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The Impossible Machine

Based on the sources provided, here is a comprehensive overview of protein quaternary structure, the factors affecting protein stability, and the mechanisms of protein folding. *Quaternary Structure and Symmetry* Quaternary structure arises from the arrangement of multiple polypeptide subunits (protomers) within a protein assembly. Most of these multi-subunit proteins exhibit specific types of **rotational or helical symmetry**: *Cyclic Symmetry ($C_n$):* Subunits are related by rotation around a single axis. For example, the protomers of hemoglobin are related by $C_2$ symmetry. *Dihedral Symmetry ($D_n$):* A more complex form where a twofold rotational axis intersects an $n$-fold axis at a right angle. *Icosahedral Symmetry:* A 12-cornered polyhedron with 20 triangular faces, common in *virus capsids* like the human poliovirus. *Helical Symmetry:* Subunits are arranged in a spiraling or "open-ended" array, as seen in the *Tobacco Mosaic Virus* and muscle **actin filaments**. *Limits to Protein Size* Protein size is generally limited by two major factors: 1. *Genetic Coding Capacity:* It is more efficient for a cell or virus to encode small subunits that can be used repeatedly to build large structures (like capsids) rather than encoding one massive polypeptide. 2. *Biosynthetic Accuracy:* The error rate during protein synthesis is roughly **one mistake per 10,000 amino acids**. As a protein's size increases, the mathematical probability of incorporating a "wrong" amino acid—and thus creating a damaged protein—becomes significantly higher. *Denaturation and the Anfinsen Experiment* *Denaturation* is the loss of a protein's three-dimensional structure sufficient to cause a loss of function. It is caused by heat (breaking hydrogen bonds), extremes of pH (altering charge), or detergents and urea (disrupting the hydrophobic core). Crucially, *Christian Anfinsen’s* 1950s experiments with *ribonuclease A* proved that the **amino acid sequence determines tertiary structure**. He showed that after completely unfolding ribonuclease using urea and a reducing agent, the protein could spontaneously refold (renature) into its active, native state once the denaturants were removed. *The Mechanism of Protein Folding* Protein folding is not a random trial-and-error process. *Levinthal’s paradox* notes that if a protein sampled every possible conformation randomly, it would take roughly $10^{77}$ years to find its native state. Instead, proteins fold through specific pathways: *Hierarchical Model:* Local secondary structures ($\alpha$ helices and $\beta$ sheets) form first, followed by longer-range interactions to form domains. *Hydrophobic Collapse:* The polypeptide spontaneously collapses into a compact state called a **molten globule**, driven by hydrophobic interactions among nonpolar residues. *Free-Energy Funnel:* Thermodynamically, folding is viewed as a "funnel" where the unfolded state has high entropy and high free energy. As folding progresses, the protein moves down the funnel, decreasing both entropy and free energy until it reaches its stable *native structure* at the bottom. *Defects in protein folding* are the molecular basis for several genetic disorders, such as **cystic fibrosis**, which results from a defect in the CFTR protein. Would you like me to create an *infographic* summarizing these different types of symmetry or perhaps a *quiz* to test your knowledge on protein denaturation and folding?