A nonlinear competitive model of the prostate tumor growth under intermittent androgen suppression.

Hormone suppression has been the primary modality of treatment for prostate cancer. However long-term androgen deprivation may induce androgen-independent (AI) recurrence. Intermittent androgen suppression (IAS) is a potential way to delay or avoid the AI relapse. Mathematical models of tumor growth and treatment are simple while they are capable of capturing the essence of complicated interactions. Game theory models have analyzed that tumor cells can enhance their fitness by adopting genetically determined survival strategies. In this paper, we consider the survival strategies as the competitive advantage of tumor cells and propose a new model to mimic the prostate tumor growth in IAS therapy. Then we investigate the competition effect in tumor development by numerical simulations. The results indicate that successfully IAS-controlled states can be achieved even though the net growth rate of AI cells is positive for any androgen level. There is crucial difference between the previous models and the new one in the phase diagram of successful and unsuccessful tumor control by IAS administration, which means that the suggestions from the models for medication can be different. Furthermore we introduce quadratic logistic terms to the competition model to simulate the tumor growth in the environment with a finite carrying capacity considering the nutrients or inhibitors. The simulations show that the tumor growth can reach an equilibrium state or an oscillatory state with the net growth rate of AI cells being androgen independent. Our results suggest that the competition and the restraint of a limited environment can enhance the possibility of relapse prevention.

A dynamical model on the network of p53-Mdm2 feedback loop regulated by p14/19ARF.

Base on new experimental results, we give a dynamical model to study the dynamical mechanism of the negative feedback loop composed of p53 and Mdm2 proteins regulated by p14/19ARF. The oscillatory behaviors for the activities of p53 and Mdm2 proteins regulated by p14/19ARF in individual of cells are described in our dynamical model. The results help us build a basal network about oscillatory behaviors among p53, Mdm2 and P14/19ARF. The dynamical model and its numerical results will help us understand the oscillatory behavior among other network of different proteins.

The use of an "effective potential" to describe the directed motion of a two-state molecular motor.

Force generation and directed motion of molecular motors using a simple two-state model are studied in the paper. Here we consider the asymmetric and periodic potential in the model. The symmetric and periodic potential is adopted to describe the interactions between motor proteins and filaments that are periodic and polar. The flux and the slope of the effective potential as functions of the temperature and transition rates are calculated in the two-state model. The ratio of the slope of the effective potential to the flux is also calculated. It is concluded that the directed motion of motor proteins is relevant to the effective potential. The slope of the effective potential corresponds to an average force. The non-vanishing force therefore implies that detailed balance is broken in the process of transition between different states. Moreover, we compare the theoretical relationship of load force and velocity with the experimental data. It is shown that they are consistent.