"The curve is strange."
Toma pointed at the graph.
"What's strange?" Kana asked.
"It's not a normal curve. It's S-shaped."
Milia smiled. "Sigmoid curve. Evidence of allosteric effect."
"Allosteric?" Rei began explaining. "Allo means 'other,' steric means 'spatial.'"
Kana wrote in her notebook. "Effect from a different location?"
"Correct. At a site different from where substrate binds, molecular shape changes."
Toma was confused. "What happens when shape changes?"
"Function changes," Milia answered. "Especially, how easily other substrates bind changes."
"Other substrates?"
Rei drew a diagram. "Hemoglobin. Made of four subunits."
"One protein?"
"A tetramer. Each subunit can bind one oxygen."
Kana asked. "All four bind oxygen?"
"They can. But the interesting part is the sequence."
Milia continued. "When first oxygen binds, shapes of other subunits change."
"Change?"
"Cooperativity. When one binds, the next binds more easily."
Toma's eyes lit up. "Chain reaction?"
"You could say that. Positive allosteric effect."
Rei emphasized. "That's why it becomes sigmoid curve. Slow at first, rapid in middle, slow again at end."
Kana traced the graph. "I'm starting to understand the S-shape meaning."
"That's mathematical expression of cooperativity."
Milia gave another example. "Also happens with enzymes. Allosteric enzymes."
"What enzymes?"
"Those involved in metabolic pathway regulation. Used for feedback control."
Rei explained. "When there's too much product, it binds to enzyme and reduces activity."
"Negative allosteric effect?"
"Yes. Stabilizes the system."
Toma got excited. "Like a switch!"
"Good metaphor. On or off, little in between."
Kana pondered. "Why is cooperativity needed?"
Milia answered. "For efficient oxygen transport. In lungs bind lots of oxygen, in tissues release quickly."
"Sigmoid curve enables that?"
"Yes. Small change in oxygen concentration causes large change in binding amount."
Rei added. "Hyperbola wouldn't work. Change too gradual."
"Hyperbola?"
"Normal enzyme reaction. Follows Michaelis-Menten equation."
Toma asked. "Allosteric enzymes don't follow?"
"Right. So special equations needed. Hill equation, Monod-Wyman-Changeux model."
Kana was surprised. "Sounds complex..."
"Complex but beautiful," Milia said. "Conveying information in molecular language."
Rei continued. "Molecules binding to allosteric sites are called effectors."
"Effectors?"
"Regulatory factors. Some increase activity, some decrease."
Toma murmured. "Molecular switches everywhere?"
"Fundamental to life activity. Metabolism, signal transduction, gene expression."
Kana was moved. "One molecule affects other molecules."
"Communication," Milia said quietly.
"Intermolecular communication?"
"Yes. Language is shape change."
Rei added. "Allosteric effect is its grammar."
Toma looked at the graph again. "S-curve, a story of cooperativity?"
"You could say that."
Kana laughed. "Equations are telling stories."
"Mathematics is nature's language," Rei acknowledged.
Milia stood up. "Do you understand allosteric effects?"
"Just a little," Toma answered.
"That's enough," Rei said. "Feeling the wonder is the first step of understanding."
The four stared at the sigmoid curve. The wonder of cooperativity certainly exists there.