Membrane Structure and Cell Size

Surrounds the cells of all living organisms and controls the entry and exit of substances.
Composed primarily of a phospholipid bilayer, along with proteins, carbohydrates, and cholesterol.
Also referred to as the plasma membrane or phospholipid bilayer.

Head Group: Contains phosphate, glycerol, and choline; polar and hydrophilic (interacts with water).
Fatty Acid Tails: Composed of saturated and unsaturated fatty acid chains; non-polar and hydrophobic (avoids water).
Membrane Fluidity: Bends in unsaturated fatty acid tails prevent phospholipids from packing too tightly, maintaining membrane fluidity.
Bilayer Assembly: Energetically unfavorable contact between hydrophobic tails and water forces tails inward to form a core, leaving hydrophilic heads facing interior and exterior aqueous environments.

Cholesterol: Regulates membrane fluidity in response to temperature variations.
Glycolipids: Carbohydrate molecules attached to phospholipids; facilitate cell-to-cell adhesion and recognition.
Glycoproteins: Carbohydrate molecules attached to proteins; enable cell cross-linking to provide structural strength to tissues.

Peripheral Proteins: Located on the inside or outside surface of the cell membrane; primarily involved in cell signaling.
Integral Proteins: Fully or partially embedded within the membrane; function in signaling and transport.
Transmembrane Proteins: Span completely across the membrane; often serve as channel proteins to move polar or large molecules.
Channel vs. Receptor Proteins:
- Channel Proteins: Transmembrane proteins featuring an internal channel used for transporting large, polar, or charged molecules across the membrane.
- Receptor Proteins: Transmembrane or peripheral proteins without an internal channel that bind specific ligands to initiate cell signaling responses.
Functional Roles of Membrane Proteins:
- Receptor: Binds chemical messengers sent by other cells, such as hormones.
- Enzyme: Catalyzes chemical breakdown of messengers to terminate their activity.
- Channel / Gated Channel: Allows solute passage continuously or opens and closes selectively.
- Cell-Identity Marker: A glycoprotein distinguishing the body's self cells from foreign cells.
- Cell-Adhesion Molecule (CAM): Binds one cell to another cell.

Allows small, non-polar molecules (such as oxygen, carbon dioxide, and water*) to diffuse freely through spaces between phospholipids.
Energetically unfavorable for molecules without these properties to interact directly with the hydrophobic core formed by fatty acid tails.

Cell Size Range: Typically spans from $10\,\mu\text{m}$ to $1\,\text{mm}$ .
Size Requirements: Must be large enough to accommodate DNA and organelles, but small enough for efficient nutrient, oxygen, and waste exchange to maintain homeostasis.
Surface Area to Volume Ratio ( $\text{SA:V}$ ):
- A high $\text{SA:V}$ ratio increases efficiency by maximizing available surface area for material exchange while minimizing internal travel distance.
- Cell projections (such as villi) significantly increase the $\text{SA:V}$ ratio.
- The rate of diffusion remains identical regardless of overall cell size.
Calculations:
- Surface Area of Cube: $\text{SA} = 6 \times a^2$
- Volume of Cube: $V = l \times w \times h$
- Example: For a cube with length $l = 3\,\text{cm}$ , width $w = 3\,\text{cm}$ , height $h = 3\,\text{cm}$ :
- $\text{SA} = 6 \times (3\,\text{cm})^2 = 54\,\text{cm}^2$
- $V = 3\,\text{cm} \times 3\,\text{cm} \times 3\,\text{cm} = 27\,\text{cm}^3$
- $\text{SA:V Ratio} = \frac{54\,\text{cm}^2}{27\,\text{cm}^3} = 2$