Partner: Je-Chiang Tsai

National Chung Cheng University (TW)

Recent publications
1.Białecki S., Kaźmierczak B., Nowicka D., Tsai J.-C., Regularity of solutions to a reaction–diffusion equation on the sphere: the Legendre series approach, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, ISSN: 0170-4214, DOI: 10.1002/mma.4390, pp.1-21, 2017
Abstract:

In the paper, we study some ‘a priori’ properties of mild solutions to a single reaction–diffusion equation with discontinuous nonlinear reaction term on the two-dimensional sphere close to its poles. This equation is the counterpart of the well-studied bistable reaction–diffusion equation on the Euclidean plane. The investigation of this equation on the sphere is mainly motivated by the phenomenon of the fertilization of oocytes or recent studies of wave propagation in a model of immune cells activation, in which the cell is modeled by a ball. Because of the discontinuous nature of reaction kinetics, the standard theory cannot guarantee the solution existence and its smoothness properties. Moreover, the singular nature of the diffusion operator near the north/south poles makes the analysis more involved. Unlike the case in the Euclidean plane, the (axially symmetric) Green's function for the heat operator on the sphere can only be represented by an infinite series of the Legendre polynomials. Our approach is to consider a formal series in Legendre polynomials obtained by assuming that the mild solution exists. We show that the solution to the equation subject to the Neumann boundary condition is C1 smooth in the spatial variable up to the north/south poles and Hölder continuous with respect to the time variable. Our results provide also a sort of ‘a priori’ estimates, which can be used in the existence proofs of mild solutions, for example, by means of the iterative methods.

Keywords:

discontinuous reaction term, stationary fronts, sphere

Affiliations:
Białecki S.-IPPT PAN
Kaźmierczak B.-IPPT PAN
Nowicka D.-IPPT PAN
Tsai J.-C.-National Chung Cheng University (TW)
2.Białecki S., Kaźmierczak B., Tsai J-C., Stationary waves on the sphere, SIAM JOURNAL ON APPLIED MATHEMATICS, ISSN: 0036-1399, DOI: 10.1137/140999384, Vol.75, No.4, pp.1761-1788, 2015
Abstract:

In this paper, we investigate stationary waves on the sphere using the bistable reaction-diffusion system. The motivation of this study arises from the study of activation waves of B cells in immune systems. We analytically establish (i) the existence and uniqueness of stationary waves; (ii) the limiting wave profile for small diffusivity of diffusing species; and (iii) the stability of the constructed stationary waves. The stability result may suggest the critical role of stationary waves in the determination of initial data for initiating propagating waves on the sphere, which is consistent with the numerical results for the B-cell activation model.

Keywords:

stationary wave, sphere, bistable kinetics

Affiliations:
Białecki S.-IPPT PAN
Kaźmierczak B.-IPPT PAN
Tsai J-C.-National Chung Cheng University (TW)
3.Cheng F.H.C., Aguda B.D., Tsai J-C., Kochańczyk M., Lin J.M.J., Chen G.C.W., Lai H-C., Nephew K.P., Hwang T-W., Chan M.W.Y., A Mathematical Model of Bimodal Epigenetic Control of miR-193a in Ovarian Cancer Stem Cells, PLOS ONE, ISSN: 1932-6203, DOI: 10.1371/journal.pone.0116050, Vol.9, No.12, pp.e116050-1-17, 2014
Abstract:

Accumulating data indicate that cancer stem cells contribute to tumor chemoresistance and their persistence alters clinical outcome. Our previous study has shown that ovarian cancer may be initiated by ovarian cancer initiating cells (OCIC) characterized by surface antigen CD44 and c-KIT (CD117). It has been experimentally demonstrated that a microRNA, namely miR-193a, targets c-KIT mRNA for degradation and could play a crucial role in ovarian cancer development. How miR-193a is regulated is poorly understood and the emerging picture is complex. To unravel this complexity, we propose a mathematical model to explore how estrogen-mediated up-regulation of another target of miR-193a, namely E2F6, can attenuate the function of miR-193a in two ways, one through a competition of E2F6 and c-KIT transcripts for miR-193a, and second by binding of E2F6 protein, in association with a polycomb complex, to the promoter of miR-193a to down-regulate its transcription. Our model predicts that this bimodal control increases the expression of c-KIT and that the second mode of epigenetic regulation is required to generate a switching behavior in c-KIT and E2F6 expressions. Additional analysis of the TCGA ovarian cancer dataset demonstrates that ovarian cancer patients with low expression of EZH2, a polycomb-group family protein, show positive correlation between E2F6 and c-KIT. We conjecture that a simultaneous EZH2 inhibition and anti-estrogen therapy can constitute an effective combined therapeutic strategy against ovarian cancer.

Keywords:

Ovarian cancer, Messenger RNA, Epigenetics, DNA methylation, Estrogens, Gene expression, Cancer treatment, Carcinogenesis

Affiliations:
Cheng F.H.C.-National Chung Cheng University (CN)
Aguda B.D.-DiseasePathways LLC (US)
Tsai J-C.-National Chung Cheng University (TW)
Kochańczyk M.-IPPT PAN
Lin J.M.J.-National Chung Cheng University (CN)
Chen G.C.W.-National Chung Cheng University (CN)
Lai H-C.-Taipei Medical University (CN)
Nephew K.P.-Indiana University School of Medicine (US)
Hwang T-W.-National Chung Cheng University (CN)
Chan M.W.Y.-National Chung Cheng University (CN)