Energy transport in the three coupled α-polypeptide chains of collagen molecule with long-range interactions effect

Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects

Understand the dynamics of cancer stem cells (CSCs), prevent the non-recurrence of cancers and develop therapeutic strategies to destroy both cancer cells and CSCs remain a challenge topic. In this paper, we study both analytically and numerically the dynamics of CSCs under radiotherapy effects. The dynamical model takes into account the diffusion of cells, the de-differentiation (or plasticity) mechanism of differentiated cancer cells (DCs) and the time delay on the interaction between microRNAs molecules (microRNAs) with DCs. The stability of the model system is studied by using a Hopf bifurcation analysis. We mainly investigate on the critical time delay τ c , that represents the time for DCs to transform into CSCs after the interaction of microRNAs with DCs. Using the system parameters, we calculate the value of τ c for prostate, lung and breast cancers. To confirm the analytical predictions, the numerical simulations are performed and show the formation of spatiotemporal circular patterns. Such patterns have been found as promising diagnostic and therapeutic value in management of cancer and various diseases. The radiotherapy is applied in the particular case of prostate model. We calculate the optimum dose of radiation and determine the probability of avoiding local cancer recurrence after radiotherapy treatment. We find numerically a complete eradication of patterns when the radiotherapy is applied before a time t < τ c . This scenario induces microRNAs to act as suppressors as experimentally observed in prostate cancer. The results obtained in this paper will provide a better concept for the clinicians and oncologists to understand the complex dynamics of CSCs and to design more efficacious therapeutic strategies to prevent the non-recurrence of cancers.

Exact Solutions for a Modified Schrödinger Equation

The aim of this paper was to propose a systematic study of a ( 1 + 1 ) -dimensional higher order nonlinear Schrödinger equation, arising in two different contexts regarding the biological science and the nonlinear optics. We performed a Lie symmetry analysis and here present exact solutions of the equation.

A Mathematical Model to Study the Mechanical Information Induced by Lifting-Thrusting Needle

Focusing on the mechanical effect of traditional Chinese acupuncture, this study builds a mathematical model that simulates the mechanical process of lifting-thrusting needle. Analytic and numerical solutions are obtained to explore the mechanical information (displacement, strain, stress, and energy) in the skin tissue. Our results show that (1) needle manipulation leads to tissue displacement and mechanical stress field, but the needle should be inserted into the right position (about π/ω cm around the acupoint, where ω is the angular frequency) and enough depth (about 2 cm in lower limbs) to achieve effective mechanical stimuli; (2) the tissue displacement decays with an increase of distance from the stimulus position, more rapidly at higher frequencies; (3) there is an inverse relationship between the area of the 'effective influence region' (where shear strain > 0.2) and the stimulus frequency, which means larger needle movement is needed at higher frequencies to achieve a better curative effect; (4) more energy is required to maintain high frequency manipulation. This study proposes a preliminary comprehension of the mechanical response around the needle during the acupuncture process.

Exact solitary wavelike solutions in a nonlinear microtubule RLC transmission line

Analytically, we study the dynamics of ionic waves in a microtubule modeled by a nonlinear resistor, inductor, and capacitor (RLC) transmission line. We show through the application of a reductive perturbation technique that the network can be reduced in the continuum limit to the dissipative nonlinear Schrödinger equation. The processes of the modulational instability are studied and, motivated with a solitary wave type of solution to the nonlinear Schrödinger (NLS) equation, we use the direct method and the Weierstrass's elliptic function method to present classes of solitary wavelike solutions to the dissipative NLS equation of the network. The results suggest that microtubules are the biological structures where short-duration nonlinear waves called electrical envelope solitons can be created and propagated. This work presents a good analytical approach of investigating the propagation of solitary waves through a microtubule modeled by a nonlinear RLC transmission line.

Fractional formalism to DNA chain and impact of the fractional order on breather dynamics

We have investigated the impact of the fractional order derivative on the dynamics of modulated waves of a homogeneous DNA chain that is based on site-dependent finite stacking and pairing enthalpies. We have reformulated the classical Lagrangian of the system by including the coordinates depending on the Riemann-Liouville time derivative of fractional order γ. From the Lagrange equation, we derived the fractional nonlinear equation of motion. We obtained the fractional breather as solutions by means of a fractional perturbation technique. The impact of the fractional order is investigated and we showed that depending on the values of γ, there are three types of waves that propagate in DNA. We have static breathers, breathers of small amplitude and high velocity, and breathers of high amplitude and small velocity.