Microeconomics of cell metabolism

Economic Principles in Cell Biology · Ch. 8 · 10.5281/zenodo.19221188

The cell as a consumer

A consumer spends a fixed income across goods to maximize utility. A cell spends a fixed proteome across pathways to maximize growth. Line them up and the correspondence is exact: income is the protein budget, price is the enzyme a pathway needs per unit product, and utility is growth rate. Consumer theory (budgets, marginal returns, substitution) is the right formalism here.

Overflow metabolism: choosing the wasteful good

The sharpest case is the one FBA couldn't explain. Respiration extracts far more ATP per glucose than fermentation, so a yield-maximizer would always respire. Yet E. coli, yeast, and tumor cells all ferment when sugar is plentiful, spilling most of their energy. Price it in protein and the paradox vanishes: respiration's machinery is bulky and slow per unit protein, fermentation's is cheap and fast. Under a tight protein budget, the cell buys ATP at the best rate per gram of enzyme, and that can be the low-yield good.

; Two ways to buy ATP from glucose, under a fixed protein budget.
;   respiration:  high yield per glucose, but expensive enzyme (slow, bulky)
;   fermentation: low yield,  but cheap enzyme (fast, lean)
(define budget 1.0)   ; proteome available to energy metabolism

; each strategy: (ATP per glucose, protein cost per unit glucose flux)
(define (atp-rate yield cost)
  (let ((flux (/ budget cost)))   ; glucose flux the budget can sustain
    (* flux yield)))              ; ATP produced per unit time

(display "respiration  ATP/time: ")
(display (atp-rate 18 6.0)) (newline)   ; 9x the yield, 12x the enzyme cost
(display "fermentation ATP/time: ")
(display (atp-rate 2 0.5)) (newline)

(display "-> fermentation wins the RATE despite losing the YIELD 9:1")

The cell that ferments is not malfunctioning. Given its budget, it is buying energy at the higher rate, and rate is what growth rewards. Yield is the wrong objective; return per unit protein is the right one. This is why the FBA of Chapter 5 mispredicts real cells until enzyme cost is folded in.

Giffen goods and diminishing returns

Push the analogy and cell metabolism reproduces consumer theory's oddities. The source shows a metabolic Giffen good, a nutrient the cell consumes more of as it gets more expensive. That's the textbook violation of the law of demand, arising here from the same budget geometry that produces it in economics. And growth shows diminishing returns: each added increment of a resource buys less extra growth than the last, the marginal-utility curve bending over exactly as it does for a consumer. Biology was doing microeconomics all along.

budget = 1.0
def atp_rate(yield_, cost):
    flux = budget / cost
    return flux * yield_

print("respiration  ATP/time:", atp_rate(18, 6.0))
print("fermentation ATP/time:", atp_rate(2, 0.5))
print("-> fermentation wins the rate despite losing the yield 9:1")

Adaptation notes

The source chapter treats the cell as an economic consumer, works the overflow-metabolism example as Giffen behavior, and derives a linear response relation and a law of diminishing returns. We make the central trade-off (rate-per-protein beating yield) runnable, and point to the source for the Giffen construction and the response relations, which deserve their full treatment.