On the Interpretation of the Normalization Constant in the Scaling Equation

The scaling equation, Y1 = βYα2, has been used empirically and explored theoretically primarily to determine the numerical value and meaning of the scaling exponent, α. The mathematical interpretation of α is clear—it is the quotient of the relative rate of change of Y1 with respect to the rate of change of Y2. In contrast, the interpretation of the normalization constant, β, is obscure, so much so that some workers have rejected the idea that it has any biological importance. With the notable exception of Steven J. Gould\u27s early work, Huxley\u27s dismissal of β largely relegated the study of its biological role to that of an academic afterthought. Here, we attempt to clarify the meaning of β by using examples from plant biology to illustrate the four primary difficulties that have obscured its importance: (1) the consistency of the units of measurement and the metric being measured (e.g., meters and body length, respectively), (2) the relationship between β and α, (3) the interpretation of scaling equations, and (4) detecting if the numerical value of β has changed and if the change is biologically meaningful. Using examples, we show that β is biologically interpretable and offers a way to quantitatively consider similarities of biological form if (1) it is expressed in terms of the relative magnitudes of Y1 or Y2 for corresponding data points in a set of Y1 = βYα2 equations, (2) the units of measurements are in the same scale, and (3) the corresponding dimensionless numbers are established based on the same units of measurement. We provide examples of where the numerical value of β or differences in the values of β are important, and we propose a research agenda examining the meaning of β values in terms of trait-based ecology

A Workflow for Lipid Nanoparticle (LNP) Formulation Optimization Using Designed Mixture-Process Experiments and Self-Validated Ensemble Models (SVEM)

We present a Quality by Design (QbD) styled approach for optimizing lipid nanoparticle (LNP) formulations, aiming to offer scientists an accessible workflow. The inherent restriction in these studies, where the molar ratios of ionizable, helper, and PEG lipids must add up to 100%, requires specialized design and analysis methods to accommodate this mixture constraint. Focusing on lipid and process factors that are commonly used in LNP design optimization, we provide steps that avoid many of the difficulties that traditionally arise in the design and analysis of mixture-process experiments by employing space-filling designs and utilizing the recently developed statistical framework of self-validated ensemble models (SVEM). In addition to producing candidate optimal formulations, the workflow also builds graphical summaries of the fitted statistical models that simplify the interpretation of the results. The newly identified candidate formulations are assessed with confirmation runs and optionally can be conducted in the context of a more comprehensive second-phase study

On the Interpretation of the Normalization Constant in the Scaling Equation

The scaling equation, Y1 = βY2α, has been used empirically and explored theoretically primarily to determine the numerical value and meaning of the scaling exponent, α. The mathematical interpretation of α is clear—it is the quotient of the relative rate of change of Y1 with respect to the rate of change of Y2. In contrast, the interpretation of the normalization constant, β, is obscure, so much so that some workers have rejected the idea that it has any biological importance. With the notable exception of Steven J. Gould's early work, Huxley's dismissal of β largely relegated the study of its biological role to that of an academic afterthought. Here, we attempt to clarify the meaning of β by using examples from plant biology to illustrate the four primary difficulties that have obscured its importance: (1) the consistency of the units of measurement and the metric being measured (e.g., meters and body length, respectively), (2) the relationship between β and α, (3) the interpretation of scaling equations, and (4) detecting if the numerical value of β has changed and if the change is biologically meaningful. Using examples, we show that β is biologically interpretable and offers a way to quantitatively consider similarities of biological form if (1) it is expressed in terms of the relative magnitudes of Y1 or Y2 for corresponding data points in a set of Y1 = βY2α equations, (2) the units of measurements are in the same scale, and (3) the corresponding dimensionless numbers are established based on the same units of measurement. We provide examples of where the numerical value of β or differences in the values of β are important, and we propose a research agenda examining the meaning of β values in terms of trait-based ecology

Co-Ingestion of Dietary Nitrate and Ascorbic Acid on Nitric Oxide Biomarkers and The Oral Microbiome in Sedentary Hispanic Women

Nitric oxide bioavailability increases following nitrate supplementation wherein oral microbiota facilitate the metabolism and absorption of nitrate. However, few studies have examined if co-ingestion of nitrate with antioxidants can further elevate nitric oxide bioavailability. Moreover, our understanding on how the oral microbiome responds to nitrate supplementation is limited, especially in women. PURPOSE: To examine the effects of ingesting dietary nitrate and ascorbic acid independently and concurrently on markers of nitric oxide bioavailability and oral microbiota species. METHODS: Twelve sedentary women of Hispanic descent (mean ± SD: age 20 ± 1 years; body mass 74 ± 15 kg; height 1.62 ± 0.09 m) consumed nitrate-rich beetroot juice (BR), nitrate-depleted beetroot juice (PL), ascorbic acid (AA), and crystal light (CRY) in four conditions: BR combined with AA (BR+AA); BR only (BR+CRY); AA only (PL+AA); and placebo-control (PL+CRY). Supplements were ingested 2.5 hours prior to a resting blood draw and buccal swab sample. Plasma [nitrate] and [nitrite] were analyzed using gas phase chemiluminescence. Buccal swab samples were used for DNA extraction and isolation. DNA was amplified using polymerase chain reaction (PCR) targeting the V3 - V4 region of the 16S rRNA gene. Following index PCR, amplicons were pooled and sequenced using the iSeq Illumina NGS sequencer. Reads were clustered into amplicon sequence variants and analyzed for alpha and beta diversity and relative abundance. RESULTS: BR increased plasma [nitrate] (BR+AA: 641 ± 252 vs. BR+CRY: 528 ± 307 vs. PL+AA: 35 ± 10 vs. PL+CRY: 35 ± 12 µM, P \u3c 0.001) and plasma [nitrite] (BR+AA: 710 ± 336 vs. BR+CRY: 578 ± 428 vs. PL+AA: 209 ± 88 vs. PL+CRY: 198 ± 82 nM, P \u3c 0.001) with no differences within BR and PL conditions. Alpha and beta diversity, and the relative abundance of higher and lower taxonomic levels were not significantly different between all conditions (P \u3e 0.05) CONCLUSION: Concurrent nitrate and AA supplementation did not elicit additional increases to nitric oxide compared to nitrate ingestion alone. Acute beetroot juice and ascorbic acid were ineffective at modulating oral microbial composition. Further research is required to understand the impact of supplementation regimen and population on the physiological effects of dietary nitrate

The Effects of Acute Beetroot Juice Ingestion on Exercise and Cognitive Performance in Female Athletes

Nitrate-rich beetroot juice can enhance intense exercise performance which is attributed to enhanced skeletal muscle contractility. However, limited data exist in females and it is unknown whether dietary nitrate has an ergogenic effect in this population. PURPOSE: To investigate the potential effects of acute nitrate ingestion on a battery of exercise performance and cognitive tests before and after fatiguing intermittent running exercise. METHODS: Fifteen female team-sport athletes were assigned in a randomized, double-blind, crossover design to consume nitrate-rich beetroot juice (BR; 12 mmol of nitrate) and nitrate-depleted beetroot juice (PL; 0.10 mmol of nitrate) 2.5 h prior to performing the exercise protocol, with a washout period of 7 days between trials. Running 10 m and 20 m sprint split times, sprint reaction time, upper- and lower-body power, handgrip strength, and cognitive flexibility were measured before and after the Yo-Yo intermittent recovery level 1 (Yo-Yo IR1) test, during which performance and rate of perceived exertion were recorded. RESULTS: There were no significant differences in any performance outcome or cognitive flexibility (P \u3e 0.05). CONCLUSION: These findings indicate that acute nitrate ingestion does not influence performance in sprints, intermittent running, power, strength, or cognitive function in young adult female team-sport athletes

Effects of Co-ingesting Dietary Nitrate and Vitamin C on Nitric Oxide Bioavailability, Blood Pressure, and Cardiovascular Reactivity in Hispanic Females

High blood pressure is a hallmark of chronic disease and is disproportionately prevalent in ethnic minorities. Dietary nitrate has been shown to lower blood pressure via increased nitric oxide (NO), but few studies have examined if combining nitrate with vitamin C (VITC) could have beneficial synergistic effects on blood pressure by augmenting NO, and limited data exist in females. PURPOSE: To investigate if combining nitrate-rich beetroot juice (BR) with VITC could further augment NO bioavailability and improve blood pressure in Hispanic females compared to BR and VITC ingested alone. METHODS: Eight sedentary Hispanic females participated in four conditions to ingest: 1) BR and VITC (BR+VITC), 2) BR and crystal light (BR+CRY), 3) nitrate-depleted BR and VITC (PL+VITC), and 4) PL and CRY (PL+CRY). A blood draw and blood pressure were obtained at rest, followed by a cardiovascular reactivity test. RESULTS: Plasma nitrate was increased in BR+VITC and BR+CRY compared to PL+VITC and PL+CRY (P0.05). Plasma nitrite was increased in BR+VITC and BR+CRY compared to PL+VITC and PL+CRY (P0.05). CONCLUSION: Co-ingestion of dietary nitrate and VITC increased plasma nitrite compared to BR alone, which could indicate augmented NO bioavailability following BR+VITC; however, there was no impact of nitrate supplementation on markers of cardiovascular health

Spiral Density Waves in a Young Protoplanetary Disk

Gravitational forces are expected to excite spiral density waves in protoplanetary disks, disks of gas and dust orbiting young stars. However, previous observations that showed spiral structure were not able to probe disk midplanes, where most of the mass is concentrated and where planet formation takes place. Using the Atacama Large Millimeter/submillimeter Array we detected a pair of trailing symmetric spiral arms in the protoplanetary disk surrounding the young star Elias 2-27. The arms extend to the disk outer regions and can be traced down to the midplane. These millimeter-wave observations also reveal an emission gap closer to the star than the spiral arms. We argue that the observed spirals trace shocks of spiral density waves in the midplane of this young disk.Comment: This is our own version of the manuscript, the definitive version was published in Science (DOI: 10.1126/science.aaf8296) on September 30, 2016. Posted to the arxiv for non-commercial us

Simulation-Based Investigation of a Model for the Interaction Between Stellar Magnetospheres and Circumstellar Accretion Disks

We examine, parametrically, the interaction between the magnetosphere of a rotating, young stellar object (YSO) and a circumstellar accretion disk using 2.5-D (cylindrically symmetric) numerical magnetoydrodynamic simulations. The interaction drives a collimated outflow, and we find that the jet formation mechanism is robust. For variations in initial disk density of a factor of 16, variations of stellar dipole strength of a factor of 4, and for various initial conditions with respect to the disk truncation radius and the existence of a disk field, outflows with similar morphologies were consistently produced. Secondly, the system is self-regulating, where the outflow properties depend relatively weakly on the parameters above. The large scale magnetic field structure rapidly evolves to a configuration that removes angular momentum from the disk at a rate that depends most strongly on the field and weakly on the rotation rate of the foot-points of the field in the disk and the mass outflow rate. Third, the simulated jets are episodic, with the timescale of jet outbursts identical to the timescale of magnetically induced oscillations of the inner edge of the disk. To better understand the physics controlling these disk oscillations, we present a semi-analytical model and confirm that the oscillation period is set by the spin down rate of the disk inner edge. Finally, our simulations offer strong evidence that it is indeed the interaction of the stellar magnetosphere with the disk, rather than some primordial field in the disk itself, that is responsible for the formation of jets from these systems.Comment: Accepted by ApJ; 34 pages, including 12 figures and 3 table