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Cellular networks realize their functions by integrating intricate information embedded within local structures such as regulatory paths and feedback loops. However, the precise mechanisms of how local topologies determine global network dynamics and induce bifurcations remain unidentified. A critical step in unraveling the integration is to identify the governing principles, which underlie the mechanisms of information flow. Here, we develop the cumulative linearized approximation (CLA) algorithm to address this issue. Based on perturbation analysis and network decomposition, we theoretically demonstrate how perturbations affect the equilibrium variations through the integration of all regulatory paths and how stability of the equilibria is determined by distinct feedback loops. Two illustrative examples, i.e., a three-variable bistable system and a more intricate epithelial-mesenchymal transition (EMT) network, are chosen to validate the feasibility of this approach. These results establish a solid foundation for understanding information flow across cellular networks, highlighting the critical roles of local topologies in determining global network dynamics and the emergence of bifurcations within these networks. This work introduces a novel framework for investigating the general relationship between local topologies and global dynamics of cellular networks under perturbations., Competing Interests: Competing interests The authors declare no competing interests., (© 2024. The Author(s).)

"The Strategy of Model Building in Population Biology" published by Richard Levins in 1966 has been cited over 2500 times. For a paper concerned with modeling approaches in population biology a surprisingly large part of the attention. The Strategy received comes from history and philosophy of biology, and specifically from accounts on model and model formulation. The Strategy is an unusual paper; it presents neither new data nor a new formal model; at times it reads like a manifesto for some modeling approach, without specifying which broader program that approach intends to support. When these peculiarities of The Strategy are even mentioned, the philosophical literature tends to explain them away by invoking Levins' Marxist commitments. In contrast, I argue that those peculiarities can be explained by examining the programmatic purpose of the paper; starting from his doctoral work, Levins was trying to establish a research program meant to account for the relations between fitness and environment in different terms than the prevalent lock-and-key view. My paper brings that program back to the discussion, explains its relation to competing approaches and examines Levins' approach to modeling in light of that context., (© 2024. The Author(s).)

The objectives of this study were to expand and implement a Computational Fluid Dynamics (CFD)-Dissolution, Absorption and Clearance (DAC)-Pharmacokinetics (PK) multi-physics modeling framework for simulating the transport of suspension-based nasal corticosteroid sprays. The mean CFD-predicted peak plasma concentration (C max ) and area under the curve (AUC) of the plasma concentration-time profile, based on three representative nasal airway models (capturing low, medium and high posterior spray deposition), were within one standard deviation of available in vivo PK data for a representative corticosteroid drug (triamcinolone acetonide). The relative differences in mean C max between predictions and in vivo data for low dose (110 µg) and high dose (220 µg) cases were 27.8% and 10.1%, respectively. The models confirmed the dose-dependent dissolution-limited behavior of nasally delivered triamcinolone acetonide observed in available in vivo data. The total uptake from the nasal cavity decreased from 68.3% to 51.3% for the medium deposition model as dose was increased from 110 to 220 µg due to concentration-limited dissolution. The modeling framework is envisioned to facilitate faster development and testing of generic locally acting suspension nasal spray products due to its ability to predict the impact of differences in spray characteristics and patient use parameters on systemic PK., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)

This paper employed a physiologically based pharmacokinetic model (PBPK) to investigate the transformations of folic acid and its metabolites in vivo. Additionally, an ultra-performance liquid chromatography (UPLC) method was developed to accurately measure the body's retention rate and conversion rate of folic acid, tetrahydrofolate, and 5-methyltetrahydrofolate. Furthermore, the bioavailability of folic acid in the body was assessed by combining this method with an evaluation technique for animal models. The study found that the gastric metabolism time was 2 h, while the small intestinal metabolism duration was 4 h. The maximum conversion rate was observed in plasma and liver after 6 h, and in the brain after 8 h. This serves as a framework for creating a model to assess the bioavailability of folic acid in living organisms, to enhance the safety and efficacy of folic acid intake., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

Musculoskeletal simulations are a useful tool for improving our understanding of the human body. However, the physiological validity of predicted kinematics and forces is highly dependent upon the correct calibration of muscle parameters and the structural integrity of a model's internal skeletal structure. In this study, we show how ill-tuned muscle parameters and unphysiological deformations of a model's skeletal structure can be detected by using muscle elements as sensors with which modelling and parameterization inconsistencies can be identified through muscle and tendon strain injury assessment. To illustrate our approach, two modelling issues were recreated. First, a model repositioning simulation using the THUMS AM50 occupant model version 5.03 was performed to show how internal model deformations can occur during a change of model posture. Second, the muscle material parameters of the OpenSim gait2354 model were varied to illustrate how unphysiological muscle forces can arise if material parameters are inadequately calibrated. The simulations were assessed for muscle and tendon strain injuries using previously published injury criteria and a newly developed method to determine tendon strain injury threshold values. Muscle strain injuries in the left and right musculus pronator teres were detected during the model repositioning. This straining was caused by an unphysiologically large gap (12.92 mm) that had formed in the elbow joint. Similarly, muscle and tendon strain injuries were detected in the modified right-hand musculus gastrocnemius medialis of the gait2354 model where an unphysiological reduction of the tendon slack length introduced large pre-strain of the muscle-tendon unit. The results of this work show that the proposed method can quantify the internal distortion behaviour of musculoskeletal human body models and the plausibility of Hill-type muscle parameter choice via strain injury assessment. Furthermore, we highlight possible actions to avoid the presented issues and inconsistencies in literature data concerning the material characteristics of human tendons., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Nölle et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

This study presents a stochastic model of seed dispersal based on a branching random walk (BRW) framework, incorporating both homogeneous and non-homogeneous Poisson point processes (PPP). Building on the model introduced by Coletti et al. (2023), we examine the effects of habitat reduction on seed dispersal dynamics. We analyze the phase transition behavior of the BRW model under varying conditions of habitat fragmentation, focusing on how these conditions influence the critical dispersal rate. Specifically, we study a BRW on the real line with a non-homogeneous PPP driven by a log-normal density, constrained between spatial barriers. Our simulations localize the critical dispersal rate with respect to barrier positions and compare this dependence between homogeneous and non-homogeneous models., Competing Interests: Declarations Competing of Interest The author declares no competing interests., (© 2024. The Author(s), under exclusive licence to Springer Nature B.V.)

Chronic spontaneous urticaria (CSU) is a typical example of an intractable skin disease with no clear cause and significantly affects daily life of patients. Because CSU is a human-specific disease and lacks proper animal model, there are many questions regarding its pathophysiological dynamics. On the other hand, most clinical symptoms of urticaria are notable as dynamic appearance of skin eruptions called wheals. In this study, we explored dynamics of wheal by dividing it into three phases using a mathematical model: onset, development, and disappearance. Our results suggest that CSU onset is critically associated with endovascular dynamics triggered by basophils positive feedback. In contrast, the development phase is regulated by mast cell dynamics via vascular gap formation. We also suggest a disappearance mechanism of skin eruptions in CSU through an extension of the mathematical model using qualitative and quantitative comparisons of wheal expansion data of real patients with urticaria. Our results suggest that the wheal dynamics of the three phases and CSU development are hierarchically related to endovascular and extravascular pathophysiological networks., Competing Interests: Declarations Code availability Numerical code is made available online on GitHub (https://github.com/seirin-lee/urticaria-code) and all other data are available from the corresponding author (SSL) on reasonable request. Conflict of interest The authors declare no Conflict of interest., (© 2024. The Author(s).)

In recent years, the micro air vehicle (MAV) oscillations caused by thrust imbalances have received more attention. This paper proposes a dual-wing thrust balance model (DTBM) that can solve the above problem by iterating the modified rotation angle formula. The core control parameter of the DTBM model is the au angle, which refers to the angle between the wing surface and the stroke plane at the mid-stroke position during the upstroke. For each degree change in the au angle, the range of variation in the dimensionless average thrust coefficient is between 0.0225-0.0268. A thrust coefficient of 0.0225 causes the dragonfly to move forward by 9.037 cm in one second, which is equivalent to 1.29 times its body length. By using DTBM, the average thrust coefficient can be reduced to below 0.001 in just a few iterations. No matter how complex the motion pattern is, the DTBM can achieve thrust balance within 0.278 s. Through our research, when selecting the deviation angle motion of real dragonflies, the dual-wing au angles exhibit a highly linear correlation with wing spacing, called linear motion. In contrast, the nonlinear variation of the au angle appears in the hindwing of the no-deviation motion and the forewing of the elliptical deviation motion. All of the nonlinear changes are referred to as nonlinear motion. Nonlinear variation of the au angle arises from larger disturbances of the lateral force during the upstroke. The stronger lateral force is closely related to the flapping trajectory. When the flapping trajectory causes the dual-wing to closely approach each other in the mid-stroke, a continuous positive pressure zone forms between the dual-wing. The collision of the leading-edge vortex and the shedding of the trailing-edge vortex is the special flow field structure in the nonlinear motion. Guided by the DTBM, future designs of MAVs will be able to better achieve thrust balance during hovering flight, requiring only the embedding of the iteration algorithm and prediction function of the DTBM in the internal chip., (© 2024 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.)

This paper is devoted to the study of optimal release strategies to control vector-borne diseases, such as dengue, Zika, chikungunya and malaria. Two techniques are considered: the sterile insect one (SIT), which consists in releasing sterilized males among wild vectors in order to perturb their reproduction, and the Wolbachia one (presently used mainly for mosquitoes), which consists in releasing vectors, that are infected with a bacterium limiting their vectorial capacity, in order to replace the wild population by one with reduced vectorial capacity. In each case, the time dynamics of the vector population is modeled by a system of ordinary differential equations in which the releases are represented by linear combinations of Dirac measures with positive coefficients determining their intensity. We introduce optimal control problems that we solve numerically using ad-hoc algorithms, based on writing first-order optimality conditions characterizing the best combination of Dirac measures. We then discuss the results obtained, focusing in particular on the complexity and efficiency of optimal controls and comparing the strategies obtained. Mathematical modeling can help testing a great number of scenarios that are potentially interesting in future interventions (even those that are orthogonal to the present strategies) but that would be hard, costly or even impossible to test in the field in present conditions., Competing Interests: Declarations Conflict of interest The authors have no conflict of interest to declare that are relevant to the content of this article., (© 2024. The Author(s).)

Cells can compensate a disruptive change in one ion channel by compensatory changes in other channels. We have simulated the adaptation of a multicellular aggregate of non-excitable cells to the electrophysiological perturbation produced by the external blocking of a cation channel. In the biophysical model employed, we consider that this blocking provokes a cell depolarization that opens a voltage-gated calcium channel, thus allowing toxic Ca 2+ levels. The cell adaptation to this externally-induced perturbation is ascribed to the multiplicity of channels available to keep the cell membrane potential within a physiological window. We propose that the cell depolarization provokes the upregulated expression of a compensatory channel protein that resets the cell potential to the correct polarized value, which prevents the calcium entry. To this end, we use two different simulation algorithms based on deterministic and stochastic methods. The simulations suggest that because of the local correlations coupling the cell potential to transcription, short-term bioelectrical perturbations can trigger long-term biochemical adaptations to novel stressors in multicellular aggregates. Previous experimental data on planarian flatworms' adaptation to a barium-containing environment is also discussed., Competing Interests: Competing interests M.L. is cofounder of the company Morphoceuticals Inc., which operates in the regenerative medicine and hopes to do regeneration by bioelectric technology. The authors declare no other competing interests., (© 2024. The Author(s).)

Petri nets are commonly applied in modeling biological systems. However, construction of a Petri net model for complex biological systems is often time consuming, and requires expertise in the research area, limiting their application. To address this challenge, we developed GINtoSPN, an R package that automates the conversion of multi-omics molecular interaction network extracted from the Global Integrative Network (GIN) into Petri nets in GraphML format. These GraphML files can be directly used for Signaling Petri Net (SPN) simulation. To demonstrate the utility of this tool, we built a Petri net model for neurofibromatosis type I. Simulation of NF1 gene knockout, compared to normal skin fibroblast cells, revealed persistent accumulation of Ras-GTPs as expected. Additionally, we identified several other genes substantially affected by the loss of NF1's function, exhibiting individual-specific variability. These results highlight the effectiveness of GINtoSPN in streamlining the modeling and simulation of complex biological systems., (© 2024. The Author(s).)

There is growing empirical evidence that animal movement patterns depend on population density. We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of diffusion at low density. For sufficiently large low-density diffusion, the wave propagates at a speed predicted by a simple linear analysis. For small or zero low-density diffusion, the linear analysis is not sufficient, but a variational approach yields exact or approximate expressions for the speed and shape of population fronts., (© 2024. The Author(s).)

A dynamical system obtains a wide variety of kinetic realizations, which is advantageous for the analysis of biochemical systems. A reaction network, derived from a dynamical system, may or may not possess some properties needed for a thorough analysis. We improve and extend the work of Johnston and Hong et al. on network translations to network transformations, where the network is modified while preserving the dynamical system. These transformations can shrink, extend, or retain the stoichiometric subspace. Here, we show that a positive dependent network can be translated to a weakly reversible network. Using the kinetic realizations of (1) calcium signaling in the olfactory system and (2) metabolic insulin signaling, we demonstrate the benefits of transformed systems with positive deficiency for analyzing biochemical systems. Furthermore, we present an algorithm for a network transformation of a weakly reversible non-complex factorizable kinetic (NFK) system to a weakly reversible complex factorizable kinetic (CFK) system, thereby enhancing the Subspace Coincidence Theorem for NFK systems of Nazareno et al. Finally, using the transformed kinetic realization of monolignol biosynthesis in Populus xylem, we study the structural and kinetic properties of transformed systems, including the invariance of concordance and variation of injectivity and mono-/multi-stationarity under network transformation., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Ecosystems with a large number of species are often modelled as Lotka-Volterra dynamical systems built around a large interaction matrix with random part. Under some known conditions, a global equilibrium exists and is unique. In this article, we rigorously study its statistical properties in the large dimensional regime. Such an equilibrium vector is known to be the solution of a so-called Linear Complementarity Problem. We describe its statistical properties by designing an Approximate Message Passing (AMP) algorithm, a technique that has recently aroused an intense research effort in the fields of statistical physics, machine learning, or communication theory. Interaction matrices based on the Gaussian Orthogonal Ensemble, or following a Wishart distribution are considered. Beyond these models, the AMP approach developed in this article has the potential to describe the statistical properties of equilibria associated to more involved interaction matrix models., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

In recent years, multi-cellular models, where cells are represented as individual interacting entities, are becoming ever popular. This has led to a proliferation of novel methods and simulation tools. The first aim of this paper is to review the numerical methods utilised by multi-cellular modelling tools and to demonstrate which numerical methods are appropriate for simulations of tissue and organ development, maintenance, and disease. The second aim is to introduce an adaptive time-stepping algorithm and to demonstrate it's efficiency and accuracy. We focus on off-lattice, mechanics based, models where cell movement is defined by a series of first order ordinary differential equations, derived by assuming over-damped motion and balancing forces. We see that many numerical methods have been used, ranging from simple Forward Euler approaches through to higher order single-step methods like Runge-Kutta 4 and multi-step methods like Adams-Bashforth 2. Through a series of exemplar multi-cellular simulations, we see that if: care is taken to have events (births deaths and re-meshing/re-arrangements) occur on common time-steps; and boundaries are imposed on all sub-steps of numerical methods or implemented using forces, then all numerical methods can converge with the correct order. We introduce an adaptive time-stepping method and demonstrate that the best compromise between L ∞ error and run-time is to use Runge-Kutta 4 with an increased time-step and moderate adaptivity. We see that a judicious choice of numerical method can speed the simulation up by a factor of 10-60 from the Forward Euler methods seen in Osborne et al. (2017), and a further speed up by a factor of 4 can be achieved by using an adaptive time-step., Competing Interests: Declaration of competing interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: James M. Osborne reports financial support was provided by Australian Research Council. The funders had no influence in the construction or findings of this study., (Copyright © 2024 The Author. Published by Elsevier Ltd.. All rights reserved.)

In vivo observations show that oxygen levels in tumours can fluctuate on fast and slow timescales. As a result, cancer cells can be periodically exposed to pathologically low oxygen levels; a phenomenon known as cyclic hypoxia. Yet, little is known about the response and adaptation of cancer cells to cyclic, rather than, constant hypoxia. Further, existing in vitro models of cyclic hypoxia fail to capture the complex and heterogeneous oxygen dynamics of tumours growing in vivo. Mathematical models can help to overcome current experimental limitations and, in so doing, offer new insights into the biology of tumour cyclic hypoxia by predicting cell responses to a wide range of cyclic dynamics. We develop an individual-based model to investigate how cell cycle progression and cell fate determination of cancer cells are altered following exposure to cyclic hypoxia. Our model can simulate standard in vitro experiments, such as clonogenic assays and cell cycle experiments, allowing for efficient screening of cell responses under a wide range of cyclic hypoxia conditions. Simulation results show that the same cell line can exhibit markedly different responses to cyclic hypoxia depending on the dynamics of the oxygen fluctuations. We also use our model to investigate the impact of changes to cell cycle checkpoint activation and damage repair on cell responses to cyclic hypoxia. Our simulations suggest that cyclic hypoxia can promote heterogeneity in cellular damage repair activity within vascular tumours., (© 2024. The Author(s).)

The purpose of this study is to construct a mortality model that reasonably explains survival curves and mortality rates in terms of the decline in biological function, which is the phenomenon of ageing. In this model, an individual organism is regarded as a collection of subsystems, and for each subsystem, the model defines human mortality by introducing positive self-repair mechanisms and stochastically generated negative external shocks. The probability density function of the time of death is derived explicitly, and the model parameters are estimated using life tables from Japan and the UK, which demonstrate the existence of multiple parameter sets that fit well with the observed data., (© 2024. The Author(s).)

Despite the primary role of cell proliferation in tissue development and homeostatic maintenance, the interplay between cell density, cell mechanoresponse, and cell growth and division is not yet understood. In this article, we address this issue by reporting on an experimental investigation of cell proliferation on all time- and length-scales of the development of a model tissue, grown on collagen-coated glass or deformable substrates. Through extensive data analysis, we demonstrate the relation between mechanoresponse and probability for cell division, as a function of the local cell density. Motivated by these results, we construct a minimal model of cell division in tissue environment that can recover the data. By parameterizing the growth and the dividing phases of the cell cycle, and introducing such a proliferation model in dissipative particle dynamics simulations, we recover the mechanoresponsive, time-dependent density profiles in 2D tissues growing to macroscopic scales. The importance of separating the cell population into growing and dividing cells, each characterized by a particular time scale, is further emphasized by calculations of density profiles based on adapted Fisher-Kolmogorov equations. Together, these results show that the mechanoresponse on the level of a constitutive cell and its proliferation results in a matrix-sensitive active pressure. The latter evokes massive cooperative displacement of cells in the invading tissue and is a key factor for developing large-scale structures in the steady state., Competing Interests: Competing interests statement:The authors declare no competing interest.

The process-based xylem formation model is an important tool for understanding the radial growth process of trees and its influencing factors. While numerous xylogenesis models for conifers have been developed, there is a lack of models available for non-coniferous trees. In this study, we present a process-based model designed for xylem formation and ring growth in broad-leaved trees, which we call the Broad-leaved Tree-Ring (BTR) model. Climate factors, including daylength, air temperature, soil moisture and vapor pressure deficit, drive daily xylem cell production (fibers and vessels) and growth (enlargement, wall deposition). The model calculates the total cell area in the simulated zone to determine the annual ring width. The results demonstrate that the BTR model can basically simulate inter-annual variation in ring width and intra-annual changes in vessel and fiber cell formation in Fraxinus mandshurica (ring-porous) and Betula platyphylla (diffuse-porous). The BTR model is a potential tool for understanding how different trees form wood and how climate change influences this process., (© The Author(s) 2024. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.)

Many animal cells that crawl on extracellular substrates exhibit durotaxis, i.e., directed migration toward stiffer substrate regions. This has implications in several biological processes including tissue development and tumor progression. Here, we introduce a phenomenological model for single-cell durotaxis that incorporates both elastic deformation-mediated cell-substrate interactions and the stochasticity of cell migration. Our model is motivated by a key observation in an early demonstration of durotaxis: a single, contractile cell at a sharp interface between a softer and a stiffer region of an elastic substrate reorients and migrates toward the stiffer region. We model migrating cells as self-propelling, persistently motile agents that exert contractile traction forces on their elastic substrate. The resulting substrate deformations induce elastic interactions with mechanical boundaries, captured by an elastic potential. The dynamics is determined by two crucial parameters: the strength of the cellular traction-induced boundary elastic interaction (A), and the persistence of cell motility (Pe). Elastic forces and torques resulting from the potential orient cells perpendicular (parallel) to the boundary and accumulate (deplete) them at the clamped (free) boundary. Thus, a clamped boundary induces an attractive potential that drives durotaxis, while a free boundary induces a repulsive potential that prevents antidurotaxis. By quantifying the steady-state position and orientation probability densities, we show how the extent of accumulation (depletion) depends on the strength of the elastic potential and motility. We compare and contrast crawling cells with biological microswimmers and other synthetic active particles, where accumulation at confining boundaries is well known. We define metrics quantifying boundary accumulation and durotaxis, and present a phase diagram that identifies three possible regimes: durotaxis, and adurotaxis with and without motility-induced accumulation at the boundary. Overall, our model predicts how durotaxis depends on cell contractility and motility, successfully explains some previous observations, and provides testable predictions to guide future experiments., Competing Interests: Declaration of interests The authors do not declare any conflicts of interest., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

Mechanical and biochemical cues intricately activate Yes-associated protein (YAP), which is pivotal for the cellular responses to these stimuli. Recent findings reveal an unexplored role of YAP in influencing the apoptotic process. It has been shown that, on soft matrices, YAP is recruited to small adhesions, phosphorylated at Y357, and translocated into the nucleus triggering apoptosis. Interestingly, YAP Y357 phosphorylation is significantly reduced in larger mature focal adhesions on stiff matrices. Building upon these novel insights, we have developed a stochastic model to delve deeper into the complex dynamics of YAP phosphorylation within integrin adhesions. Our findings emphasize several key points: firstly, increasing the cytosolic diffusion rate of YAP correlates with higher levels of phosphorylated YAP (pYAP); secondly, increasing the number of binding sites and distributing them across the membrane surface, mimicking smaller adhesions, leads to higher pYAP levels, particularly at lower diffusion rates. Moreover, we show that the binding and release rate of YAP to adhesions as well as adhesion lifetimes significantly influence the size effect of adhesion-induced YAP phosphorylation. The results highlight the complex and dynamic interplay between adhesion lifetime, the rate of pYAP unbinding from adhesions, and dephosphorylation rates, collectively shaping overall pYAP levels. In summary, our work advances the understanding of YAP mechanotransduction and opens avenues for experimental validation., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

The parameter region of multistationarity of a reaction network contains all the parameters for which the associated dynamical system exhibits multiple steady states. Describing this region is challenging and remains an active area of research. In this paper, we concentrate on two biologically relevant families of reaction networks that model multisite phosphorylation and dephosphorylation of a substrate at n sites. For small values of n, it had previously been shown that the parameter region of multistationarity is connected. Here, we extend these results and provide a proof that applies to all values of n. Our techniques are based on the study of the critical polynomial associated with these reaction networks together with polyhedral geometric conditions of the signed support of this polynomial., (© 2024. The Author(s).)

There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain Ω ⊂ R d containing a set of small subdomains or interior compartments U j , j = 1 , … , N (singularly-perturbed diffusion problems). The domain Ω could represent the cell membrane, the cell cytoplasm, the cell nucleus or the extracellular volume, while an individual compartment could represent a synapse, a membrane protein cluster, a biological condensate, or a quorum sensing bacterial cell. In this review we use a combination of matched asymptotic analysis and Green's function methods to solve a general type of singular boundary value problems (BVP) in 2D and 3D, in which an inhomogeneous Robin condition is imposed on each interior boundary ∂ U j . This allows us to incorporate a variety of previous studies of singularly perturbed diffusion problems into a single mathematical modeling framework. We mainly focus on steady-state solutions and the approach to steady-state, but also highlight some of the current challenges in dealing with time-dependent solutions and randomly switching processes., (© 2024. The Author(s).)

The increasing availability of enzyme turnover number measurements from experiments and of turnover number predictions from deep learning models prompts the use of these enzyme parameters in precise metabolic engineering. Yet, there is no computational approach that allows the prediction of metabolic engineering strategies that rely on the modification of turnover numbers. It is also unclear if modifications of turnover numbers without alterations in the host's transcriptional regulatory machinery suffice to increase the production of chemicals of interest. Here, we present a constraint-based modeling approach, termed Overcoming Kinetic rate Obstacles (OKO), that uses enzyme-constrained metabolic models to predict in silico strategies to increase the production of a given chemical, while ensuring specified cell growth. We demonstrate that the application of OKO to enzyme-constrained metabolic models of Escherichia coli and Saccharomyces cerevisiae results in strategies that can at least double the production of over 40 compounds with little penalty to growth. Interestingly, we show that the overproduction of compounds of interest does not entail only an increase in the values of turnover numbers. Lastly, we demonstrate that a refinement of OKO, allowing also for manipulation of enzyme abundance, facilitates the usage of the available compendia and deep learning models of turnover numbers in the design of precise metabolic engineering strategies. Our results expand the usage of genome-scale metabolic models toward the identification of targets for protein engineering, allowing their direct usage in the generation of innovative metabolic engineering designs for various biotechnological applications., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Razaghi-Moghadam et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Background: The kallikrein-kinin system (KKS) is a complex biochemical pathway that plays a crucial role in regulating several physiological processes, including inflammation, coagulation, and blood pressure. Dysregulation of the KKS has been associated with several pathological conditions such as hereditary angioedema (HAE), hypertension, and stroke. Developing an accurate quantitative model of the KKS may provide a better understanding of its role in health and disease and facilitate the rapid and targeted development of effective therapies for KKS-related disorders., Objectives: Here, we present a novel, detailed mechanistic model of the plasma KKS, elucidating the processes of Factor XII (FXII) activation, the kallikrein feedback loop, cleavage of high molecular weight kininogen leading to bradykinin (BK) production, and the impact of inhibitors., Methods: The model incorporates both surface and solution-phase reactions of all proteins in the KKS, describing how binding site concentration affects the rate of surface reactions. The model was calibrated and validated using a variety of published and in-house experimental datasets, which encompass a range of dextran sulphate (DXS) concentrations to initiate contact activation and various KKS inhibitors to block bradykinin production., Results: Our mathematical model showed that a trace amount of activated FXII is required for subsequent FXII activation. The model also reveals a bell-shaped curve relationship between the activation of the KKS and the number of DXS surface binding sites. Simulations of BK generation in healthy and HAE plasma demonstrated the impact of C1 esterase inhibitor (C1inh) deficiency via increased peak BK levels and accelerated formation in HAE plasma. The efficacy of KKS inhibitors, such as CSL312, ecallantide, and C1inh, was also evaluated, with CSL312 showing the most potent inhibition of BK generation., Conclusions: The present model represents a valuable framework for studying the intricate interactions within the plasma KKS and provides a better understanding of the mechanism of action of various KKS-targeted therapies., Competing Interests: I have read the journal’s policy, and the authors of this manuscript have the following competing interests: AR, HL, MP, CP, and IM are employees of CSL Limited. AR, HL, SD, MP, CP, and IM hold shares in CSL Limited., (Copyright: © 2024 Rezvani-Sharif et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Drugs exhibiting nonlinear pharmacokinetics hold significant importance in drug research and development. However, evaluating drug exposure accurately is challenging with the current formulae established for linear pharmacokinetics. This article aims to investigate the steady-state drug exposure for a one-compartment pharmacokinetic (PK) model with sigmoidal Hill elimination, focusing on three key topics: the comparison between steady-state drug exposure of repeated intravenous (IV) bolus ( AUC ss ) and total drug exposure after a single IV bolus ( AUC 0 - ∞ ); the evolution of steady-state drug concentration with varying dosing frequencies; and the control of drug pharmacokinetics in multiple-dose therapeutic scenarios. For the first topic, we established conditions for the existence of AUC ss , derived an explicit formula for its calculation, and compared it with AUC 0 - ∞ . For the second, we identified the trending properties of steady-state average and trough concentrations concerning dosing frequency. For the third, we developed formulae to compute dose and dosing time for both regular and irregular dosing scenarios. As an example, our findings were applied to a real drug model of progesterone used in lactating dairy cows. In conclusion, these results provide a theoretical foundation for designing rational dosage regimens and conducting therapeutic trials., (© 2024. The Author(s), under exclusive licence to the Society for Mathematical Biology.)

Understanding how organisms make choices about what to eat is a fascinating puzzle explored in this study, which employs stoichiometric modeling and optimal foraging principles. The research delves into the intricate balance of nutrient intake with foraging strategies, investigating quality and quantity-based food selection through mathematical models. The stoichiometric models in this study, encompassing producers and a grazer, unveils the dynamics of decision-making processes, introducing fixed and variable energetic foraging costs. Analysis reveals cell quota-dependent predation behaviors, elucidating biological phenomena such as "compensatory foraging behaviors" and the "stoichiometric extinction effect". The Marginal Value Theorem quantifies food selection, highlighting the profitability of prey items and emphasizing its role in optimizing foraging strategies in predator-prey dynamics. The environmental factors like light and nutrient availability prove pivotal in shaping optimal foraging strategies, with numerical results from a multi-species model contributing to a comprehensive understanding of the intricate interplay between organisms and their environment., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Application of biomechanical models relies on model parameters estimated from experimental data. Parameter non-identifiability, when the same model output can be produced by many sets of parameter values, introduces severe errors yet has received relatively little attention in biomechanics and is subtle enough to remain unnoticed in the absence of deliberate verification. The present work develops a global identifiability analysis method in which cluster analysis and singular value decomposition are applied to vectors of parameter-output variable correlation coefficients. This method provides a visual representation of which specific experimental design elements are beneficial or harmful in terms of parameter identifiability, supporting the correction of deficiencies in the test protocol prior to testing physical specimens. The method was applied to a representative nonlinear biphasic model for cartilaginous tissue, demonstrating that confined compression data does not provide identifiability for the biphasic model parameters. This result was confirmed by two independent analyses: local analysis of the Hessian of a sum-of-squares error cost function and observation of the behaviour of two optimization algorithms. Therefore, confined compression data are insufficient for the calibration of general-purpose biphasic models. Identifiability analysis by these or other methods is strongly recommended when planning future experiments.

The Bateman gradient is a central concept in sexual selection theory that relates reproductive success to mate number, with important consequences for sex-specific selection. The conventional expectation is that Bateman gradients are steeper in males than females, implying that males benefit more from multiple mating than females do. This claim is supported by much empirical evidence as well as mathematical modelling. However, under some reproductive systems, reversed Bateman gradients are observed, perhaps most notably in syngnathid fishes with male pregnancy. Unlike conventional Bateman gradients, the causal basis of such reversed Bateman gradients has never been modelled mathematically. Here, we present a sex-neutral mathematical model demonstrating how restrictions in capacity for carrying or incubating gametes and embryos (brooding) interact with anisogamy, generating both conventional and reversed Bateman gradients from a single mathematical model. The results clearly demonstrate how anisogamy tends to cause conventional Bateman gradients, but diminishing male brooding capacity under male pregnancy or nesting causes a gradual reversal from conventional to fully 'reversed' Bateman gradients.

Numerous studies have explored the link between bacterial swimming and the number of flagella, a distinguishing feature of motile multi-flagellated bacteria. We revisit this open question using augmented slender-body theory simulations, in which we resolve the full hydrodynamic interactions within a bundle of helical filaments rotating and translating in synchrony. Unlike previous studies, our model considers the full torque-speed relationship of the bacterial flagellar motor, revealing its significant impact on multi-flagellated swimming. Because the viscous load per motor decreases with the flagellar number, the bacterial flagellar motor transitions from the high-load to the low-load regime at a critical number of filaments, leading to bacterial slowdown as further flagella are added to the bundle. We explain the physical mechanism behind the observed slowdown as an interplay between the load-dependent generation of torque by the motor, and the load-reducing cooperativity between flagella, which consists of both hydrodynamic and non-hydrodynamic components. The theoretically predicted critical number of flagella is remarkably close to the values reported for the model organism Escherichia coli . Our model further predicts that the critical number of flagella increases with viscosity, suggesting that bacteria can enhance their swimming capacity by growing more flagella in more viscous environments, consistent with empirical observations.

AbstractFor species that partition resources, the classic expectation is that increasing resource diversity allows for increased species diversity. On the other hand, for neutral species, such as those competing equally for a single resource, diversity reflects a balance between the rate of introduction of novelty (e.g., by immigration or speciation) and the rate of extinction. Recent models of microbial metabolism have identified scenarios where metabolic trade-offs among species partitioning multiple resources can produce emergent neutral-like dynamics. In this hybrid scenario, one might expect that both resource diversity and immigration will act to boost species diversity. We show, however, that the reverse may be true: when metabolic trade-offs hold and population sizes are sufficiently large, increasing resource diversity can act to reduce species diversity, sometimes drastically. This reversal is explained by a generic transition between neutral- and niche-like dynamics, driven by the diversity of resources. The inverted resource-diversity relationship that results may be a signature of consumer-resource systems with strong metabolic trade-offs.

Ground reaction forces (GRFs) and center of pressure (COP) are essential for understanding human motion and evaluating biomechanical parameters, but measuring them with force plates is often limited in many scenarios. In this study, we propose a novel methodology for estimating GRFs and COP during normal gait based on a rigid foot-ground contact model, referred to as the COP phase transition continuity model (COP-PTCM). The GRFs and COP are calculated based on the Newton-Euler Equations during the single support phase (SSP). Considering the spatiotemporal continuity of the COP trajectory during normal gait, the COP data for the double support phase (DSP) is obtained by an improved logistic function fitted using the COP data from the SSP. GRFs during the DSP are optimized using the minimum energy hypothesis. The COP-PTCM method is used to estimate the GRFs and COP of ten participants during normal gait, and the results are compared with simultaneously measured force plate data, yielding the relative root mean square error (rRMSE) between measured and estimated GRFs in the anterior-posterior, vertical, and medial-lateral directions are 10.90±2.09 %, 4.73±1.44 %, and 15.17±1.69 %, respectively. Additionally, the rRMSE between measured and estimated COP in the anterior-posterior direction is 11.23±0.03 %. The above comparison validates the effectiveness and accuracy of the proposed method., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

Background and Objective: Voriconazole (VRC), a broad-spectrum antifungal drug, exhibits nonlinear pharmacokinetics (PK) due to saturable metabolic processes, autoinhibition and metabolite-mediated inhibition on their own formation. VRC PK is also characterised by high inter- and intraindividual variability, primarily associated with cytochrome P450 (CYP) 2C19 genetic polymorphism. Additionally, recent in vitro findings indicate that VRC main metabolites, voriconazole N-oxide (NO) and hydroxyvoriconazole (OHVRC), inhibit CYP enzymes responsible for VRC metabolism, adding to its PK variability. This variability poses a significant risk of therapeutic failure or adverse events, which are major challenges in VRC therapy. Understanding the underlying processes and sources of these variabilities is essential for safe and effective therapy. This work aimed to develop a whole-body physiologically-based pharmacokinetic (PBPK) modelling framework that elucidates the complex metabolism of VRC and the impact of its metabolites, NO and OHVRC, on the PK of the parent, leveraging both in vitro and in vivo clinical data in a middle-out approach., Methods: A coupled parent-metabolite PBPK model for VRC, NO and OHVRC was developed in a stepwise manner using PK-Sim ® and MoBi ® . Based on available in vitro data, NO formation was assumed to be mediated by CYP2C19, CYP3A4, and CYP2C9, while OHVRC formation was attributed solely to CYP3A4. Both metabolites were assumed to be excreted via renal clearance, with hepatic elimination also considered for NO. Inhibition functions were implemented to describe the complex interaction network of VRC autoinhibition and metabolite-mediated inhibition on each CYP enzyme., Results: Using a combined bottom-up and middle-out approach, incorporating data from multiple clinical studies and existing literature, the model accurately predicted plasma concentration-time profiles across various intravenous dosing regimens in healthy adults, of different CYP2C19 genotype-predicted phenotypes. All (100%) of the predicted area under the concentration-time curve (AUC) and 94% of maximum concentration (C max ) values of VRC met the 1.25-fold acceptance criterion, with overall absolute average fold errors of 1.12 and 1.14, respectively. Furthermore, all predicted AUC and C max values of NO and OHVRC met the twofold acceptance criterion., Conclusion: This comprehensive parent-metabolite PBPK model of VRC quantitatively elucidated the complex metabolism of the drug and emphasised the substantial impact of the primary metabolites on VRC PK. The comprehensive approach combining bottom-up and middle-out modelling, thereby accounting for VRC autoinhibition, metabolite-mediated inhibition, and the impact of CYP2C19 genetic polymorphisms, enhances our understanding of VRC PK. Moreover, the model can be pivotal in designing further in vitro experiments, ultimately allowing for extrapolation to paediatric populations, enhance treatment individualisation and improve clinical outcomes., Competing Interests: Declarations Funding Open Access funding was enabled and organised by Projekt DEAL. Conflicts of Interest Charlotte Kloft and Wilhelm Huisinga report grants from an industry consortium (AbbVie Deutschland GmbH & Co. K.G., AstraZeneca, Boehringer Ingelheim Pharma GmbH & Co. K.G., Grünenthal GmbH, F. Hoffmann-La Roche Ltd, Merck KGaA, Novo Nordisk A/S and Sanofi) for the graduate research training programme PharMetrX. In addition, Charlotte Kloft reports research grants from the Innovative Medicines Initiative-Joint Undertaking (‘DDMoRe’), from H2020-EU.3.1.3 (‘FAIR’), Diurnal Ltd and the Federal Ministry of Education and Research within the Joint Programming Initiative on Antimicrobial Resistance Initiative (‘JPIAMR’), all outside the submitted work. Ayatallah Saleh, Josefine Schulz, Jan-Frederik Schlender, Linda B.S. Aulin, Amrei-Pauline Konrad, Franziska Kluwe, Gerd Mikus, and Robin Michelet declare no competing interests that may be relevant to the contents of this work. Ethics Approval All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. All trial protocols were approved by the responsible Ethics Committees and the respective competent authorities. Informed Consent Written informed consent was obtained from all individual study participants before inclusion. Written informed consent was obtained from all individual study participants before inclusion. Availability of Data and Material The datasets generated and/or analysed during the current study are not publicly available as patients did not provide consent for sharing their data in a public database. The datasets are available from the corresponding author upon reasonable request. Availability of Code The PBPK model will be available on the AK-Kloft GitHub website and can be freely downloaded. Author Contributions Conceptualisation: AS, RM, CK. Clinical data collection: GM, CK. In vitro data generation: JS, CK. Planning of analysis: AS, FK, RM, CK. Formal analysis and investigation: AS, RM, JFS, WH, GM, CK. Writing – original draft preparation: AS, RM. Writing – review and editing: All authors contributed to discussion of the results as well as reviewing and editing the manuscript., (© 2024. The Author(s).)

Background: Intraoperation hypotension (IOH) is commonly observed in patients undergoing surgery under general anesthesia, and even a brief episode of IOH can lead to unfavorable outcomes. To reduce the risk, blood pressure is closely measured during general anesthesia, and norepinephrine (NE) is frequently administered if hypotension is detected. Despite its routine application, information on the dose-exposure-response relationship of NE remains limited. Additionally, quantification of the influence of general anesthesia on the pharmacokinetics (PK) of NE is lacking., Objective: In this study, we aimed to describe NE PK in healthy volunteers and the influence of general anesthesia on its PK., Methods: A single-center, cross-over study was conducted in healthy volunteers. The volunteers received a step-up NE dosing scheme (0.04, 0.08, 0.12, 0.16 and 0.20 mcg -1 /kg -1 /min -1 ) first in the awake state and then under general anesthesia. General anesthesia was administered using a propofol/remifentanil Eleveld target-controlled infusion. During general anesthesia, a 30-second electrical stimulus was given as surrogate for surgical incision to the volunteers at each dosage step. Blood samples were drawn before the initial dosing and after each dosing step, and plasma NE, propofol and remifentanil concentrations were subsequently determined. A population PK model was developed using non-linear mixed effects modelling. Simulations were conducted to predict the plasma NE concentration in patients at different measured propofol concentrations., Results: A total of 1219 samples were analyzed from 36 volunteers. A two-compartment model with a first-order elimination best described the data. Weight, age, and session effect (awake vs general anesthesia) were identified as relevant covariates on the clearance (CL) of NE. A 10% decrease in NE CL was observed after general anesthesia induction. This difference between sessions is better explained by the measured concentration of propofol, rather than the anticipated impact of cardiac output. The estimated post-stimulation NE concentration is 0.66 nmol/L -1 (95% CI 0.06-1.20 nmol/L -1 ) lower than the pre-stimulation NE concentration. Model simulation indicates that patients at a higher measured propofol concentration (e.g., 6 mcg/mL -1 ) exhibited higher NE concentrations (95% PI 18.10-43.89 nmol/L -1 ) than patients at a lower measured propofol concentration (e.g., 3 mcg/mL -1 ) (95% PI 16.81-38.91 nmol L -1 )., Conclusion: The NE PK is well described with a two-compartment model with a first-order elimination. NE CL exhibiting a 10% decrease under general anesthesia, with this difference being attributed to the measured concentration of propofol. The impact of stimulation on NE PK under general anesthesia is very limited., Clinical Trials Registration Number: NL9312., Competing Interests: Declarations Funding The study is supported by the Department of Anesthesiology at University Medical Center Groningen, The Netherlands. Conflicts of Interest M.M.R.F Struys: His research group/department received (over the last 3 years) research grants and consultancy fees from The Medicines Company (Parsippany, NJ, USA), Masimo (Irvine, CA, USA), Becton Dickinson (Eysins, Switzerland), Fresenius (Bad Homburg, Germany), Dräger (Lübeck, Germany), Paion (Aachen, Germany), Medtronic (Dublin, Ireland). He receives royalties on intellectual property from Demed Medical (Sinaai, Belgium) and the Ghent University (Gent, Belgium). He is an editorial board member and Director for the British Journal of Anaesthesia. D.J. Eleveld: Has received travel from Becton Dickenson and is an editorial board member of Anesthesiology journal. P.J. Colin: Over the last 3 years his research group has been involved in contract research for PAION UK Ltd. (London, England) and Acacia Pharma Ltd. (Cambridge, England). Yingxue Li, Jeroen V. Koomen, Johannes P. van den Berg, Jaap Jan Vos, Ilonka N. de Keijzer declare that they have no conflicts of interest that are relevant to the content of this article. Ethics Approval The protocol of the study has been approved by the local medical ethics committee. Consent to Participate Informed consent was acquired from each individual participant incorporated in the study. Consent for Publication Not applicable. Availability of Data and Material The data and material are accessible upon reasonable request by contacting the corresponding author. Code Availability The model code is accessible upon reasonable request by contacting the corresponding author. Authors’ Contributions M.M.R.F. Struys, P.J. Colin, J.P. Van den Berg, J.J. Vos: conception and design of the study and manuscript revision; J.P. Van den Berg, J.J. Vos, I.N. de Keijzer: data collection, bioanalysis and manuscript revision; Y Li, J.V. Koomen, D.J. Eleveld, P.J. Colin: data analysis and interpretation, modelling, manuscription preparation and revision., (© 2024. The Author(s).)

Background and Objective: Population pharmacokinetic/pharmacodynamic (PK/PD) modelling of antibiotics including C-reactive protein (C-RP) dynamics could be helpful in predicting the efficacy of antimicrobials. We developed a PK/PD model for assessing the impact of continuous infusion (CI) meropenem PK/PD target attainment on C-RP dynamics in critically ill patients with documented Gram-negative hospital- (HAP) or ventilator-acquired pneumonia (VAP)., Methods: Patients were grouped according to the type of antibiotic treatment received [meropenem monotherapy; meropenem plus empirical anti-MRSA (methicillin-resistant Staphylococcus aureus) therapy; meropenem in combination with another anti-Gram-negative active agent; meropenem plus a targeted anti-MRSA therapy]. A one-compartment population PK model of CI meropenem was developed by including all patients. A full C-RP production inhibition model was developed for fitting the PD data by including only patients receiving meropenem monotherapy or meropenem plus empirical anti-MRSA therapy. Monte Carlo simulations explored the relationship between the type of PK/PD target attainment of CI meropenem, defined as optimal (steady-state plasma concentration [C ss ] to minimum inhibitory concentration [MIC] ratio = 4-8), quasi-optimal (C ss /MIC = 1-4) and sub-optimal (C ss /MIC < 1) and the magnitude of C-RP production inhibition over time., Results: A total of 64 patients providing 211 meropenem concentrations were included in the PK analysis, whereas 47 patients providing 328 C-RP data were included in the PD model. Simulations showed that optimal PK/PD target attainment was associated with the highest and most rapid C-RP production inhibition (44% and 56% at days 2 and 4, respectively). Conversely, sub-optimal PK/PD target attainment was shown to be almost ineffective (< 5% at day 4 and < 10% at day 10)., Conclusion: Our PK/PD model predicted that attaining optimal PK/PD target with CI meropenem may grant prompt and intense C-RP decrease among critically ill patients receiving targeted monotherapy for Gram-negative HAP/VAP, thus anticipating efficacy., Competing Interests: Declarations Ethics Approval and Consent to Participate The study was approved by the Local Ethics Committee (No. 308/2021/Oss/AOUBo on 24 May 2021). Consent for Publication Due to the retrospective nature of this investigation, informed written consent was waived. Availability of Data and Materials The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request. Competing Interests The authors declare that they have no competing interests. Funding This project has received funding from European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No 861323. Authors' Contributions CT analyzed and wrote the initial manuscript; PGC wrote the manuscript and interpreted patient data; MR collected patient data; TT collected and analyzed patient data; AS collected and analyzed patient data; CvH, PV and FP supervised the project., (© 2024. The Author(s).)

Background and Objective: Different empirical lactation models have been published to predict the milk-to-plasma (M/P) ratio of drugs to gain knowledge on the extent of drug distribution to the breastmilk. M/P ratios will likely vary across the lactation period due to differences in physiological milk pH and fat content, which are not routinely reported in clinical lactation pharmacokinetic studies. This work aims to evaluate the sensitivity of two (a theory-based phase distribution and a log-transformed regression) lactation models for M/P prediction at different physiological milk pH and fat content., Methods: A literature search was conducted to collate reported M/P ratios for different drugs and their physicochemical parameters required for the prediction of the M/P ratio. Two distribution models were used for M/P ratio predictions. The M/P ratio of drugs was predicted under the physiological milk pHs of 6.8, 7.0, 7.2, and 7.4 and at of 1%, 3%, and 6% fat content. Calculated M/P ratios were compared with the observed M/P ratios., Results: A total of 200 M/P ratios for 130 compounds (40 acids and 90 bases) were collected from clinical studies and included in the analysis. For both model, precision decreases and bias increases outside the milk pH range 7.0-7.2 and fat contents more than 3%. Significant variability exists in the observed M/P ratios. Both milk pH and fat content are important parameters for model prediction., Conclusion: Calculated M/P ratios are influenced by multiple covariates, including milk pH and fat content. The phase distribution model is less sensitive to these covariates than the log-transformed model, especially for acidic compounds. For complex matrices such as breastmilk, the actual physiological parameters of the sampled milk, at least milk fat and pH, and their distributions are required covariates to improve the prediction outcomes, design lactation pharmacokinetic studies, and inform the potential breastfed infant dose., Competing Interests: Declarations Funding No funding was provided for this work. Conflict of interest K.A. is a full-time employee of Certara Predictive Technologies, UK, and may hold shares in Certara. M.F. is a full-time employee of UCB and was a former employee of Certara, UK. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Authors’ contributions K.A. and M.F. collected the data; K.A. and M.F. analyzed the data; and K.A. and M.F. wrote the manuscript. Data availability statement All data generated or analyzed during this study are included in this published article (and its supplementary information files). Ethics approval For this study, ethical approval was not required. Code availability Not applicable. Consent to participate Not applicable. Consent for publication Not applicable., (© 2024. The Author(s), under exclusive licence to Springer Nature Switzerland AG.)

Background and Objective: Codeine metabolism in humans is complex due to the involvement of multiple cytochrome P450 (CYP) enzymes, and has a strong genetic underpinning, which determines the levels of relevant CYP450 enzyme expression in vivo. Polymorphic CYP2D6 metabolises codeine to morphine via O-demethylation, while a strong correlation between CYP2D6 phenotype and opioidergic adverse effects of codeine is well documented. The aim of this study was to quantify the effect of CYP2D6 genotype on the biotransformation of codeine., Methods: We conducted a prospective clinical trial with 1000 patients, during which ambulatory patients were administered 60 mg of codeine preoperatively and the association between CYP2D6 activity and morphine exposure across various CYP2D6 genotypes was quantified using a population pharmacokinetic model. Plasma concentration data for codeine and its primary metabolites were obtained from 997 patients and CYP2D6 genotype was screened for study subjects, and respective sums of activity scores assigned for each CYP2D6 allele were used as covariates in model development., Results: Our final model predicts the disposition of codeine and the formation of morphine, codeine-6-glucuronide and morphine-3-glucuronide adequately while accounting for variability in morphine exposure on the basis of CYP2D6 genotype. In agreement with previous results, patients with decreased function alleles (CYP2D6*10 and *41) showed varying levels of decrease in CYP2D6 activity that were inconsistent with increasing activity scores. Model simulations demonstrate that morphine concentrations in ultrarapid CYP2D6 metabolisers reach systemic concentrations that can potentially cause respiratory depression (over 9.1 ng/mL), and have 218% higher exposure (19 versus 8.7 µg · h/L, p < 0.001) to morphine than normal metabolisers. Similarly, poor and intermediate metabolisers had significantly reduced morphine exposure (1.0 and 3.7 versus 8.7 µg · h/L, p < 0.001) as compared with normal metabolisers., Conclusions: Our final model leads the way in implementing model-informed precision dosing in codeine therapy and identifies the use of genetic testing as an integral component in the effort to implement rational pharmacotherapy with codeine., Competing Interests: Declarations Funding Open Access funding provided by University of Turku (including Turku University Central Hospital). M.W.A. has received funding from University of Turku Graduate School and Finnish Cultural Foundation, Varsinais-Suomi Regional fund. This study was partially funded by state funding for university-level health research to Turku University Hospital (#11147 for M.W.A. and #13821 for T.I.S.) and to HUS Helsinki University Hospital (TYH2016239 for S.P., K.T.O. and V.K; TYH2019300 for J.B.; and TYH2019240 for M.N.), as well as the Sigrid Jusélius Foundation, Helsinki, Finland (M.N.). Competing Interests This study was a non-commercial, investigator-initiated trial and has not received any funding from the industry. The authors have no financial or proprietary interests in any material discussed in this article. Ethics Approval The study protocol was reviewed and approved by approved by the Coordinating Ethics Committee of the Helsinki and Uusimaa Hospital District (3/2016) and the Finnish National Agency for Medicines (KL no. 4/2016). Consent to Participate All participants provided written informed consent before study participation. Consent for Publication All authors approved this manuscript for publication. Availability of Data Patient-level data for data on file in this manuscript are not available for sharing as there is a reasonable likelihood that individual patients could be re-identified. Further information can be requested from the authors. Author Contributions S.P., K.T.O. and V.K. conceived the idea and designed the study, contributed to the interpretation of the manuscript and gave final approval of the version to be published; M.Ne, J.I.K, J.B. and M.Ni. contributed to data analyses, interpretation of the manuscript and gave final approval of the version to be published; M.W.A. and T.I.S. supported in study design, collected model information and performed simulations and wrote and finalised the manuscript., (© 2024. The Author(s).)

One strand of modern coexistence theory (MCT) partitions invader growth rates (IGR) to quantify how different mechanisms contribute to species coexistence, highlighting fluctuation-dependent mechanisms. A general conclusion from the classical analytic MCT theory is that coexistence mechanisms relying on temporal variation (such as the temporal storage effect) are generally less effective at promoting coexistence than mechanisms relying on spatial or spatiotemporal variation (primarily growth-density covariance). However, the analytic theory assumes continuous population density, and IGRs are calculated for infinitesimally rare invaders that have infinite time to find their preferred habitat and regrow, without ever experiencing intraspecific competition. Here we ask if the disparity between spatial and temporal mechanisms persists when individuals are, instead, discrete and occupy finite amounts of space. We present a simulation-based approach to quantifying IGRs in this situation, building on our previous approach for spatially non-varying habitats. As expected, we found that spatial mechanisms are weakened; unexpectedly, the contribution to IGR from growth-density covariance could even become negative, opposing coexistence. We also found shifts in which demographic parameters had the largest effect on the strength of spatial coexistence mechanisms. Our substantive conclusions are statements about one model, across parameter ranges that we subjectively considered realistic. Using the methods developed here, effects of individual discreteness should be explored theoretically across a broader range of conditions, and in models parameterized from empirical data on real communities., (© 2024 The Ecological Society of America.)

The skin is a multilayered organ with microstructural and antomical heterogeneities that contribute to its unique mechanophysiology. Between the epidermis layer at the top and the dermis layer below, the basal keratinocytes form an interface with sinusoidal-like geometry termed rete ridges. In previous computational work we showed that the rete ridges contribute to lower delamination risk by increasing surface area and reducing the stress jump across the interface. Experimentally, we and others have shown that upon repeated tissue expansion and growth, physiological rete ridge frequency is preserved. Here we implement a 2D multilayered skin model where each layer is able to grow in response to applied loading toward recovering the layer-specific homeostatic stretch. Our simulations support the hypothesis that mechanics of growing tissue can explain secondary buckling and new rete ridge formation in tissue expansion. The process is robust with respect to parameters such as homeostatic stretch, layer thicknesses, and shear moduli of the different layers. Thicker epidermis suppresses higher frequency features, and so does a stiffer epidermis with respect to the basal layer. Interestingly, new rete ridge valleys are formed at locations that were originally peaks of the sine wave, whereas original valleys remain valleys. This pattern might have a connection to the localization of stem cell and transient amplifying cells in the epidermis. This study does not discard the role of cell-cell signaling dynamics, but rather emphasizes the possibility of achieving robust geometric patterns with simple rules of growing tissue, even in the absence of complex regulatory networks., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

The micro-pipette aspiration technique is a classical experiment used to characterize the physical properties of inert fluids and biological soft materials such as cellular aggregates. The physical parameters of the fluid, as viscosity and interfacial tension, are obtained by studying how the fluid enters the pipette when the suction pressure is increased and how it relaxes when the suction pressure is put to zero. A mathematical model representative of the experiment is needed to extrapolate the physical parameters of the fluid-like matter; however, for biological materials as cells or cell aggregates mathematical models are always based on strong starting hypotheses that impact the significance of the identified parameters. In this article, starting from the bi-constituent nature of the cell aggregate, we derive a general mathematical model based of a Cahn-Hilliard-Navier-Stokes set of equations. The model is applied to describe quantitatively the aspiration-retraction dynamics of a cell-aggregate into and out of a pipette. We demonstrate the predictive capability of the model and highlight the impact of the assumptions made on the identified parameters by studying two cases: one with a non-wetting condition between the cells and the wall of the pipette (classical assumption in the literature) and the second one, which is more realistic, with a partial wetting condition (contact angle θ s = 150°). Furthermore, our results provide a purely physical explanation to the asymmetry between the aspiration and retraction responses which is alternative to the proposed hypothesis of an mechano-responsive alteration of the surface tension of the cell aggregate. STATEMENT OF SIGNIFICANCE: Our study introduces a general mathematical model, based on the Cahn-Hilliard-Navier-Stokes equations, tailored to model micro-pipette aspiration of cell aggregates. The model accounts for the multi-component structure of the cell aggregate and its intrinsic viscoelastic rheology. By challenging prevailing assumptions, particularly regarding perfect non-wetting conditions and the mechano-responsive alteration of cell surface tension, we demonstrate the reliability of the mathematical model and elucidate the mechanisms at play, offering a purely physical explanation for observed asymmetries between the aspiration and retraction stages of the experiment., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

Topographic heterogeneity sets the stage for community assembly, but its effects on ecosystem functioning remain poorly understood. Here, we test the hypothesis that topographic heterogeneity underpins multiple cascading species interactions and functional pathways that indirectly control multifunctionality. To do so, we combined experimental manipulation of a form of topographic heterogeneity on rocky shores (holes of various sizes) with a comprehensive assessment of naturally assembled communities and multifunctionality. Structural equation modeling indicated that heterogeneity: (1) enhanced biodiversity by supporting filter feeder richness; (2) triggered a facilitation cascade via reef-forming (polychaete) and biomass-dominant (macroalga) foundation species, which in turn broadly supported functionally diverse epibiotic and understory assemblages; and (3) inhibited a key consumer (limpet). The model supported that these mechanisms exerted complementary positive effects on individual functions (e.g., water filtration, ecosystem metabolism, nutrient uptake) and, in turn, collectively enhanced multifunctionality. Topographic heterogeneity may therefore serve as a cornerstone physical attribute by initiating multiple cascades that propagate through ecological communities via foundation species, ultimately manifesting disproportionate effects on ecosystem multifunctionality., (© 2024 The Author(s). Ecology published by Wiley Periodicals LLC on behalf of The Ecological Society of America.)

Ecological forecasting models play an increasingly important role for managing natural resources and assessing our fundamental knowledge of processes driving ecological dynamics. As global environmental change pushes ecosystems beyond their historical conditions, the utility of these models may depend on their transferability to novel conditions. Because species interactions can alter resource use, timing of reproduction, and other aspects of a species' realized niche, changes in biotic conditions, which can arise from community reorganization events in response to environmental change, have the potential to impact model transferability. Using a long-term experiment on desert rodents, we assessed model transferability under novel biotic conditions to better understand the limitations of ecological forecasting. We show that ecological forecasts can be less accurate when the models generating them are transferred to novel biotic conditions and that the extent of model transferability can depend on the species being forecast. We also demonstrate the importance of incorporating uncertainty into forecast evaluation with transferred models generating less accurate and more uncertain forecasts. These results suggest that how a species perceives its competitive landscape can influence model transferability and that when uncertainties are properly accounted for, transferred models may still be appropriate for decision making. Assessing the extent of the transferability of forecasting models is a crucial step to increase our understanding of the limitations of ecological forecasts., (© 2024 The Ecological Society of America.)

This paper presents a bond graph model for the dynamics of sit-to-stand (SiTSt) and stand-to-sit (StTSi) motions. It is hypothesized that, for these motions, the central nervous system (CNS) controls the trajectory of the centre of mass of the body (COMB). The model comprises two identical submodels: one submodel emulates the working of the CNS, and the other represents the human body. Reference trajectories of the COMB determined through experimentation are input to the submodel representing the working of CNS, which automatically determines the required joint angle trajectories. Based on the required and actual joint angle trajectories, proportional integral derivative controllers at the joints (j-PID) provide the required joint torques to actuate the human body submodel. Simulation results show that during SiTSt or StTSi motions, the centre of mass of the human body submodel follows the commanded trajectories. The joint angle trajectories from the submodel representing the working of CNS closely follow the respective experimental joint angle trajectories. Also, for each motion, joint angles, torques and powers are presented, which agree with earlier studies. These findings provide adequate confidence in proposed hypothesis and indicate the potential of developed model for other biomechanical investigations of SiTSt and StTSi motions., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

Cellulose nanocrystals (CNC) are increasingly recognized for their potential in various applications, including packaging, cosmetics, and biomedical engineering. Due to their gelation properties influenced by pH and ionic strength, CNC could impact gastric emptying and satiety, beneficial for managing obesity and diabetes. This study investigated the gastric emptying of CNC (4 % and 8 %, w/w) in comparison with sodium alginate (2 %, w/w) and pectin (2 %, w/w), exploring the effect of divalent cations (Ca 2+  and Mg 2+ ) using a dynamic gastric digestion model. CNC, in the presence of Ca 2+ and Mg 2+ , formed a high-viscosity gel network under gastric conditions, leading to delayed gastric emptying. While alginate formed strong gels with Ca 2+ , it did not significantly delay gastric emptying due to the poor water-holding capacity of its gel network. Pectin showed minimal impact on gastric emptying. Among the treatments, the half-time (t 1/2 ) of gastric emptying for 8 % CNC with Ca 2+ was observed to be the longest at 215.4 ± 23.7 min, compared to the shortest times observed with pectin at 15.1 ± 1.4 min. The results suggest that different mechanisms are involved in the gastric emptying effect of different dietary fibers, and CNC is more effective than alginate and pectin assisting in promoting gastric retention and aiding in the management of body weight. This study also introduced a novel application of the dynamic gastric digestion model for estimating digestion energy expenditure, providing insights into the impact of dietary fiber on gastric emptying and satiety enhancement., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)

Several investigations have recently been conducted using microfluidic channels to sort highly motile sperm and thereby increase the probability of fertilization. To further enhance the efficiency of sperm sorting, predicting sperm movement in microfluidic channels through simulation techniques could be beneficial. In this study, we constructed a sperm swimming model based on the concept of an agent-based model. This model allows analysis at the same spatio-temporal scale similar to microfluidic channels. Sperm movement was simplistically modeled as a random walk, utilizing the distribution of sperm velocity and deflection angle obtained from experimental data. We have developed a thigmotaxis model to describe the phenomenon where sperm near the wall exhibit a reduced tendency to move away from it. Additionally, we created a rheotaxis model, in which sperm reorient in the direction opposite to the flow depending on the shear rate. Using these models, we investigated sperm behaviors within a microchannel featuring a tapered area. The results reveal that sperm accumulate within the tapered area, leading to a significant increase in sperm concentration for specific flow velocity ranges in the microchannel. This model provides valuable information for predicting the effects of sperm sorting in various microfluidic channels., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

Intermittent androgen-deprivation therapy (IADT) can be beneficial to delay the occurrence of treatment resistance and cancer relapse compared to the standard continuous therapy. To study the effect of IADT in controlling prostate cancer, we developed a Filippov prostate cancer model with a joint threshold function: therapy is implemented once the total population of androgen-dependent cells (AC-Ds) and androgen-independent cells (AC-Is) is greater than the threshold value ET, and it is suspended once the population is less than ET. As the parameters vary, our model undergoes a series of sliding bifurcations, including boundary node, focus, saddle, saddle-node and tangency bifurcations. We also obtained the coexistence of one, two or three real equilibria and the bistability of two equilibria. Our results demonstrate that the population of AC-Is can be contained at a predetermined level if the initial population of AC-Is is less than this level, and we choose a suitable threshold value., Competing Interests: Declaration of competing interest The authors declare no conflict of interest., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

Vultures play a crucial role in scavenging communities as apex scavengers. Scavenging communities in turn are a key component of terrestrial ecosystems, ensuring that dead biomass is removed quickly and efficiently. Anthropogenic disturbances, particularly mass poisonings, have caused crashes in vulture populations in Africa and Asia. We ask if vultures can re-establish themselves in a scavenging community from a point of near extirpation. To allow for maximum knowledge transfer across ecosystems, we focus on an ecosystem that is otherwise considered pristine. We chose Kruger National Park (KNP), a well-documented African scavenging community, as our focal ecosystem and parameterised a mathematical model of scavenging-community dynamics using field data from the park. We predicted the upper limit of vulture population size in an ecosystem like KNP. We then analysed vultures' path to recovery, using this empirically parameterised scavenging-community model. We used perturbation methods to determine how parameter values that may be specific to KNP influence our predictions. Comparisons of predicted vulture carrying capacity with recent population estimates suggest that the cumulative effect of human activities on vulture abundance is larger than previously believed. Our analysis shows that vulture populations can reach their carrying capacity approximately five decades after a poisoning event that would almost extirpate the population. Over shorter time scales, we predict a decade of enhanced mammal abundance (i.e. mesoscavenger release) before the mammals are excluded from the scavenging community. In our study system, jackals and hyenas are the mammalian groups predicted to benefit from the absence of vultures. However, neither group removes biomass as efficiently as vultures and animal carcasses are predicted to accumulate in the ecosystem while the vulture population recovers. In our framework, the carrying capacity for vulture populations is determined by carcass availability. As evidence for an alternative regulating factor is lacking, we conclude that present-day vulture population densities are orders of magnitude below their upper limits. Our results therefore suggest that with a recovery plan in place, the long-term prospects for vulture species and the associated ecosystems are positive., (© 2024 The Author(s). Journal of Animal Ecology published by John Wiley & Sons Ltd on behalf of British Ecological Society.)

Background: Ultra-high dose rate irradiation (≥40 Gy/s, FLASH) has been shown to reduce normal tissue toxicity, while maintaining tumor control compared to conventional dose-rate radiotherapy. The radiolytic oxygen (O 2 ) depletion (ROD) resulting from FLASH has been proposed to explain the normal tissue protection effect; however, in vivo experiments have not confirmed that FLASH induced global tissue hypoxia. Nonetheless, the experiments reported are based on volume-averaged measurement, which have inherent limitations in detecting microscopic phenomena, including the potential preservation of stem cells niches due to local FLASH-induced O 2 depletion. Computational modeling offers a complementary approach to understand the ROD caused by FLASH at the microscopic level., Purpose: We developed a comprehensive model to describe the spatial and temporal dynamics of O 2 consumption and transport in response to irradiation in vivo. The change of oxygen enhancement ratio (OER) was used to quantify and investigate the FLASH effect as a function of physiological and radiation parameters at microscopic scale., Methods: We considered time-dependent O 2 supply and consumption in a 3D cylindrical geometry, incorporating blood flow linking the O 2 concentration ([O 2 ]) in the capillary to that within the tissue through the Hill equation, radial and axial diffusion of O 2 , metabolic and zero-order radiolytic O 2 consumption, and a pulsed radiation structure. Time-evolved distributions of [O 2 ] were obtained by numerically solving perfusion-diffusion equations. The model enables the computation of dynamic O 2 distribution and the relative change of OER (δ ROD ) under various physiological and radiation conditions in vivo., Results: Initial [O 2 ] level and the subsequent changes during irradiation determined δ ROD distribution, which strongly depends on physiological parameters, i.e., intercapillary spacing, ultimately determining the tissue area with enhanced radioresistance. We observed that the δ ROD /FLASH effect is affected by and sensitive to the interplay effect among physiological and radiation parameters. It renders that the FLASH effect can be tissue environment dependent. The saturation of FLASH normal tissue protection upon dose and dose rate was shown. Beyond ∼60 Gy/s, no significant decrease in radiosensitivity within tissue region was observed. In turn, for a given dose rate, the change of radiosensitivity became saturated after a certain dose level. Pulse structures with the same dose and instantaneous dose rate but with different delivery times were shown to have distinguishable δ ROD thus tissue sparing, suggesting the average dose rate could be a metric assessing the FLASH effect and demonstrating the capability of our model to support experimental findings., Conclusion: On a macroscopic scale, the modeling results align with the experimental findings in terms of dose and dose rate thresholds, and it also indicates that pulse structure can vary the FLASH effect. At the microscopic level, this model enables us to examine the spatially resolved FLASH effect based on physiological and irradiation parameters. Our model thus provides a complementary approach to experimental methods for understanding the underlying mechanism of FLASH radiotherapy. Our results show that physiological conditions can potentially determine the FLASH efficacy in tissue protection. The FLASH effect may be observed under optimal combination of physiological parameters, not limited to radiation conditions alone., (© 2024 The Author(s). Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Background: An increase in Staphylococcus aureus infections has been reported in pediatric patients with cystic fibrosis (CF) over the last few years. This pathogen is commonly treated with vancomycin, an antibiotic for which therapeutic drug monitoring (TDM) is recommended. Updated guidelines were recently published regarding new targets of exposure for the TDM of vancomycin through a Bayesian approach, using population pharmacokinetic (popPK) models., Objectives: This study aims to assess the predictive performance of vancomycin popPK models in pediatric patients with CF and to recommend optimal initial dosing regimens based on simulations., Methods: Patient data were collected from two centers in Canada, and a literature review was conducted to identify all published vancomycin popPK models for pediatric CF patients. External evaluation and simulations were performed according to patient and occasion of treatment., Results: A total of 53 vancomycin concentrations were collected from six pediatric CF patients. Only two popPK models of vancomycin for pediatric CF patients were identified through the literature review. The external evaluation results for both centers combined revealed a population bias of 28.1% and an imprecision of 33.7%. A re-estimation of parameters was performed to improve predictive performance. The optimal initial dosing regimen was 15 mg/kg/dose administered every 6 hours according to the per occasion remodel., Conclusion: The predictive performance and identified optimal initial dosing regimens associated with the model were different depending on the data used, showing external evaluation's importance before implementing a model in clinical practice., (© 2024. The Author(s), under exclusive licence to Springer Nature Switzerland AG.)

Extracellular auxin maxima and minima are important to control plant developmental programs. Auxin gradients are provided by the concerted action of proteins from the three major plasma membrane (PM) auxin transporter classes AUX1/LAX, PIN and ATP-BINDING CASSETTE subfamily B (ABCB) transporters. But neither genetic nor biochemical nor modeling approaches have been able to reliably assign the individual roles and interplay of these transporter types. Based on the thermodynamic properties of the transporters, we show here by mathematical modeling and computational simulations that the concerted action of different auxin transporter types allows the adjustment of specific transmembrane auxin gradients. The dynamic flexibility of the 'auxin homeostat' comes at the cost of an energy-consuming 'auxin cycling' across the membrane. An unexpected finding was that potential functional ABCB-PIN synchronization appears to allow an optimization of the trade-off between the speed of PM auxin gradient adjustment on the one hand and ATP consumption and disturbance of general anion homeostasis on the other. In conclusion, our analyses provide fundamental insights into the thermodynamic constraints and flexibility of transmembrane auxin transport in plants., (© 2024 The Author(s). New Phytologist © 2024 New Phytologist Foundation.)