Dynamics of two granules

Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...

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,...

An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...

An object undergoing circular motion, like a race car, is accelerating because it is changing the direction of its velocity. This centrally directed acceleration is called centripetal acceleration. This acceleration acts along the radius of the curved path (thus is also referred to as radial acceleration).
Any acceleration must be produced by some force. Therefore, any force or combination of forces can cause centripetal acceleration. A few examples include the tension in the rope on a...

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...

Vesicle budding is orchestrated by distinct cytosolic proteins such as adaptor proteins, coat proteins, and GTPases. To initiate vesicle budding, membrane-bending proteins containing crescent-shaped BAR domains bind to the lipid heads in the bilayer and distort the membrane to form a protein-coated vesicle bud. Adaptors proteins such as AP2 for clathrin-coated vesicles can nucleate on the deformed membrane. Finally, coat proteins such as clathrin or COPI and COPII assemble into a coat forming...