Modelling deuterium labelling of lymphocytes with temporal and/or kinetic heterogeneity

To study the kinetics of lymphocytes, models have divided the cell population into subpopulations with different turnover rates. These have been called ‘kinetic heterogeneity models’ so as to distinguish them from ‘temporal heterogeneity models’, in which a cell population may have different turnover rates at different times, e.g. when resting versus when activated. We model labelling curves for temporally heterogeneous populations, and predict that they exhibit equal biphasic up- and downslopes. We show when cells divide only once upon activation, these slopes are dominated by the slowest exponent, yielding underestimates of the average turnover rate. When cells undergo more than one division, the labelling curves allow fitting of the two exponential slopes in the temporal heterogeneity model. The same data can also be described with a two-compartment kinetic heterogeneity model. In both instances, the average turnover rate is correctly estimated. Because both models assume a different cell biology but describe the data equally well, the parameters of either model have no simple biological interpretation, as each parameter could reflect a combination of parameters of another biological process. Thus, even if there are sufficient data to reliably estimate all exponentials, one can only accurately estimate an average turnover rate. We illustrate these issues by re-fitting labelling data from healthy and HIV-infected individuals.     

Development and validation of a two-dimensional population balance model for a supercritical CO2 antisolvent batch crystallization process

In this study, a two-dimensional population balance model with solvent removal kinetics has been developed to predict the dynamic behavior of carbamazepine form II crystals produced by a supercritical CO₂ antisolvent batch crystallization process. The model was simulated and validated using experimental crystal size distribution data (CSD). The model was able to accurately predict the behavior of CSD with a change in process operating conditions. The model was also applied to study the time evolution of aspect ratio, average crystal length, and solute concentration in the solution. Finally, solvent removal kinetics were modeled to evaluate the solvent content and drying temperature of the drying gas during the solvent removal process. The developed mathematical model and the presented results suggest the ability of the discussed approach to make suitable model predictions, which can significantly reduce the number of experimental trials required for process design, optimization, and control.     

Mathematical modelling of the evolution of protein distribution within single PLGA microspheres: prediction of local concentration profiles and release kinetics

Protein release from poly(D,L-lactide-co-glycolide) (PLGA) microspheres in an aqueous environment is governed by the diffusion of the protein through an autocatalytically degrading polymeric matrix. Many attempts have been made to model the release rate of proteins from biodegrading matrices, but the transport parameters involved in the process are not fully established at the microscale level. The aim of this work was to develop a new mathematical model taking into account the temporal evolution of the radial protein distribution during release, and to provide physical insight into the relation between local transport features and microsphere degradation. The model was validated by comparing its predictions with the experimentally determined protein concentration profiles in PLGA microspheres loaded with tetramethylrhodamine-labelled bovine serum albumin (BSA-Rhod) as a model protein. Morphological studies were carried out by scanning electron microscopy (SEM), while release kinetics and time-dependent BSA-Rhod concentration profiles within the microspheres were studied by a confocal laser scanning microscopy (CLSM)-assisted technique. The model, based on a modification of Fick's second law of diffusion, could closely fit the experimental protein radial distribution profiles in the microspheres as a function of time. It is also a useful tool to ab initio design protein release devices using degrading matrices.     

Lattice modeling of chloride diffusion in sound and cracked concrete

Reinforced concrete structures are frequently exposed to aggressive environmental conditions. Most notably, chloride ions from sea water or de-icing salts are potentially harmful since they promote corrosion of steel reinforcement. Concrete cover of sufficient quality and depth can ensure protection of the steel reinforcement. However, it is necessary to study the effects of material heterogeneity and cracking on chloride ingress in concrete. This is done herein by proposing a three-dimensional lattice model capable of simulating chloride transport in saturated sound and cracked concrete. Means of computationally determining transport properties of individual phases in heterogeneous concrete (aggregate, mortar, and interface), knowing the concrete composition and its averaged transport properties, are presented and discussed. Based on numerical experimentation and available literature, a relation between the effective diffusion coefficient of cracked lattice elements and the crack width was adopted. The proposed model is coupled with a lattice fracture model to enable simulation of chloride ingress in cracked concrete. The model was validated on data from the literature, showing good agreement with experimental results.     

Effects of heterogeneity in infection-exposure history and immunity on the dynamics of a protozoan parasite

Infection systems where traits of the host, such as acquired immunity, interact with the infection process can show complex dynamic behaviour with counter-intuitive results. In this study, we consider the traits ‘immune status’ and ‘exposure history’, and our aim is to assess the influence of acquired individual heterogeneity in these traits. We have built an individual-based model of Eimeria acervulina infections, a protozoan parasite with an environmental stage that causes coccidiosis in chickens. With the model, we simulate outbreaks of the disease under varying initial contaminations. Heterogeneity in the traits arises stochastically through differences in the dose and frequency of parasites that individuals pick up from the environment. We find that the relationship between the initial contamination and the severity of an outbreak has a non-monotonous ‘wave-like’ pattern. This pattern can be explained by an increased heterogeneity in the host population caused by the infection process at the most severe outbreaks. We conclude that when dealing with these types of infection systems, models that are used to develop or evaluate control measures cannot neglect acquired heterogeneity in the host population traits that interact with the infection process.     

A model of averaged radiation transfer in two-phase heterogeneous medium

Presently employed for describing the radiation transfer in heterogeneous media is the radiation transfer equation (RTE) which is rigorously validated only for homogeneous media, although the hypothesis of the validity of one and the same model for both homogeneous and heterogeneous media is questionable. The local intensities of radiation in different phases of heterogeneous medium may significantly differ; therefore, the only averaged radiation intensity employed in the RTE model is insufficient. A model of radiation transfer is obtained for two-phase heterogeneous medium in the geometrical optics limit, which consists of two transfer equations for partial radiation intensities averaged in each phase separately. These equations resemble ordinary RTEs but include the exchange of radiation between the phases; therefore, they are referred to as the vector model of RTE. This model reduces to ordinary RTE if one of two phases is nontransparent or one phase prevails in the volume. It is demonstrated that the vector model of RTE in these two extreme cases does not contradict the known results of calculations by the ray optics and Monte-Carlo methods, as well as the experimental data. The suggested vector model is necessary if both phases are transparent or semitransparent and their volume fractions are comparable, because no adequate mathematical models are available in this case. The vector model describes the known results of Monte-Carlo simulation of packed beds of semitransparent spheres. The use of the vector model of RTE for experimental identification of the radiative properties is illustrated with the example of normal-directional reflectance of packed bed of semitransparent SiC particles. The results of numerical calculations confirm the general experimentally observed tendency for increase in reflectance with increasing angle of reflection. The main contribution to the error is made by the boundary conditions for vector RTEs; therefore, detailed analysis of the suggested model in boundary regions is required.     

Role of cell cycle on the cellular uptake and dilution of nanoparticles in a cell population

Nanoparticles are considered a primary vehicle for targeted therapies because they can pass biological barriers and enter and distribute within cells by energy-dependent pathways. So far, most studies have shown that nanoparticle properties, such as size and surface, can influence how cells internalize nanoparticles. Here, we show that uptake of nanoparticles by cells is also influenced by their cell cycle phase. Although cells in different phases of the cell cycle were found to internalize nanoparticles at similar rates, after 24 h the concentration of nanoparticles in the cells could be ranked according to the different phases: G2/M > S > G0/G1. Nanoparticles that are internalized by cells are not exported from cells but are split between daughter cells when the parent cell divides. Our results suggest that future studies on nanoparticle uptake should consider the cell cycle, because, in a cell population, the dose of internalized nanoparticles in each cell varies as the cell advances through the cell cycle.     

Computational modelling of mitotic exit in budding yeast: the role of separase and Cdc14 endocycles

The operating principles of complex regulatory networks are best understood with the help of mathematical modelling rather than by intuitive reasoning. Hereby, we study the dynamics of the mitotic exit (ME) control system in budding yeast by further developing the Queralt''s model. A comprehensive systems view of the network regulating ME is provided based on classical experiments in the literature. In this picture, Cdc20–APC is a critical node controlling both cyclin (Clb2 and Clb5) and phosphatase (Cdc14) branches of the regulatory network. On the basis of experimental situations ranging from single to quintuple mutants, the kinetic parameters of the network are estimated. Numerical analysis of the model quantifies the dependence of ME control on the proteolytic and non-proteolytic functions of separase. We show that the requirement of the non-proteolytic function of separase for ME depends on cyclin-dependent kinase activity. The model is also used for the systematic analysis of the recently discovered Cdc14 endocycles. The significance of Cdc14 endocycles in eukaryotic cell cycle control is discussed as well.     

Mass Cytometry and Single‐Cell RNA‐seq Profiling of the Heterogeneity in Human Peripheral Blood Mononuclear Cells Interacting with Silver Nanoparticles

Understanding the interactions between nanoparticles (NPs) and human immune cells is necessary for justifying their utilization in consumer products and biomedical applications. However, conventional assays may be insufficient in describing the complexity and heterogeneity of cell–NP interactions. Herein, mass cytometry and single‐cell RNA‐sequencing (scRNA‐seq) are complementarily used to investigate the heterogeneous interactions between silver nanoparticles (AgNPs) and primary immune cells. Mass cytometry reveals the heterogeneous biodistribution of the positively charged polyethylenimine‐coated AgNPs in various cell types and finds that monocytes and B cells have higher association with the AgNPs than other populations. scRNA‐seq data of these two cell types demonstrate that each type has distinct responses to AgNP treatment: NRF2‐mediated oxidative stress is confined to B cells, whereas monocytes show Fcγ‐mediated phagocytosis. Besides the between‐population heterogeneity, analysis of single‐cell dose–response relationships further reveals within‐population diversity for the B cells and naïve CD4⁺ T cells. Distinct subsets having different levels of cellular responses with respect to their cellular AgNP doses are found. This study demonstrates that the complementary use of mass cytometry and scRNA‐seq is helpful for gaining in‐depth knowledge on the heterogeneous interactions between immune cells and NPs and can be incorporated into future toxicity assessments of nanomaterials.     

A stochastic mathematical model of 4D tumour spheroids with real-time fluorescent cell cycle labelling

In vitro tumour spheroids have been used to study avascular tumour growth and drug design for over 50 years. Tumour spheroids exhibit heterogeneity within the growing population that is thought to be related to spatial and temporal differences in nutrient availability. The recent development of real-time fluorescent cell cycle imaging allows us to identify the position and cell cycle status of individual cells within the growing spheroid, giving rise to the notion of a four-dimensional (4D) tumour spheroid. We develop the first stochastic individual-based model (IBM) of a 4D tumour spheroid and show that IBM simulation data compares well with experimental data using a primary human melanoma cell line. The IBM provides quantitative information about nutrient availability within the spheroid, which is important because it is difficult to measure these data experimentally.     

The dynamic balance of import and export of zinc in Escherichia coli suggests a heterogeneous population response to stress

Zinc is essential for life, but toxic in excess. Thus all cells must control their internal zinc concentration. We used a systems approach, alternating rounds of experiments and models, to further elucidate the zinc control systems in Escherichia coli. We measured the response to zinc of the main specific zinc import and export systems in the wild-type, and a series of deletion mutant strains. We interpreted these data with a detailed mathematical model and Bayesian model fitting routines. There are three key findings: first, that alternate, non-inducible importers and exporters are important. Second, that an internal zinc reservoir is essential for maintaining the internal zinc concentration. Third, our data fitting led us to propose that the cells mount a heterogeneous response to zinc: some respond effectively, while others die or stop growing. In a further round of experiments, we demonstrated lower viable cell counts in the mutant strain tested exposed to excess zinc, consistent with this hypothesis. A stochastic model simulation demonstrated considerable fluctuations in the cellular levels of the ZntA exporter protein, reinforcing this proposal. We hypothesize that maintaining population heterogeneity could be a bet-hedging response allowing a population of cells to survive in varied and fluctuating environments.     

A dimensionless ordered pull-through model of the mammalian lens epithelium evidences scaling across species and explains the age-dependent changes in cell density in the human lens

We present a mathematical (ordered pull-through; OPT) model of the cell-density profile for the mammalian lens epithelium together with new experimental data. The model is based upon dimensionless parameters, an important criterion for inter-species comparisons where lens sizes can vary greatly (e.g. bovine (approx. 18 mm); mouse (approx. 2 mm)) and confirms that mammalian lenses scale with size. The validated model includes two parameters: β/α, which is the ratio of the proliferation rate in the peripheral and in the central region of the lens; and γ_GZ, a dimensionless pull-through parameter that accounts for the cell transition and exit from the epithelium into the lens body. Best-fit values were determined for mouse, rat, rabbit, bovine and human lens epithelia. The OPT model accounts for the peak in cell density at the periphery of the lens epithelium, a region where cell proliferation is concentrated and reaches a maximum coincident with the germinative zone. The β/α ratio correlates with the measured FGF-2 gradient, a morphogen critical to lens cell survival, proliferation and differentiation. As proliferation declines with age, the OPT model predicted age-dependent changes in cell-density profiles, which we observed in mouse and human lenses.     

Mixed model assembly system with multiple secondary feeder lines: layout design and balancing procedure for ATO environment

The constant research for efficiency and flexibility has forced assembly systems to change from simple/single assembly lines to mixed model assembly lines, while the necessity to reduce inventory has led the transition from single to multi-line systems, where some components are assembled in secondary lines, called feeder lines, connected to the main one by a ‘pull philosophy’. A possible approach to configure such an assembly system is to balance the main line first and use the retrieved cycle time to balance each feeder line separately, which is a questionable solution, especially if operators can perform tasks on both the feeder and the main line. Moreover for its complexity the mixed model balancing problem is usually solved transforming it into a single model by creating a single ‘virtual average model’, representative of the whole production mix. The use of a virtual average model assumes that the processing times of some models are higher or lower than the cycle time, which creates overload/idle time at the stations. This approach, especially in complex multi line production systems, largely reduces the assembly line productivity and increases the buffers dimensions. This paper faces the mixed model assembly line balancing problem in the presence of multiple feeder lines, introducing an innovative integrated main-feeder lines balancing procedure in case of unpaced assembly systems. The proposed approach is compared with the classical one and validated through simulation and industrial applications.     

Study of cohabitation and interconnection effects on normal and leukaemic stem cells dynamics in acute myeloid leukaemia

On the basis of recent studies, understanding the intimate relationship between normal and leukaemic stem cells is very important in leukaemia treatment. The authors’ aim in this work is to clarify and assess the effect of coexistence and interconnection phenomenon on the healthy and cancerous stem cell dynamics. To this end, they perform the analysis of two time‐delayed stem cell models in acute myeloid leukaemia. The first model is based on decoupled healthy and cancerous stem cell populations (i.e. there is no interaction between cell dynamics) and the second model includes interconnection between both population''s dynamics. By using the positivity of both systems, they build new linear functions that permit to derive global stability conditions for each model. Moreover, knowing that most common types of haematological diseases are characterised by the existence of oscillations, they give conditions for the existence of a limit cycle (oscillations) in a particularly interesting healthy situation based on Poincare–Bendixson theorem. The obtained results are simulated and interpreted to be significant in understanding the effect of interconnection and would lead to an improvement in leukaemia treatment.Inspec keywords: cellular biophysics, cancer, blood, stability, patient treatmentOther keywords: healthy stem cell dynamics, cancerous stem cell dynamics, time‐delayed stem cell models, acute myeloid leukaemia, cancerous stem cell populations, leukaemia treatment, normal stem cells dynamics, leukaemic stem cells dynamics, intimate relationship, interconnection effects, cohabitation effects, decoupled stem cell populations, global stability conditions, haematological diseases, oscillations, limit cycle, Poincare–Bendixson theorem     

A probabilistic model for multiaxial high cycle fatigue

A probabilistic framework developed to model multiaxial high cycle fatigue tests is proposed. Up to now, with a probabilistic point of view (i.e., Weibull law), models account for the stress heterogeneity effect by introducing the concept of effective volume. It is proposed to extend this concept to multiaxial load histories. It consists in introducing a factor representing the distribution of activated slip directions. The non‐proportionality effect is taken into account with no additional parameter with respect to traditional (i.e., Weibull) probabilistic approaches. The proposed model is validated on a large experimental data base and compared with other models.     

MP-PIC modeling of CFB risers with homogeneous and heterogeneous drag models

In this paper, the MP-PIC (multiphase particle-in-cell) approach is used for three-dimensional (3D) modeling of the gas-solid flows in two types of circulating fluidized bed (CFB) risers with Geldart group A and B particles by incorporating the homogeneous and heterogeneous drag force models in the MP-PIC method, respectively. First, the effects of the three important simulation parameters, namely, the grid cell number, numerical particle-parcel size and time step, are investigated. Having determined the appropriate values for the three parameters, the hydrodynamic characteristics predicted by different drag force models are rigorously analyzed. The homogeneous drag models considered are the six models, the Wen-Yu, Wenyu-Ergun, Syamlal-O’Brien, Gidaspow, HKL, and BVK models, while the four heterogeneous models considered are Sarkar and EMMS-based models (EMMS-Yang, EMMS-Matrix and EMMS-QL). For the riser 1 with the Geldart A particles, all the six homogeneous models predict extremely high solid fluxes and inconsistent void fraction distributions compared with experimental results. The heterogeneous Sarkar and EMMS-based models can effectively improve the simulation accuracy and predict a typical core-annulus flow structure. The lately-developed EMMS-QL model produces the most accurate solid flux. For the riser 2 with the Geldart B particles, both the heterogeneous and homogeneous drag force models can predict a reasonable flow structure. Further, there are no significant differences in the void fraction and velocity profiles due to the choice of a drag force model over the other. These drag force models also successfully capture the meso-scale local particle clusters. Of these drag-force models, the Wenyu-Ergun drag-forec model predicts comparatively accurate solid flux. Generally, MP-PIC combined with heterogeneous Sarkar and EMMS-based drag force models reasonably improve the simulation accuracy for the Geldart A particles, while these heterogeneous models have no superiority over the homogeneous drag models for the Geldart B particles.     

Airborne laser-induced oceanic chlorophyll fluorescence: solar-induced quenching corrections by use of concurrent downwelling irradiance measurements

Airborne laser-induced (and water Raman-normalized) spectral fluorescence emissions from oceanic chlorophyll were obtained during variable downwelling irradiance conditions induced by diurnal variability and patchy clouds. Chlorophyll fluorescence profiles along geographically repeated inbound and outbound flight track lines, separated in time by ~3-6 h and subject to overlying cloud movement, were found to be identical after corrections made with concurrent downwelling irradiance measurements. The corrections were accomplished by a mathematical model containing an exponential of the ratio of the instantaneous-to-average downwelling irradiance. Concurrent laser-induced phycoerythrin fluorescence and chromophoric dissolved organic matter fluorescence were found to be invariant to downwelling irradiance and thus, along with sea-surface temperature, established the near constancy of the oceanic surface layer during the experiment and validated the need for chlorophyll fluorescence quenching corrections over wide areas of the ocean.     

Effect of Process Variables on Kinetics and Gas Consumption in Rotor-Degassing Assisted by Physical and Mathematical Modeling

Mathematical and physical models of water deoxidation in a batch aluminum degassing reactor using the rotor-injector technique were developed. The mathematical model was successfully validated against measured degassing kinetics. The physical model was employed to perform a process analysis using a two-level factorial experimental design to determine the influence of gas flow rate, impeller angular velocity, and gas injection points on gas consumption efficiency and degassing kinetics. A combination of higher rotor speeds and gas flow rates results in fast degassing kinetics. However, moderate gas flow rates are recommended to save gas.     

Edge-based compartmental modelling for infectious disease spread

The primary tool for predicting infectious disease spread and intervention effectiveness is the mass action susceptible–infected–recovered model of Kermack & McKendrick. Its usefulness derives largely from its conceptual and mathematical simplicity; however, it incorrectly assumes that all individuals have the same contact rate and partnerships are fleeting. In this study, we introduce edge-based compartmental modelling, a technique eliminating these assumptions. We derive simple ordinary differential equation models capturing social heterogeneity (heterogeneous contact rates) while explicitly considering the impact of partnership duration. We introduce a graphical interpretation allowing for easy derivation and communication of the model and focus on applying the technique under different assumptions about how contact rates are distributed and how long partnerships last.     

A quantitative assessment of heterogeneity for surface-immobilized proteins

Many biotechnological applications use protein receptors immobilized on solid supports. Although, in solution, these receptors display homogeneous binding affinities and association/dissociation kinetics for their complementary ligand, they often display heterogeneous binding characteristics after immobilization. In this study, a fluorescence-based fiber-optic biosensor was used to quantify the heterogeneity associated with the binding of a soluble analyte, fluorescently labeled trinitrobenzene, to surface-immobilized monoclonal anti-TNT antibodies. The antibodies were immobilized on silica fiber-optic probes via five different immobilization strategies. We used the Sips isotherm to assesses and compare the heterogeneity in the antibody binding affinity and kinetic rate parameters for these different immobilization schemes. In addition, we globally analyzed kinetic data with a two-compartment transport-kinetic model to analyze the heterogeneity in the analyte-antibody kinetics. These analyses provide a quantitative tool by which to evaluate the relative homogeneity of different antibody preparations. Our results demonstrate that the more homogeneous protein preparations exhibit more uniform affinities and kinetic constants.