A Generalized Theory of Semiflexible Polymers

NA bending on length scales shorter than a persistence length plays an integral role in the translation of genetic information from DNA to cellular function. Quantitative experimental studies of these biological systems have led to a renewed interest in the polymer mechanics relevant for describing the conformational free energy of DNA bending induced by protein-DNA complexes. Recent experimental results from DNA cyclization studies have cast doubt on the applicability of the canonical semiflexible polymer theory, the wormlike chain (WLC) model, to DNA bending on biologically relevant length scales. This paper develops a theory of the chain statistics of a class of generalized semiflexible polymer models. Our focus is on the theoretical development of these models and the calculation of experimental observables. To illustrate our methods, we focus on a specific, illustrative model of DNA bending. We show that the WLC model generically describes the long-length-scale chain statistics of semiflexible polymers, as predicted by renormalization group arguments. In particular, we show that either the WLC or our present model adequately describes force-extension, solution scattering, and long-contour-length cyclization experiments, regardless of the details of DNA bend elasticity. In contrast, experiments sensitive to short-length-scale chain behavior can in principle reveal dramatic departures from the linear elastic behavior assumed in the WLC model. We demonstrate this explicitly by showing that our toy model can reproduce the anomalously large short-contour-length cyclization factors recently measured by Cloutier and Widom. Finally, we discuss the applicability of these models to DNA chain statistics in the context of future experiments

Biological Consequences of Tightly Bent DNA: The Other Life of a Macromolecular Celebrity

The mechanical properties of DNA play a critical role in many biological functions. For example, DNA packing in viruses involves confining the viral genome in a volume (the viral capsid) with dimensions that are comparable to the DNA persistence length. Similarly, eukaryotic DNA is packed in DNA-protein complexes (nucleosomes) in which DNA is tightly bent around protein spools. DNA is also tightly bent by many proteins that regulate transcription, resulting in a variation in gene expression that is amenable to quantitative analysis. In these cases, DNA loops are formed with lengths that are comparable to or smaller than the DNA persistence length. The aim of this review is to describe the physical forces associated with tightly bent DNA in all of these settings and to explore the biological consequences of such bending, as increasingly accessible by single-molecule techniques.Comment: 24 pages, 9 figure

A generalized theory of semiflexible polymers

DNA bending on length scales shorter than a persistence length plays an integral role in the translation of genetic information from DNA to cellular function. Quantitative experimental studies of these biological systems have led to a renewed interest in the polymer mechanics relevant for describing the conformational free energy of DNA bending induced by protein-DNA complexes. Recent experimental results from DNA cyclization studies have cast doubt on the applicability of the canonical semiflexible polymer theory, the wormlike chain (WLC) model, to DNA bending on biological length scales. This paper develops a theory of the chain statistics of a class of generalized semiflexible polymer models. Our focus is on the theoretical development of these models and the calculation of experimental observables. To illustrate our methods, we focus on a specific toy model of DNA bending. We show that the WLC model generically describes the long-length-scale chain statistics of semiflexible polymers, as predicted by the Renormalization Group. In particular, we show that either the WLC or our new model adequate describes force-extension, solution scattering, and long-contour-length cyclization experiments, regardless of the details of DNA bend elasticity. In contrast, experiments sensitive to short-length-scale chain behavior can in principle reveal dramatic departures from the linear elastic behavior assumed in the WLC model. We demonstrate this explicitly by showing that our toy model can reproduce the anomalously large short-contour-length cyclization J factors observed by Cloutier and Widom. Finally, we discuss the applicability of these models to DNA chain statistics in the context of future experiments

Exact theory of kinkable elastic polymers

The importance of nonlinearities in material constitutive relations has long been appreciated in the continuum mechanics of macroscopic rods. Although the moment (torque) response to bending is almost universally linear for small deflection angles, many rod systems exhibit a high-curvature softening. The signature behavior of these rod systems is a kinking transition in which the bending is localized. Recent DNA cyclization experiments by Cloutier and Widom have offered evidence that the linear-elastic bending theory fails to describe the high-curvature mechanics of DNA. Motivated by this recent experimental work, we develop a simple and exact theory of the statistical mechanics of linear-elastic polymer chains that can undergo a kinking transition. We characterize the kinking behavior with a single parameter and show that the resulting theory reproduces both the low-curvature linear-elastic behavior which is already well described by the Wormlike Chain model, as well as the high-curvature softening observed in recent cyclization experiments.Comment: Revised for PRE. 40 pages, 12 figure

High flexibility of DNA on short length scales probed by atomic force microscopy

The mechanics of DNA bending on intermediate length scales (5–100 nm) plays a key role in many cellular processes, and is also important in the fabrication of artificial DNA structures, but previous experimental studies of DNA mechanics have focused on longer length scales than these. We use high-resolution atomic force microscopy on individual DNA molecules to obtain a direct measurement of the bending energy function appropriate for scales down to 5 nm. Our measurements imply that the elastic energy of highly bent DNA conformations is lower than predicted by classical elasticity models such as the worm-like chain (WLC) model. For example, we found that on short length scales, spontaneous large-angle bends are many times more prevalent than predicted by the WLC model. We test our data and model with an interlocking set of consistency checks. Our analysis also shows how our model is compatible with previous experiments, which have sometimes been viewed as confirming the WLC

The Promise of Prediction Markets

Prediction markets are markets for contracts that yield payments based on the outcome of an uncertain future event, such as a presidential election. Using these markets as forecasting tools could substantially improve decision making in the private and public sectors. We argue that U.S. regulators should lower barriers to the creation and design of prediction markets by creating a safe harbor for certain types of small stakes markets. We believe our proposed change has the potential to stimulate innovation in the design and use of prediction markets throughout the economy, and in the process to provide information that will benefit the private sector and government alike.Technology and Industry

The evolution of methods for establishing evolutionary timescales

The fossil record is well known to be incomplete. Read literally, it provides a distorted view of the history of species divergence and extinction, because different species have different propensities to fossilize, the amount of rock fluctuates over geological timescales, as does the nature of the environments that it preserves. Even so, patterns in the fossil evidence allow us to assess the incompleteness of the fossil record. While the molecular clock can be used to extend the time estimates from fossil species to lineages not represented in the fossil record, fossils are the only source of information concerning absolute (geological) times in molecular dating analysis. We review different ways of incorporating fossil evidence in modern clock dating analyses, including node-calibrations where lineage divergence times are constrained using probability densities and tip-calibrations where fossil species at the tips of the tree are assigned dates from dated rock strata. While node-calibrations are often constructed by a crude assessment of the fossil evidence and thus involves arbitrariness, tip-calibrations may be too sensitive to the prior on divergence times or the branching process and influenced unduly affected by well-known problems of morphological character evolution, such as environmental influence on morphological phenotypes, correlation among traits, and convergent evolution in disparate species. We discuss the utility of time information from fossils in phylogeny estimation and the search for ancestors in the fossil record. This article is part of the themed issue ‘Dating species divergences using rocks and clocks’

Chemistry of floral rewards: intra- and interspecific variability of nectar and pollen secondary metabolites across taxa

Floral chemistry mediates plant interactions with pollinators, pathogens, and herbivores, with major consequences for fitness of both plants and flower visitors. The outcome of such interactions often depends on compound dose and chemical context. However, chemical diversity and intraspecific variation of nectar and pollen secondary chemistry are known for very few species, precluding general statements about their composition. We analyzed methanol extracts of flowers, nectar, and pollen from 31 cultivated and wild plant species, including multiple sites and cultivars, by liquid chromatography-mass spectrometry. To depict the 29 chemical niche of each tissue type, we analyzed differences in nectar and pollen chemical richness, absolute and proportional concentrations, and intraspecific variability. We hypothesized that pollen would have higher concentrations and more compounds than nectar, consistent with Optimal Defense Theory and pollen’s importance as a male gamete. To investigate chemical correlations across and within tissues, which could reflect physiological constraints, we quantified chemical overlap between conspecific nectar and pollen, and phenotypic integration of individual compounds within tissue types Nectar and pollen were chemically differentiated both across and within species. Of 102 compounds identified, most occurred in only one species. Machine-learning algorithms assigned samples to the correct species and tissue type with 98.6% accuracy. Consistent with our hypothesis, pollen had 23.8- to 235-fold higher secondary chemical concentrations and 63% higher chemical richness than nectar. The most common secondary compound classes were flavonoids, alkaloids, terpenoids, and phenolics (primarily phenylpropanoids including chlorogenic acid). The most common specific compound types were quercetin and kaempferol glycosides, known to mediate biotic and abiotic effects. Pollens were distinguished from nectar by high concentrations of hydroxycinnamoyl-spermidine conjugates, which affect plant development, abiotic stress tolerance, and herbivore resistance. Although chemistry was qualitatively consistent within species and tissue types, concentrations varied across cultivars and sites, which could influence pollination, herbivory, and disease in wild and agricultural plants. Analyses of multivariate trait space showed greater overlap across sites and cultivars in nectar than pollen chemistry; this overlap reflected greater within-site and within-cultivar variability of nectar. Our analyses suggest different ecological roles of nectar and pollen mediated by chemical concentration, composition, and variability

Secondary metabolites from nectar and pollen: A resource for ecological and evolutionary studies

Floral chemistry mediates plant interactions with herbivores, pathogens, and pollinators. The chemistry of floral nectar and pollen—the primary food rewards for pollinators—can affect both plant reproduction and pollinator health. Although the existence and functional significance of nectar and pollen secondary metabolites has long been known, comprehensive quantitative characterizations of secondary chemistry exist for only a few species. Moreover, little is known about intraspecific variation in nectar and pollen chemical profiles. Because the ecological effects of secondary chemicals are dose-dependent, heterogeneity across genotypes and populations could influence floral trait evolution and pollinator foraging ecology. To better understand within- and across species heterogeneity in nectar and pollen secondary chemistry, we undertook exhaustive LC-MS and LC-UV-based chemical characterizations of nectar and pollen methanol extracts from 31 cultivated and wild plant species. Nectar and pollen were collected from farms and natural areas in Massachusetts, Vermont, and California, USA, in 2013 and 2014. For wild species, we aimed to collect 10 samples from each of 3 sites. For agricultural and horticultural species, we aimed for 10 samples from each of 3 cultivars. Our dataset (1535 samples, 102 identified compounds) identifies and quantifies each compound recorded in methanolic extracts, and includes chemical metadata that describe the molecular mass, retention time, and chemical classification of each compound. A reference phylogeny is included for comparative analyses. We found that each species possessed a distinct chemical profile; moreover, within species, few compounds were found in both nectar and pollen. The most common secondary chemical classes were flavonoids, terpenoids, alkaloids and amines, and chlorogenic acids. The most common compounds were quercetin and kaempferol glycosides. Pollens contained high concentrations of hydroxycinnamoyl-spermidine conjugates, mainly triscoumaroyl and trisferuloyl spermidine, found in 71% of species. When present, pollen alkaloids and spermidines had median nonzero concentrations of 23,000 μM (median 52% of recorded micromolar composition). Although secondary chemistry was qualitatively consistent within each species and sample type, we found significant quantitative heterogeneity across cultivars and sites. These data provide a standard reference for future ecological and evolutionary research on nectar and pollen secondary chemistry, including its role in pollinator health and plant reproduction