Associations between dietary iron intake from different sources and non-alcoholic fatty liver disease in adults.

BACKGROUND AND OBJECTIVES: Non-alcoholic fatty liver disease (NAFLD) has become a worldwide public health problem. Current evidence on the association between dietary iron intake and the risk of NAFLD is limited. The present study aimed to investigate the associations of animal-derived dietary iron (ADDI) intake, plant-derived dietary iron (PDDI) intake, and the ratio of PDDI:ADDI with NAFLD risk among U.S. adult population. METHODS AND STUDY DESIGN: This was a repeated cross-sectional study. Data were collected from the National Health and Nutrition Examination Survey (NHANES) 2007-2018. NAFLD was defined as a United States Fatty Lives Index ≥30, and dietary iron intake was assessed through two 24-h dietary recall in-terviews. Logistic regression and restricted cubic spline models were applied to examine the associations between dietary iron intake from different sources and NAFLD risk. RESULTS: A total of 9478 participants aged ≥20 years were enrolled in the present study. After adjustment for multiple confounding factors, relative to the lowest quartile, the odds ratio (OR) and 95% confidence interval (CI) of NAFLD for the highest quartile was 1.01(95% CI, 0.82-1.24) for ADDI intake, 0.82 (95% CI, 0.64-0.99) for PDDI intake, and 1.00 (95% CI, 0.81-1.24) for the PDDI: ADDI intake ratio. In stratified analysis by sex and age, the significantly negative associations of PDDI intake with NAFLD was observed in women and participants older than 45 years. Dose-response analyses indicated that NAFLD was negatively associated with PDDI intake in a non-linear manner. CONCLUSIONS: PDDI intake was negatively associated with NAFLD in U.S. adults.

A near-IR ratiometric fluorescent probe for the precise tracking of senescence: a multidimensional sensing assay of biomarkers in cell senescence pathways.

Senescence is a complex physiological process that can be induced by a range of factors, and cellular damage caused by reactive oxygen species (ROS) is one of the major triggers. In order to learn and solve age-related diseases, tracking strategies through biomarkers, including senescence-associated ß-galactosidase (SA-ß-gal), with high sensitivity and accuracy, have been considered as a promising solution. However, endogenous ß-gal accumulation is not only associated with senescence but also with other physiological processes. Therefore, additional assays are needed to define cellular senescence further. In this work, a fancy fluorescent probe SA-HCy-1 for accurately monitoring senescence is developed, with SA-ß-gal and HClO as targets under high lysosomal pH conditions (pH > 6.0) specifically, on account of the role ß-gal commonly played as an ovarian cancer biomarker. Therefore, precise tracking of cellular senescence could be achieved in view of these three dimensions, with response in dual fluorescence channels providing a ratiometric sensing pattern. This elaborate strategy has been verified to be suitable for biological applications by skin photo-aging evaluation and cellular passage tracing, displaying a significantly improved sensitivity compared with the commercial X-gal kit measurement.

Application of topical gentamicin ointment in the treatment of Nagashima-type palmoplantar keratosis in children with a nonsense mutation.

Importance: Nagashima-type palmoplantar keratosis (NPPK) is a hereditary dermatosis mostly caused by a nonsense mutation in SERPINB7. Despite the increasing interest in readthrough gentamicin treatment of NPPK, clinical evidence for this treatment is limited. Objective: This study aimed to provide further evidence for the use of topical gentamicin in the treatment of NPPK in children with nonsense mutations. Methods: We designed a bilaterally controlled study of topical gentamicin ointment. Children diagnosed with NPPK carrying nonsense mutations were enrolled in this study. A 0.1% gentamicin ointment was applied to one hand and an emollient to the other for 3 months. A bilateral comparison of the visual analog scale scores for clinical manifestations and safety was performed. Results: Ten children with NPPK were included in this study. In comparison with the emollient side, the topical gentamicin side showed significant improvements in hyperkeratosis, erythema, maceration, and desquamation after 1 and 3 months of treatment (P < 0.05). However, hyperhidrosis and odor did not improve significantly. No adverse events were observed during the systemic safety monitoring examinations. Interpretation: Topical gentamicin ointment showed good safety in the treatment of NPPK with nonsense mutations, indicating that it is a promising therapeutic choice in children with NPPK.

Dynamic behavior of P53-Mdm2-Wip1 gene regulatory network under the influence of time delay and noise.

The tumor suppressor protein P53 can regulate the cell cycle, thereby preventing cell abnormalities. In this paper, we study the dynamic characteristics of the P53 network under the influence of time delay and noise, including stability and bifurcation. In order to study the influence of several factors on the concentration of P53, bifurcation analysis on several important parameters is conducted; the results show that the important parameters could induce P53 oscillations within an appropriate range. Then we study the stability of the system and the existing conditions of Hopf bifurcation by using Hopf bifurcation theory with time delays as the bifurcation parameter. It is found that time delay plays a key role in inducing Hopf bifurcation and regulating the period and amplitude of system oscillation. Meanwhile, the combination of time delays can not only promote the oscillation of the system but it also provides good robustness. Changing the parameter values appropriately can change the bifurcation critical point and even the stable state of the system. In addition, due to the low copy number of the molecules and the environmental fluctuations, the influence of noise on the system is also considered. Through numerical simulation, it is found that noise not only promotes system oscillation but it also induces system state switching. The above results may help us to further understand the regulation mechanism of the P53-Mdm2-Wip1 network in the cell cycle.

[Evolution of auditory brainstem response in 0-6 years old normal hearing children and characteristics of children with abnormal acoustic conduction].

Objective:To explore the normal reference range of Click-ABR latency and interwave period in 0-6 years old children, and to analyze the clinical characteristics of Click-ABR in children with sound transmission function is abnormal. Methods:A total of 1791（3582 ears） normal hearing children aged 0-6 years and 176（258 ears） conductive hearing loss children were selected for Click-ABR. The differences of Click-ABR parameters in children of different months were analyzed, and the correlation between the degree of conductive hearing loss and Click-ABR parameters was explored. Results:The incubation period of wave Ⅰ was not correlated with the age of month, while the incubation period of wave Ⅲ, wave Ⅴ, waveⅠ-Ⅲ and wave Ⅰ-Ⅴ were highly correlated with the age of month. There was a positive correlation between the latency of wave Ⅰ and hearing threshold in the children with sound transmission function is abnormal under 80 dB nHL stimulation, and there was no difference between the standard values of wave Ⅰ-Ⅲ and Ⅰ-Ⅴ in the children with sound transmission function is abnormal and normal children. Conclusion:The latency of ABR wave Ⅲ and Ⅴ, and the interval between wave Ⅰ-Ⅲ and Ⅰ-Ⅴ shorten with the increase of age in children aged 0-6 years. The normal ABR values of children of different ages should be established in each hearing clinic for children as a reference. Combined with Click-ABR threshold and 80 dB nHL acoustic subwave Ⅰlatency, the abnormal conduction function can be preliminatively screened out, which should be further supplemented with other combinations of hearing diagnosis.

New Biomarkers Based on Dendritic Cells for Breast Cancer Treatment and Prognosis Diagnosis.

Dendritic cells(DCs) play a protective role in the antitumor immunity of most cancers, which can be divided into conventional dendritic cells (cDCs) and plasmacytoid dendritic cells (pDCs). Most current studies are only based on either cDCs or pDCs for the study of the relationship between DCs and breast cancer prognosis, without combining the two together. We aimed to select new biomarkers from pDCs and cDCs. In this paper, the xCell algorithm was first used to calculate the cellular abundance of 64 types of immune cells and stromal cells in tumor samples from the TCGA database, and the high-abundance pDC group and cDC group were divided according to the results of a survival analysis. Then, we looked for the co-expressed gene module of highly infiltrating pDC and cDC patients with a weighted correlation network analysis (WGCNA) and screened out the hub genes, including RBBP5, HNRNPU, PEX19, TPR, and BCL9. Finally, we analyzed the biological functions of the hub genes, and the results showed that RBBP5, TPR, and BCL9 were significantly related to the immune cells and prognosis of patients, and RBBP5 and BCL9 were involved in responding to TCF-related instructions of the Wnt pathway. In addition, we also evaluated the response of pDCs and cDCs with different abundances to chemotherapy, and the results showed that the higher the abundance of pDCs and cDCs, the higher their sensitivity to drugs. This paper revealed new biomarkers related to DCs-among them, BCL9, TPR, and RBBP5 were proven to be closely related to dendritic cells in cancer. For the first time, this paper puts forward that HNRNPU and PEX19 are related to the prognosis of dendritic cells in cancer, which also provides new possibilities for finding new targets for breast cancer immunotherapy.

[Application of auditory brainstem response to different types of hearing loss in infants].

Objective:The aim of this study is to analyze the variation characteristics of ABR wave latency and wave interval in different functional states of middle ear and different hearing levels, and to explore the value of ABR detection method in hearing assessment of infants. Methods:A total of 670 children were enrolled in the Pediatric Hearing Diagnosis and Treatment Center of the Department of Otolaryngology head and Neck Surgery, Beijing Children's Hospital, Capital Medical University from May 2020 to April 2021. According to the hearing test results, they were divided into group A normal group（632 ears）. Group B consisted of normal middle ear function and abnormal hearing（157 ears）, further divided into mild hearing loss subgroup（49 ears）, moderate hearing loss subgroup（47 ears） and severe to very severe hearing loss subgroup（61 ears）. Group C was a group with abnormal middle ear function（551 ears）, which was further divided into normal hearing subgroup（307 ears）, mild hearing loss subgroup（110 ears）, moderate hearing loss subgroup（107 ears） and severe to very severe hearing loss subgroup（27 ears）. The differences of Ⅰ, Ⅲ, Ⅴ Wave Latency, Ⅰ-Ⅲ, Ⅰ-Ⅴ wave interval between subgroups B and C and Group A, and between subgroups B and C were analyzed. Results:When the stimulus intensity was 80 dB nHL, there was no significant difference in ABR latency and wave interval between group B and group A, and there was no significant difference between group B and group A（P>0.05）, nor between the two groups（P>0.05）. In the subgroup of severe to very severe hearing loss, some ABRⅠ, Ⅲ and Ⅴwaves could not be elicited, only Ⅲ and Ⅴ waves were elicited from 4 ears and Ⅴ waves were elicited from 7 ears. The mean latency of 11 ear Ⅲ and Ⅴ waves was （5.20±0.44） ms and （6.80±0.75） ms, respectively, which was longer than that of mild and moderate hearing loss subgroups. Compared with group A, the latency of normal hearing subgroup in group C was significantly prolonged only for wave Ⅰ, and the latency of wave I, Ⅲ and Ⅴin other subgroups was significantly prolonged（P<0.01）. In terms of Ⅰ-Ⅲ and Ⅰ-Ⅴ wave intervals, there was no significant difference between group C and group A in normal hearing subgroup and mild loss subgroup. The subgroup of moderate hearing loss and the subgroup of severe to very severe hearing loss were significantly shorter than the group A（P<0.01）. Compared with the normal group, the latency of Ⅰ, Ⅲ and Ⅴ waves in group C were significantly longer（P<0.01）. The latency of wave Ⅰ, in the moderate hearing loss group was significantly longer than that in the mild hearing loss group（P<0.001）. The latency of each wave in severe to very severe hearing loss subgroup was significantly longer than that in mild and moderate hearing loss subgroup（P<0.001）. There was no difference between mild hearing loss subgroup and normal hearing subgroup（P>0.05）. The subgroup of moderate hearing loss and severe to very severe hearing loss were significantly shorter than the subgroup of normal hearing and the subgroup of mild hearing loss, and there was a significant difference between the two groups（P<0.01）. Conclusion:In sensorineural hearing loss, mild and moderate hearing loss had no significant effect on the latency and interwave period of ABR. The latency of each wave in severe to very severe hearing loss cannot be elicited normally or only Ⅲ and Ⅴ waves can be elicited, and it is significantly prolonged. The latency of ABR Ⅰwave was significantly prolonged when middle ear function was abnormal. The latency of each wave was significantly prolonged when middle ear function was abnormal and hearing was abnormal. When hearing loss reaches a certain degree, the interwave period is shortened significantly. Therefore, for mild to moderate hearing loss, the prolonged latency of ABRⅠ wave is of certain value for the qualitative diagnosis of hearing loss, and the prolonged latency of ABR Ⅰwave is of significance for judging middle ear dysfunction in infants.

Circadian Rhythm Regulated by Tumor Suppressor p53 and Time Delay in Unstressed Cells.

Circadian function and p53 network are interconnected on the molecular level, but the dynamics induced by the interaction between the circadian factor Per2 and the tumor suppressor p53 remains poorly understood. Here, we constructed an integrative model composed of a circadian clock module and a p53-Mdm2 feedback module to study the dynamics of p53-Per2 network in unstressed cells. As expected, the model can accurately predict the circadian rhythm, which is consistent with diverse experimental observations. In addition, using a combination of theoretical analysis and numerical simulation, the results demonstrated that p53 expression enhances the phase advance of circadian rhythm and reduces the robustness of circadian rhythm. Furthermore, the time delay required for the transcription and translation of Per2 protein induces oscillations by undergoing a supercritical Hopf bifurcation, and improves the robustness of circadian rhythm. In summary, this work shows that the p53-Per2 interaction and the time delay are two essential factors for circadian functions.

A turn on fluorescent assay for γ-glutamyltransferase activity and its application in biological imaging.

γ-glutamyltransferase (GGT) is widely presented in living cells and overexpressed in many tumor tissues. Therefore, it is generally considered as an important biomarker for the detection of tumor, especially for liver cancer. Accurate determination of its activity is helpful for early diagnosis and treatment of related diseases. In this work, a "turn on" fluorescent probe NSA-GGT for the detection of GGT activity based on glutamine bond was designed and synthesized by employing dansylamino as fluorophore. The probe shows good water solubility and can be well dispersed in aqueous buffer. After incubated with GGT in phosphate buffer, the fluorescence of NSA-GGT centered at ∼523 nm increased over 25-fold. This sensing pattern exhibits an intriguing sensing sensitivity for GGT, and has good performance on intracellular GGT staining, serving as a promising candidate for GGT measurement. Subsequent biological experiments showed that probe NSA-GGT could also be used for fluorescent imaging of GGT activity in living cells and animal tissues.

A Dual-Control Strategy by Phosphate Ions and Local Microviscosity for Tracking Adenosine Triphosphate Metabolism in Mitochondria and Cellular Activity Dynamically.

Adenosine triphosphate (ATP) acts as the main energy source for growth and development in organisms, and the disorder reflects the mitochondrial damage to a large extent. Therefore, an efficient tool for the evaluation of the ATP metabolic level is important to track mitochondrial health, providing an additional perspective for an in-depth long-term study on living activities. Herein, a twisted intramolecular charge transfer (TICT) framework is utilized to build up a sensitive receptor, Mito-VP, with a negligible background to target mitochondrial ATP metabolism by monitoring the phosphate ion (Pi) level upon ATP hydrolysis under the overall consideration of the structural and functional features of mitochondria. The responsive fluorescence could be lighted on under the dual control of Pi and local microviscosity, and the two steps of ATP hydrolysis could be captured through fluorescence. In addition to the well-behaved mitochondrial targeting, the energy metabolism at cellular and organism levels has been clarified via mitosis and zebrafish development, respectively.

Dynamic behavior of the p53-Mdm2 core module under the action of drug Nutlin and dual delays.

Nutlin is a family of p53-targeting drugs. It is able to bind to Mdm2, thereby accelerate the accumulation of p53 that is a prominent tumor suppressor. An integrated module of the Nutlin PBK and p53 pathway is composed of positive feedback mediated by Mdm2 mRNA as well as the drug Nutlin and negative feedback mediated by Mdm2 protein. The main research content of our paper is how the time delay of protein synthesis, response time delay of Nutlin drug, the degradation rate of Mdm2, the degradation rate of p53 depended on Mdm2 and the actual dose of Nutlin in the cell affect the oscillatory behavior caused by Hopf bifurcation in the integrated network system of Nutlin PBK and p53 pathways. The stability of the unique positive equilibrium point and the existence of Hopf bifurcation are studied by taking the time delays as the bifurcation parameters and applying bifurcation theory. Based on the normal form theory and central manifold theorem, explicit criteria to determine the Hopf bifurcation direction and stability of the bifurcated periodic solution are established. It is found that the time delays and key parameters in the integrated network system of Nutlin PBK and p53 pathways play an important role in the amplitude and period of p53 oscillation according to the results from the numerical simulation and theoretical calculation. These results may provide us with a better understanding of the biological functions of the p53 pathway and some clues for cancer treatment.

Modelling and analysing biological oscillations in quorum sensing networks.

Recent experiments have shown that the biological oscillation of quorum sensing (QS) system play a vital role not only in the process of bacterial synthesis but also in the treatment of cancer by releasing drugs. As known, these five substances TetR, CI, LacI, AiiA and AI are the core components of the QS system. However, the effects of AiiA and protein synthesis time delay on QS system are often ignored in the theoretical model, which is taken as a priority in the proposed research. Therefore, the authors developed a new mathematical model to explore the effects of AiiA and time delay on the dynamical behaviour of QS system theoretically and numerically. The results show that time delay can induce oscillation of QS system. Concretely, there exists a time delay threshold [inline-formula removed]. When time delay is less than [inline-formula removed], the system is stable. With the increasing of time delay and once it passes [inline-formula removed], oscillation behaviour occurs. Moreover, the length of time delay determines the amplitude and period of the QS oscillation. In addition, the value of [inline-formula removed] is sensitive to AiiA. These results may enhance the understanding of QS oscillations and provide new insights for bacterial release drugs to treat cancer.

Dynamic Behavior of p53 Driven by Delay and a Microrna-34a-Mediated Feedback Loop.

The tumor suppressor protein p53 is a critical hub in the comprehensive transcriptional network that inhibits the growth of cells after acute stress stimulation. In this paper, an integrated model of the p53 signaling pathway in response to DNA damage is proposed and the p53 stability and oscillatory dynamics are analyzed. Through theoretical analysis and numerical simulation, we find that the delay as a bifurcation parameter can drive the p53-Mdm2 module to undergo a supercritical Hopf bifurcation, thereby producing oscillation behavior. Moreover, we demonstrate how the positive feedback loop formed by p53* and microRNA-34a (miR-34a) with the feature of double-negative regulation produces limit-cycle oscillations. Further, we find that miR-34a can affect the critical value of Hopf bifurcation in delay-induced p53 networks. In addition, we show that ATM, once activated by DNA damage, makes p53* undergo two Hopf bifurcations. These results revealed that both time delay and miR-34a can have tumor suppressing roles by promoting p53 oscillation or high level expression, which will provide a perspective for promoting the development of anti-cancer drugs by targeting miR-34a and time delay.

Oscillatory Dynamics of p53-Mdm2 Circuit in Response to DNA Damage Caused by Ionizing Radiation.

Although the dynamical behavior of the p53-Mdm2 loop has been extensively studied, the understanding of the mechanism underlying the regulation of this pathway still remains limited. Herein, we developed an integrated model with five basic components and three ubiquitous time delays for the p53-Mdm2 interaction in response to DNA damage following ionizing radiation (IR). We showed that a sufficient amount of activated ATM level can initiate the p53 oscillations with nearly the same amplitude over a wide range of the ATM level; a proper range of p53 level is also required for generating the oscillations, for too high or too low levels it would fail to generate the oscillations; and increased Mdm2 level leads to decreased amplitude of the p53 oscillation and reduced expression of the p53 activity. Moreover, we found that the negative feedback loop formed between p53 and nuclear Mdm2 plays a dominant role in determining the p53 dynamics, whereas when interaction strength of the negative feedback loop becomes weaker, the positive feedback loop formed between p53 and cytoplasmatic Mdm2 can induce different types of dynamics. Furthermore, we demonstrated that the total time delay required for protein production and nuclear translocation of Mdm2 can induce p53 oscillations even when the p53 level is at a certain stable high steady state or at a certain stable low steady state. In addition, the two important features of the oscillatory dynamics-amplitude and period-can be controlled by such time delay. These results are in agreement with multiple experimental observations and may enrich our understanding of the dynamics of the p53 network.

Oscillation Expression of NF- κ B Driven by Transcription and Translation Time Delays.

Oscillation expression of NF- [Formula: see text] signaling system can lead to nuclear NF- [Formula: see text] accumulation which involving various important cellular processes including immune response, inflammation and cancer development. Negative feedback circuits involved in NF- [Formula: see text] signaling system are generally believed to be responsible for the oscillation expression. In view of feedback loops involving time delays resulting from transcription, transcript splicing and processing, and protein synthesis, in this paper, a mathematical model with time delay to describe the core negative feedback circuits centered on NF- [Formula: see text] including [Formula: see text] and A20 -like proteins is developed. Here, the time delay refer to the time demand of transcription and translation process of [Formula: see text]. First, the results suggest that time delay can drive oscillation dynamics of NF- [Formula: see text] signaling system. Concretely, there exists a critical value of time delay. When the time delay exceeds the critical value, the system exhibits oscillation dynamics, and with the increase of time delay, the amplitude and period increase accordingly. Second, analysis indicate that A20 -like proteins are able to change the amplitude and period of the nuclear NF- [Formula: see text] oscillations. In addition, the effects of several important parameters on the nuclear NF- [Formula: see text] oscillations are also discussed. Finally, a prediction is formed, which is shortening time delay, repairing and maintaining the function of A20 -like proteins, and increasing [Formula: see text] transcription rate may be new clues to related disease treatment.

Oscillation induced by Hopf bifurcation in the p53-Mdm2 feedback module.

This study develops an integrated model of the p53-Mdm2 interaction composed of five basic components and time delay in the DNA damage response based on the existing research work. Some critical factors, including time delay, system parameters, and their interactions in the p53-Mdm2 system are investigated to examine their effects on the oscillatory behaviour induced by Hopf bifurcation. It is shown that the positive feedback formed between p53 and the activity of Mdm2 in the cytoplasm can cause a slight decrease in the amplitude of the p53 oscillation. The length of the time delay plays an important role in determining the amplitude and period of the oscillation and can significantly extend the parameter range for the system to demonstrate oscillatory behaviour. The numerical simulation results are found to be in good agreement with the published experimental observation. It is expected that the results of this research would be helpful to better understand the biological functions of p53 pathway and provide some clues in the treatment of cancer.

Oscillatory dynamics mechanism induced by protein synthesis time delay in quorum-sensing system.

Recent experimental evidence reports that the oscillatory behavior of quorum sensing plays an extremely important role in the process of bacterial synthesis and release drug to fight cancer. As we know, the six substances AiiA, LuxI, internal AHL, external AHL, AHL substrate, and H_{2}O_{2} are the core parts of the quorum-sensing system. Here, the effects of several important factors, including time delay, variable H_{2}O_{2}, AHL synthesis rate induced by LuxI, and AHL degradation rate induced by AiiA on the oscillatory behavior of the quorum-sensing system are studied theoretically based on a part of mathematical model describing the interaction of the above six substances proposed by Prindle et al. [Nature 508, 387 (2014)10.1038/nature13238]. The results show that the time delay is a prerequisite for inducing oscillation of the quorum-sensing system. Furthermore, the length of time delay can determine the amplitude and period of oscillation. As a further matter, the change of H_{2}O_{2} concentration can induce the oscillatory behavior of the quorum-sensing system. In addition, under the regulation of H_{2}O_{2}, the period robustness of the quorum-sensing system is increased. Similarly, the quorum-sensing system exhibits periodic oscillation when AHL synthesis rate induced by LuxI less than a certain critical value, unless it displays a steady state. Additionally, a too-high or too-low level of AHL degradation rate induced by AiiA will fail to generate oscillation of the quorum-sensing system, only the intermediate level will cause oscillation. Finally, the two and three parameter regions in which the quorum-sensing system exhibits oscillation behavior are generated.

Contribution of time delays to p53 oscillation in DNA damage response.

Although the oscillatory dynamics of the p53 network have been extensively studied, the understanding of the mechanism of delay-induced oscillations is still limited. In this paper, a comprehensive mathematical model of p53 network is studied, which contains two delayed negative feedback loops. By studying the model with and without explicit delays, the results indicate that the time delay of Mdm2 protein synthesis can well control the pulse shape but cannot induce p53 oscillation alone, while the time delay required for Wip1 protein synthesis induces a Hopf bifurcation to drive p53 oscillation. In addition, the synergy of the two delays will cause the p53 network to oscillate in advance, indicating that p53 begins the repair process earlier in the damaged cell. Furthermore, the stability and bifurcation of the model are addressed, which may highlight the role of time delay in p53 oscillations.

Oscillatory Dynamics of p53 Genetic Network Induced by Feedback Loops and Time Delays.

DNA damage caused by γ -irradiation initiates oscillatory expression of the p53 genetic network. Although many studies revealed the effects of the p53-Mdm2 circuit on p53 dynamics, a few studies explored the contribution of upstream kinases to p53 oscillation. In this paper, an integrated mathematical model of the p53 network in response to γ -irradiation is studied, which consists of five basic components, two ubiquitous time delays, and two negative feedback loops. It is found that recurrent p53 pulses are externally initiated by ataxia telangiectasia mutated (ATM), and the negative feedback loop formed between ATM and p53, via Wip1, plays a dominant role in generating p53 oscillation. In addition, p53 oscillation requires not only an appropriate Mdm2 negative strength but also a threshold level of Wip1 negative strength. Furthermore, the time delays required for transcription and translation of Mdm2 and Wip1 proteins are essential for p53 oscillation. In particular, the critical value of time delay for inducing oscillation and the properties of delay-driven Hopf bifurcation are theoretically analyzed. As expected, the results are clearly in consistence with biological experiments and observations.

Oscillatory Dynamics of P53 Network With Time Delays.

AIMS AND OBJECTIVE: A large number of experimental evidences report that the oscillatory dynamics of p53 would regulate the cell fate decisions. Moreover, multiple time delays are ubiquitous in gene expression which have been demonstrated to lead to important consequences on dynamics of genetic networks. Although delay-driven sustained oscillation in p53-based networks is commonplace, the precise roles of such delays during the processes are not completely known. METHOD: Herein, an integrated model with five basic components and two time delays for the network is developed. Using such time delays as the bifurcation parameter, the existence of Hopf bifurcation is given by analyzing the relevant characteristic equations. Moreover, the effects of such time delays are studied and the expression levels of the main components of the system are compared when taking different parameters and time delays. RESULT AND CONCLUSION: The above theoretical results indicated that the transcriptional and translational delays can induce oscillation by undergoing a super-critical Hopf bifurcation. More interestingly, the length of these delays can control the amplitude and period of the oscillation. Furthermore, a certain range of model parameter values is essential for oscillation. Finally, we illustrated the main results in detail through numerical simulations.