Hysteresis modeling for calcium-mediated ciliary beat frequency in airway epithelial cells

Mathematical Modeling Reveals the Role of Hypoxia in the Promotion of Human Mesenchymal Stem Cell Long-Term Expansion

Many experimental studies have found that human mesenchymal stem cells (MSCs) in long-term culture exhibited enhanced cell proliferation and prolonged lifespan under hypoxia (around 1%–7% oxygen) against the normoxic condition (about 21% oxygen). Inspired by the experimental findings, we aimed to investigate the hypoxic effects on MSC expansion quantitatively through mathematical modeling to elucidate the corresponding biological mechanism. A two-compartment model based on ordinary differential equations (ODEs), which incorporate cellular division and senescence via state transition, was developed to describe the MSC expansion process. Parameters of this model were fitted to experimental data and used to interpret the different proliferative capacities of MSCs under hypoxia and normoxia along with model sensitivity analysis. The proposed model was tested on data from two separate experimental studies, and it could reproduce the observed growth characteristics in both conditions. Overall, this compartmental model with a logistic state transition rate was sufficient to explain the experimental findings and highlighted the promotive role of hypoxia in MSC proliferation. This in silico study suggests that hypoxia can enhance MSC long-term expansion mainly by delaying replicative senescence, which is indicated by the slowdown of the state transition rate in our model. Therefore, this explanatory model may provide theoretical proof for the experimentally observed MSC growth superiority under hypoxia and has the potential to further optimize MSC culture protocols for regenerative medicine applications.

Adaptation of the modified Bouc-Wen model to compensate for hysteresis in respiratory motion for the list-mode binning of cardiac SPECT and PET acquisitions: testing using MRI

PURPOSE

Binning list-mode acquisitions as a function of a surrogate signal related to respiration has been employed to reduce the impact of respiratory motion on image quality in cardiac emission tomography (SPECT and PET). Inherent in amplitude binning is the assumption that there is a monotonic relationship between the amplitude of the surrogate signal and respiratory motion of the heart. This assumption is not valid in the presence of hysteresis when heart motion exhibits a different relationship with the surrogate during inspiration and expiration. The purpose of this study was to investigate the novel approach of using the Bouc-Wen (BW) model to provide a signal accounting for hysteresis when binning list-mode data with the goal of thereby improving motion correction. The study is based on the authors' previous observations that hysteresis between chest and abdomen markers was indicative of hysteresis between abdomen markers and the internal motion of the heart.

METHODS

In 19 healthy volunteers, they determined the internal motion of the heart and diaphragm in the superior-inferior direction during free breathing using MRI navigators. A visual tracking system (vts) synchronized with MRI acquisition tracked the anterior-posterior motions of external markers placed on the chest and abdomen. These data were employed to develop and test the Bouc-Wen model by inputting the vts derived chest and abdomen motions into it and using the resulting output signals as surrogates for cardiac motion. The data of the volunteers were divided into training and testing sets. The training set was used to obtain initial values for the model parameters for all of the volunteers in the set, and for set members based on whether they were or were not classified as exhibiting hysteresis using a metric derived from the markers. These initial parameters were then employed with the testing set to estimate output signals. Pearson's linear correlation coefficient between the abdomen, chest, average of chest and abdomen markers, and Bouc-Wen derived signals versus the true internal motion of the heart from MRI was used to judge the signals match to the heart motion.

RESULTS

The results show that the Bouc-Wen model generated signals demonstrated strong correlation with the heart motion. This correlation was slightly larger on average than that of the external surrogate signals derived from the abdomen marker, and average of the abdomen and chest markers, but was not statistically significantly different from them.

CONCLUSIONS

The results suggest that the proposed model has the potential to be a unified framework for modeling hysteresis in respiratory motion in cardiac perfusion studies and beyond.

Asymmetric distribution of dynamic calcium signals in the node of mouse embryo during left-right axis formation

In the node of mouse embryo, rotational movements of cilia generate an external liquid flow known as nodal flow, which determines left-right asymmetric gene expression. How nodal flow is converted into asymmetric gene expression is still controversial, but the increase of Ca(2+) levels in endodermal cells to the left of the node has been proposed to play a role. However, Ca(2+) signals inside the node itself have not yet been described. By our optimized Ca(2+) imaging method, we were able to observe dynamic Ca(2+) signals in the node in live mouse embryos. Pharmacological disruption of Ca(2+) signals did not affect ciliary movements or nodal flow, but did alter the expression patterns of the Nodal and Cerl-2 genes. Quantitative analyses of Ca(2+) signal frequencies and distributions showed that during left-right axis establishment, formerly symmetric Ca(2+) signals became biased to the left side. In iv/iv mutant embryos that showed randomized laterality due to ciliary immotility, Ca(2+) signals were found to be variously left-sided, right-sided, or bilateral, and thus symmetric on average. In Pkd2 mutant embryos, which lacked polycystin-2, a Ca(2+)-permeable cation channel necessary for left-right axis formation, the Ca(2+) signal frequency was lower than in wild-type embryos. Our data support a model in which dynamic Ca(2+) signals in the node are involved in left-right patterning.

Modeling of hysteresis in gene regulatory networks

Hysteresis, observed in many gene regulatory networks, has a pivotal impact on biological systems, which enhances the robustness of cell functions. In this paper, a general model is proposed to describe the hysteretic gene regulatory network by combining the hysteresis component and the transient dynamics. The Bouc-Wen hysteresis model is modified to describe the hysteresis component in the mammalian gene regulatory networks. Rigorous mathematical analysis on the dynamical properties of the model is presented to ensure the bounded-input-bounded-output (BIBO) stability and demonstrates that the original Bouc-Wen model can only generate a clockwise hysteresis loop while the modified model can describe both clockwise and counter clockwise hysteresis loops. Simulation studies have shown that the hysteresis loops from our model are consistent with the experimental observations in three mammalian gene regulatory networks and two E.coli gene regulatory networks, which demonstrate the ability and accuracy of the mathematical model to emulate natural gene expression behavior with hysteresis. A comparison study has also been conducted to show that this model fits the experiment data significantly better than previous ones in the literature. The successful modeling of the hysteresis in all the five hysteretic gene regulatory networks suggests that the new model has the potential to be a unified framework for modeling hysteresis in gene regulatory networks and provide better understanding of the general mechanism that drives the hysteretic function.

Engineering airway epithelium

Airway epithelium is constantly presented with injurious signals, yet under healthy circumstances, the epithelium maintains its innate immune barrier and mucociliary elevator function. This suggests that airway epithelium has regenerative potential (I. R. Telford and C. F. Bridgman, 1990). In practice, however, airway regeneration is problematic because of slow turnover and dedifferentiation of epithelium thereby hindering regeneration and increasing time necessary for full maturation and function. Based on the anatomy and biology of the airway epithelium, a variety of tissue engineering tools available could be utilized to overcome the barriers currently seen in airway epithelial generation. This paper describes the structure, function, and repair mechanisms in native epithelium and highlights specific and manipulatable tissue engineering signals that could be of great use in the creation of artificial airway epithelium.