System-based strategies for p53 recovery

Robust p53 recovery using chattering free sliding mode control and a gain-scheduled modified Utkin observer

p53 protein plays an essential role in protecting the genomic integrity of mammalian cells. A drastic decrease in the amount of p53 protein has been observed in cancerous cells. By using Nutlin-based small molecule drugs, the concentration of p53 can be restored to the desired level. This paper presents the drug-dosage design for p53 pathway, based on a control-oriented nonlinear model. A chattering free sliding mode control (CFSMC) strategy is employed to track the desired trajectory of p53 concentration for both of its dynamic behaviors, i.e., sustained and oscillatory responses. A gain-scheduled modified Utkin observer (GSMUO) is designed for robust state reconstruction and disturbance estimation. The simulation results show that CFSMC and GSMUO exhibit desired robustness and performance properties in the presence of parametric variations, an input disturbance and measurement noise. Moreover, a comprehensive simulation study, along with a detailed quantitative analysis is performed to compare CFSMC-GSMUO with four different techniques: a sliding mode control (SMC) with an equivalent control based sliding mode observer (SMO) and GSMUO, respectively, and a dynamic sliding mode control (DSMC) with SMO and GSMUO, respectively. The analysis demonstrates that the tracking error and utilization of the control energy is the least in the case of CFSMC-GSMUO as compared to its counterparts.

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.

Effect of pharmacodynamical interaction between nutlin-3a and aspirin in the activation of p53

BACKGROUND AND OBJECTIVE

p53, an anti-tumour protein, is significantly inactivated in most tumours. A small molecule of nutlin-3a is used to activate its function by repressing (Mouse double minute 2 homolog) Mdm2 protein which inhibits its activity. In cancer patients, a high risk of drug-drug interactions (DDIs) is observed owing to their multi-dosing prescriptions, which may lead them to harmful effects. In the presented work, we have aimed to investigate the effect of pharmacodynamical interaction between two anti-cancer drugs, nutlin-3a and aspirin in the activation of p53 protein.

METHODS

We have adapted control system techniques and designed a Proportional-Integral-Derivative (PID) controller. This controller is used to activate p53 protein. A drug interaction parameter is used to incorporate the effect of both drugs. Extensive simulation is performed using two different doses of aspirin, i.e. a low and a high dose of aspirin.

RESULTS

The result shows no harmful effects of pharmacodynamical interaction when a low dose is administered along with nutlin-3a. When a high dose of aspirin is administered it acts as input disturbance and leads to undesirable over-expression of p53 protein. This can further harm other growth cells, thus inducing harmful effects. A comparative analysis is also tabulated with different dosing regimens which shows that a combination of nutlin-3a and a low dose of aspirin provides better results than a high dose of aspirin.

CONCLUSION

Overall, the work provides an insight to the activation of p53 protein in cancer patients under the presence of pharmacodynamical interaction and might contribute to the effective management of cancer patients.

Sliding mode controller-observer pair for p53 pathway

A significant loss of p53 protein, an anti-tumour agent, is observed in early cancerous cells. Induction of small molecules based drug is by far the most prominent technique to revive and maintain wild-type p53 to the desired level. In this study, a sliding mode control (SMC) based robust non-linear technique is presented for the drug design of a control-oriented p53 model. The control input generated by conventional SMC is discontinuous; however, depending on the physical nature of the system, drug infusion needs to be continuous. Therefore, to obtain a smooth control signal, a dynamic SMC (DSMC) is designed. Moreover, the boundedness of the zero-dynamics is also proved. To make the model-based control design possible, the unknown states of the system are estimated using an equivalent control based, reduced-order sliding mode observer. The robustness of the proposed technique is assessed by introducing input disturbance and parametric uncertainty in the system. The effectiveness of the proposed control scheme is witnessed by performing in-silico trials, revealing that the sustained level of p53 can be achieved by controlled drug administration. Moreover, a comparative quantitative analysis shows that both controllers yield similar performance. However, DSMC consumes less control energy.