Cancer as a Model System for Testing Metabolic Scaling Theory

Biological allometries, such as the scaling of metabolism to mass, are hypothesized to result from natural selection to maximize how vascular networks fill space yet minimize internal transport distances and resistance to blood flow. Metabolic scaling theory argues two guiding principles—conservation of fluid flow and space-filling fractal distributions—describe a diversity of biological networks and predict how the geometry of these networks influences organismal metabolism. Yet, mostly absent from past efforts are studies that directly, and independently, measure metabolic rate from respiration and vascular architecture for the same organ, organism, or tissue. Lack of these measures may lead to inconsistent results and conclusions about metabolism, growth, and allometric scaling. We present simultaneous and consistent measurements of metabolic scaling exponents from clinical images of lung cancer, serving as a first-of-its-kind test of metabolic scaling theory, and identifying potential quantitative imaging biomarkers indicative of tumor growth. We analyze data for 535 clinical PET-CT scans of patients with non-small cell lung carcinoma to establish the presence of metabolic scaling between tumor metabolism and tumor volume. Furthermore, we use computer vision and mathematical modeling to examine predictions of metabolic scaling based on the branching geometry of the tumor-supplying blood vessel networks in a subset of 56 patients diagnosed with stage II-IV lung cancer. Examination of the scaling of maximum standard uptake value with metabolic tumor volume, and metabolic tumor volume with gross tumor volume, yield metabolic scaling exponents of 0.64 (0.20) and 0.70 (0.17), respectively. We compare these to the value of 0.85 (0.06) derived from the geometric scaling of the tumor-supplying vasculature. These results: (1) inform energetic models of growth and development for tumor forecasting; (2) identify imaging biomarkers in vascular geometry related to blood volume and flow; and (3) highlight unique opportunities to develop and test the metabolic scaling theory of ecology in tumors transitioning from avascular to vascular geometries.

Body Shape Indices in Adolescents Based on the 2009–2012 Korea National Health and Nutrition Examination Survey

A Body Shape Index (ABSI) is a recently proposed index for standardizing waist circumference (WC) for body mass index (BMI) and height in adults, using 2/3 and 1/2 as scaling exponents, respectively. However, ABSI has limited applicability to children and adolescents, as the relationship between height and weight changes with age and varies according to sex. This study aimed to investigate whether ABSI can be applied to adolescents and to analyze the relationships among BMI, WC, height, weight, and body shape index (BSI) in Korean adolescents. The data of 1023 adolescents aged 10–19 years from the 2009–2012 Korea National Health and Nutrition Examination Survey were collected. Body measurements (height, weight, WC, and BMI) were analyzed to estimate the BSI using log-linear regression. The scaling exponents for standardizing WC for weight and height were estimated according to age (per year) and sex. The scaling exponents for standardizing WC for weight and height were 0.698 and −1.090 for boys and 0.646 and −0.855 for girls, respectively. The exponents also differed according to age. BSI was negatively correlated with height, weight, and BMI in boys and girls, and these correlations differed in direction from those in adults. ABSI cannot be applied to adolescents. In adolescents, the BSI is dependent on age and sex and is associated with growth and puberty. Further studies are required to evaluate the association between BSI and other biomarkers, to improve its applicability as a parameter for predicting the risk of chronic diseases in adolescents.

Finding self-similar behavior in quantum many-body dynamics via persistent homology

Inspired by topological data analysis techniques, we introduce persistent homology observables and apply them in a geometric analysis of the dynamics of quantum field theories. As a prototype application, we consider data from a classical-statistical simulation of a two-dimensional Bose gas far from equilibrium. We discover a continuous spectrum of dynamical scaling exponents, which provides a refined classification of nonequilibrium self-similar phenomena. A possible explanation of the underlying processes is provided in terms of mixing strong wave turbulence and anomalous vortex kinetics components in point clouds. We find that the persistent homology scaling exponents are inherently linked to the geometry of the system, as the derivation of a packing relation reveals. The approach opens new ways of analyzing quantum many-body dynamics in terms of robust topological structures beyond standard field theoretic techniques.

Scaling of joint mass and metabolism fluctuations in in silico cell-laden spheroids

Variations and fluctuations are characteristic features of biological systems and are also manifested in cell cultures. Here, we describe a computational pipeline for identifying the range of three-dimensional (3D) cell-aggregate sizes in which nonisometric scaling emerges in the presence of joint mass and metabolic rate fluctuations. The 3D cell-laden spheroids with size and single-cell metabolic rates described by probability density functions were randomly generated in silico. The distributions of the resulting metabolic rates of the spheroids were computed by modeling oxygen diffusion and reaction. Then, a method for estimating scaling exponents of correlated variables through statistically significant data collapse of joint probability distributions was developed. The method was used to identify a physiologically relevant range of spheroid sizes, where both nonisometric scaling and a minimum oxygen concentration (0.04 mol⋅m−3) is maintained. The in silico pipeline described enables the prediction of the number of experiments needed for an acceptable collapse and, thus, a consistent estimate of scaling parameters. Using the pipeline, we also show that scaling exponents may be significantly different in the presence of joint mass and metabolic-rate variations typically found in cells. Our study highlights the importance of incorporating fluctuations and variability in size and metabolic rates when estimating scaling exponents. It also suggests the need for taking into account their covariations for better understanding and interpreting experimental observations both in vitro and in vivo and brings insights for the design of more predictive and physiologically relevant in vitro models.

Multiple macroecological laws do characterize various aspects of microbiota dynamics

In this letter we address the potential confusion related to our recent demonstration that multiple macroecological laws describe short- and long-term dynamics of microbial communities. Specifically, we clarify that these laws, similarly to many other relationships observed in nature, are characterized not just by the existence of scaling, but also by certain characteristic values of the scaling exponents. By performing proper statistical analysis, we demonstrate that the relationships sensitive to temporal bacterial dynamics are not reproduced in the shuffled data. We also discuss that there is no clear evidence in the data that macroecological relationships in microbiota are primarily driven by external or environmental factors. Proper statistical analyses of the data suggest that the dynamics of gut microbiota, even on a constant diet, contains rich temporal structure. Therefore, it is likely that complex and non-linear internal dynamics may be primarily responsible for the observed macroecological laws in microbiota and other ecological communities.

Viscoelasticity and Noise Properties Reveal the Formation of Biomemory in Cells

Living cells are neither perfectly elastic nor liquid and return a viscoelastic response to external stimuli. Nanoindentation provides force distance curves allowing the investigation of cell mechanical properties, and yet, these curves can differ from point to point on cell surface revealing its inhomogeneous character. In the present work, we propose a mathematical method to estimate both viscoelastic and noise properties of cells, as these are depicted on the values of the scaling exponents of relaxation function and power spectral density respectively. The method uses as input the time derivative of the response force in a nanoindentation experiment. Generalized moments method and/or rescaled range analysis are used to study the resulting time series depending on their non-stationary or stationary nature. We conducted experiments in living Ulocladium Chartarum spores. We found that spores, in the approaching phase present a viscoelastic behavior with the corresponding scaling exponent in the range 0.25-0.52, and in the retracting phase present a liquid-like behavior with exponents in the range 0.67-0.85. This substantial difference of the scaling exponents in the two phases suggests the formation of biomemory as response of the spores to the indenting AFM mechanical stimulus. The retracting phase may be described as a process driven by bluish noises, while the approaching one is driven by persistent noise.

Within-species relationship of patchiness to both abundance and occupancy, as exemplified by seagrass macrobenthos

For the first time, intraspecific relationships between the macroecological metrics patchiness (P) and both abundance (A) and occupancy (O) were investigated in a faunal assemblage. As a companion study to recent work on interspecific P, A and O patterns at the same localities, intraspecific patterns were documented within each of the more dominant invertebrates forming the seagrass macrobenthos of warm–temperate Knysna estuarine bay (South Africa) and of sub-tropical Moreton Bay (Australia). As displayed interspecifically, individual species showed strong A–O patterns (mean scaling coefficient − 0.76 and mean R2 > 0.8). All P–O relations were negative and most (67%) were statistically significant, although weaker (mean R2 0.5) than A–O ones; most P–A ones were also negative but fewer (43%) achieved significance, and were even weaker (mean R2 0.4); 33% of species showed no significant interrelations of either O or A with P. No species showed only a significant P–A relationship. Compared with interspecific P–A–O data from the same assemblages, power–law scaling exponents were equivalent, but R2 values were larger. Larviparous species comprised 70% of the total studied, but 94% of those displaying significant patchiness interrelationships; 5 of the 9 showing no P–A or P–O relationships, however, were also larviparous. At Knysna, though not in Moreton Bay, larviparous species also showed higher levels of occupancy than non-larviparous ones, whilst non-larviparous species showed higher levels of patchiness. Dominant Moreton Bay species, but not those at Knysna, exhibited homogeneously sloped P–O relationships.

Whether the CMIP5 Models Can Reproduce the Long-Range Correlation of Daily Precipitation?

In this study, we investigated the performance of nine CMIP5 models for global daily precipitation by comparing with NCEP data from 1960 to 2005 based on the detrended fluctuation analysis (DFA) method. We found that NCEP daily precipitation exhibits long-range correlation (LRC) characteristics in most regions of the world. The LRC of daily precipitation over the central of North American continent is the strongest in summer, while the LRC of precipitation is the weakest for the equatorial central Pacific Ocean. The zonal average scaling exponents of NCEP daily precipitation are smaller in middle and high latitudes than those in the tropics. The scaling exponents are above 0.9 over the tropical middle and east Pacific Ocean for the year and four seasons. Most CMIP5 models can capture the characteristic that zonal mean scaling exponents of daily precipitation reach the peak in the tropics, and then decrease rapidly with the latitude increasing. The zonal mean scaling exponents simulated by CMCC-CMS, GFDL-ESM2G and IPSL-CM5A-MR show consistencies with those of NCEP, while BCC_CSM1.1(m) and FGOALS-g2 cannot capture the seasonal variations of daily precipitation’s LRC. The biases of scaling exponents between CMIP5 models and NCEP are smaller in the high latitudes, and even less than the absolute value of 0.05 in some regions, including Arctic Ocean, Siberian, Southern Ocean and Antarctic. However, for Western Africa, Eastern Africa, Tropical Eastern Pacific and Northern South America, the simulated biases of scaling exponents are greater than the absolute value of 0.05 for the year and all four seasons. In general, the spatial biases of LRC simulated by GFDL-ESM2G, HadGEM2-AO and INM-CM4 are relatively small, which indicating that the LRC characteristics of daily precipitation are well simulated by these models.