Parameter identification and qualitative analysis with differential evolution of the calcium standard kinetics model

Calcium signaling is an intensively studied area, which establishes calcium ion (Ca
²⁺
) as a key player in the control of cell's basic functions. Calcium is a highly versatile intracellular signal present throughout the cell's life cycle as birth, life, and death, regulating many cellular functions. In this work, we study a mathematical model previously reported called Standard Kinetics (SK), which tries to explain the apparent paradox in ryanodine receptors (RyR) driven calcium release from the sarcoplasmic reticulum (SR), where the relation between free and total calcium concentration in the SR is calculated according to the basic chemical reaction for Ca
²⁺
buffering proposed by Nobel Prize Erwin Neher. We prove the generalization of the SK model by identifying the model parameters with Differential Evolution (DE) solving a bi-objective function to fit simultaneously and independently the recording of the two states variables representing the intracellular calcium concentration [Ca
²⁺
]
_i
and the Ca
²⁺
level in the SR in smooth muscle cells (SMC).