The Working Cell Study Guide

Cell Size and Surface Area-to-Volume Ratio

Limits to Cell Size

The size of cells is limited by the need to efficiently exchange materials with their environment. As cells grow, their volume increases faster than their surface area, which restricts the rate at which substances can enter or leave the cell.

• Surface Area-to-Volume Ratio (SA/V): Smaller cells have a larger SA/V ratio, allowing for more efficient exchange of oxygen, nutrients, and waste.

• Volume: Determines the amount of metabolism in the cytoplasm.

• Surface Area: Determines the rate of exchange of materials between the cell and its environment.

Example Table:

Size (μm)	Surface Area (μm²)	Volume (μm³)	SA/V Ratio
1	6	1	6
2	24	8	3
3	54	27	2
4	96	64	1.5
5	150	125	1.2
6	216	216	1

Key Point: As cell size increases, the SA/V ratio decreases, making exchange less efficient.

Adaptations to Increase Surface Area

• Cells may develop extensions (e.g., microvilli in the intestine) or flatten into thin films to increase surface area without significantly increasing volume.

• Multicellular organisms may divide cytoplasm into smaller volumes or develop branched structures (e.g., plant roots) to maximize exchange.

Microscopy and Field of View Calculations

Field of View (FOV) Calculations

Microscopes are used to estimate the size of specimens using the field of view (FOV). The actual length of a specimen can be calculated using the ratio:

$\frac{\text{Length of specimen in picture (mm)}}{\text{Length of FOV in picture (mm)}} = \frac{\text{Actual Length of specimen (μm)}}{\text{Actual FOV (μm)}}$

• Measure the specimen and FOV in the image (mm).

• Use the actual FOV (μm) provided by the microscope.

• Solve for the actual length of the specimen (μm).

Example: If the specimen is 2.0 mm, FOV is 6.8 mm, and actual FOV is 300 μm:

$\frac{2.0}{6.8} = \frac{x}{300}$ $x = \frac{2.0}{6.8} \times 300 = 88\ \mu m$

Cell Membranes: Structure and Function

Fluid Mosaic Model

The plasma membrane is described by the fluid mosaic model, which highlights its dynamic and complex structure.

• Phospholipid Bilayer: Forms a waterproof barrier; hydrophilic heads face outward, hydrophobic tails face inward.

• Selective Permeability: Only certain molecules can pass through freely (e.g., small, nonpolar molecules like O2 and CO2).

Membrane Proteins

• Transport Proteins: Allow specific ions or molecules to enter or exit the cell (e.g., channel and carrier proteins).

• Enzymes: Catalyze chemical reactions at the membrane surface.

• Attachment Proteins: Anchor the membrane to the cytoskeleton and extracellular matrix.

• Glycoproteins: Serve as ID tags for cell recognition.

• Receptor Proteins: Bind signaling molecules and relay messages into the cell.

Cell Transport Mechanisms

Passive Transport

• Diffusion: Movement of particles from high to low concentration due to entropy; does not require energy.

• Simple Diffusion: Small, nonpolar molecules move directly through the phospholipid bilayer.

• Facilitated Diffusion: Ions and larger molecules move through channel or carrier proteins; still passive (no energy required).

Concentration Gradient: The difference in concentration of a substance across a space or membrane.

Osmosis

• Definition: The diffusion of water across a selectively permeable membrane.

• Water moves from an area of high water concentration (low solute) to low water concentration (high solute) to balance solute concentrations.

Tonicity and Water Balance

• Tonicity: The ability of a surrounding solution to cause a cell to gain or lose water.

• Hypertonic Solution: Higher solute concentration outside; cells lose water and shrink.

• Hypotonic Solution: Lower solute concentration outside; cells gain water and swell.

• Isotonic Solution: Equal solute concentrations; no net water movement.

Example Table:

Solution Type	Animal Cell	Plant Cell
Hypotonic	Lyse (burst)	Turgid (normal)
Isotonic	Normal	Flaccid
Hypertonic	Shriveled	Plasmolyzed

Active Transport

• Requires energy (ATP) to move substances against their concentration gradient.

• Protein Pumps: Transport ions and molecules across the membrane using energy.

• Endocytosis: Movement of materials into the cell via vesicles (includes phagocytosis and receptor-mediated endocytosis).

• Exocytosis: Movement of materials out of the cell via vesicles.

Neuronal Membrane Transport and Action Potentials

Resting and Action Potentials

• Resting Potential: The electrical charge difference across the neuron's membrane when not transmitting a signal (about -70 mV).

• Sodium-Potassium Pump: Maintains resting potential by pumping Na+ out and K+ in (active transport).

• Action Potential: A rapid change in membrane potential that travels along the neuron, involving the opening and closing of voltage-gated Na+ and K+ channels.

Phases of Action Potential:

1. Resting state

2. Threshold reached

3. Depolarization (Na+ influx)

4. Repolarization (K+ efflux)

5. Refractory period (hyperpolarization/undershoot)

6. Return to resting state

Summary of Key Concepts

• Cell size is limited by the surface area-to-volume ratio, which affects the efficiency of material exchange.

• The plasma membrane's fluid mosaic structure allows selective permeability, with proteins serving diverse roles.

• Transport across membranes can be passive (diffusion, osmosis, facilitated diffusion) or active (requiring ATP).

• Osmosis and tonicity are crucial for maintaining water balance in cells.

• Neurons use active and passive transport to generate and propagate action potentials.

Additional info: These notes are based on slides and class notes for Chapter 5, covering cell membranes, transport, and related laboratory activities. For further study, review enzyme structure and function, which is also part of this chapter but not fully detailed in the provided slides.