In silico simulation of reversible and irreversible swelling of mitochondria: The role of membrane rigidity

Abstract

Mitochondria have been widely accepted as the main source of ATP in the cell. The inner mitochondrial membrane (IMM) is important for the maintenance of ATP production and other functions of mitochondria. The electron transport chain (ETC) generates an electrochemical gradient of protons known as the proton-motive force across the IMM and thus produces the mitochondrial membrane potential that is critical to ATP synthesis. One of the main factors regulating the structural and functional integrity of the IMM is the changes in the matrix volume. Mild (reversible) swelling regulates mitochondrial metabolism and function; however, excessive (irreversible) swelling causes mitochondrial dysfunction and cell death. The central mechanism of mitochondrial swelling includes the opening of non-selective channels known as permeability transition pores (PTPs) in the IMM by high mitochondrial Ca 2+ and reactive oxygen species (ROS). The mechanisms of reversible and irreversible mitochondrial swelling and transition between these two states are still unknown. The present study elucidates an upgraded biophysical model of reversible and irreversible mitochondrial swelling dynamics. The model provides a description of the PTP regulation dynamics using an additional differential equation. The rigidity tensor was used in numerical simulations of the mitochondrial parameter dynamics with different initial conditions defined by Ca 2+ concentration in the sarco/endoplasmic reticulum. We were able to estimate the values of the IMM rigidity tensor components by fitting the model to the previously reported experimental data. Overall, the model provides a better description of the reversible and irreversible mitochondrial swelling dynamics.

On the Effects of Mechanical Stress of Biological Membranes in Modeling of Swelling Dynamics of Biological Systems

“…that are strongly coupled to the internal membrane parameters. For an axisymmetric oblate ellipsoid (a = b), we obtain g' xx = g' yy 24,25 . Using the material resistance theory 36 , diagonal tensor components may be presented as:…”

“…Several computational models describing changes in the mitochondrial volume have been developed, reproducing swelling dynamics of these organelles [26][27][28] . Recently, we have proposed a simplified mathematical approach to the analysis of mitochondrial swelling dynamics, which includes stretching mechanical properties of the inner mitochondrial membrane 24,25 . This approach allowed to describe transition from the reversible (physiological) to the irreversible (pathological) mitochondrial swelling mode.…”

“…In a biological system, osmotic pressure induces cell swelling through the influx of water. The membrane properties defining its mechanical stress due to swelling may be described by a second-rank rigidity tensor, in a biological object with an arbitrary 3D configuration 24,25 .…”

“…Figure 1 also shows a referential that is rigidly connected to the biological system, with its Cartesian x-, y-, and z-axes directed respectively along with the a, b, and c axes of the oblate ellipsoid. The rigidity tensor becomes diagonal in this referential 24,25 , with only the diagonal components g' ii (i = x, y, z) different from zero. Note that these tensor components are directly dependent on the membrane properties including its biochemical composition and structure, its permeability with respect to transport of different ionic and neutral species, its mechanical stability, and its physicochemical activity.…”

“…xx These expressions of the rigidity tensor components include membrane disruption at large mechanical deformations (irreversible pathological swelling), where β i (i = 0 and z) and n 1 are the respective phenomenological parameters, introduced to describe the reduction in stress at large deformations 24,25 . The ellipsoid deformations are Δr along the x and y axes, and Δz along the z axis, respectively.…”