**Plasma Membrane: The Most Fluid Bio-Membrane**

The plasma membrane is the bio-membrane with the highest degree of fluidity among the options provided (thylakoid membrane, chloroplast envelope, outer membrane of mitochondria, and plasma membrane). This fluidity is crucial for the proper functioning of the cell. Let us delve into the reasons why the plasma membrane exhibits such high fluidity:

**Lipid Composition:**

- The plasma membrane consists of a phospholipid bilayer, which is primarily composed of phospholipids. These phospholipids have two hydrophobic fatty acid tails and a hydrophilic phosphate head.
- The fatty acid tails can vary in length and saturation, affecting the fluidity of the membrane. Shorter and unsaturated fatty acid tails increase fluidity, while longer and saturated tails decrease fluidity.
- The plasma membrane contains a high proportion of unsaturated phospholipids, which are more fluid due to the presence of double bonds in their fatty acid tails. This unsaturation prevents tight packing of the lipids, resulting in increased fluidity.

**Cholesterol Content:**

- The plasma membrane also contains cholesterol, which is interspersed between the phospholipids. Cholesterol plays a crucial role in modulating membrane fluidity.
- At high temperatures, cholesterol restricts the movement of phospholipids, reducing fluidity. Conversely, at low temperatures, cholesterol prevents the phospholipids from solidifying, maintaining fluidity.
- Cholesterol acts as a buffer, maintaining the optimal fluidity of the plasma membrane by preventing excessive fluidity or rigidity.

**Integral Membrane Proteins:**

- Integral membrane proteins are embedded within the phospholipid bilayer of the plasma membrane and play vital roles in various cellular functions.
- These proteins can diffuse laterally within the membrane, contributing to its fluidity.
- The fluid nature of the plasma membrane allows these proteins to move and interact with other molecules, facilitating cellular processes such as signal transduction and membrane transport.

**Conclusion:**

In summary, the plasma membrane exhibits the highest degree of fluidity among the given options due to its specific lipid composition, including a high proportion of unsaturated phospholipids, the presence of cholesterol, and the lateral movement of integral membrane proteins. This fluidity is essential for various cellular processes, including membrane trafficking, signaling, and cell-cell communication.

I think it is plasma membrane which is phospholipid bilayer consisting flowing proteins and cholesterol.