Oscillatory Gene Expression by the microRAN Mediating Delayed Negative Feedback Loop

More and more experiments show that microRNAs can regulate gene expression by stimulating degradation of mRNA or repression of translation of mRNA. In this paper, we incorporate the microRNA into a previous mathematical model of gene expression through forming a microRNA-induced silencing complex(RISC). Our findings demonstrate the dynamical behavior of the constructed system. By Hopf theories, we derive the theoretical results of globally asymptotical stability and provide the sufficient conditions for the oscillation of the simple gene regulatory system, and by numerical simulation further demonstrate how the amplitudes against the change of delay in the gene regulatory network.

Review Study of Detection of Diabetes Models through Delay Differential Equations

Mathematical models based on advanced differential equations are utilized to analyze the glucose-insulin regulatory system, and how it affects the detection of Type I and Type II diabetes. In this paper, we have incorporated several models of prominent mathematicians in this field of work. Three of these models are single time delays, where either there is a time delay of how long it takes insulin produced by the pancreas to take effect, or a delay in the glucose production after the insulin has taken effect on the body. Three other models are two-time delay models, and based on the specific models, the time delay takes place in some sort of insulin production delay or glucose production delay. The intent of this paper is to use these multiple delays to analyze the glucose-insulin regulatory system, and how if it is not properly working at any point, the high risk of diabetes becomes a reality.

Kinetic analysis of p53 gene network with time delays and PIDD

p53 kinetics plays a key role in regulating cell fate.Based on the p53 gene regulatory network composed by the core regulatory factors ATM,Mdm2,Wipl,and PIDD,the effect of the delays in the process of transcription and translation of Mdm2 and Wipl on the dynamics of p53 is studied theoretically and numerically.The results show that these two time delays can affect the stability of the positive equilibrium.With the increase of delays,the dynamics of p53 presents an oscillating state.Further,we also study the effects of PIDD and chemotherapeutic drug etoposide on the kinetics of p53.The model indicates that(i)PIDD low-level expression does not significantly affect p53 oscillatory behavior,but high-level expression could induce two-phase kinetics of p53;(ii)Too high and too low concentration of etoposide is not conducive to p53 oscillation.These results are in good agreement with experimental findings.Finally,we consider the infuence of internal noise on the system through Binomial r-leap algorithm.Stochastic simulations reveal that high-intensity noise completely destroys p53 dynamics in the deterministic model,whereas low-intensity noise does not alter p53 dynamics.Interestingly,for the stable focus,the internal noise with appropriate intensity can induce quasi-limit cycle oscillations of the system.Our work may provide the useful insights for the development of anticancer therapy.

A novel model-free approach for reconstruction of time-delayed gene regulatory networks

Reconstruction of genetic networks is one of the key scientific challenges in functional genomics. This paper describes a novel approach for addressing the regulatory dependencies be-tween genes whose activities can be delayed by multiple units of time. The aim of the proposed ap-proach termed TdGRN (time-delayed gene regulatory networking) is to reversely engineer the dy-namic mechanisms of gene regulations, which is realized by identifying the time-delayed gene regu-lations through supervised decision-tree analysis of the newly designed time-delayed gene expres-sion matrix, derived from the original time-series microarray data. A permutation technique is used to determine the statistical classification threshold of a tree, from which a gene regulatory rule(s) is ex-tracted. The proposed TdGRN is a model-free approach that attempts to learn the underlying regula-tory rules without relying on any model assumptions. Compared with model-based approaches, it has several significant advantages: it requires neither any arbitrary threshold for discretization of gene transcriptional values nor the definition of the number of regulators (k). We have applied this novel method to the publicly available data for budding yeast cell cycling. The numerical results demonstrate that most of the identified time-delayed gene regulations have current biological knowledge supports.

Global stability analysis of fractional-order gene regulatory networks with time delay

Fractional-order gene regulatory networks with time delay(DFCIRNs)have proven that they are more suitable to model gene regulation mechanism than integer-order.In this paper,a novel DFGRN is proposed.The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions.On this basis,the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN,and the stability conditions are dependent on the fractional-order q.Finally,numerical simulations show that the obtained results arc reasonable.

Is nonlinear model predictive control with fuzzy predictive model proper for managing the blood glucose level in typeI diabetes?

In recent decades, due to the increasing risk of diabetes, the measurement and control of the blood sugar is of great importance. In typeI diabetes, because of the lack of insulin secretion, the cells cannot absorb glucose, and thus have a low level of glucose. To control blood glucose, the insulin must be injected to the body. In fact, the injection must be in a completely controlled environment. If the level of the insulin exceeds the physiological limits, it may cause death. This paper presents an online approach to control the blood glucose level using a nonlinear model predictive control. This method, maintains the level of blood glucose concentration within a normal range. Thus, the blood glucose level is measured in each minute and predicted for the next time interval. If that is not in the normal range, amount of the insulin which must be injected will be determined. The proposed control approach includes important features such as model uncertainties and prevents acute decrease in the blood glucose level, and instability. In order to assess performance of the proposed controller, computer simulations have been carried out in Matlab/Simulink. Simulation results will reveal the effectiveness of the proposed nonlinear model predictive controller in adjusting the blood glucose level by injecting required insulin. So if the nutrition of the person decreases instantly, the hypoglycemia does not happen.

Stability and bifurcation analysis of a fractional-order single-gene regulatory model with delays under a novel PD^α control law

In this paper,we propose a novel fractional-order proportional-derivative(PD)strategy to achieve the control of bifurcation of a fractional-order gene regulatory model with delays.The stability theory of fractional differential equations proved that with delays,some explicit conditions for the local asymptotical stability and Hopf bifurcation are given for the controlled fractional-order genetic model.It is demonstrated that the fractional-order gene regulatory model becomes controllable by adjusting the control gain parameters.In addition,the effect of fractional-order parameter on the dynamical behaviors is shown.Finally,numerical simulations are carried out to testify the validity of the main results and the availability of the fractional-order PD controller.

Existence and exponential stability of weighted pseudo-almost periodic solutions for genetic regulatory networks with time-varying delays

The importance of prediction for genetic regulatory network(GRNs)makes mathematical modeling a prominent tool.In this paper,we consider weighted pseudo-almost periodic solutions for a class of GRNs with time-varying delays.We establish the existence,uniqueness,and global exponential stability by employing the theory of dichotomy,the fixed point theorem,and differential inequality.A numerical example along with a graphical illustration are presented to support our main results.Our results extend existing GRNs models using almost periodic functions to support a wider range of regulatory processes.

Downregulation of Na^＋/Ca^2＋ Exchanger Isoform 1 Protects Isolated Hearts by Sevoflurane Postconditioning but Not by Delayed Remote Ischemic Preconditioning in Rats

Background：Calcium regulatory proteins-L-type Ca^2＋ channels （LTCCs）,ryanodine receptor 2 （RyR2）,and Na^＋/Ca^2＋ exchanger isoform 1 （NCX1） have been recognized as important protective mechanisms during myocardial ischemia-reperfusion injury （I/RI）.Both sevofturane postconditioning （SevoPoC） and delayed remote ischemic preconditioning （DRIPC） have been shown to protect the heart against I/RI.In this study,we aimed to compare the effects of SevoPoC and DRIPC on the expression of the three calcium regulatory proteins in an isolated rat heart model.Methods：After 30-min balanced perfusion,isolated hearts from rats were subjected to 30-min ischemia followed by 60-min reperfusion.Totally 40 isolated hearts were randomly assigned to four groups （n =10/group）：time control group,I/RI group,SevoPoC group,and DRIPC group.The effect of SevoPoC （3% v/v） and DRIPC were observed.Myocardial infarct size （IS）,cardiac troponin I level,and heart function were measured.The protein and messenger RNA levels of LTCCs,RyR2,and NCX1 were determined.Results：Both SevoPoC and DRIPC improved the recovery of myocardial function,and reduced cardiac troponin Ⅰ release after I/RI.The decrease in IS was more significant in the SevoPoC group than that in the DRIPC group （16.50% ± 4.54% in the SevoPoC group [P =0.0006],and 22.34% ± 4.02% in the DRIPC group [P =0.0007] vs.35.00% ± 5.24% in the I/RI group,respectively）.SevoPoC,but not DRIPC significantly inhibited the activity of NCX 1 （0.59 ＋ 0.09 in the I/RI group vs.0.32 ± 0.16 in the SevoPoC group,P =0.006;vs.0.57 ± 0.14 in the DRIPC group,P =0.072）.No statistical significant differences were observed in the expression of LTCCs and RyR2 between SevoPoC and DRIPC.In addition,subsequent correlation analysis showed a significantly positive relationship between the cardiac troponin Ⅰ level and the protein expression ofNCX1 （r =0.505,P =0.023）.Conclusion：SevoPoC may be more effective in the cardioprotection than DRIPC partly due to the deactivation of NCX1.