The fourth dimension of life: fractal geometry and allometric scaling of organisms

Stability and robustness of kinetochore dynamics under sudden perturbations and stochastic influences

Understanding the dynamic behavior of kinetochores is crucial for understanding the mechanisms of accurate chromosome segregation during cell division. In this study, we introduced non-linear exponents p and q into two new systems to capture the complex movements that govern the intersister movement of kinetochores during chromosome segregation. Our analysis revealed a power-law relationship between these exponents and the maximum amplitude A of sister kinetochore 2, indicating that even small adjustments in p and q lead to significant changes in kinetochore movement. This sensitivity suggests that kinetochore dynamics are governed by scale-invariant principles, potentially reflecting intrinsic properties of the kinetochore-microtubule interface such as motor protein activity. We observed that the Type II model with perturbation functions, demonstrated stability with rapidly dampening oscillations across various forms of noise and sudden shocks. This highlights the effectiveness of adaptable regulatory mechanisms in maintaining stability during mitosis. In contrast, the Type I model without such regulatory parameters exhibited sustained, bounded oscillations that did not dampen over time and showed significant fragility under stochastic noise, potentially compromising chromosome segregation fidelity. Our findings highlight the role of the exponents p and q in modulating kinetochore behavior and suggest that enhancing or mimicking these regulatory mechanisms could be a potential strategy for improving cell division fidelity as shown in our theoretical work.

Does death drive the scaling of life?

The magnitude of many kinds of biological structures and processes scale with organismal size, often in regular ways that can be described by power functions. Traditionally, many of these "biological scaling" relationships have been explained based on internal geometric, physical, and energetic constraints according to universal natural laws, such as the "surface law" and "3/4-power law". However, during the last three decades it has become increasingly apparent that biological scaling relationships vary greatly in response to various external (environmental) factors. In this review, I propose and provide several lines of evidence supporting a new ecological perspective that I call the "mortality theory of ecology" (MorTE). According to this viewpoint, mortality imposes time limits on the growth, development, and reproduction of organisms. Accordingly, small, vulnerable organisms subject to high mortality due to predation and other environmental hazards have evolved faster, shorter lives than larger, more protected organisms. A MorTE also includes various corollary, size-related internal and external causative factors (e.g. intraspecific resource competition, geometric surface area to volume effects on resource supply/transport and the protection of internal tissues from environmental hazards, internal homeostatic regulatory systems, incidence of pathogens and parasites, etc.) that impact the scaling of life. A mortality-centred approach successfully predicts the ranges of body-mass scaling slopes observed for many kinds of biological and ecological traits. Furthermore, I argue that mortality rate should be considered the ultimate (evolutionary) driver of the scaling of life, that is expressed in the context of other proximate (functional) drivers such as information-based biological regulation and spatial (geometric) and energetic (metabolic) constraints.

The island rule-like patterns of plant size variation in a young land-bridge archipelago: Roles of environmental circumstance and biotic competition

The island rule, a general pattern of dwarfism in large species to gigantism in small species on islands relative to mainland, is typically seen as a macroevolutionary phenomenon. However, whether the ecological processes associated with abiotic and biotic factors generate a pattern of plant size variation similar to the island rule remains unknown. We measured plant height for 29,623 individuals of 50 common woody plant species across 43 islands in the Zhoushan Archipelago (8500 years old and yet to undergo major evolutionary adaptation) and the adjacent mainlands in China. We found pronounced variations in plant height, similar to those of the island rule. Interestingly, islands with low resource availability, such as low soil organic matter content and low precipitation, had a high degree of dwarfism; islands experiencing high environmental stress, such as high soil pH, had a high degree of dwarfism; and islands experiencing less plant-plant competition had a high degree of gigantism. The magnitude of plant dwarfism was higher on small and remote islands than on larger and nearer islands. These results highlight the importance of ecological processes associated with abiotic and biotic conditions in shaping the island rule-like patterns of plant size variation. Since our studied archipelago is too young to undergo major evolution, ecological processes likely played a prominent role in generating the observed pattern, challenging the notion that the evolutionary process is the dominant factor underlying the island rule. Future studies on the island rule need to perform experiments to disentangle evolutionary from ecological mechanisms.

Metabolic ecology in aquatic ecosystems: Viewed from trophic compartments and communities in food webs

A different perspective in metabolic ecology is presented using food web data, based on trophic compartments and communities in aquatic ecosystems (coastal areas, shelves and estuaries in marine ecosystems, and lake ecosystems), including primary producers (phytoplankton and aquatic plants). The relationships among the metabolic traits (biomass, respiration and production) in aquatic communities are expressed through power laws, hence, the value of one of the three metabolic traits provides the values of the other two. Noteworthily, these metabolic traits (biomass, respiration, production) are related to those of primary producers according to various power laws. That is: the metabolic traits of communities can be estimated from those of primary producers alone. These power laws appear to be universal in marine ecosystems but vary among different lake ecosystems.

Principles Entailed by Complexity, Crucial Events, and Multifractal Dimensionality

Complexity is one of those descriptive terms adopted in science that we think we understand until it comes time to form a coherent definition upon which everyone can agree. Suddenly, we are awash in conditions that qualify this or that situation, much like we were in the middle of the last century when it came time to determine the solutions to differential equations that were not linear. Consequently, this tutorial is not an essay on the mathematics of complexity nor is it a rigorous review of the recent growth spurt of complexity science, but is rather an exploration of how physiologic time series (PTS) in the life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions are discarded and so-called ordinary statistical events in PTS are replaced with crucial events (CEs) using mutifractal dimensionality as the working measure of complexity. The empirical datasets considered include respiration, electrocardiograms (ECGs), and electroencephalograms (EEGs), and as different as these time series appear from one another when recorded, they are in fact shown to be in synchrony when properly processed using the technique of modified diffusion entropy analysis (MDEA). This processing reveals a new synchronization mechanism among the time series which simultaneously measures their complexity by means of the multifractal dimension of each time series and are shown to track one another across time. These results reveal a set of priciples that capture the manner in which information is exchanged among physiologic organ networks.

Complexity, Uncertainty, and Entropy: Applications to Food Sensory Perception and Other Complex Phenomena

Complexity has been studied in various areas of science, such as ecology and sensory science. One important aspect is the quantification of the complexity of a system. There exist a multitude of different approaches. One approach relates complexity to information, with its measure introduced by Shannon. This is equal to the negative value of entropy, or uncertainty. In this review, we discuss the different approaches that are used to quantify and measure complexity in the realm of food sensory perception. We address how the food sensory field could benefit from an approach that is based on an information-theoretical footing, to allow for one quantitative measure, thus improving comparison and reproducibility among different laboratories. Reversely, the review is intended to inspire the physics community to explore complex phenomena, such as sensory perception, in terms of a general information-theoretical measure, such as entropy and other fields.

Fractal analysis of healthy and diseased vasculature in pediatric Moyamoya disease

BACKGROUND AND PURPOSE

Fractal dimension is an objective metric for the notion of structural complexity. We sought to investigate differences in structural complexity between healthy and affected territories of cerebral vasculature in moyamoya, as well as associated scalp vasculature and native transdural collaterals in patients with moyamoya by comparing their respective fractal dimensions.

METHODS

Our cohort consisted of 15 transdural collaterals from 12 patients with unilateral anterior circulation moyamoya. Frames of distal arterial vasculature from internal and external carotid angiograms were selected then automatically segmented and also manually annotated by a cerebrovascular surgeon. In the affected hemisphere, the region with transdural collateral supply was compared to the contralateral region. The resulting skeletonized angiograms were analyzed for their fractal dimensions.

RESULTS

We found the average fractal dimension (Df) of the moyamoya-side ICA was 1.82 with slightly different means for the anteroposterial (AP) and lateral views (mean  =  1.82; mean  =  1.81). The overall mean for healthy cerebral vasculature was also found to be 1.82 (AP: mean  =  1.83; lateral: mean  =  1.81). Mean Df of native transdural collaterals was found to be 1.82 (AP: mean  =  1.83; lateral: mean  =  1.81). The mean Df difference between autosegmented and manually segmented images was 0.013.

CONCLUSION

In accordance with the clinical understanding of moyamoya disease, the distal arterial structural complexity is not affected in moyamoya, and is maintained by transdural collaterals formed by vasculogenesis. Autosegmentation of cerebral vasculature is also shown to be accurate when compared to manual segmentation.

Impact of developmental temperature on neural growth, connectivity, and function

Environmental temperature dictates the developmental pace of poikilothermic animals. In Drosophila, slower development at lower temperatures results in higher brain connectivity, but the generality of such scaling across temperatures and brain regions and its impact on function are unclear. Here, we show that brain connectivity scales continuously across temperatures, in agreement with a first-principle model that postulates different metabolic constraints for the growth of the brain and the organism. The model predicts brain wiring under temperature cycles and the nonuniform temporal scaling of neural development across temperatures. Developmental temperature has notable effects on odor-driven behavior. Dissecting the circuit architecture and function of neurons in the olfactory pathway, we demonstrate that developmental temperature does not alter odor encoding in first- and second-order neurons, but it shifts the specificity of connections onto third-order neurons that mediate innate behaviors. We conclude that while some circuit computations are robust to the effects of developmental temperature on wiring, others exhibit phenotypic plasticity with possible adaptive advantages.

The impact of age and renal function on the pharmacokinetics and protein binding characteristics of fludarabine in paediatric and adult patients undergoing allogeneic haematopoietic stem cell transplantation conditioning

AIM

To evaluate the population pharmacokinetics of unbound F-Ara-A (the circulating metabolite of fludarabine) in 211 patients (age range, 0.1-63.4 years) undergoing allogeneic haematopoietic stem cell transplantation conditioning.

METHODS

Total (n = 2480) and unbound (n = 1403) F-Ara-A concentrations were measured in blood samples collected at timed intervals after fludarabine doses ranging from 10 to 50 mg/m2 and infused over 0.42-1.5 h. A three-compartment population pharmacokinetic model was developed based on unbound plasma concentrations and used to estimate F-Ara-A unbound pharmacokinetic parameters and fraction unbound (fu). A number of covariates, including glomerular filtration rate (GFR) and post-menstrual age (PMA), were evaluated for inclusion in the model.

RESULTS

The base population mean estimates ± relative standard error (%RSE) for unbound clearance from the central compartment (CLu) and inter-compartmental clearances (Q2u, Q3u) were 3.42 ± 3%, 6.54 ± 24% and 1.47 ± 16% L/h/70 kg, respectively. The population mean estimates (%RSE) for the unbound volume of distribution into the central (V1u) and peripheral compartments (V2u, V3u) were 9.65 ± 8%, 8.17 ± 9% and 16.4 ± 10% L/70 kg, respectively, and that for fu was 0.877 ± 1%. Covariate model development involved differentiating F-Ara-A CLu into non-renal (1.81 ± 9% L/h/70 kg) and renal components (1.02 ± 9%*GFR L/h/70 kg). A sigmoidal maturation factor was applied to renal CLu, with population mean estimates for the Hill exponent and PMA at 50% mature of 2.97 ± 4% and 69.1 ± 8% weeks, respectively.

CONCLUSION

Patient age and GFR are predictors of unbound F-Ara-A CLu. This has the potential to impact dose requirements. Dose individualisation by target concentration intervention will be facilitated by this model once it is externally validated.

An allometry perspective on crops

Understanding trait-trait coordination is essential for successful plant breeding and crop modeling. Notably, plant size drives variation in morphological, physiological, and performance-related traits, as described by allometric laws in ecology. Yet, as allometric relationships have been limitedly studied in crops, how they influence and possibly limit crop performance remains unknown. Here, we review how an allometry perspective on crops gains insights into the phenotypic evolution during crop domestication, the breeding of varieties adapted to novel conditions, and the prediction of crop yields. As allometry is an active field of research, modeling and manipulating crop allometric relationships can help to develop more resilient and productive agricultural systems to face future challenges.

Constructing stability: optimal learning in noisy ecological niches

Organisms can learn in response to environmental inputs as well as actively modify their environments through niche construction on slower evolutionary time scales. How quickly should an organism respond to a changing environment, and when possible, should organisms adjust the time scale of environmental change? We formulate these questions using a model of learning costs that considers optimal time scales of both memory and environment. We derive a general, sublinear scaling law for optimal memory as a function of environmental persistence. This encapsulates a trade-off between remembering and forgetting. We place learning strategies within a niche construction dynamics in a game theoretic setting. Niche construction is found to reduce or stabilize environmental volatility when learned environmental resources can be monopolized. When learned resources are shared, niche destructors evolve to degrade the shared environment. We integrate these results into a metabolic scaling framework in order to derive learning strategies as a function of body size.

Multi-scaling allometry in human development, mammalian morphology, and tree growth

Various animal and plant species exhibit allometric relationships among their respective traits, wherein one trait undergoes expansion as a power-law function of another due to constraints acting on growth processes. For instance, the acknowledged consensus posits that tree height scales with the two-thirds power of stem diameter. In the context of human development, it is posited that body weight scales with the second power of height. This prevalent allometric relationship derives its nomenclature from fitting two variables linearly within a logarithmic framework, thus giving rise to the term "power-law relationship." Here, we challenge the conventional assumption that a singular power-law equation adequately encapsulates the allometric relationship between any two traits. We strategically leverage quantile regression analysis to demonstrate that the scaling exponent characterizing this power-law relationship is contingent upon the centile within these traits' distributions. This observation fundamentally underscores the proposition that individuals occupying disparate segments of the distribution may employ distinct growth strategies, as indicated by distinct power-law exponents. We introduce the innovative concept of "multi-scale allometry" to encapsulate this newfound insight. Through a comprehensive reevaluation of (i) the height-weight relationship within a cohort comprising 7, 863, 520 Japanese children aged 5-17 years for which the age, sex, height, and weight were recorded as part of a national study, (ii) the stem-diameter-height and crown-radius-height relationships within an expansive sample of 498, 838 georeferenced and taxonomically standardized records of individual trees spanning diverse geographical locations, and (iii) the brain-size-body-size relationship within an extensive dataset encompassing 1, 552 mammalian species, we resolutely substantiate the viability of multi-scale allometric analysis. This empirical substantiation advocates a paradigm shift from uni-scaling to multi-scaling allometric modeling, thereby affording greater prominence to the inherent growth processes that underlie the morphological diversity evident throughout the living world.

Advancing fine branch biomass estimation with lidar and structural models

BACKGROUND AND AIMS

Lidar is a promising tool for fast and accurate measurements of trees. There are several approaches to estimate above-ground woody biomass using lidar point clouds. One of the most widely used methods involves fitting geometric primitives (e.g. cylinders) to the point cloud, thereby reconstructing both the geometry and topology of the tree. However, current algorithms are not suited for accurate estimation of the volume of finer branches, because of the unreliable point dispersions from, for example, beam footprint compared to the structure diameter.

METHOD

We propose a new method that couples point cloud-based skeletonization and multi-linear statistical modelling based on structural data to make a model (structural model) that accurately estimates the above-ground woody biomass of trees from high-quality lidar point clouds, including finer branches. The structural model was tested at segment, axis and branch level, and compared to a cylinder fitting algorithm and to the pipe model theory.

KEY RESULTS

The model accurately predicted the biomass with 1.6 % normalized root mean square error (nRMSE) at the segment scale from a k-fold cross-validation. It also gave satisfactory results when scaled up to the branch level with a significantly lower error (13 % nRMSE) and bias (-5 %) compared to conventional cylinder fitting to the point cloud (nRMSE: 92 %, bias: 82 %), or using the pipe model theory (nRMSE: 31 %, bias: -27 %). The model was then applied to the whole-tree scale and showed that the sampled trees had more than 1.7 km of structures on average and that 96 % of that length was coming from the twigs (i.e. <5 cm diameter). Our results showed that neglecting twigs can lead to a significant underestimation of tree above-ground woody biomass (-21 %).

CONCLUSIONS

The structural model approach is an effective method that allows a more accurate estimation of the volumes of smaller branches from lidar point clouds. This method is versatile but requires manual measurements on branches for calibration. Nevertheless, once the model is calibrated, it can provide unbiased and large-scale estimations of tree structure volumes, making it an excellent choice for accurate 3D reconstruction of trees and estimating standing biomass.

Population pharmacokinetic modeling of sotatercept in healthy participants and patients with pulmonary arterial hypertension

Sotatercept is a breakthrough, first-in-class biologic, that is FDA-approved for the treatment of pulmonary arterial hypertension (PAH). A population pharmacokinetic (PopPK) model was developed using data from two phase 1 studies in healthy participants, and two phase 2 studies and one phase 3 study in participants with PAH. The pooled sotatercept PK data encompassed single intravenous (IV) or subcutaneous (SC) doses ranging from 0.01 to 3.0 mg/kg, as well as multiple SC doses ranging from 0.03 to 1.0 mg/kg, with PK samples collected up to a maximum of ~150 weeks following Q3W and Q4W dosing regimens. The final PopPK analysis included 350 participants, with 30 and 320 participants receiving sotatercept IV and SC, respectively. A two-compartment model with a first-order absorption rate constant and a linear disposition from central compartment well-described sotatercept PK. The estimated bioavailability is ~66%; bioavailability, clearance (CL), and central volume (VC) have low to moderate inter-individual variability. Time-varying body weight and baseline albumin concentration were statistically significant predictors of PK; CL and VC were predicted to increase with increasing body weight, while CL was predicted to decrease with increasing baseline albumin concentration. However, the magnitude of covariate effects is not predicted to meaningfully alter the disposition of sotatercept. Altogether, the PopPK modeling results demonstrate favorable PK characteristics (low to moderate variability and typical bioavailability), supporting sotatercept as a SC biological agent for the treatment of patients with PAH.

Size matters in metabolic scaling: Critical role of the thermodynamic efficiency of ATP synthesis and its dependence on mitochondrial H+ leak across mammalian species

In this last article of the trilogy, the unified biothermokinetic theory of ATP synthesis developed in the previous two papers is applied to a major problem in comparative physiology, biochemistry, and ecology-that of metabolic scaling as a function of body mass across species. A clear distinction is made between intraspecific and interspecific relationships in energy metabolism, clearing up confusion that had existed from the very beginning since Kleiber first proposed his mouse-to-elephant rule almost a century ago. It is shown that the overall mass exponent of basal/standard metabolic rate in the allometric relationship [Formula: see text] is composed of two parts, one emerging from the relative intraspecific constancy of the slope (b), and the other (b') arising from the interspecific variation of the mass coefficient, a(M) with body size. Quantitative analysis is shown to reveal the hidden underlying relationship followed by the interspecific mass coefficient, a(M)=P0M0.10, and a universal value of P0=3.23 watts, W is derived from empirical data on mammals from mouse to cattle. The above relationship is shown to be understood only within an evolutionary biological context, and provides a physiological explanation for Cope's rule. The analysis also helps in fundamentally understanding how variability and a diversity of scaling exponents arises in allometric relations in biology and ecology. Next, a molecular-level understanding of the scaling of metabolism across mammalian species is shown to be obtained by consideration of the thermodynamic efficiency of ATP synthesis η, taking mitochondrial proton leak as a major determinant of basal metabolic rate in biosystems. An iterative solution is obtained by solving the mathematical equations of the biothermokinetic ATP theory, and the key thermodynamic parameters, e.g. the degree of coupling q, the operative P/O ratio, and the metabolic efficiency of ATP synthesis η are quantitatively evaluated for mammals from rat to cattle. Increases in η (by ∼15%) over a 2000-fold body size range from rat to cattle, primarily arising from an ∼3-fold decrease in the mitochondrial H+ leak rate are quantified by the unified ATP theory. Biochemical and mechanistic consequences for the interpretation of basal metabolism, and the various molecular implications arising are discussed in detail. The results are extended to maximum metabolic rate, and interpreted mathematically as a limiting case of the general ATP theory. The limitations of the analysis are pointed out. In sum, a comprehensive quantitative analysis based on the unified biothermokinetic theory of ATP synthesis is shown to solve a central problem in biology, physiology, and ecology on the scaling of energy metabolism with body size.

Polyphenol-Derived Carbonaceous Frameworks with Multiscale Porosity for High-Power Electrochemical Applications

With the escalating global demand for electric vehicles and sustainable energy solutions, increasing focus is placed on developing electrochemical systems that offer fast charging and high-power output, primarily governed by mass transport. Accordingly, porous carbons have emerged as highly promising electrochemically active or supporting materials due to expansive surface areas, tunable pore structures, and superior electrical conductivity, accelerating surface reaction. Yet, while substantial research has been devoted to crafting various porous carbons to increase specific surface areas, the optimal utilization of the surfaces remains underexplored. This review emphasizes the critical role of the fluid dynamics within multiscale porous carbonaceous electrodes, leading to substantially enhanced pore utilization in electrochemical systems. It elaborates on strategies of using sacrificial templates for incorporating meso/macropores into microporous carbon matrix, while exploiting the unique properties of polyphenol moieties such as sustainable carbons derived from biomass, inherent adhesive/cohesive interactions with template materials, and facile complexation capabilities with diverse materials, thereby enabling adaptive structural modulations. Furthermore, it explores how multiscale pore configurations influence pore-utilization efficiency, demonstrating advantages of incorporating multiscale pores. Finally, synergistic impact on the high-power electrochemical systems is examined, attributed to improved fluid-dynamic behavior within the carbonaceous frameworks, providing insights for advancing next-generation high-power electrochemical applications.

The Fastest Capillary Flow in Root-like Networks under Gravity

Capillary flow has garnered significant attention due to its unique dynamic characteristics that require no external force. Creating a quantitative analytical model to evaluate capillary flow behaviors in root-like networks is essential for enhancing fluid control properties in functional textiles. In this study, we explore the capillary dynamics within root-like networks under the influence of gravity and derive the most rapid capillary flow via structural optimization. The flow time in a capillary is dominated by the capillary pressure, viscous pressure loss, and gravity, each of which exhibits diverse sensitivities to the structures of root-like networks. We scrutinize various structural parameters to understand their impact on capillary flow in root-like networks. Subsequently, optimal structural parameters (namely, the mother tube diameter and diameter ratio) are identified to minimize capillary flow time. Moreover, we discovered that the correlation between flow time and distance for capillary flow in root-like networks does not obey the classical Lucas-Washburn equation. These results affirm that root-like networks can enhance capillary flow, providing critical insights for numerous capillary-flow-dependent engineering applications.

Unraveling power-law scaling through exponential cell division dynamics

A primary objective of biology is the development of universal laws that define how organic form develops and how it evolves as a function of size, both ontogenetically and across evolutionary time. Scaling theory has been essential in reaching this goal by giving a complete perspective point, particularly in illuminating the fundamental biological features produced within scaling exponents defining families of equations. Nonetheless, the theoretical basis of the allometric equation within scaling theory are inadequately explained, particularly when it comes to establishing links between micro-level processes at the cellular level and macro-level phenomena. We proposed an unlimited cell bipartition, resulting in an exponential growth in cell numbers during an individual's lifespan, to bridge this conceptual gap between cellular processes and allometric scaling. The power-law scaling between body mass and organ weight was produced by the synchronous exponential increments and the allometric exponent is rate of logarithmic cell proliferation rate. Substituting organ weight for erythrocyte weight aided in the development of a power-law scaling relationship between body mass and metabolic rate. Furthermore, it is critical to understand how cell size affects the exponent in power-law scaling. We find that a bigger exponent will result from an increase in the average weight of organ cells or a decrease in the average weight of all cells. Furthermore, cell proliferation dynamics showed a complex exponential scaling between body mass and longevity, defying the previously reported power-law scaling. We discovered a quadratic link between longevity and logarithmic body mass. Notably, all of the parameters included in these relationships are explained by indices linked to cell division and embryonic development. This research adds to our understanding of the complex interaction between cellular processes and overarching scaling phenomena in biology.

Dissipative scaling of development and aging in multicellular organisms

Evolution, self-replication and ontogenesis are highly dynamic, irreversible and self-organizing processes dissipating energy. While progress has been made to decipher the role of thermodynamics in cellular fission, it is not yet clear how entropic balances shape organism growth and aging. This paper derives a general dissipation theory for the life history of organisms. It implies a self-regulated energy dissipation facilitating exponential growth within a hierarchical and entropy lowering self-organization. The theory predicts ceilings in energy expenditures imposed by geometric constrains, which promote thermal optimality during development, and a dissipative scaling across organisms consistent with ecological scaling laws combining isometric and allometric terms. The theory also illustrates how growing organisms can tolerate damage through continuous extension and production of new dissipative structures low in entropy. However, when organisms reduce their rate of cell division and reach a steady adult state, they become thermodynamically unstable, increase internal entropy by accumulating damage, and age.

Metabolic scaling as an emergent outcome of variation in metabolic rate

The allometric scaling of metabolic rate and what drives it are major questions in biology with a long history. Since the metabolic rate at any level of biological organization is an emergent property of its lower-level constituents, it is an outcome of the intrinsic heterogeneity among these units and the interactions among them. However, the influence of lower-level heterogeneity on system-level metabolic rate is difficult to investigate, given the tightly integrated body plan of unitary organisms. In this context, social insects such as honeybees can serve as important model systems because unlike unitary organisms, these superorganisms can be taken apart and reassembled in different configurations to study metabolic rate and its various drivers at different levels of organization. This commentary discusses the background of such an approach and how combining it with artificial selection to generate heterogeneity in metabolic rate with an analytical framework to parse out the different mechanisms that contribute to the effects of heterogeneity can contribute to the various models of metabolic scaling. Finally, the absence of the typical allometric scaling relationship among different species of honeybees is discussed as an important prospect for deciphering the role of top-down ecological factors on metabolic scaling. This article is part of the theme issue 'The evolutionary significance of variation in metabolic rates'.

The scaling of elemental stoichiometry and growth rate over the course of bamboo ontogeny

Stoichiometric rules may explain the allometric scaling among biological traits and body size, a fundamental law of nature. However, testing the scaling of elemental stoichiometry and growth to size over the course of plant ontogeny is challenging. Here, we used a fast-growing bamboo species to examine how the concentrations and contents of carbon (C), nitrogen (N) and phosphorus (P), relative growth rate (G), and nutrient productivity scale with whole-plant mass (M) at the culm elongation and maturation stages. The whole-plant C content vs M and N content vs P content scaled isometrically, and the N or P content vs M scaled as a general 3/4 power function across both growth stages. The scaling exponents of G vs M and N (and P) productivity in newly grown mass vs M relationships across the whole growth stages decreased as a -1 power function. These findings reveal the previously undocumented generality of stoichiometric allometries over the course of plant ontogeny and provide new insights for understanding the origin of ubiquitous quarter-power scaling laws in the biosphere.

New ways for (in)validating the forest carbon neutrality hypothesis

Over 50 years ago, Eugene Odum postulated that mature or climax forests reside in carbon neutrality. As climate change rose to prominence in the international environmental agenda, the neutrality hypothesis transformed from an ecological principle to a justification for using forest management in combating climate change. Despite persistent efforts, Odum's neutrality hypothesis has resisted both confirmation and refutation. In this opinion we show the limitations of past efforts to (in)validate Odum's neutrality hypothesis and propose new research directions for the community to permit a more general confirmation or refutation with current and near-future observations. We then demonstrate such an approach by using metabolic theory to formulate testable predictions for the total sink strength considering soil, litter, and biomass of mature or climax forests based on observations of tree biomass and individual density. In doing so, we show that ecological theory can create additional relevant, testable hypotheses to provide timely support to decision-makers seeking to address one of the world's most pressing environmental challenges.

A Self-Similarity Logic May Shape the Organization of the Nervous System

From the morphological point of view, the nervous system exhibits a fractal, self-similar geometry at various levels of observations, from single cells up to cell networks. From the functional point of view, it is characterized by a hierarchical organization in which self-similar structures (networks) of different miniaturizations are nested within each other. In particular, neuronal networks, interconnected to form neuronal systems, are formed by neurons, which operate thanks to their molecular networks, mainly having proteins as components that via protein-protein interactions can be assembled in multimeric complexes working as micro-devices. On this basis, the term "self-similarity logic" was introduced to describe a nested organization where, at the various levels, almost the same rules (logic) to perform operations are used. Self-similarity and self-similarity logic both appear to be intimately linked to the biophysical evidence for the nervous system being a pattern-forming system that can flexibly switch from one coherent state to another. Thus, they can represent the key concepts to describe its complexity and its concerted, holistic behavior.

The Fractal Geometry of the Brain: AnOverview

The first chapter of this book introduces some history, philosophy, and basic concepts of fractal geometry and discusses how the neurosciences can benefit from applying computational fractal-based analysis. Further, it compares fractal with Euclidean approaches to analyzing and quantifying the brain in its entire physiopathological spectrum and presents an overview of the first section of this book as well.

Fractal Analysis in Clinical Neurosciences: An Overview

Over the last years, fractals have entered into the realms of clinical neurosciences. The whole brain and its components (i.e., neurons and astrocytes) have been studied as fractal objects, and even more relevant, the fractal-based quantification of the geometrical complexity of histopathological and neuroradiological images as well as neurophysiopathological time series has suggested the existence of a gradient in the pattern representation of neurological diseases. Computational fractal-based parameters have been suggested as potential diagnostic and prognostic biomarkers in different brain diseases, including brain tumors, neurodegeneration, epilepsy, demyelinating diseases, cerebrovascular malformations, and psychiatric disorders as well. This chapter and the entire third section of this book are focused on practical applications of computational fractal-based analysis into the clinical neurosciences, namely, neurology and neuropsychiatry, neuroradiology and neurosurgery, neuropathology, neuro-oncology and neurorehabilitation, neuro-ophthalmology, and cognitive neurosciences, with special emphasis on the translation of the fractal dimension and other fractal parameters as clinical biomarkers useful from bench to bedside.

A Nonlinear Dynamical View of Kleiber's Law on the Metabolism of Plants and Animals

Kleiber's empirical law, which describes that metabolism increases as the mass to the power 3/4, has arguably remained life sciences' enigma since its formal uncovering in 1930. Why is this behavior sustained over many orders of magnitude? There have been quantitative rationalizations put forward for both plants and animals based on realistic mechanisms. However, universality in scaling laws of this kind, like in critical phenomena, has not yet received substantiation. Here, we provide an account, with quantitative reproduction of the available data, of the metabolism for these two biology kingdoms by means of broad arguments based on statistical mechanics and nonlinear dynamics. We consider iterated renormalization group (RG) fixed-point maps that are associated with an extensive generalized (Tsallis) entropy. We find two unique universality classes that satisfy the 3/4 power law. One corresponds to preferential attachment processes-rich gets richer-and the other to critical processes that suppress the effort for motion. We discuss and generalize our findings to other empirical laws that exhibit similar situations, using data based on general but different concepts that form a conjugate pair that gives rise to the same power-law exponents.

Reference standard analysis of multiple new and old plasma clearance models and renal clearance with special attention to measurement of reduced glomerular filtration rate

Nine models were evaluated as candidate glomerular filtration rate (GFR) reference standards in three datasets using [51Cr(EDTA)]- or [169Yb(DTPA)]2- anions in 98 studies. Noncompartmental methods formed an upper limit for estimating mass excreted and voluntary urine collection formed a lower limit. For current models and methods, reduced GFR in adults resulted in inflated clearance estimates. Two different logarithmic models with exponential tails were created and may have underestimated reduced clearance. The logarithmic formulae can be used with only two plasma samples, and fit 13 multiple time-samples from 5 min to 24 h with an 8% standard deviation of residuals compared to 20% error for monoexponentials. For shorter times (4 or 5 h) the fit errors decreased but the ratio of errors remained at circa 2.5 times lesser for the logarithmic versus monoexponential models. Adaptively regularised gamma variate, Tk-GV, models that are well documented, but not in common use, were largely contained within the reference extreme values, were unbiased for different levels of clearance and were the only models to be uncorrelated to volume of distribution from mean residence time divided by weight. Using Tk-GV as a candidate reference standard, potentially better methods for routine clinical usage were discussed. Prospective clinical testing, and metabolic scaling of decreased renal function is advised for potential changes to patient triage.

A physiological approach to renal clearance: From premature neonates to adults

AIMS

We propose using glomerular filtration rate (GFR) as the physiological basis for distinguishing components of renal clearance.

METHODS

Gentamicin, amikacin and vancomycin are thought to be predominantly excreted by the kidneys. A mixed-effects joint model of the pharmacokinetics of these drugs was developed, with a wide dispersion of weight, age and serum creatinine. A dataset created from 18 sources resulted in 27,338 drug concentrations from 9,901 patients. Body size and composition, maturation and renal function were used to describe differences in drug clearance and volume of distribution.

RESULTS

This study demonstrates that GFR is a predictor of two distinct components of renal elimination clearance: (1) GFR clearance associated with normal GFR and (2) non-GFR clearance not associated with normal GFR. All three drugs had GFR clearance estimated as a drug-specific percentage of normal GFR (gentamicin 39%, amikacin 90% and vancomycin 57%). The total clearance (sum of GFR and non-GFR clearance), standardized to 70 kg total body mass, 176 cm, male, renal function 1, was 5.58 L/h (95% confidence interval [CI] 5.50-5.69) (gentamicin), 7.77 L/h (95% CI 7.26-8.19) (amikacin) and 4.70 L/h (95% CI 4.61-4.80) (vancomycin).

CONCLUSIONS

GFR provides a physiological basis for renal drug elimination. It has been used to distinguish two elimination components. This physiological approach has been applied to describe clearance and volume of distribution from premature neonates to elderly adults with a wide dispersion of size, body composition and renal function. Dose individualization has been implemented using target concentration intervention.

How and Why Does Metabolism Scale with Body Mass?

Most explanations for the relationship between body size and metabolism invoke physical constraints; such explanations are evolutionarily inert, limiting their predictive capacity. Contemporary approaches to metabolic rate and life history lack the pluralism of foundational work. Here, we call for reforging of the lost links between optimization approaches and physiology.

Comparing the spreading characteristics of monkeypox (MPX) and COVID-19: Insights from a quantitative model

Climate change is acknowledged to directly affect not only the environment, economy, and society but also the transmission dynamics of infectious diseases, thereby impacting public health. The recent experiences with the spread of SARS-CoV-2 and Monkeypox have highlighted the complex and interconnected nature of infectious diseases, which are strongly linked to various determinants of health. Considering these challenges, adopting a new vision such as the trans-disciplinary approach appears to be imperative. This paper proposes a new theory about viruses' spread, based on a biological model, accounting for the optimisation of energy and material resources for organisms' survival and reproduction in the environment. The approach applies Kleiber's law scaling theory, originally developed in biology, to model community dynamics in cities. A simple equation can be used to model pathogen spread without accounting for each species' physiology by leveraging the superlinear scaling of variables with population size. This general theory offers several advantages, including the ability to explain the rapid and surprising spread of both SARS-CoV-2 and Monkeypox. The proposed model shows similarities in the spreading processes of both viruses, based on the resulting scaling factors, and opens new avenues for research. By fostering cooperation and integrating knowledge from different disciplines to effectively tackle the multifaceted dimensions of disease outbreaks, we can work towards preventing future health emergencies.

The Pulmonary Vasculature

The pulmonary circulation is a low-pressure, low-resistance circuit whose primary function is to deliver deoxygenated blood to, and oxygenated blood from, the pulmonary capillary bed enabling gas exchange. The distribution of pulmonary blood flow is regulated by several factors including effects of vascular branching structure, large-scale forces related to gravity, and finer scale factors related to local control. Hypoxic pulmonary vasoconstriction is one such important regulatory mechanism. In the face of local hypoxia, vascular smooth muscle constriction of precapillary arterioles increases local resistance by up to 250%. This has the effect of diverting blood toward better oxygenated regions of the lung and optimizing ventilation-perfusion matching. However, in the face of global hypoxia, the net effect is an increase in pulmonary arterial pressure and vascular resistance. Pulmonary vascular resistance describes the flow-resistive properties of the pulmonary circulation and arises from both precapillary and postcapillary resistances. The pulmonary circulation is also distensible in response to an increase in transmural pressure and this distention, in addition to recruitment, moderates pulmonary arterial pressure and vascular resistance. This article reviews the physiology of the pulmonary vasculature and briefly discusses how this physiology is altered by common circumstances.

Scale in Language

A central concern of the cognitive science of language since its origins has been the concept of the linguistic system. Recent approaches to the system concept in language point to the exceedingly complex relations that hold between many kinds of interdependent systems, but it can be difficult to know how to proceed when "everything is connected." This paper offers a framework for tackling that challenge by identifying *scale* as a conceptual mooring for the interdisciplinary study of language systems. The paper begins by defining the scale concept-simply, the possibility for a measure to be larger or smaller in different instances of a system, such as a phonemic inventory, a word's frequency value in a corpus, or a speaker population. We review sites of scale difference in and across linguistic subsystems, drawing on findings from linguistic typology, grammatical description, morphosyntactic theory, psycholinguistics, computational corpus work, and social network demography. We consider possible explanations for scaling differences and constraints in language. We then turn to the question of *dependencies between* sites of scale difference in language, reviewing four sample domains of scale dependency: in phonological systems, across levels of grammatical structure (Menzerath's Law), in corpora (Zipf's Law and related issues), and in speaker population size. Finally, we consider the implications of the review, including the utility of a scale framework for generating new questions and inspiring methodological innovations and interdisciplinary collaborations in cognitive-scientific research on language.

Allometric relationships between stem diameter, height and crown area of associated trees of cocoa agroforests of Ghana

Allometric models which are used to describe the structure of trees in agroforestry systems are usually extrapolated from models developed for trees in forest ecosystems. This makes quantitative assessment of the functions of shade trees in agroforestry systems challenging since increased availability of light and space in these systems may induce structural differences from those growing under forest conditions. We addressed this issue by providing species-specific allometric information on the structural characteristics of associated shade trees on cocoa agroforestry systems and assessed if allometries conformed to theoretical predictions. At the plot level, stand and soil characteristics affecting tree structural characteristics were assessed. The study was conducted in cocoa agroforestry systems at Suhum, Ghana. The height-diameter at breast height (H-DBH) allometry had the best fits (R2 = 53-89%), followed by the crown area (CA)-DBH allometry (R2 = 27-87%) and then the CA-H allometry (R2 = 22-73%). In general, the scaling exponents of the CA-DBH, H-CA and H-DBH allometries conformed to the metabolic scaling theory (MST). However, both the CA-DBH and H-DBH allometries diverged from the geometric similarity model. Though forest tree species had similar crown areas as fruit trees, they were slenderer than fruit trees. Tree slenderness coefficients were positively correlated with soil P, Ca, Cu and the ratios (Ca + Mg):K, (Ca + Mg):(K + Na) and Ca:Mg, but not C:N while DBH and H were correlated with soil P and C:N ratio. Our results show that critical soil nutrients and their ratios affects shade tree structural attributes (e.g. slenderness and CA), which possibly restrict variations in species-specific allometries to a narrow range on cocoa systems. Furthermore, shade tree species richness and density are better predictors of relative canopy projection area (a proxy for shade intensity) than tree species diversity. In conclusion, the results have implications for shade tree species selection, monitoring of woody biomass and maintenance of biodiversity.

Scale-free dynamics of COVID-19 in a Brazilian city

A common basis to address the dynamics of directly transmitted infectious diseases, such as COVID-19, are compartmental (or SIR) models. SIR models typically assume homogenous population mixing, a simplification that is convenient but unrealistic. Here we validate an existing model of a scale-free fractal infection process using high-resolution data on COVID-19 spread in São Caetano, Brazil. We find that transmission can be described by a network in which each infectious individual has a small number of susceptible contacts, of the order of 2-5. This model parameter correlated tightly with physical distancing measured by mobile phone data, such that in periods of greater distancing the model recovered a lower average number of contacts, and vice versa. We show that the SIR model is a special case of our scale-free fractal process model in which the parameter that reflects population structure is set at unity, indicating homogeneous mixing. Our more general framework better explained the dynamics of COVID-19 in São Caetano, used fewer parameters than a standard SIR model and accounted for geographically localized clusters of disease. Our model requires further validation in other locations and with other directly transmitted infectious agents.

The Relevance of Time in Biological Scaling

Various phenotypic traits relate to the size of a living system in regular but often disproportionate (allometric) ways. These "biological scaling" relationships have been studied by biologists for over a century, but their causes remain hotly debated. Here, I focus on the patterns and possible causes of the body-mass scaling of the rates/durations of various biological processes and life-history events, i.e., the "pace of life". Many biologists have regarded the rate of metabolism or energy use as the master driver of the "pace of life" and its scaling with body size. Although this "energy perspective" has provided valuable insight, here I argue that a "time perspective" may be equally or even more important. I evaluate various major ways that time may be relevant in biological scaling, including as (1) an independent "fourth dimension" in biological dimensional analyses, (2) a universal "biological clock" that synchronizes various biological rates/durations, (3) a scaling method that uses various biological time periods (allochrony) as scaling metrics, rather than various measures of physical size (allometry), as traditionally performed, (4) an ultimate body-size-related constraint on the rates/timing of biological processes/events that is set by the inevitability of death, and (5) a geological "deep time" approach for viewing the evolution of biological scaling patterns. Although previously proposed universal four-dimensional space-time and "biological clock" views of biological scaling are problematic, novel approaches using allochronic analyses and time perspectives based on size-related rates of individual mortality and species origination/extinction may provide new valuable insights.

An interactive deep learning-based approach reveals mitochondrial cristae topologies

The convolution of membranes called cristae is a critical structural and functional feature of mitochondria. Crista structure is highly diverse between different cell types, reflecting their role in metabolic adaptation. However, their precise three-dimensional (3D) arrangement requires volumetric analysis of serial electron microscopy and has therefore been limiting for unbiased quantitative assessment. Here, we developed a novel, publicly available, deep learning (DL)-based image analysis platform called Python-based human-in-the-loop workflow (PHILOW) implemented with a human-in-the-loop (HITL) algorithm. Analysis of dense, large, and isotropic volumes of focused ion beam-scanning electron microscopy (FIB-SEM) using PHILOW reveals the complex 3D nanostructure of both inner and outer mitochondrial membranes and provides deep, quantitative, structural features of cristae in a large number of individual mitochondria. This nanometer-scale analysis in micrometer-scale cellular contexts uncovers fundamental parameters of cristae, such as total surface area, orientation, tubular/lamellar cristae ratio, and crista junction density in individual mitochondria. Unbiased clustering analysis of our structural data unraveled a new function for the dynamin-related GTPase Optic Atrophy 1 (OPA1) in regulating the balance between lamellar versus tubular cristae subdomains.

Fractal-like geometry as an evolutionary response to predation?

Fractal-like, intricate morphologies are known to exhibit beneficial mechanical behavior in various engineering and technological domains. The evolution of fractal-like, internal walls of ammonoid cephalopod shells represent one of the most clear evolutionary trends toward complexity in biology, but the driver behind their iterative evolution has remained unanswered since the first hypotheses introduced in the early 1800s. We show a clear correlation between the fractal-like morphology and structural stability. Using linear and nonlinear computational mechanical simulations, we demonstrate that the increase in the complexity of septal geometry leads to a substantial increase in the mechanical stability of the entire shell. We hypothesize that the observed tendency is a driving force toward the evolution of the higher complexity of ammonoid septa, providing the animals with superior structural support and protection against predation. Resolving the adaptational value of this unique trait is vital to fully comprehend the intricate evolutionary trends between morphology, ecological shifts, and mass extinctions through Earth's history.

Toward a cohesive understanding of ecological complexity

Ecological systems are quintessentially complex systems. Understanding and being able to predict phenomena typical of complex systems is, therefore, critical to progress in ecology and conservation amidst escalating global environmental change. However, myriad definitions of complexity and excessive reliance on conventional scientific approaches hamper conceptual advances and synthesis. Ecological complexity may be better understood by following the solid theoretical basis of complex system science (CSS). We review features of ecological systems described within CSS and conduct bibliometric and text mining analyses to characterize articles that refer to ecological complexity. Our analyses demonstrate that the study of complexity in ecology is a highly heterogeneous, global endeavor that is only weakly related to CSS. Current research trends are typically organized around basic theory, scaling, and macroecology. We leverage our review and the generalities identified in our analyses to suggest a more coherent and cohesive way forward in the study of complexity in ecology.

Declining metabolic scaling parallels an ontogenetic change from elongate to deep-bodied shapes in juvenile Brown trout

Body shape and metabolic rate can be important determinants of animal performance, yet often their effects on influential traits are evaluated in a non-integrated way. This creates an important gap because the integration between shape and metabolism may be crucial to evaluate metabolic scaling theories. Here, we measured standard metabolic rate in 1- and 2-years old juvenile brown trout Salmo trutta, and used a geometric morphometrics approach to extricate the effects of ontogeny and size on the link between shape and metabolic scaling. We evidenced near-isometric ontogenetic scaling of metabolic rate with size, but also a biphasic pattern driven by a significant change in metabolic scaling, from positive to negative allometry. Moreover, the change in metabolic allometry parallels an ontogenetic change from elongate to deep-bodied shapes. This is consistent with the dynamic energy budget (DEB) and surface area (SA) theories, but not with the resource transport network theory which predicts increasing allometric exponents for trends towards more robust, three-dimensional bodies. In addition, we found a relationship between body shape and size independent metabolic rate, with a positive correlation between robustness and metabolic rate, which fits well within the view of Pace-of-Life Syndromes (POLS). Finally, our results align with previous studies that question the universality of metabolic scaling exponents and propose other mechanistic models explaining the diversity of metabolic scaling relationships or emphasizing the potential contribution of ecological factors.

The fractal brain: scale-invariance in structure and dynamics

The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.

Vascularized organ bioprinting: From strategy to paradigm

Over the past two decades, bioprinting has become a popular research topic worldwide, as it is the most promising approach for manufacturing vascularized organ in vitro. However, transitioning bioprinting from simple tissue models to real biomedical applications is still a challenge due to the lack of interdisciplinary theoretical knowledge and perfect multitechnology integration. This review examines the goals of vasculature manufacturing and proposes the objectives in three stages. We then outline a bidirectional manufacturing strategy consisting of top-down reproduction (bioprinting) and bottom-up regeneration (cellular behaviour). We also provide an in-depth analysis of the views from the four aspects of design, ink, printing, and culture. Furthermore, we present the 'constructing-comprehension cycle' research paradigm in Strategic Priority Research Program and the 'math-model-based batch insights generator' research paradigm for the future, which have the potential to revolutionize the biomedical field.

Mechanical analogue for cities

Motivated from the increasing need to develop a science-based, predictive understanding of the dynamics and response of cities when subjected to natural hazards, in this paper, we apply concepts from statistical mechanics and microrheology to develop mechanical analogues for cities with predictive capabilities. We envision a city to be a matrix where cell-phone users are driven by the city's economy and other incentives while using the collection of its infrastructure networks in a similar way that thermally driven Brownian particles are moving within a complex viscoelastic material. Mean-square displacements of thousands of cell-phone users are computed from GPS location data to establish the creep compliance and the resulting impulse response function of a city. The derivation of these time-response functions allows the synthesis of simple mechanical analogues that model satisfactorily the city's behaviour under normal conditions. Our study concentrates on predicting the response of cities to acute shocks (natural hazards) that are approximated with a rectangular pulse; and we show that the derived solid-like mechanical networks predict that cities revert immediately to their pre-event response suggesting an inherent resilience. Our findings are in remarkable good agreement with the recorded response of the Dallas metroplex following the February 2021 North American winter storm.

Empirical parameterisation and dynamical analysis of the allometric Rosenzweig-MacArthur equations

Allometric settings of population dynamics models are appealing due to their parsimonious nature and broad utility when studying system level effects. Here, we parameterise the size-scaled Rosenzweig-MacArthur differential equations to eliminate prey-mass dependency, facilitating an in depth analytic study of the equations which incorporates scaling parameters' contributions to coexistence. We define the functional response term to match empirical findings, and examine situations where metabolic theory derivations and observation diverge. The dynamical properties of the Rosenzweig-MacArthur system, encompassing the distribution of size-abundance equilibria, the scaling of period and amplitude of population cycling, and relationships between predator and prey abundances, are consistent with empirical observation. Our parameterisation is an accurate minimal model across 15+ orders of mass magnitude.

A Physiological-Based Pharmacokinetic Model Embedded with a Target-Mediated Drug Disposition Mechanism Can Characterize Single-Dose Warfarin Pharmacokinetic Profiles in Subjects with Various CYP2C9 Genotypes under Different Cotreatments

Warfarin, a commonly prescribed oral anticoagulant medication, is highly effective in treating deep vein thrombosis and pulmonary embolism. However, the clinical dosing of warfarin is complicated by high interindividual variability in drug exposure and response and its narrow therapeutic index. CYP2C9 genetic polymorphism and drug-drug interactions (DDIs) are substantial contributors to this high variability of warfarin pharmacokinetics (PK), among numerous factors. Building a physiology-based pharmacokinetic (PBPK) model for warfarin is not only critical for a mechanistic characterization of warfarin PK but also useful for investigating the complicated dose-exposure relationship of warfarin. Thus, the objective of this study was to develop a PBPK model for warfarin that integrates information regarding CYP2C9 genetic polymorphisms and their impact on DDIs. Generic PBPK models for both S- and R-warfarin, the two enantiomers of warfarin, were constructed in R with the mrgsolve package. As expected, a generic PBPK model structure did not adequately characterize the warfarin PK profile collected up to 15 days following the administration of a single oral dose of warfarin, especially for S-warfarin. However, following the integration of an empirical target-mediated drug disposition (TMDD) component, the PBPK-TMDD model well characterized the PK profiles collected for both S- and R-warfarin in subjects with different CYP2C9 genotypes. Following the integration of enzyme inhibition and induction effects, the PBPK-TMDD model also characterized the PK profiles of both S- and R-warfarin in various DDI settings. The developed mathematic framework may be useful in building algorithms to better inform the clinical dosing of warfarin. SIGNIFICANCE STATEMENT: The present study found that a traditional physiology-based pharmacokinetic (PBPK) model cannot sufficiently characterize the pharmacokinetic profiles of warfarin enantiomers when warfarin is administered as a single dose, but a PBPK model with a target-mediated drug disposition mechanism can. After incorporating CYP2C9 genotypes and drug-drug interaction information, the developed model is anticipated to facilitate the understanding of warfarin disposition in subjects with different CYP2C9 genotypes in the absence and presence of both cytochrome P450 inhibitors and cytochrome P450 inducers.

Population pharmacokinetic and pharmacodynamic model of propofol externally validated in Korean elderly subjects

The Eleveld propofol pharmacokinetic (PK) model, which was developed based on a broad range of populations, showed greater bias (- 27%) in elderly subjects in a previous validation study conducted by Vellinga and colleagues. We aimed to develop and externally validate a new PK-pharmacodynamic (PK-PD) model of propofol for elderly subjects. A population PK-PD model was constructed using propofol plasma concentrations and bispectral index (BIS) values that were obtained from 31 subjects aged 65 years older in previously published phase I studies. The predictive performance of the newly-developed PK-PD model (Choi model) was assessed in a separate Korean elderly population and compared with that of the Eleveld model. A three-compartment mammillary model using an allometric expression and a sigmoid E_max model well-described the time courses of propofol concentrations and BIS values. The V₁, V₂, V₃, Cl, Q₁, Q₂, E₀, E_max, Ce₅₀, γ, and k_e0 of a 60-kg subject were 8.36, 58.0, 650 L, 1.26, 0.917, 0.669 L/min, 92.1, 18.7, 2.21 μg/mL, 2.89, and 0.138 /min, respectively. In the Choi model and Eleveld model, pooled biases (95% CI) of the propofol concentration were 7.78 ( 3.09-12.49) and 16.70 (9.46-23.93) and pooled inaccuracies were 22.84 (18.87-26.81) and 24.85 (18.07-31.63), respectively. The Choi PK model was less biased than the Eleveld PK model in Korean elderly subjects (age range: 65.0-79.0 yr; weight range: 45.0-75.3 kg). Our results suggest that the Choi PK model, particularly, is applicable to target-controlled infusion in non-obese Korean elderly subjects.

Allometric scaling relationships in mouse placenta

Fetal growth and maturation are highly intertwined with placental development during pregnancy. Here we used placental vascular morphology measurements (depth and span) as well as the umbilical artery (UA) diameter of previously published studies on three different mouse strains (C57BL6/J, CD-1 and BALB/c), which were exposed to different conditions (combination antiretroviral therapy, chronic maternal hypoxia and malaria infection) at different embryonic days, to test the hypothesis that placental vascularization and specifically the UA size affect conceptus weight. Interaction of each study parameter with embryonic day, strain and exposure to treatments are studied to investigate the stability of the scaling relationships across and/or within strains and conditions. In addition, the effect of UA diameter on the placental growth measurements (depth and span) is studied. These results show that the power-law scaling relationship of conceptus weight and placental depth with the UA diameter is conserved across strains and conditions with the scaling exponent of approximately 3/8 and 5/8, respectively. By contrast, the relationship between conceptus weight and either the placental span or depth is different between strains and conditions, suggesting multiple mechanisms of vascular adaptation.

Flow similarity, stochastic branching, and quarter-power scaling in plants

The origin of allometric scaling patterns that are multiples of one-fourth has long fascinated biologists. While not universal, quarter-power scaling relationships are common and have been described in all major clades. Several models have been advanced to explain the origin of such patterns, but questions regarding the discordance between model predictions and empirical data have limited their widespread acceptance. Notable among these is a fractal branching model that predicts power-law scaling of both metabolism and physical dimensions. While a power law is a useful first approximation to some data sets, nonlinear data compilations suggest the possibility of alternative mechanisms. Here, we show that quarter-power scaling can be derived using only the preservation of volume flow rate and velocity as model constraints. Applying our model to land plants, we show that incorporating biomechanical principles and allowing different parts of plant branching networks to be optimized to serve different functions predicts nonlinearity in allometric relationships and helps explain why interspecific scaling exponents covary along a fractal continuum. We also demonstrate that while branching may be a stochastic process, due to the conservation of volume, data may still be consistent with the expectations for a fractal network when one examines sub-trees within a tree. Data from numerous sources at the level of plant shoots, stems, and petioles show strong agreement with our model predictions. This theoretical framework provides an easily testable alternative to current general models of plant metabolic allometry.

Comparison of fractal and grid electrodes for studying the effects of spatial confinement on dissociated retinal neuronal and glial behavior

Understanding the impact of the geometry and material composition of electrodes on the survival and behavior of retinal cells is of importance for both fundamental cell studies and neuromodulation applications. We investigate how dissociated retinal cells from C57BL/6J mice interact with electrodes made of vertically-aligned carbon nanotubes grown on silicon dioxide substrates. We compare electrodes with different degrees of spatial confinement, specifically fractal and grid electrodes featuring connected and disconnected gaps between the electrodes, respectively. For both electrodes, we find that neuron processes predominantly accumulate on the electrode rather than the gap surfaces and that this behavior is strongest for the grid electrodes. However, the 'closed' character of the grid electrode gaps inhibits glia from covering the gap surfaces. This lack of glial coverage for the grids is expected to have long-term detrimental effects on neuronal survival and electrical activity. In contrast, the interconnected gaps within the fractal electrodes promote glial coverage. We describe the differing cell responses to the two electrodes and hypothesize that there is an optimal geometry that maximizes the positive response of both neurons and glia when interacting with electrodes.