Estimation of cell proliferation dynamics using CFSE data

Ironing out Persisters? Revisiting the Iron Chelation Strategy to Target Planktonic Bacterial Persisters Harboured in Carbapenem-Resistant Escherichia coli

Antibiotic resistance is a global health crisis. Notably, carbapenem-resistant Enterobacterales (CRE) pose a significant clinical challenge due to the limited effective treatment options. This problem is exacerbated by persisters that develop upon antibiotic exposure. Bacteria persisters can tolerate high antibiotic doses and can cause recalcitrant infections, potentially developing further antibiotic resistance. Iron is a critical micronutrient for survival. We aimed to evaluate the utility of iron chelators, alone and in combination with antibiotics, in managing persisters. We hypothesized that iron chelators eradicate CRE persisters in vitro, when administered in combination with antibiotics. Our screening revealed three clinical isolates with bacteria persisters that resuscitated upon antibiotic removal. These isolates were treated with both meropenem and an iron chelator (deferoxamine mesylate, deferiprone or dexrazoxane) over 24 h. Against our hypothesis, bacteria persisters survived and resuscitated upon withdrawing both the antibiotic and iron chelator. Pursuing our aim, we next hypothesized that iron chelation is feasible as a post-antibiotic treatment in managing and suppressing persisters' resuscitation. We exposed bacteria persisters to an iron chelator without antibiotics. Flow cytometric assessments revealed that iron chelators are inconsistent in suppressing persister resuscitation. Collectively, these results suggest that the iron chelation strategy may not be useful as an antibiotic adjunct to target planktonic bacteria persisters.

Modelling count data with partial differential equation models in biology

Partial differential equation (PDE) models are often used to study biological phenomena involving movement-birth-death processes, including ecological population dynamics and the invasion of populations of biological cells. Count data, by definition, is non-negative, and count data relating to biological populations is often bounded above by some carrying capacity that arises through biological competition for space or nutrients. Parameter estimation, parameter identifiability, and making model predictions usually involves working with a measurement error model that explicitly relating experimental measurements with the solution of a mathematical model. In many biological applications, a typical approach is to assume the data are normally distributed about the solution of the mathematical model. Despite the widespread use of the standard additive Gaussian measurement error model, the assumptions inherent in this approach are rarely explicitly considered or compared with other options. Here, we interpret scratch assay data, involving migration, proliferation and delays in a population of cancer cells using a reaction-diffusion PDE model. We consider relating experimental measurements to the PDE solution using a standard additive Gaussian measurement error model alongside a comparison to a more biologically realistic binomial measurement error model. While estimates of model parameters are relatively insensitive to the choice of measurement error model, model predictions for data realisations are very sensitive. The standard additive Gaussian measurement error model leads to biologically inconsistent predictions, such as negative counts and counts that exceed the carrying capacity across a relatively large spatial region within the experiment. Furthermore, the standard additive Gaussian measurement error model requires estimating an additional parameter compared to the binomial measurement error model. In contrast, the binomial measurement error model leads to biologically plausible predictions and is simpler to implement. We provide open source Julia software on GitHub to replicate all calculations in this work, and we explain how to generalise our approach to deal with coupled PDE models with several dependent variables through a multinomial measurement error model, as well as pointing out other potential generalisations by linking our work with established practices in the field of generalised linear models.

Investigating cell death responses associated with histotripsy ablation of canine osteosarcoma

BACKGROUND

Osteosarcoma (OS) is the most frequently occurring primary bone tumor in dogs and people and innovative treatment options are profoundly needed. Histotripsy is an emerging tumor ablation modality, and it is essential for the clinical translation of histotripsy to gain knowledge about the outcome of nonablated tumor cells that could remain postablation. The objective of this study was to characterize the cell death genetic signature and proliferation response of canine OS cells post a near complete histotripsy ablation (96% ± 1.5) and to evaluate genetic cell death signatures associated with histotripsy ablation and OS in vivo.

METHODS

In the current study, we ablated three canine OS cell lines with a histotripsy dose that resulted in near complete ablation to allow for a viable tumor cell population for downstream analyses. To assess the in vivo cell death genetic signature, we characterized cell death genetic signature in histotripsy-ablated canine OS tumors collected 24-h postablation.

RESULTS

Differential gene expression changes observed in the 4% viable D17 and D418 cells, and histotripsy-ablated OS tumor samples, but not in Abrams cells, were associated with immunogenic cell death (ICD). The 4% viable OS cells demonstrated significantly reduced proliferation, compared to control OS cells, in vitro.

CONCLUSION

Histotripsy ablation of OS cell lines leads to direct and potentially indirect cell death as evident by, reduced proliferation in remaining viable OS cells and cell death genetic signatures suggestive of ICD both in vitro and in vivo.

In silico ADMET prediction, evaluation of cytotoxicity in mouse splenocytes and preliminary evaluation of in vitro antimalarial activity of 4-(4-chlorophenyl)thiazole compounds

In this work, an in silico study and evaluation of the cytotoxicity of 4-(4-chlorophenyl)thiazole compounds against mouse splenocytes and the chloroquine-sensitive Plasmodium falciparum 3D7 strain are reported. The in silico results showed that the compounds have important pharmacokinetic properties for compounds with potential drug candidates. Regarding cytotoxicity assays against splenocytes, the compounds have low cytotoxicity. In addition, they were able to promote activation of these cells by increasing nitric oxide production without promoting cell death. Finally, they were able to promote cell proliferation. Regarding the in vitro anti-P. falciparum activity assays, it was observed that the compounds were able to inhibit the parasite's growth, presenting IC50 values ​​ranging from 0.79 to greater than 10 µM. These results are promising when compared to chloroquine. Therefore, this study showed that 4-(4-chlorophenyl)thiazole compounds are promising candidates for antimalarials.

Integration of quantitative methods and mathematical approaches for the modeling of cancer cell proliferation dynamics

Physiological processes rely on the control of cell proliferation, and the dysregulation of these processes underlies various pathological conditions, including cancer. Mathematical modeling can provide new insights into the complex regulation of cell proliferation dynamics. In this review, we first examine quantitative experimental approaches for measuring cell proliferation dynamics in vitro and compare the various types of data that can be obtained in these settings. We then explore the toolbox of common mathematical modeling frameworks that can describe cell behavior, dynamics, and interactions of proliferation. We discuss how these wet-laboratory studies may be integrated with different mathematical modeling approaches to aid the interpretation of the results and to enable the prediction of cell behaviors, specifically in the context of cancer.

Artesunate Inhibits the Cell Growth in Colorectal Cancer by Promoting ROS-Dependent Cell Senescence and Autophagy

Although artesunate has been reported to be a promising candidate for colorectal cancer (CRC) treatment, the underlying mechanisms and molecular targets of artesunate are yet to be explored. Here, we report that artesunate acts as a senescence and autophagy inducer to exert its inhibitory effect on CRC in a reactive oxygen species (ROS)-dependent manner. In SW480 and HCT116 cells, artesunate treatment led to mitochondrial dysfunction, drastically promoted mitochondrial ROS generation, and consequently inhibited cell proliferation by causing cell cycle arrest at G0/G1 phase as well as subsequent p16- and p21-mediated cell senescence. Senescent cells underwent endoplasmic reticulum stress (ERS), and the unfolded protein response (UPR) was activated via IRE1α signaling, with upregulated BIP, IRE1α, phosphorylated IRE1α (p-IRE1α), CHOP, and DR5. Further experiments revealed that autophagy was induced by artesunate treatment due to oxidative stress and ER stress. In contrast, N-Acetylcysteine (NAC, an ROS scavenger) and 3-Methyladenine (3-MA, an autophagy inhibitor) restored cell viability and attenuated autophagy in artesunate-treated cells. Furthermore, cellular free Ca²⁺ levels were increased and could be repressed by NAC, 3-MA, and GSK2350168 (an IRE1α inhibitor). In vivo, artesunate administration reduced the growth of CT26 cell-derived tumors in BALB/c mice. Ki67 and cyclin D1 expression was downregulated in tumor tissue, while p16, p21, p-IRE1α, and LC3B expression was upregulated. Taken together, artesunate induces senescence and autophagy to inhibit cell proliferation in colorectal cancer by promoting excessive ROS generation.

Cyton2: A Model of Immune Cell Population Dynamics That Includes Familial Instructional Inheritance

Lymphocytes are the central actors in adaptive immune responses. When challenged with antigen, a small number of B and T cells have a cognate receptor capable of recognising and responding to the insult. These cells proliferate, building an exponentially growing, differentiating clone army to fight off the threat, before ceasing to divide and dying over a period of weeks, leaving in their wake memory cells that are primed to rapidly respond to any repeated infection. Due to the non-linearity of lymphocyte population dynamics, mathematical models are needed to interrogate data from experimental studies. Due to lack of evidence to the contrary and appealing to arguments based on Occam’s Razor, in these models newly born progeny are typically assumed to behave independently of their predecessors. Recent experimental studies, however, challenge that assumption, making clear that there is substantial inheritance of timed fate changes from each cell by its offspring, calling for a revision to the existing mathematical modelling paradigms used for information extraction. By assessing long-term live-cell imaging of stimulated murine B and T cells in vitro, we distilled the key phenomena of these within-family inheritances and used them to develop a new mathematical model, Cyton2, that encapsulates them. We establish the model’s consistency with these newly observed fine-grained features. Two natural concerns for any model that includes familial correlations would be that it is overparameterised or computationally inefficient in data fitting, but neither is the case for Cyton2. We demonstrate Cyton2’s utility by challenging it with high-throughput flow cytometry data, which confirms the robustness of its parameter estimation as well as its ability to extract biological meaning from complex mixed stimulation experiments. Cyton2, therefore, offers an alternate mathematical model, one that is, more aligned to experimental observation, for drawing inferences on lymphocyte population dynamics.

Advancements in Assessments of Bio-Tissue Engineering and Viable Cell Delivery Matrices Using Bile Acid-Based Pharmacological Biotechnologies

The utilisation of bioartificial organs is of significant interest to many due to their versatility in treating a wide range of disorders. Microencapsulation has a potentially significant role in such organs. In order to utilise microcapsules, accurate characterisation and analysis is required to assess their properties and suitability. Bioartificial organs or transplantable microdevices must also account for immunogenic considerations, which will be discussed in detail. One of the most characterized cases is the investigation into a bioartificial pancreas, including using microencapsulation of islets or other cells, and will be the focus subject of this review. Overall, this review will discuss the traditional and modern technologies which are necessary for the characterisation of properties for transplantable microdevices or organs, summarizing analysis of the microcapsule itself, cells and finally a working organ. Furthermore, immunogenic considerations of such organs are another important aspect which is addressed within this review. The various techniques, methodologies, advantages, and disadvantages will all be discussed. Hence, the purpose of this review is providing an updated examination of all processes for the analysis of a working, biocompatible artificial organ.

A probabilistic view on the long-time behaviour of growth-fragmentation semigroups with bounded fragmentation rates

The growth-fragmentation equation models systems of particles that grow and reproduce as time passes. An important question concerns the asymptotic behaviour of its solutions. Bertoin and Watson (2018) developed a probabilistic approach relying on the Feynman-Kac formula, that enabled them to answer to this question for sublinear growth rates. This assumption on the growth ensures that microscopic particles remain microscopic. In this work, we go further in the analysis, assuming bounded fragmentations and allowing arbitrarily small particles to reach macroscopic mass in finite time. We establish necessary and sufficient conditions on the coefficients of the equation that ensure Malthusian behaviour with exponential speed of convergence to the asymptotic profile. Furthermore, we provide an explicit expression of the latter.

Learning Equations from Biological Data with Limited Time Samples

Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets; however, the performance of these methods in the presence of common challenges from biological data has not been thoroughly explored. We present an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data. The performance of this methodology is thoroughly investigated in the face of several common challenges presented by biological data, namely, sparse data sampling, large noise levels, and heterogeneity between datasets. We find that this methodology can accurately infer the correct underlying equation and predict unobserved system dynamics from a small number of time samples when the data are sampled over a time interval exhibiting both linear and nonlinear dynamics. Our findings suggest that equation learning methods can be used for model discovery and selection in many areas of biology when an informative dataset is used. We focus on glioblastoma multiforme modeling as a case study in this work to highlight how these results are informative for data-driven modeling-based tumor invasion predictions.

Learning partial differential equations for biological transport models from noisy spatio-temporal data

We investigate methods for learning partial differential equation (PDE) models from spatio-temporal data under biologically realistic levels and forms of noise. Recent progress in learning PDEs from data have used sparse regression to select candidate terms from a denoised set of data, including approximated partial derivatives. We analyse the performance in using previous methods to denoise data for the task of discovering the governing system of PDEs. We also develop a novel methodology that uses artificial neural networks (ANNs) to denoise data and approximate partial derivatives. We test the methodology on three PDE models for biological transport, i.e. the advection-diffusion, classical Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) and nonlinear Fisher-KPP equations. We show that the ANN methodology outperforms previous denoising methods, including finite differences and both local and global polynomial regression splines, in the ability to accurately approximate partial derivatives and learn the correct PDE model.

Determining the Development of Persisters in Extensively Drug-Resistant Acinetobacter baumannii upon Exposure to Polymyxin B-Based Antibiotic Combinations Using Flow Cytometry

Polymyxin B-based combinations are increasingly prescribed as a last-line option against extensively drug-resistant (XDR) Acinetobacter baumannii It is unknown if such combinations can result in the development of nondividing persister cells in XDR A. baumannii We investigated persister development upon exposure of XDR A. baumannii to polymyxin B-based antibiotic combinations using flow cytometry. Time-kill studies (TKSs) were conducted in three nonclonal XDR A. baumannii strains with 5 log₁₀ CFU/ml bacteria against polymyxin B alone and polymyxin B-based two-drug combinations over 24 h. At different time points, samples were obtained and enumerated by viable plating and flow cytometry. Propidium iodide and carboxyfluorescein succinimidyl ester dyes were used to differentiate between live and dead cells and between dividing and nondividing cells, respectively, at the single-cell level, and nondividing live cells were resuscitated and characterized phenotypically. Our results from viable plating showed that polymyxin B plus meropenem and polymyxin B plus rifampin were each bactericidal (>99.9% kill compared to the initial inoculum) against 2/3 XDR A. baumannii strains at 24 h. By flow cytometry, however, none of the combinations were bactericidal against XDR A. baumannii at 24 h. Further analysis using cellular dyes in flow cytometry revealed that upon exposure to polymyxin B-based combinations, XDR A. baumannii entered a viable but nondividing persister state. These bacterial cells reinitiated division upon the removal of antibiotic pressure and did not have a growth deficit compared to the parent strain. We conclude that persister cells develop in XDR A. baumannii upon exposure to polymyxin B-based combinations and that nonplating methods appear to complement viable-plating methods in describing the killing activity of polymyxin B-based combinations against XDR A. baumannii.

Estimation methods for heterogeneous cell population models in systems biology

Heterogeneity among individual cells is a characteristic and relevant feature of living systems. A range of experimental techniques to investigate this heterogeneity is available, and multiple modelling frameworks have been developed to describe and simulate the dynamics of heterogeneous populations. Measurement data are used to adjust computational models, which results in parameter and state estimation problems. Methods to solve these estimation problems need to take the specific properties of data and models into account. The aim of this review is to give an overview on the state of the art in estimation methods for heterogeneous cell population data and models. The focus is on models based on the population balance equation, but stochastic and individual-based models are also discussed. It starts with a brief discussion of common experimental approaches and types of measurement data that can be obtained in this context. The second part describes computational modelling frameworks for heterogeneous populations and the types of estimation problems occurring for these models. The third part starts with a discussion of observability and identifiability properties, after which the computational methods to solve the various estimation problems are described.

Nongenetic origins of cell-to-cell variability in B lymphocyte proliferation

Rapid antibody production in response to invading pathogens requires the dramatic expansion of pathogen-derived antigen-specific B lymphocyte populations. Whether B cell population dynamics are based on stochastic competition between competing cell fates, as in the development of competence by the bacterium Bacillus subtilis, or on deterministic cell fate decisions that execute a predictable program, as during the development of the worm Caenorhabditis elegans, remains unclear. Here, we developed long-term live-cell microscopy of B cell population expansion and multiscale mechanistic computational modeling to characterize the role of molecular noise in determining phenotype heterogeneity. We show that the cell lineage trees underlying B cell population dynamics are mediated by a largely predictable decision-making process where the heterogeneity of cell proliferation and death decisions at any given timepoint largely derives from nongenetic heterogeneity in the founder cells. This means that contrary to previous models, only a minority of genetically identical founder cells contribute the majority to the population response. We computationally predict and experimentally confirm nongenetic molecular determinants that are predictive of founder cells' proliferative capacity. While founder cell heterogeneity may arise from different exposure histories, we show that it may also be due to the gradual accumulation of small amounts of intrinsic noise during the lineage differentiation process of hematopoietic stem cells to mature B cells. Our finding of the largely deterministic nature of B lymphocyte responses may provide opportunities for diagnostic and therapeutic development.

An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations

We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach.

Numerical rate function determination in partial differential equations modeling cell population dynamics

This paper introduces a method to solve the inverse problem of determining an unknown rate function in a partial differential equation (PDE) based on discrete measurements of the modeled quantity. The focus is put on a size-structured population balance equation (PBE) predicting the evolution of the number distribution of a single cell population as a function of the size variable. Since the inverse problem at hand is ill-posed, an adequate regularization scheme is required to avoid amplification of measurement errors in the solution method. The technique developed in this work to determine a rate function in a PBE is based on the approximate inverse method, a pointwise regularization scheme, which employs two key ideas. Firstly, the mollification in the directions of time and size variables are separated. Secondly, instable numerical data derivatives are circumvented by shifting the differentiation to an analytically given function. To examine the performance of the introduced scheme, adapted test scenarios have been designed with different levels of data disturbance simulating the model and measurement errors in practice. The success of the method is substantiated by visualizing the results of these numerical experiments.

Analysis of CFSE time-series data using division-, age- and label-structured population models

MOTIVATION

In vitro and in vivo cell proliferation is often studied using the dye carboxyfluorescein succinimidyl ester (CFSE). The CFSE time-series data provide information about the proliferation history of populations of cells. While the experimental procedures are well established and widely used, the analysis of CFSE time-series data is still challenging. Many available analysis tools do not account for cell age and employ optimization methods that are inefficient (or even unreliable).

RESULTS

We present a new model-based analysis method for CFSE time-series data. This method uses a flexible description of proliferating cell populations, namely, a division-, age- and label-structured population model. Efficient maximum likelihood and Bayesian estimation algorithms are introduced to infer the model parameters and their uncertainties. These methods exploit the forward sensitivity equations of the underlying partial differential equation model for efficient and accurate gradient calculation, thereby improving computational efficiency and reliability compared with alternative approaches and accelerating uncertainty analysis. The performance of the method is assessed by studying a dataset for immune cell proliferation. This revealed the importance of different factors on the proliferation rates of individual cells. Among others, the predominate effect of cell age on the division rate is found, which was not revealed by available computational methods.

AVAILABILITY AND IMPLEMENTATION

The MATLAB source code implementing the models and algorithms is available from http://janhasenauer.github.io/ShAPE-DALSP/Contact: jan.hasenauer@helmholtz-muenchen.de

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Immune Response of Calves Vaccinated with Brucella abortus S19 or RB51 and Revaccinated with RB51

Brucella abortus S19 and RB51 strains have been successfully used to control bovine brucellosis worldwide; however, currently, most of our understanding of the protective immune response induced by vaccination comes from studies in mice. The aim of this study was to characterize and compare the immune responses induced in cattle prime-immunized with B. abortus S19 or RB51 and revaccinated with RB51. Female calves, aged 4 to 8 months, were vaccinated with either vaccine S19 (0.6-1.2 x 1011 CFU) or RB51 (1.3 x 1010 CFU) on day 0, and revaccinated with RB51 (1.3 x 1010 CFU) on day 365 of the experiment. Characterization of the immune response was performed using serum and peripheral blood mononuclear cells. Blood samples were collected on days 0, 28, 210, 365, 393 and 575 post-immunization. Results showed that S19 and RB51 vaccination induced an immune response characterized by proliferation of CD4+ and CD8+ T-cells; IFN-ɣ and IL-17A production by CD4+ T-cells; cytotoxic CD8+ T-cells; IL-6 secretion; CD4+ and CD8+ memory cells; antibodies of IgG1 class; and expression of the phenotypes of activation in T-cells. However, the immune response stimulated by S19 compared to RB51 showed higher persistency of IFN-ɣ and CD4+ memory cells, induction of CD21+ memory cells and higher secretion of IL-6. After RB51 revaccination, the immune response was chiefly characterized by increase in IFN-ɣ expression, proliferation of antigen-specific CD4+ and CD8+ T-cells, cytotoxic CD8+ T-cells and decrease of IL-6 production in both groups. Nevertheless, a different polarization of the immune response, CD4+- or CD8+-dominant, was observed after the booster with RB51 for S19 and RB51 prime-vaccinated animals, respectively. Our results indicate that after prime vaccination both vaccine strains induce a strong and complex Th1 immune response, although after RB51 revaccination the differences between immune profiles induced by prime-vaccination become accentuated.

A Stochastic Model for CD4+ T Cell Proliferation and Dissemination Network in Primary Immune Response

The study of the initial phase of the adaptive immune response after first antigen encounter provides essential information on the magnitude and quality of the immune response. This phase is characterized by proliferation and dissemination of T cells in the lymphoid organs. Modeling and identifying the key features of this phenomenon may provide a useful tool for the analysis and prediction of the effects of immunization. This knowledge can be effectively exploited in vaccinology, where it is of interest to evaluate and compare the responses to different vaccine formulations. The objective of this paper is to construct a stochastic model based on branching process theory, for the dissemination network of antigen-specific CD4+ T cells. The devised model is validated on in vivo animal experimental data. The model presented has been applied to the vaccine immunization context making references to simple proliferation laws that take into account division, death and quiescence, but it can also be applied to any context where it is of interest to study the dynamic evolution of a population.

Valproic acid enhances neuronal differentiation of sympathoadrenal progenitor cells

The antiepileptic drug valproic acid (VPA) has been shown to influence the neural differentiation and neurite outgrowth of neural stem cells. Sympathoadrenal progenitor cells share properties with neural stem cells and are considered a potential cell source in the treatment of neurodegenerative diseases. The present study therefore aims at modulating the neural differentiation potential of these cells by treatment with the histone deacetylase inhibitor VPA. We studied the epigenetic effects of VPA in two culture conditions: suspension conditions aimed to expand adrenomedullary sympathoadrenal progenitors within free-floating chromospheres and adherent cell cultures optimized to derive neurons. Treatment of chromospheres with VPA may launch neuronal differentiation mechanisms and improve their neurogenic potential upon transplantation. However, also transplantation of differentiated functional neurons could be beneficial. Treating chromospheres for 7 days with clinically relevant concentrations of VPA (2 mm) revealed a decrease of neural progenitor markers Nestin, Notch2 and Sox10. Furthermore, VPA initiated catecholaminergic neuronal differentiation indicated by upregulation of the neuronal marker β-III-tubulin, the dopaminergic transcription factor Pitx3 and the catecholaminergic enzymes TH and GTPCH. In adherent neural differentiation conditions, VPA treatment improved the differentiation of sympathoadrenal progenitor cells into catecholaminergic neurons with significantly elevated levels of nor- and epinephrine. In conclusion, similar to neural stem cells, VPA launches differentiation mechanisms in sympathoadrenal progenitor cells that result in increased generation of functional neurons. Thus, data from this study will be relevant to the potential use of chromaffin progenitors in transplantation therapies of neurodegenerative diseases.

Using carboxyfluorescein diacetate succinimidyl ester to monitor intracellular protein glycation

Protein glycation is a ubiquitous process involved in vascular complications observed in diabetes. Glyoxal (GO), an intracellular reactive oxoaldehyde that is one of the most potent glycation agents, readily reacts with amines present on proteins to produce the lysine-derived adduct carboxymethyllysine, which is a prevalent advanced glycation end-product (AGE). Our group previously showed that cell exposure to GO leads to an alteration in the cell contractile activity that could occur as a result of the glycation of various proteins regulating the cell contractile machinery. Here, we measured the extent of glycation on three functionally distinct proteins known to participate in cell contraction and cytoskeletal organization-Rho-kinase (ROCK), actin, and gelsolin (GSN)-using an assay based on the reaction of the cell membrane-permeable fluorescent probe carboxyfluorescein diacetate succinimidyl ester (CFDA-SE), which reacts with primary amine groups of proteins. By combining CFDA-SE fluorescence and Western blot detection, we observed (following GO incubation) increased glycation of actin and ROCK as well as an increased interaction between actin and GSN as observed by co-immunoprecipitation. Thus, we conclude that the use of the fluorescent probe CFDA-SE offers an interesting alternative to perform a comparative analysis of the extent of intracellular protein glycation in live cells.

Paradoxical signaling by a secreted molecule leads to homeostasis of cell levels

A widespread feature of extracellular signaling in cell circuits is paradoxical pleiotropy: the same secreted signaling molecule can induce opposite effects in the responding cells. For example, the cytokine IL-2 can promote proliferation and death of T cells. The role of such paradoxical signaling remains unclear. To address this, we studied CD4(+) T cell expansion in culture. We found that cells with a 30-fold difference in initial concentrations reached a homeostatic concentration nearly independent of initial cell levels. Below an initial threshold, cell density decayed to extinction (OFF-state). We show that these dynamics relate to the paradoxical effect of IL-2, which increases the proliferation rate cooperatively and the death rate linearly. Mathematical modeling explained the observed cell and cytokine dynamics and predicted conditions that shifted cell fate from homeostasis to the OFF-state. We suggest that paradoxical signaling provides cell circuits with specific dynamical features that are robust to environmental perturbations.

Mathematical models for CFSE labelled lymphocyte dynamics: asymmetry and time-lag in division

Since their invention in 1994, fluorescent dyes such as carboxyfluorescein diacetate succinimidyl ester (CFSE) are used for cell proliferation analysis in flow cytometry. Importantly, the interpretation of such assays relies on the assumption that the label is divided equally between the daughter cells upon cell division. However, recent experimental studies indicate that division of cells is not perfectly symmetric and there is unequal distribution of protein between sister cell pairs. The uneven partition of protein or mass to daughter cells can lead to an overlap in the generations of CFSE-labelled cells with straightforward consequences for the resolution of individual generations. Numerous mathematical models developed so far for the analysis of CFSE proliferation assay incorporate the premise that the CFSE fluorescence intensity is halved in the two daughter cells. Here, we propose a novel modelling approach for the analysis of the CFSE cell proliferation assays which are characterized by poorly resolved peaks of cell generations in flow cytometric histograms. We formulate a mathematical model in the form of a system of delay hyperbolic partial differential equations which provides a good agreement with the CFSE histograms time-series data and allows an analytical treatment. The model is a further generalization of the recently proposed class of division- and label-structured models as it considers an asymmetric cell division. In addition, the basic structure of the cell cycle, i.e. the resting and cycling cell compartments, is taken into account. The model is used to estimate fundamental parameters such as activation rate, duration of the cell cycle, apoptosis rate, CFSE decay rate and asymmetry factor in cell division of monoclonal T cells during cognate interaction with dendritic cells.

Monitoring the cycling activity of cultured human keratinocytes using a CFSE-based dye tracking approach

The development of methods and tools suitable for functional analysis of keratinocytes placed in an in vitro context is of great importance for characterizing properties associated with their normal state, for detecting abnormalities related to pathological states, or for studying the effects of extrinsic factors. In the present chapter, we describe the use of the intracellular fluorescent dye carboxyfluorescein succinimidyl ester (CFSE) to monitor cell division in mass cultures of normal human keratinocytes. We detail the preparation of CFSE-labeled keratinocyte samples and the identification by flow cytometry of cell subpopulations exhibiting different cycling rates in a mitogenic culture context. In addition, we show that the CFSE-based division-tracking approach enables the monitoring of keratinocyte responsiveness to growth modulators, which is here exemplified by the cell-cycling inhibition mediated by the growth factor TGF-β1. Finally, we show that keratinocyte subpopulations, separated according to their mitotic history using CFSE fluorescence tracking, can be sorted by flow cytometry and used for further functional characterization, including determination of clone-forming efficiency.

Asymmetry of Cell Division in CFSE-Based Lymphocyte Proliferation Analysis

Flow cytometry-based analysis of lymphocyte division using carboxyfluorescein succinimidyl ester (CFSE) dye dilution permits acquisition of data describing cellular proliferation and differentiation. For example, CFSE histogram data enable quantitative insight into cellular turnover rates by applying mathematical models and parameter estimation techniques. Several mathematical models have been developed using different types of deterministic or stochastic approaches. However, analysis of CFSE proliferation assays is based on the premise that the label is halved in the two daughter cells. Importantly, asymmetry of protein distribution in lymphocyte division is a basic biological feature of cell division with the degree of the asymmetry depending on various factors. Here, we review the recent literature on asymmetric lymphocyte division and CFSE-based lymphocyte proliferation analysis. We suggest that division- and label-structured mathematical models describing CFSE-based cell proliferation should take into account asymmetry and time-lag in cell proliferation. Utilization of improved modeling algorithms will permit straightforward quantification of essential parameters describing the performance of activated lymphocytes.

A structured population modeling framework for quantifying and predicting gene expression noise in flow cytometry data

We formulated a structured population model with distributed parameters to identify mechanisms that contribute to gene expression noise in time-dependent flow cytometry data. The model was validated using cell population-level gene expression data from two experiments with synthetically engineered eukaryotic cells. Our model captures the qualitative noise features of both experiments and accurately fit the data from the first experiment. Our results suggest that cellular switching between high and low expression states and transcriptional re-initiation are important factors needed to accurately describe gene expression noise with a structured population model.

Quantifying T lymphocyte turnover

Peripheral T cell populations are maintained by production of naive T cells in the thymus, clonal expansion of activated cells, cellular self-renewal (or homeostatic proliferation), and density dependent cell life spans. A variety of experimental techniques have been employed to quantify the relative contributions of these processes. In modern studies lymphocytes are typically labeled with 5-bromo-2'-deoxyuridine (BrdU), deuterium, or the fluorescent dye carboxy-fluorescein diacetate succinimidyl ester (CFSE), their division history has been studied by monitoring telomere shortening and the dilution of T cell receptor excision circles (TRECs) or the dye CFSE, and clonal expansion has been documented by recording changes in the population densities of antigen specific cells. Proper interpretation of such data in terms of the underlying rates of T cell production, division, and death has proven to be notoriously difficult and involves mathematical modeling. We review the various models that have been developed for each of these techniques, discuss which models seem most appropriate for what type of data, reveal open problems that require better models, and pinpoint how the assumptions underlying a mathematical model may influence the interpretation of data. Elaborating various successful cases where modeling has delivered new insights in T cell population dynamics, this review provides quantitative estimates of several processes involved in the maintenance of naive and memory, CD4(+) and CD8(+) T cell pools in mice and men.

Quantifying CFSE Label Decay in Flow Cytometry Data

We developed a series of models for the label decay in cell proliferation assays when the intracellular dye carboxyfluorescein succinimidyl ester (CFSE) is used as a staining agent. Data collected from two healthy patients were used to validate the models and to compare the models with the Akiake Information Criteria. The distinguishing features of multiple decay rates in the data are readily characterized and explained via time dependent decay models such as the logistic and Gompertz models.

A novel statistical analysis and interpretation of flow cytometry data

A recently developed class of models incorporating the cyton model of population generation structure into a conservation-based model of intracellular label dynamics is reviewed. Statistical aspects of the data collection process are quantified and incorporated into a parameter estimation scheme. This scheme is then applied to experimental data for PHA-stimulated CD4+T and CD8+T cells collected from two healthy donors. This novel mathematical and statistical framework is shown to form the basis for accurate, meaningful analysis of cellular behaviour for a population of cells labelled with the dye carboxyfluorescein succinimidyl ester and stimulated to divide.

An efficient kinetic model for assemblies of amyloid fibrils and its application to polyglutamine aggregation

Protein polymerization consists in the aggregation of single monomers into polymers that may fragment. Fibrils assembly is a key process in amyloid diseases. Up to now, protein aggregation was commonly mathematically simulated by a polymer size-structured ordinary differential equations (ODE) system, which is infinite by definition and therefore leads to high computational costs. Moreover, this Ordinary Differential Equation-based modeling approach implies biological assumptions that may be difficult to justify in the general case. For example, whereas several ordinary differential equation models use the assumption that polymerization would occur at a constant rate independently of polymer size, it cannot be applied to certain protein aggregation mechanisms. Here, we propose a novel and efficient analytical method, capable of modelling and simulating amyloid aggregation processes. This alternative approach consists of an integro-Partial Differential Equation (PDE) model of coalescence-fragmentation type that was mathematically derived from the infinite differential system by asymptotic analysis. To illustrate the efficiency of our approach, we applied it to aggregation experiments on polyglutamine polymers that are involved in Huntington’s disease. Our model demonstrates the existence of a monomeric structural intermediate acting as a nucleus and deriving from a non polymerizing monomer (). Furthermore, we compared our model to previously published works carried out in different contexts and proved its accuracy to describe other amyloid aggregation processes.

Analysis and simulation of division- and label-structured population models : a new tool to analyze proliferation assays

In most biological studies and processes, cell proliferation and population dynamics play an essential role. Due to this ubiquity, a multitude of mathematical models has been developed to describe these processes. While the simplest models only consider the size of the overall populations, others take division numbers and labeling of the cells into account. In this work, we present a modeling and computational framework for proliferating cell populations undergoing symmetric cell division, which incorporates both the discrete division number and continuous label dynamics. Thus, it allows for the consideration of division number-dependent parameters as well as the direct comparison of the model prediction with labeling experiments, e.g., performed with Carboxyfluorescein succinimidyl ester (CFSE), and can be shown to be a generalization of most existing models used to describe these data. We prove that under mild assumptions the resulting system of coupled partial differential equations (PDEs) can be decomposed into a system of ordinary differential equations (ODEs) and a set of decoupled PDEs, which drastically reduces the computational effort for simulating the model. Furthermore, the PDEs are solved analytically and the ODE system is truncated, which allows for the prediction of the label distribution of complex systems using a low-dimensional system of ODEs. In addition to modeling the label dynamics, we link the label-induced fluorescence to the measure fluorescence which includes autofluorescence. Furthermore, we provide an analytical approximation for the resulting numerically challenging convolution integral. This is illustrated by modeling and simulating a proliferating population with division number-dependent proliferation rate.

A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays

Some key features of a mathematical description of an immune response are an estimate of the number of responding cells and the manner in which those cells divide, differentiate, and die. The intracellular dye CFSE is a powerful experimental tool for the analysis of a population of dividing cells, and numerous mathematical treatments have been aimed at using CFSE data to describe an immune response [30,31,32,37,38,42,48,49]. Recently, partial differential equation structured population models, with measured CFSE fluorescence intensity as the structure variable, have been shown to accurately fit histogram data obtained from CFSE flow cytometry experiments [18,19,52,54]. In this report, the population of cells is mathematically organized into compartments, with all cells in a single compartment having undergone the same number of divisions. A system of structured partial differential equations is derived which can be fit directly to CFSE histogram data. From such a model, cell counts (in terms of the number of divisions undergone) can be directly computed and thus key biological parameters such as population doubling time and precursor viability can be determined. Mathematical aspects of this compartmental model are discussed, and the model is fit to a data set. As in [18,19], we find temporal and division dependence in the rates of proliferation and death to be essential features of a structured population model for CFSE data. Variability in cellular autofluorescence is found to play a significant role in the data, as well. Finally, the compartmental model is compared to previous work, and statistical aspects of the experimental data are discussed.

A novel nonradioactive CFDA assay to monitor the cellular immune response in myeloid leukemia

BACKGROUND

Donor lymphocyte transfusion (DLT) may induce the graft-versus-leukemia (GVL) effect for patients with AML relapsed after transplant. However, AML is a highly diverse disease and the limited overall efficacy of DLT in clinical practice emphasizes the importance of identifying a specific subgroup of patients who might benefit from this treatment approach.

OBJECTIVE

To monitor the cellular immune response after DLT, we developed an active specific immunization strategy using in vitro generated AML-trained T cells to induce a highly specific antileukemic T-cell response and thus established a novel nonradioactive assay system to assess the antileukemia immunity by flow cytometry, correlated with [3H]-thymidine uptake.

METHODS

The myeloid blasts derived from five patients with AML relapsed post-allogeneic hematopoietic stem cell transplantation (allo-HSCT) were first labeled with CFDA (5,6-carboxyfluorescein diacetate succinimidyl ester). To analyze the growth inhibitory potential of the donor T cells trained by AML progenitor cells, the myeloid blasts were induced to proliferate by means of a cytokine cocktail (50ng/mL of SCF; 25ng/mL of IL-3; 100ng/mL of GM-CSF; 100ng/mL of G-CSF; 2U/mL of EPO; 0.47g/L of transferrin; and 5×10(-5)mmol/L of 2-ME). The T cell mediated growth inhibitory potential was detected after 5 days by flow cytometry and correlated with [3H]-thymidine uptake. The simultaneous use of TO-PRO-dye and calibrate beads allowed not only the cell viability to be known but also allowed quantification of the effector function.

RESULTS

Here, we applied a CFDA dye to track the proliferation and expansion of AML blasts in response to the cytokine cocktail in vitro. AML-trained T cells, expressed high levels of the activation markers CD25 and CD69, and were generated to recognize the leukemic progenitor cells and inhibit cytokine-induced leukemic cell proliferation, which is an active specific immunization strategy circumventing the identification of leukemia-associated antigens. The capability of proliferation inhibition of AML-trained T cells evaluated with our nonradioactive, CFDA-based assay provided comparable results with the classic [3H]-thymidine assay with an even lower ratio of effector to target cells.

CONCLUSION

Taken together, the novel, nonradioactive, CFDA-based assay was a robust tool to monitor the antileukemic immune response after DLT in myeloid leukemias.

Nonlinear stochastic Markov processes and modeling uncertainty in populations

We consider an alternative approach to the use of nonlinear stochastic Markov processes (which have a Fokker-Planck or Forward Kolmogorov representation for density) in modeling uncertainty in populations. These alternate formulations, which involve imposing probabilistic structures on a family of deterministic dynamical systems, are shown to yield pointwise equivalent population densities. Moreover, these alternate formulations lead to fast efficient calculations in inverse problems as well as in forward simulations. Here we derive a class of stochastic formulations for which such an alternate representation is readily found.

A new model for the estimation of cell proliferation dynamics using CFSE data

CFSE analysis of a proliferating cell population is a popular tool for the study of cell division and divisionlinked changes in cell behavior. Recently Banks et al. (2011), Luzyanina et al. (2009), Luzyanina et al. (2007), a partial differential equation (PDE) model to describe lymphocyte dynamics in a CFSE proliferation assay was proposed. We present a significant revision of this model which improves the physiological understanding of several parameters. Namely, the parameter used previously as a heuristic explanation for the dilution of CFSE dye by cell division is replaced with a more physical component, cellular autofluorescence. The rate at which label decays is also quantified using a Gompertz decay process. We then demonstrate a revised method of fitting the model to the commonly used histogram representation of the data. It is shown that these improvements result in a model with a strong physiological basis which is fully capable of replicating the behavior observed in the data.

Identification of models of heterogeneous cell populations from population snapshot data

Background

Most of the modeling performed in the area of systems biology aims at achieving a quantitative description of the intracellular pathways within a "typical cell". However, in many biologically important situations even clonal cell populations can show a heterogeneous response. These situations require study of cell-to-cell variability and the development of models for heterogeneous cell populations.

Results

In this paper we consider cell populations in which the dynamics of every single cell is captured by a parameter dependent differential equation. Differences among cells are modeled by differences in parameters which are subject to a probability density. A novel Bayesian approach is presented to infer this probability density from population snapshot data, such as flow cytometric analysis, which do not provide single cell time series data. The presented approach can deal with sparse and noisy measurement data. Furthermore, it is appealing from an application point of view as in contrast to other methods the uncertainty of the resulting parameter distribution can directly be assessed.

Conclusions

The proposed method is evaluated using artificial experimental data from a model of the tumor necrosis factor signaling network. We demonstrate that the methods are computationally efficient and yield good estimation result even for sparse data sets.

Label Structured Cell Proliferation Models

We present a general class of cell population models that can be used to track the proliferation of cells which have been labeled with a fluorescent dye. The mathematical models employ fluorescence intensity as a structure variable to describe the evolution in time of the population density of proliferating cells. While cell division is a major component of changes in cellular fluorescence intensity, models developed here also address overall label degradation.