Fractional order interdependent nonlinear chaotic spatiotemporal calcium and Aβ dynamics in a neuron cell

Abstract

The formation of β-amyloid (Aβ) and its accumulation depend on the calcium ([Ca2+]) signaling in neurons. The individual and independent dynamics of calcium and β-amyloid give very limited information about different cellular mechanisms. Some researchers have explored the interdependent system dynamics of integer-order calcium and β-amyloid, which provides some more crucial information on different regulatory and dysregulatory processes in neurons. However, these integer-order systems are not capable of generating the information on the superdiffusion, cell memory and Brownian motion effects in neuron cells. A nonlinear mathematical model has been framed to explore the fractional-order interdependent chaotic spatiotemporal [Ca2+] and Aβ dynamics in neurons. The proposed model integrates the two-way feedback mechanism between [Ca2+] and Aβ dynamics in neurons. The Crank-Nicolson scheme with the Grunwald approximation is employed for space fractional derivatives and the L1 formula is employed for time fractional derivatives. The Gauss-Seidel iterations are utilized to solve the resultant system of nonlinear algebraic equations. The effects of cell memory, Brownian motion and superdiffusion phenomena with different crucial mechanisms like buffer, source influx, ryanodine receptor, etc. on the spatiotemporal interdependent [Ca2+] and Aβ dynamics have been explored in neurons. The numerical findings give novel insights on the regulatory and dysregulatory effects of cell memory, Brownian motion and superdiffusion on the system dynamics of [Ca2+] and Aβ in neuron cells and the conditions that may cause the different neurodegenerative illnesses like Alzheimer’s disease.

Modeling and analysis of fractional order calcium distribution model with Amyloid beta and Orai channel

“…All the values of these parameters are given in Table 1. incorporating the equations (14)(15)(16)(17)(18)(19)(20)(21)(22)(23). we obtain the proposed model,…”

“…Naik modeled the Bazykin-Berezovskaya model for diffusion system [18]. Pawar and Pardasani have modeled the amyloid beta and calcium dynamics on cellular degeneration [19]. Y Jagtap and N. Adlakha have studied the calcium and IPR dynamics by using the finite volume method [20].…”

Mechanistic insights of COVID-19 dynamics by considering the influence of neurodegeneration and memory trace

“…The impact of age-wise transmission dynamics of COVID-19 patterns has been studied in the given literature [22,23]. However, the mathematical model to examine the impact of various physiological parameters that disturb nerve cells and invite neurodegenerative conditions has been studied in the given literature [24][25][26][27][28][29][30][31][32][33][34][35]. The co-dynamics of COVID-19 with diabetes [36], comorbidity [37], bacterial pneumonia [38], and tuberculosis [39] are proposed and analyzed.…”

Nonlinear system dynamics of calcium and nitric oxide due to cell memory and superdiffusion in neurons

“…It is reported that the occurrence of superdiffusive behavior is contingent upon the absence of equilibrium between birth and death processes in tumor cells [77]. The influences of memory and superdiffusion on the systems of calcium and Aβ and calcium and IP 3 were studied in neurons [78,79].…”