組織內部的細胞受到外在的環境因素，會決定是要分裂或是要死亡。雖然組織受到外在的損害後，經過一段時間後通常可以復原，但有時候卻無法回到原來的狀況，而產生傷疤，所以組織可能存在多重穩定態。本論文研究的重點就是組織什麼情況下可以存在雙穩態。我們首先建立一個簡單的population model，population model只考慮細胞的數目，我們假設可分裂細胞的daughter cells有兩種不同配體來決定它們要變成可分裂的細胞或是不可分裂的細胞，如果兩種配體與受體結合後對daughter cells的決定有相反的影響，組織可能存在著雙穩態。另外為了描述組織裏不同區域細胞行為的差異，我們也建立spatial model，我們假設可分裂的細胞可以分泌morphogen分子且不可分裂的細胞可以吸收morphogen，我們發現morphogen產生率要在某個範圍且組織存在兩種配體與受體結合後對daughter cells的決定有相反的影響，我們才可以得到雙穩態的成果。;It is known that cells receive outside environmental factors, and decide to divide or undergo apoptosis. Usually a damaged tissue can evolve back to its homeostasis state, but tissue sometimes develops keloid and hypertrophic scars. Therefore tissues might have multiple stable states. In this thesis we explore possible mechanisms for a tissue to have bistable state. First, we construct a simple population model with cell lineage. In our model we only distinguish proliferative cells and non-proliferative cells. We find that when the decision of a daughter to differentiate into a nonproliferative cell or becomes a proliferatice cell is controlled by signal from two types of receptors with opposite effects, the tissue has bistable states. Since in a tissue cell growth is directional, we propose a spatial model for tissue. We assume that non-proliferative cells secrete signaling molecules, and proliferative cells absorb signaling molecules. We also assume that decision of a daughter cell is controlled by two types of ligands, and these two types of ligands have opposite effects on daughter cell decision. Finally, in the numerical solution we find multiple steady states in a range of morphogen production rate.
