Crossover Scales at the Critical Points of Fluids with Electrostatic Interactions

Criticality in a fluid of dielectric constant D that exhibits Ising-type behavior is studied as additional electrostatic (i.e., ionic) interactions are turned on. An exploratory perturbative calculation is performed for small ionicity as measured by the ratio of the electrostatic energy to the strength of the short-range nonionic (i.e., van der Waals) interactions in the uncharged fluid. With the aid of distinct transformations for the short-range and for the Coulombic interactions, an effective Hamiltonian with coefficients depending on the ionicity is derived at the Debye-Hueckel limiting-law level for a fully symmetric model. The crossover between classical (mean-field) and Ising behavior is then estimated using a Ginzburg criterion. This indicates that the reduced crossover temperature depends only weakly on the ionicity (and on the range of the nonionic potentials); however, the trends do correlate with the, much stronger, dependence observed experimentally.Comment: 25 pages, 4 figure; submitted to J. Chem. Phy

Stochastic Lag Time in Nucleated Linear Self-Assembly

Protein aggregation is of great importance in biology, e.g., in amyloid fibrillation. The aggregation processes that occur at the cellular scale must be highly stochastic in nature because of the statistical number fluctuations that arise on account of the small system size at the cellular scale. We study the nucleated reversible self-assembly of monomeric building blocks into polymer-like aggregates using the method of kinetic Monte Carlo. Kinetic Monte Carlo, being inherently stochastic, allows us to study the impact of fluctuations on the polymerisation reactions. One of the most important characteristic features in this kind of problem is the existence of a lag phase before self-assembly takes off, which is what we focus attention on. We study the associated lag time as a function of the system size and kinetic pathway. We find that the leading order stochastic contribution to the lag time before polymerisation commences is inversely proportional to the system volume for large-enough system size for all nine reaction pathways tested. Finite-size corrections to this do depend on the kinetic pathway

Chain-Length-Dependent Termination in Radical Polymerization of Acrylates

The technique of SP PLP EPR, which is single-pulse pulsed-laser polymerization (SP PLP) in conjunction with electron paramagnetic resonance (EPR) spectroscopy, is used to carry out a detailed investigation of secondary (chain-end) radical termination of acrylates. Measurements are performed on methyl acrylate, n-butyl acrylate and dodecyl acrylate in bulk and in toluene solution at –40 °C. The reason for the low temperature is to avoid formation of mid-chain radicals, a complicating factor that has imparted ambiguity to the results of previous studies of this nature. Consistent with these previous studies, composite-model behavior for chain-length-dependent termination rate coefficients, kt i,i, is found in this work. However, lower and more reasonable values of α s, the exponent for variation of kt i,i at short chain lengths, are found in the present study. Most likely this is because of the absence of mid-chain radicals, thereby validating the methodology of this work. Family-type termination behavior is observed, with the following average parameter values adequately describing all results, regardless of acrylate or the presence of toluene: α s = 0.79, α l = 0.21 (long chains) and ic ≈ 30 (crossover chain length). All indications are that these values carry over to termination of acrylate chain-end radicals at higher, more practical temperatures. Further, these values largely make sense in terms of what is understood about the physical meaning of the parameters. Variation of the rate coefficient for termination between monomeric radicals, kt 1,1, is found to be well described by the simple Smoluchowski and Stokes-Einstein equations. This allows easy prediction of kt 1,1 for different alkyl acrylates, solvent and temperature. Through all this the unrivalled power of SP PLP EPR for measuring and understanding (chain-length-dependent) termination rate coefficients shines through

Recent Advances in the Understanding of Termination in Radical Polymerization from Using the SP-PLP-EPR Technique

Since at least the 1940s, workers have been seeking to understand the kinetics of the fundamental radical-polymerization reaction of termination. This quest has not proven to be easy. Just under a decade ago, two game-changing advances were made that have unleashed rapid progress in the field: (1) The so-called ‘composite model’ was proposed: short radicals and long radicals are characterized by different scaling-law behavior in their rate of termination. (2) Single-pulse pulsed-laser polymerization (SP PLP) was coupled with electron paramagnetic resonance (EPR) spectroscopy to produce a remarkably potent new method for measuring chain-length-dependent termination (CLDT) rate coefficients, in particular those of short radicals. Essentially without exception, the SP-PLP-EPR method has revealed termination behavior in accord with the composite model. Here we summarize three recent SP-PLP-EPR studies, all involving new directions for the application of this technique

New Tetromycin Derivatives with Anti-Trypanosomal and Protease Inhibitory Activities †

Four new tetromycin derivatives, tetromycins 1–4 and a previously known one, tetromycin B (5) were isolated from Streptomyces axinellae Pol001T cultivated from the Mediterranean sponge Axinella polypoides. Structures were assigned using extensive 1D and 2D NMR spectroscopy as well as HRESIMS analysis. The compounds were tested for antiparasitic activities against Leishmania major and Trypanosoma brucei, and for protease inhibition against several cysteine proteases such as falcipain, rhodesain, cathepsin L, cathepsin B, and viral proteases SARS-CoV Mpro, and PLpro. The compounds showed antiparasitic activities against T. brucei and time-dependent inhibition of cathepsin L-like proteases with Ki values in the low micromolar range

Cancer Biomarker Discovery: The Entropic Hallmark

Background: It is a commonly accepted belief that cancer cells modify their transcriptional state during the progression of the disease. We propose that the progression of cancer cells towards malignant phenotypes can be efficiently tracked using high-throughput technologies that follow the gradual changes observed in the gene expression profiles by employing Shannon's mathematical theory of communication. Methods based on Information Theory can then quantify the divergence of cancer cells' transcriptional profiles from those of normally appearing cells of the originating tissues. The relevance of the proposed methods can be evaluated using microarray datasets available in the public domain but the method is in principle applicable to other high-throughput methods. Methodology/Principal Findings: Using melanoma and prostate cancer datasets we illustrate how it is possible to employ Shannon Entropy and the Jensen-Shannon divergence to trace the transcriptional changes progression of the disease. We establish how the variations of these two measures correlate with established biomarkers of cancer progression. The Information Theory measures allow us to identify novel biomarkers for both progressive and relatively more sudden transcriptional changes leading to malignant phenotypes. At the same time, the methodology was able to validate a large number of genes and processes that seem to be implicated in the progression of melanoma and prostate cancer. Conclusions/Significance: We thus present a quantitative guiding rule, a new unifying hallmark of cancer: the cancer cell's transcriptome changes lead to measurable observed transitions of Normalized Shannon Entropy values (as measured by high-throughput technologies). At the same time, tumor cells increment their divergence from the normal tissue profile increasing their disorder via creation of states that we might not directly measure. This unifying hallmark allows, via the the Jensen-Shannon divergence, to identify the arrow of time of the processes from the gene expression profiles, and helps to map the phenotypical and molecular hallmarks of specific cancer subtypes. The deep mathematical basis of the approach allows us to suggest that this principle is, hopefully, of general applicability for other diseases