for a whole interval below the adsorption transition, one can not exclude a contiuous variation with temperature of this exponent. Deep into the adsorbed phase we are able to verify that knot localization is strong and well described in terms of the flat knot model.Comment: 27 pages, 10 figures. Submitter to Phys. Rev.