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In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...

Microtubules are thick hollow cylindrical proteins that help form the cytoskeleton. Microtubules have varied roles in the cell. These filaments help form cellular appendages like cilia and flagella, which are responsible for locomotion. The cilia arise from basal bodies, separated from the main body by a membrane-like structure forming the transition zone. This zone is the gate for the entry of lipids and proteins, creating a unique composition of lipids and proteins in the ciliary membrane and...

The torque-free motion refers to the movement of a rigid body in space when no external torques are acting upon it. This type of motion can be observed in environments where there are no external forces or frictions, like in outer space. For example, a rotation of Mars in space is a torque-free motion. Mars is an axisymmetric object, meaning it has an axis of symmetry along which it rotates, designated as the z-axis. The rotating frame of reference is defined such that the center of mass of...

In eukaryotic cells,  cytoskeletal filaments such as actin, microtubules, and intermediate filaments form a mesh-like cytoskeletal network. These filaments serve as tracks for transporting cellular cargo. Specialized motor proteins use the chemical energy stored in adenosine triphosphate (ATP) for this transport. During interphase, microtubules are polarized, with the plus-end towards the cell periphery and the minus-end towards the cell center. Two microtubule-associated motor proteins,...

Actin filaments undergo polymerization and depolymerization from either end. The polymerization and depolymerization rates depend on the cytosolic concentration of free G-actins. The polymerization rate is generally higher at the plus or barbed end, while the depolymerization rate is higher at the minus or pointed end. At a steady state, critical concentration describes the concentration of free G-actin monomers at which the polymerization rate at the plus end is equal to that of the...