###### Regulation of p53 by siRNA in radiation treated cells: Simulation studies

Ionizing radiation activates a large variety of intracellular mechanisms responsible for maintaining appropriate cell functionality or activation of apoptosis which eliminates damaged cells from the population. The mechanism of such induced cellular death is widely used in radiotherapy in order to eliminate cancer cells, although in some cases it is highly limited by increased cellular radio-resistance due to aberrations in molecular regulation mechanisms of malignant cells. Despite the positive correlation between the radiation dose and the number of apoptotic cancer cells, radiation has to be limited because of extensive side effects. Therefore, additional control signals whose role will be to maximize the cancer cells death-ratio while minimizing the radiation dose and by that the potential side effects are worth considering. In this work we present the results of simulation studies showing possibilities of single gene regulation by *small interfering RNA *(siRNA) that can increase radio-sensitivity of malignant cells showing aberrations in the p53 signaling pathway, responsible for DNA damage-dependant apoptosis. By blocking the production of the p53 inhibitor Mdm2, radiation treated cancer cells are pushed into the apoptotic state on a level normally achievable only with high radiation doses. The presented approach, based on a simulation study originating from experimentally validated regulatory events, concerns one of the basic problems of radiotherapy dosage limitations, which, as will be shown, can be partially avoided by using the appropriate siRNA based control mechanism.

###### Immunotherapy with Interleukin-2: A Study Based on Mathematical Modeling

-112. Bodnar M. and Foryś U. (2000b). Periodic dynamics in the model of immune system, International Journal of Applied Mathematics and Computer Science 10 (1): 113-126. Bodnar M. and Foryś U. (2003a). Time delays in proliferation process for solid avascular tumor, Mathematical and Computer Modeling 37 (11): 1201-1209. Bodnar M. and Foryś U. (2003b). Time delays in regulatory apoptosis for solid avascular tumor, Mathematical and Computer Modeling 37 (11): 1211-1220. Byrne H. M. (1997). The

###### Machine learning techniques combined with dose profiles indicate radiation response biomarkers

variance and bias, Bioinformatics 19 (2): 185–193. Brenner, D.J., Doll, R., Goodhead, D.T., Hall, E.J., Land, C.E., Little, J.B., Lubin, J.H., Preston, D.L., Preston, R.J., Puskin, J.S., Ron, E., Sachs, R.K., Samet, J.M., Setlow, R.B. and Zaider, M. (2003). Cancer risks attributable to low doses of ionizing radiation: Assessing what we really know, Proceedings of the National Academy of Sciences 100 (24): 13761–13766. Brodsky, R.A., Vala, M.S., Barber, J.P., Medof, M.E. and Jones, R.J. (1997). Resistance to apoptosis caused by PIG-A gene mutations in

###### Nuclei segmentation for computer-aided diagnosis of breast cancer

morphologies in breast cancer cells undergoing apoptosis using generalized Cauchy field, Computerized Medical Imaging and Graphics 32(7): 631-637. National Cancer Registry in Poland (2012). http://85.128.14.124/krn. Nikolova, N.K. (2011). Microwave imaging for breast cancer, IEEE Microwave Magazine 12(7): 78-94. Niwas, S.I., Palanisamy, P., Sujathan, K. and Bengtsson, E. (2013). Analysis of nuclei textures of fine needle aspirated cytology images for breast cancer diagnosis using complex Daubechies wavelets, Signal Processing

###### A coherent modeling procedure to describe cell activation in biological systems

populations, Bull. Math. Biol., vol. 77, no. 2, pp. 1132–1165, 2015. 20. H. S. Bell, I. R. Whittle, M. Walker, H. A. Leaver, and S. B. Wharton, The development of necrosis and apoptosis in glioma: experimental findings using spheroid culture systems, Neuropathol. Appl. Neurobiol., vol. 27, pp. 291–304, 2001. 21. M. L. Puiffe, C. L. Page, A. Filali-Mouhim, M. Zietarska, V. Ouellet, P. N. Toniny, M. Chevrette, D. M. Provencher, and A. M. Mes-Masson, Characterization of ovarian cancer ascites on cell invasion, proliferation, spheroid formation

###### Optimal control problems for differential equations applied to tumor growth: state of the art

even if apoptosis is not induced. The remaining fraction (1 -u ) a 2 N 2 suffers cell division and therefore the controlled mathematical model becomes (3) N ˙ 1 ( t ) = − a 1 N 1 ( t ) + 2 ( 1 − u ) a 2 N 2 ( t ) , N 1 ( 0 ) = N 10 , $$\begin{eqnarray}\dot{N}_1(t)&=&-a_1N_1(t)+2(1-u)a_2N_2(t),\quad N_1(0)=N_{10},\\ \end{eqnarray}$$ (4) N ˙ 2 ( t ) = a 1 N 1