Mathematical modeling and application of IL-1ß/TNF signaling pathway in regulating chondrocyte apoptosis.

Introduction: Mathematical model can be used to model complex biological processes, and have shown potential in describing apoptosis in chondrocytes. Method: In order to investigate the regulatory mechanisms of TNF signaling pathway in regulating chondrocyte apoptosis, a fractional-order differential equation model is proposed to describe the dynamic behavior and mutual interaction of apoptosis-related genes under the activation of TNF signaling pathway. Compared with the traditional molecular biology techniques, the proposed mathematical modeling has advantages to providing a more comprehensive understanding of the regulatory mechanisms of TNF signaling pathway in chondrocyte apoptosis. Result: In this paper, differentially expressed genes induced by IL-1ß in human chondrocyte apoptosis are screened using high-throughput sequencing. It is found that they were significantly enriched in the TNF signaling pathway. Therefore, a mathematical model of the TNF signaling pathway is built. Using real-time PCR experiments, mRNA data is measured and used to identify the model parameters, as well as the correlation coefficient. Finally, the sensitivity of the model parameters is discussed by using numerical simulation methods, which can be used to predict the effects of different interventions and explore the optimal intervention strategies for regulating chondrocyte apoptosis. Discussion: Therefore, fractional-order differential equation modeling plays an important role in understanding the regulatory mechanisms of TNF signaling pathway in chondrocyte apoptosis and its potential clinical applications.

One-step fabrication of cell sheet-laden hydrogel for accelerated wound healing.

Full-thickness skin wounds are have continued to be reconstructive challenges in dermal and skin appendage regeneration, and skin substitutes are promising tools for addressing these reconstructive procedures. Herein, the one-step fabrication of a cell sheet integrated with a biomimetic hydrogel as a tissue engineered skin for skin wound healing generated in one step is introduced. Briefly, cell sheets with rich extracellular matrix, high cell density, and good cell connections were integrated with biomimetic hydrogel to fabricate gel + human skin fibroblasts (HSFs) sheets and gel + human umbilical vein endothelial cells (HUVECs) sheets in one step for assembly as a cell sheet-laden hydrogel (CSH). The designed biomimetic hydrogel formed with UV crosslinking and ionic crosslinking exhibited unique properties due to the photo-generated aldehyde groups, which were suitable for integrating into the cell sheet, and ionic crosslinking reduced the adhesive force toward the substrate. These properties allowed the gel + cell sheet film to be easily released from the substrate. The cells in the harvested cell sheet maintained excellent viability, proliferation, and definite migration abilities inside the hydrogel. Moreover, the CSH was implanted into a full-thickness skin defects to construct a required dermal matrix and cell microenvironment. The wound closure rate reached 60.00 ± 6.26% on the 2nd day, accelerating mature granulation and dermis formation with skin appendages after 14 days. This project can provide distinct guidance and strategies for the complete repair and regeneration of full-thickness skin defects, and provides a material with great potential for tissue regeneration in clinical applications.

Fractional differential equation modeling of the HBV infection with time delay and logistic proliferation.

In this article, a fractional-order differential equation model of HBV infection was proposed with a Caputo derivative, delayed immune response, and logistic proliferation. Initially, infection-free and infection equilibriums and the basic reproduction number were computed. Thereafter, the stability of the two equilibriums was analyzed based on the fractional Routh-Hurwitz stability criterion, and the results indicated that the stability will change if the time delay or fractional order changes. In addition, the sensitivity of the basic reproduction number was analyzed to find out the most sensitive parameter. Lastly, the theoretical analysis was verified by numerical simulations. The results showed that the time delay of immune response and fractional order can significantly affect the dynamic behavior in the HBV infection process. Therefore, it is necessary to consider time delay and fractional order in modeling HBV infection and studying its dynamics.

Forecasting sensitive targets of the kynurenine pathway in pancreatic adenocarcinoma using mathematical modeling.

In this study, a new mathematical model was established and validated to forecast and define sensitive targets in the kynurenine pathway (Kynp) in pancreatic adenocarcinoma (PDAC). Using the Panc-1 cell line, genetic profiles of Kynp molecules were tested. qPCR data were implemented in the algorithm programming (fmincon and lsqnonlin function) to estimate 35 parameters of Kynp variables by Matlab 2017b. All tested parameters were defined as non-negative and bounded. Then, based on experimental data, the function of the fmincon equation was employed to estimate the approximate range of each parameter. These calculations were confirmed by qPCR and Western blot. The correlation coefficient (R) between model simulation and experimental data (72 hours, in intervals of 6 hours) of every variable was >0.988. The analysis of reliability and predictive accuracy depending on qPCR and Western blot data showed high predictive accuracy of the model; R was >0.988. Using the model calculations, kynurenine (x3, a6), GPR35 (x4, a8), NF-kßp105 (x7, a16), and NF-kßp65 (x8, a18) were recognized as sensitive targets in the Kynp. These predicted targets were confirmed by testing gene and protein expression responses. Therefore, this study provides new interdisciplinary evidence for Kynp-sensitive targets in the treatment of PDAC.

Modeling the COVID-19 Epidemic With Multi-Population and Control Strategies in the United States.

As of January 19, 2021, the cumulative number of people infected with coronavirus disease-2019 (COVID-19) in the United States has reached 24,433,486, and the number is still rising. The outbreak of the COVID-19 epidemic has not only affected the development of the global economy but also seriously threatened the lives and health of human beings around the world. According to the transmission characteristics of COVID-19 in the population, this study established a theoretical differential equation mathematical model, estimated model parameters through epidemiological data, obtained accurate mathematical models, and adopted global sensitivity analysis methods to screen sensitive parameters that significantly affect the development of the epidemic. Based on the established precise mathematical model, we calculate the basic reproductive number of the epidemic, evaluate the transmission capacity of the COVID-19 epidemic, and predict the development trend of the epidemic. By analyzing the sensitivity of parameters and finding sensitive parameters, we can provide effective control strategies for epidemic prevention and control. After appropriate modifications, the model can also be used for mathematical modeling of epidemics in other countries or other infectious diseases.

A mathematical model for predicting intracranial pressure based on noninvasively acquired PC-MRI parameters in communicating hydrocephalus.

To develop and validate a mathematical model for predicting intracranial pressure (ICP) noninvasively using phase-contrast cine MRI (PC-MRI). We performed a retrospective analysis of PC-MRI from patients with communicating hydrocephalus (n = 138). The patients were recruited from Shenzhen Second People's Hospital between November 2017 and April 2020, and randomly allocated into training (n = 97) and independent validation (n = 41) groups. All participants underwent lumbar puncture and PC-MRI in order to evaluate ICP and cerebrospinal fluid (CSF) parameters (i.e., aqueduct diameter and flow velocity), respectively. A novel ICP-predicting model was then developed based on the nonlinear relationships between the CSF parameters, using the Levenberg-Marquardt and general global optimisation methods. There was no significant difference in baseline demographic characteristics between the training and independent validation groups. The accuracy of the model for predicting ICP was 0.899 in the training cohort (n = 97) and 0.861 in the independent validation cohort (n = 41). We obtained an ICP-predicting model that showed excellent performance in the noninvasive diagnosis of clinically significant communicating hydrocephalus.

Noncoding RNAs in subchondral bone osteoclast function and their therapeutic potential for osteoarthritis.

Osteoclasts are the only cells that perform bone resorption. Noncoding RNAs (ncRNAs) are crucial epigenetic regulators of osteoclast biological behaviors ranging from osteoclast differentiation to bone resorption. The main ncRNAs, including miRNAs, circRNAs, and lncRNAs, compose an intricate network that influences gene transcription processes related to osteoclast biological activity. Accumulating evidence suggests that abnormal osteoclast activity leads to the disturbance of subchondral bone remodeling, thus initiating osteoarthritis (OA), a prevalent joint disease characterized mainly by cartilage degradation and subchondral bone remodeling imbalance. In this review, we delineate three types of ncRNAs and discuss their related complex molecular signaling pathways associated with osteoclast function during bone resorption. We specifically focused on the involvement of noncoding RNAs in subchondral bone remodeling, which participate in the degradation of the osteochondral unit during OA progression. We also discussed exosomes as ncRNA carriers during the bone remodeling process. A better understanding of the roles of ncRNAs in osteoclast biological behaviors will contribute to the treatment of bone resorption-related skeletal diseases such as OA.

Modeling and forecasting the spread tendency of the COVID-19 in China.

To forecast the spread tendency of the COVID-19 in China and provide effective strategies to prevent the disease, an improved SEIR model was established. The parameters of our model were estimated based on collected data that were issued by the National Health Commission of China (NHCC) from January 10 to March 3. The model was used to forecast the spread tendency of the disease. The key factors influencing the epidemic were explored through modulation of the parameters, including the removal rate, the average number of the infected contacting the susceptible per day and the average number of the exposed contacting the susceptible per day. The correlation of the infected is 99.9% between established model data in this study and issued data by NHCC from January 10 to February 15. The correlation of the removed, the death and the cured are 99.8%, 99.8% and 99.6%, respectively. The average forecasting error rates of the infected, the removed, the death and the cured are 0.78%, 0.75%, 0.35% and 0.83%, respectively, from February 16 to March 3. The peak time of the epidemic forecast by our established model coincided with the issued data by NHCC. Therefore, our study established a mathematical model with high accuracy. The aforementioned parameters significantly affected the trend of the epidemic, suggesting that the exposed and the infected population should be strictly isolated. If the removal rate increases to 0.12, the epidemic will come to an end on May 25. In conclusion, the proposed mathematical model accurately forecast the spread tendency of COVID-19 in China and the model can be applied for other countries with appropriate modifications.

Analysis of an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway.

In this paper, an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway is proposed for the first time. The uniqueness, nonnegativity, and boundedness of solutions are studied. In a two cells model, there are two equilibriums (no-expression of Delta and normal expression of Delta). Local asymptotic stability is proved for both cases. Stability analysis shows that the orders of the fractional-order differential equation model can significantly affect the equilibriums in the two cells model. Numerical simulations are presented to illustrate the conclusions. Next, the sensitivity of model parameters is calculated, and the calculation results show that different parameters have different sensitivities. The most and least sensitive parameters in the two cells model and the 60 cells model are verified by numerical simulations. What is more, we compare the fractional-order model with the integer-order model by simulations, and the results show that the orders can significantly affect the dynamic and the phenotypes.

The Effects of Graded Levels of Calorie Restriction XV: Phase Space Attractors Reveal Distinct Behavioral Phenotypes.

Calorie restriction (CR) has a positive impact on health and life span. Previous work, however, does not reveal the whole underlying mechanism of behavioral phenotypes under CR. We propose a new approach based on phase space reconstruction (PSR) to analyze the behavioral responses of mice to graded CR. This involved reconstructing high-dimensional attractors which topologically represent the intrinsic dynamics of mice based on low-dimensional time series of movement counts observed during the 90-day time course of restriction. PSR together with correlation dimensions (CD), Kolmogorov entropy (KE), and multifractal spectra builds a map from internal attractors to the phenotype of mice and reveals the mice with increasing CR levels undergo significant changes from a normal to a new state. Features of the attractors (CD and KE) were significantly associated with gene expression profiles in the hypothalamus of the same individuals.

Modeling and Control of a Delayed Hepatitis B Virus Model with Incubation Period and Combination Treatment.

In this paper, a hepatitis B virus (HBV) model with an incubation period and delayed state and control variables is firstly proposed. Furthermore, the combination treatment is adopted to have a longer-lasting effect than mono-therapy. The equilibrium points and basic reproduction number are calculated, and then the local stability is analyzed on this model. We then present optimal control strategies based on the Pontryagin's minimum principle with an objective function not only to reduce the levels of exposed cells, infected cells and free viruses nearly to zero at the end of therapy, but also to minimize the drug side-effect and the cost of treatment. What's more, we develop a numerical simulation algorithm for solving our HBV model based on the combination of forward and backward difference approximations. The state dynamics of uninfected cells, exposed cells, infected cells, free viruses, CTL and ALT are simulated with or without optimal control, which show that HBV is reduced nearly to zero based on the time-varying optimal control strategies whereas the disease would break out without control. At last, by the simulations, we prove that strategy A is the best among the three kinds of strategies we adopt and further comparisons have been done between model (1) and model (2).

Modeling and analysis of the Delta-Notch dependent boundary formation in the Drosophila large intestine.

BACKGROUND: The boundary formation in the Drosophila large intestine is widely studied as an important biological problem. It has been shown that the Delta-Notch signaling pathway plays an essential role in the formation of boundary cells. RESULTS: In this paper, we propose a mathematical model for the Delta-Notch dependent boundary formation in the Drosophila large intestine in order to better interpret related experimental findings of this biological phenomenon. To achieve this, we not only perform stability analysis on the model from a theoretical point of view, but also perform numerical simulations to analyze the model with and without noises, the phenotype change with the change of Delta or Notch expression, and the perturbation influences of binding and inhibition parameters on the boundary formation. CONCLUSIONS: By doing all these work, we can assure that our model can better interpret the biological findings related to the boundary formation in the Drosophila large intestine.

Analysis of a New Delayed HBV Model with Exposed State and Immune Response to Infected Cells and Viruses.

We propose a comprehensive delayed HBV model, which not only considers the immune response to both infected cells and viruses and a time delay for the immune system to clear viruses but also incorporates an exposed state and the proliferation of hepatocytes. We prove the positivity and boundedness of solutions and analyze the global stability of two boundary equilibria and then study the local asymptotic stability and Hopf bifurcation of the positive (infection) equilibrium and also the stability of the bifurcating periodic solutions. Moreover, we illustrate how the factors such as the time delay, the immune response to infected cells and viruses, and the proliferation of hepatocytes affect the dynamics of the model by numerical simulation.

Serum amyloid A promotes osteosarcoma invasion via upregulating αvß3 integrin.

Serum amyloid A (SAA) is regarded as an important acute phase protein involved in tumor progression and metastasis. However, at present there is no evidence of its involvement in osteosarcoma. The present study aimed to investigate the effect of SAA on the invasion of osteosarcoma cells. The effects of SAA on the migration and invasion of osteosarcoma cells were detected using scratch wound healing and transwell assays, respectively. The expression of αvß3 integrin was detected at the protein and mRNA levels in U2OS cells. Agonists, inhibitors or siRNA of formyl peptide receptor like­1 (FPRL­1), mitogen­activated protein kinases and αvß3 integrin were used to investigate the mechanism underlying the effects of SAA on the regulation of U2OS cell migration and invasion. The present study revealed that SAA promoted osteosarcoma cell migration and invasion. SAA upregulated the expression of αvß3 integrin in a concentration­ and time­dependent manner. When inhibiting αvß3 integrin with its antagonist, the migration and invasion abilities of the U2OS cells were markedly inhibited. SAA­induced αvß3 integrin production was significantly downregulated by inhibiting FPRL­1 with siRNA and inhibitors. The present study also found that extracellular signal­regulated kinase (ERK) 1/2, but not c­Jun N­terminal kinase or p38, was important in this process. These findings demonstrated that SAA regulated osteosarcoma cell migration and invasion via the FPRL­1/ERK/αvß3 integrin pathway.

Stable superhydrophobic surface of hierarchical carbon nanotubes on Si micropillar arrays.

It is of great importance to construct a stable superhydrophobic surface with low sliding angle (SA) for various applications. We used hydrophobic carbon nanotubes (CNTs) to construct the superhydrophobic hierarchical architecture of CNTs on silicon micropillar array (CNTs/Si-µp), which have a large contact angle of 153° to 155° and an ultralow SA of 3° to 5°. Small water droplets with a volume larger than 0.3 µL can slide on the CNTs/Si-µp with a tilted angle of approximately 5°. The CNTs growing on planar Si wafer lose their superhydrophobic properties after exposing to tiny water droplets. However, the CNTs/Si-µp still show superhydrophobic properties even after wetting using tiny water droplets. The CNTs/Si-µp still have a hierarchical structure after wetting, resulting in a stable superhydrophobic surface.