Self assembly of different globular and filamentous proteins in the eukaryotic cell throughout the entire cell cycle is ubiquitous and helps a cell to perform various tasks such as migration from one place to another, intake of food from the outside world, cell division, etc. The organization of individual microtubule filaments into bundles during the formation of the mitotic spindle is an example of such a phenomenon when a cell enters mitosis. At the beginning of prometaphase, experimentally it is found that at the midplane of a vertically oriented spindle, microtubules form a mist-like distribution which transits to well-formed droplet like structures as time progresses. We construct a free energy description of this system using the density of microtubules and cross-linking proteins as field variables considering attractive and repulsive interactions between them. Further, dynamical equations governing the time evolution of density fields are obtained by minimizing the free energy and incorporating a non-equilibrium process of microtubule polymerization and depolymerization. Linear stability analysis shows that the system transits from homogeneous distribution of microtubules to a phase consisting of multiple bundles of microtubules once the density of cross-linking proteins crosses a threshold and the bundles do not collapse into a single large bundle over time.
 On the other hand, pattern formation on the cell membrane is linked with the contractile active force generated by the actomyosin cortex beneath it and outward push coming due to polymerization of filamentous actin attached to the membrane surface. Membrane associated proteins act as the nucleating centers of actin polymerization, and the proteins couple to the membrane surface in a curvature dependent manner modifying the local bending modulus of the membrane. These competing equilibrium and non-equilibrium forces acting on cell membrane allow a cell to deform, and mediate cell motility and division. We use coupled evolution of fields to perform linear stability analysis and numerical calculations. As activity overcomes the stabilizing factors such as surface tension and bending rigidity, the spherical membrane shows instability towards pattern formation, localized pulsation, and running pulsation between poles.