STEM Readiness: Pre-Calculus Readiness - Sequences/Series: Sigma Notation - Writing and Evaluating Sums, Index Manipulation

Must?Know (20–25 detailed bullets)

• Prokaryotic cells range from 0.1–5.0 ?m in diameter; eukaryotic cells range from 10–100 ?m.
• Prokaryotes include bacteria and archaea; eukaryotes include animals, plants, fungi, and protists.
• Prokaryotic DNA is located in the nucleoid, a region without a membrane; eukaryotic DNA is enclosed within a membrane-bound nucleus.
• Prokaryotes have 70S ribosomes (30S + 50S subunits); eukaryotes have 80S ribosomes (40S + 60S subunits).
• Mitochondria and chloroplasts in eukaryotes contain 70S ribosomes, supporting their origin via endosymbiosis.
• Prokaryotic cell walls typically contain peptidoglycan (e.g., Escherichia coli); archaea lack peptidoglycan and have different wall chemistry.
• Plant cell walls are composed of cellulose; fungal cell walls contain chitin; animal cells lack a cell wall.
• Both prokaryotes and eukaryotes have a phospholipid bilayer plasma membrane with embedded proteins.
• Eukaryotes have internal membrane systems including the endoplasmic reticulum (ER), Golgi apparatus, and lysosomes; prokaryotes do not.
• Mitochondria are present in nearly all eukaryotic cells and are sites of aerobic respiration; absent in prokaryotes.
• Chloroplasts are found in plant cells and some protists (e.g., Chlamydomonas); they perform photosynthesis and are absent in prokaryotes (except in cyanobacteria, which have thylakoid membranes but not chloroplasts).
• Cyanobacteria are prokaryotes that perform oxygenic photosynthesis using thylakoid membranes, not chloroplasts.
• Eukaryotic flagella are composed of microtubules (9+2 arrangement) and are covered by the plasma membrane; prokaryotic flagella are made of flagellin protein, lack microtubules, and are not membrane-bound.
• Plasmids are small, circular extrachromosomal DNA molecules common in prokaryotes; rare in eukaryotes (e.g., 2-micron plasmid in Saccharomyces cerevisiae).
• Binary fission is the method of asexual reproduction in prokaryotes; eukaryotes divide by mitosis and cytokinesis.
• Mycoplasma species are bacteria without a cell wall; they are the smallest known cells capable of independent growth (~0.2 ?m).
• Human red blood cells lack a nucleus and mitochondria in maturity, making them an exception among eukaryotic cells.
• Nuclear envelope in eukaryotes is a double membrane with nuclear pores that regulate transport; absent in prokaryotes.
• Endosymbiotic theory proposes that mitochondria and chloroplasts originated from engulfed prokaryotes; evidence includes their own circular DNA, 70S ribosomes, and ability to replicate independently.
• Lysosomes are membrane-bound organelles in animal cells containing hydrolytic enzymes; absent in most plant cells (vacuoles perform similar function).
• Plant cells have a large central vacuole that maintains turgor pressure; animal cells have small or temporary vacuoles.
• Centrioles are present in animal cells and involved in spindle formation during mitosis; absent in most plant and fungal cells.
• Peptidoglycan is a polymer of N-acetylglucosamine (NAG) and N-acetylmuramic acid (NAM) cross-linked by peptides; targeted by penicillin.
• Gram-positive bacteria have a thick peptidoglycan layer and retain crystal violet stain; Gram-negative have a thin layer and outer membrane with lipopolysaccharide (LPS).
• Archaea lack peptidoglycan and have ether-linked lipids in their membranes; some live in extreme environments (e.g., Methanogens in anaerobic conditions).

Difficulty Level

Intermediate – requires distinguishing structural and functional differences across domains and recognizing exceptions common in introductory biology exams.

Common Traps (3–5 factual traps)

Trap: All cells with cell walls have peptidoglycan – Fact: Only bacteria have peptidoglycan; plant cell walls are made of cellulose, fungal walls of chitin, and archaeal walls lack peptidoglycan.
Trap: Mitochondria and chloroplasts use 80S ribosomes like the rest of the eukaryotic cell – Fact: These organelles have 70S ribosomes, similar to prokaryotes, supporting endosymbiotic origin.
Trap: Prokaryotes have no internal membranes at all – Fact: Some prokaryotes (e.g., cyanobacteria) have thylakoid membranes for photosynthesis, though they lack membrane-bound organelles.
Trap: The nucleus evolved from the nucleoid through membrane invagination – Fact: The nuclear envelope likely formed via infolding of the plasma membrane or endoplasmic reticulum development, but direct evolutionary pathway remains uncertain; nucleoid is not ancestral to nucleus in a structural sense.
Trap: Eukaryotic flagella and cilia are homologous to prokaryotic flagella – Fact: They are not homologous; eukaryotic flagella are microtubule-based (9+2), while prokaryotic flagella are flagellin-based and structurally unrelated.

Practice MCQs (5–7 questions)

Question: Which of the following is a feature found in prokaryotic cells but not in eukaryotic cells?
A) Circular DNA
B) 70S ribosomes
C) Peptidoglycan in the cell wall
D) Plasma membrane with phospholipid bilayer
Answer: C
Explanation: Peptidoglycan is unique to bacterial cell walls and absent in eukaryotes.
Why the top distractor is wrong: 70S ribosomes (B) are also found in mitochondria and chloroplasts of eukaryotes, so not exclusive to prokaryotes.

Question: Which structure is present in plant cells but not in animal cells?
A) Mitochondria
B) Golgi apparatus
C) Central vacuole
D) Plasma membrane
Answer: C
Explanation: The large central vacuole is a defining feature of mature plant cells.
Why the top distractor is wrong: Mitochondria (A) are present in both plant and animal cells.

Question: Which of the following provides the strongest evidence for the endosymbiotic theory?
A) Mitochondria are surrounded by a double membrane
B) Mitochondria contain 70S ribosomes and circular DNA
C) Mitochondria divide by binary fission
D) Mitochondria are found in all eukaryotic cells
Answer: B
Explanation: The presence of 70S ribosomes and circular DNA in mitochondria closely resembles free-living prokaryotes.
Why the top distractor is wrong: While a double membrane (A) is consistent with engulfment, it is not as specific as ribosome and DNA evidence.

Question: Which organism lacks a cell wall entirely?
A) Escherichia coli
B) Saccharomyces cerevisiae
C) Mycoplasma pneumoniae
D) Arabidopsis thaliana
Answer: C
Explanation: Mycoplasma species are bacteria without a cell wall.
Why the top distractor is wrong: Saccharomyces cerevisiae (B) is a fungus and has a chitin-containing cell wall.

Question: Where is DNA located in a prokaryotic cell?
A) Inside the nucleus
B) In the nucleolus
C) In the nucleoid region
D) Bound to histone proteins
Answer: C
Explanation: Prokaryotes lack a nucleus; DNA is concentrated in the nucleoid.
Why the top distractor is wrong: A nucleus (A) is only present in eukaryotes.

Question: Which of the following is true about ribosomes in eukaryotic cells?
A) All ribosomes are 80S, including those in mitochondria
B) Ribosomes are only found free in the cytoplasm
C) 80S ribosomes are located in the cytoplasm and on the rough ER
D) Ribosomes are enclosed within lysosomes
Answer: C
Explanation: 80S ribosomes are found free in the cytosol and attached to the rough ER.
Why the top distractor is wrong: Mitochondria and chloroplasts have 70S ribosomes, not 80S (A).

Question: Which cell type lacks a nucleus at maturity?
A) Neuron
B) Leukocyte
C) Human red blood cell
D) Hepatocyte
Answer: C
Explanation: Mature human red blood cells eject their nucleus to accommodate more hemoglobin.
Why the top distractor is wrong: Leukocytes (B) are nucleated white blood cells.

Last?Minute Revision (20–25 one?liners)

• Prokaryotic cell size: 0.1–5.0 ?m; eukaryotic: 10–100 ?m.
• Prokaryotes: nucleoid; eukaryotes: nucleus with double membrane.
• Prokaryotic ribosome = 70S; eukaryotic cytoplasmic ribosome = 80S.
• Mitochondria and chloroplasts have 70S ribosomes and circular DNA – evidence of endosymbiosis.
• Bacteria: peptidoglycan cell wall; archaea: no peptidoglycan.
• Plant cell wall: cellulose; fungal: chitin; animal: no cell wall.
• Both domains have phospholipid bilayer plasma membranes.
• Eukaryotes have membrane-bound organelles; prokaryotes do not.
• Mycoplasma – smallest known cells, no cell wall.
• Human red blood cells lack a nucleus and mitochondria.
• Nuclear pores regulate RNA and protein transport across nuclear envelope.
• Endoplasmic reticulum (ER): rough ER has ribosomes; smooth ER synthesizes lipids.
• Golgi apparatus: modifies, sorts, and packages proteins for secretion or delivery.
• Lysosomes: contain acid hydrolases, function in intracellular digestion (mainly in animals).
• Plant vacuoles perform lysosomal functions and maintain turgor.
• Mitochondria: site of ATP production via oxidative phosphorylation.
• Chloroplasts: contain thylakoids and grana, perform photosynthesis.
• Cyanobacteria are prokaryotes with thylakoid membranes but no chloroplasts.
• Eukaryotic flagella: 9+2 microtubule arrangement; powered by dynein.
• Prokaryotic flagella: made of flagellin, rotates like a propeller.
• Plasmids: small circular DNA, common in bacteria.
• Binary fission: prokaryotic cell division; mitosis: eukaryotic nuclear division.
• Centrioles: present in animal cells, organize spindle fibers; absent in most plants.
• Archaeal membranes have ether linkages; bacterial and eukaryotic have ester linkages.
• Gram-positive: thick peptidoglycan, no outer membrane; Gram-negative: thin peptidoglycan + outer LPS membrane.
• Verify from standard textbook: exact origin of nuclear envelope.