Cell Size, SA:V, Microscopy, and Cell Types — Study Notes

Cell Size, Surface Area, and Volume

• Maximum size concept: cells will die if they grow too large because transport cannot meet metabolic demands.
• Key relationship: as a cell increases in size, both surface area and volume increase, but volume increases faster than surface area.
• Geometry cue: for a spherical cell, the surface area and volume follow:
  SA = 4\pi r^2, \quad V = \frac{4}{3}\pi r^3, \quad \frac{SA}{V} = \frac{3}{r}.
• Example with radius change from 1 mm to 10 mm:
  • For r = 1 mm: SA = 4\pi(1)^2 \approx 12.57\ \text{mm}^2, \quad V = \frac{4}{3}\pi(1)^3 \approx 4.19\ \text{mm}^3. \frac{SA}{V} \approx 3.0.
  • For r = 10 mm: SA = 4\pi(10)^2 = 4\pi\cdot100 \approx 1256.64\ \text{mm}^2, \quad V = \frac{4}{3}\pi(10)^3 = \frac{4}{3}\pi\cdot1000 \approx 4188.79\ \text{mm}^3. \frac{SA}{V} \approx 0.30.
• Size effect summary:
  • Surface area increases by a factor of 100 when radius grows by a factor of 10 (since SA ∝ r^2).
  • Volume increases by a factor of 1000 (since V ∝ r^3).
  • Therefore, SA increases slower than V; the SA:V ratio decreases with size.
• Significance of SA:V ratio:
  • Smaller cells have a greater SA:V, enabling faster transport of nutrients and wastes and faster overall metabolism.
  • Metabolic rate and transport capacity are higher relative to volume in small cells, enabling rapid growth.
  • This helps explain why bacteria reproduce quickly (generation times ~15–20 minutes) compared to plants/animals (days to months).
• Real-world implication: metabolism and transport depend on surface area to volume; a larger cell requires more resources but has a relatively smaller surface area for exchange, which can bottleneck growth and necessitate division.

Metabolism and the Surface Area–Volume Link

• Photosynthesis example in a plant cell (metabolism link):
  • Overall photosynthesis equation (reactants → products):
    6\text{CO}2 + 6\text{H}2\text{O} + \text{light} \rightarrow \text{C}6\text{H}{12}\text{O}6 + 6\text{O}2.
  • Oxygen is produced as a waste product in photosynthesis.
  • Location of metabolism: photosynthesis occurs inside chloroplasts within the cell while exchange of reactants and wastes occurs across the plasma membrane.
• Transport dependence:
  • The rate of transport of reactants in and waste out depends on the plasma membrane surface area (SA).
  • The volume of the cell determines how much metabolic production/consumption occurs inside the cell.
  • For a given cell size, SA per unit volume is higher when the cell is smaller, enabling faster exchange relative to the cell’s needs.
• Conceptual note:
  • Amount of surface area per unit volume varies with cell size: smaller cells have a relatively larger SA:V than larger cells.
  • If a cell becomes large, SA:V decreases, making it harder to supply all regions of the cell and to remove wastes quickly enough, threatening survival without division.
• Analogy: compare a small infant vs a large adult; a bigger organism requires more resources, and with less SA:V, exchange processes may lag.

What Limits Cell Size?

• Main limiter: surface area to volume ratio (SA:V).
• The SA:V ratio governs the efficiency of material transport across the cell boundary.
• Flowchart takeaway: as SA:V decreases with increasing cell size, viability becomes constrained; thus cells tend to stay small or divide to restore a favorable SA:V.
• Typical scale discussion:
  • Bacteria: very small (often 1–2 µm in diameter).
  • Elephant vs ant: despite gigantic body size differences, individual cells remain small; entire size difference is due to cell number, not large changes in single cell size.

Microscopy: Resolving Power, Magnification, and Optics

• Two general types of microscopes: light microscope and electron microscope.
• Core idea: microscopes render objects larger than their actual size by altering the light/path of rays, not by changing the actual size of the specimen.
• Wavelength and resolution:
  • Wavelength is the distance between successive wave crests; shorter wavelengths yield higher resolving power.
  • Visible spectrum range: ext{λ} \in [400, 700]\ \text{nm}. Violet has shorter wavelength than red (≈ 400 nm vs ≈ 700 nm).
  • Shorter wavelengths (e.g., blue/violet, and even ultraviolet) have higher resolving power than longer wavelengths (red).
• Resolution vs. limit of resolution:
  • Resolution (clarity) is the ability to distinguish two points as separate.
  • Limit of resolution is the minimum distance between two points that can be seen as distinct.
  • Our eyes have a limit of resolution around 0.1\ \text{mm} = 100\ \mu\text{m}. A light microscope has a smaller limit than the eye, and an electron microscope has an even smaller limit.
  • If two points are separated by a distance greater than the limit, they are resolved; if smaller, they appear as one (unresolved).
• Example analogy: two headlights on distant cars appear as one if the distance is below the limit, but as two headlights if closer to the observer (and hence above the limit of resolution).
• Why electron vs light microscopy:
  • Electron microscopy provides higher resolution (smaller limit) than light microscopy due to shorter effective wavelength of electrons.
• Magnification concepts:
  • Magnification is the apparent increase in size; it does not add new information, it merely enlarges the image.
  • Total magnification for a light microscope is the product of the magnifications of the objective and the ocular (eyepiece) lenses:
    M{ ext{total}} = M{ ext{objective}} \times M_{ ext{ocular}}.
  • Typical lab setup: oculars are often M_{ ext{ocular}} = 10\times. Objectives can include 4×, 10×, 40×, 100× (oil immersion).
  • Example calculations:
  • If objective = 10× and ocular = 10×, then M_{ ext{total}} = 10\times 10 = 100\times.
  • If objective = 40× and ocular = 10×, then M_{ ext{total}} = 40\times 10 = 400\×.
  • If objective = 100× (oil) and ocular = 10×, then M_{ ext{total}} = 1000\×.
• Image inversion: due to refraction at the lens, the observed image is inverted relative to the object.
• Refraction basics:
  • Light travels from air (less dense) into glass (more dense) and bends (refracts) due to changes in optical density.
  • The bending occurs both at entry and exit of the lens, culminating in a focused image.
  • This refraction is also responsible for the apparent inversion of the image.
• Contrast and staining:
  • Contrast can be low (poor contrast) without staining; staining increases contrast and can improve apparent resolution.
  • Discussed as a practical note: staining enhances visibility of structures.
• Types of microscopes in typical teaching labs:
  • Light microscopes (bright-field) are common; electron microscopes provide much higher resolution but require different preparation.

Prokaryotes vs Eukaryotes: Key Cellular Differences

• Prokaryotes (includes archaea and bacteria):
  • Nucleus: absent (nucleoid region contains DNA).
  • Membrane-bound organelles: absent in general (no mitochondria, no chloroplasts, etc.).
  • Plasma membrane: present; many essential functions regulated at the membrane.
  • Cell wall: typically present; provides shape and protection.
  • DNA: circular, not enclosed in a nucleus.
  • Ribosomes: present (70S in prokaryotes).
  • Cytoskeleton: simple or absent; has some structural elements but not the complex cytoskeleton of eukaryotes.
  • Other features mentioned in the transcript: pili/fimbriae for attachment, capsules for attachment, flagella for movement.
  • Metabolism: ATP generation largely linked to the plasma membrane; photosynthetic bacteria perform photosynthesis at the plasma membrane.
  • Cytoplasm contains water and dissolved substances; nucleoid houses DNA.
• Eukaryotes:
  • Nucleus: present; encloses genetic material.
  • Membrane-bound organelles: present (ER, Golgi, mitochondria, chloroplasts in plants/algae, etc.).
  • Plasma membrane: present; regulates transport.
  • Cytoskeleton: present; provides internal structure and transport routes.
  • DNA: linear and enclosed within the nucleus.
• Note on table-style features in transcript:
  • Prokaryotes lack a nucleus and membrane-bound organelles (negative for these features).
  • Eukaryotes possess a nucleus and membrane-bound organelles (positive for these features).
  • Some components (e.g., ribosomes, plasma membrane, DNA) are present in both, but the details (size/composition) differ.
• Quick caveat:
  • The transcript also mentions peroxisomes, central vacuoles, and chloroplasts in a plant/animal context; here are the standard distinctions:
  • Peroxisomes: common in both plant and animal cells (not exclusive to one group).
  • Central vacuole: prominent in plant cells.
  • Chloroplasts: present in plants and algae, not in animal cells.
  • Food vacuoles: more typical in some animal cells.
• Practical takeaway: structural differences underpin function and organismal biology (e.g., energy production, storage, photosynthesis, and intercellular interactions).

Plant Cells vs Animal Cells: Organelles and Features

• Plant cell features:
  • Cell wall: present (rigid outer wall providing shape and protection).
  • Chloroplasts: present (site of photosynthesis).
  • Central vacuole: present (large storage/maintains turgor).
  • Mitochondria: present (ATP production).
  • Plasma membrane: present; regulates exchange.
  • Vesicles, endomembrane system: present (ER, Golgi, etc.).
  • Nucleus and DNA: present.
• Animal cell features:
  • No cell wall (only plasma membrane).
  • No chloroplasts (no photosynthesis).
  • Central vacuole typically absent or small.
  • Peroxisomes, mitochondria, ER, Golgi: present.
  • Lysosomes/food vacuoles: more prominent in some animal cells.
  • Flagella and cilia: present in some animal cells.
• Shared features (present in both plant and animal cells):
  • Plasma membrane, nucleus, mitochondria, general endomembrane system, ribosomes, cytoskeleton, DNA, vesicles.
• Important reminder from the session notes:
  • Some organelles’ presence can vary by cell type and organism; the listed distinctions help distinguish typical plant vs animal cells.

Quick Review: True/False Check (from the session cues)

• If a cell increases in size, its volume increases. True.
• If a cell increases in size, its surface area increases. True (but less than volume, leading to a smaller SA:V).
• The volume increases faster than the surface area as cell size grows. True.
• The SA:V ratio decreases as the cell grows larger. True.
• Smaller cells have greater SA:V than larger cells, which supports faster metabolism and transport. True.

Connections to Theory and Real-World Relevance

• Foundational principle: SA:V drives limits on cell size and shapes metabolic rates, transport efficiency, and growth.
• Real-world relevance:
  • Microbial growth is rapid due to high SA:V; this informs understanding of growth rates, antibiotic action, and ecological dynamics.
  • In multicellular organisms, maintaining small cell sizes in many tissues enhances nutrient uptake and waste removal, which supports tissue function and homeostasis.
  • Microscopy principles underpin how we observe cells and interpret cellular structures, making accurate interpretation of images possible.
• Ethical/practical implications (implicit in practice): understanding cell size and transport helps in areas like drug design, tissue engineering, and diagnostics, where imaging and interpretation impact outcomes.

Key Formulas to Remember

• Sphere-like cell relationships:
  SA = 4\pi r^2, \quad V = \frac{4}{3}\pi r^3, \quad \frac{SA}{V} = \frac{3}{r}.
• SA:V implications: as radius r increases, SA:V decreases.
• Photosynthesis (global equation):
  6\text{CO}2 + 6\text{H}2\text{O} + \text{light} \rightarrow \text{C}6\text{H}{12}\text{O}6 + 6\text{O}2.
• Microscopy magnification:
  M{ ext{total}} = M{ ext{objective}} \times M_{ ext{ocular}}.
• Visible spectrum range (for reference):
  ext{λ} \in [400, 700]\ \text{nm}.
• Note on image orientation: refraction in lenses causes image inversion under typical light microscopes.

Practical Notes for Exam Preparation

• Remember the qualitative trend: smaller cells have higher SA:V, enabling faster metabolism and transport relative to volume; this explains rapid growth in bacteria vs larger organisms.
• Be able to describe why larger cells struggle with exchange across the boundary and how division mitigates this constraint.
• Understand the difference between magnification and resolution, and why both matter for viewing cells.
• Be prepared to distinguish general features of prokaryotic vs eukaryotic cells and plant vs animal cells, including typical organelles and their functions.
• Know the basic steps and implications of light vs electron microscopy, including why staining is used and how it affects contrast and resolution.