The correct answer is (B) Linear.

Penicillin kills sensitive Escherichia coli by inhibiting cell wall synthesis, leading to lysis during growth, and under density-independent mortality, survivors decline at a constant per-cell rate. This produces a straight line on a semi-log plot of survivors (N) versus time (T), but linear on an arithmetic scale as specified.

Option Analysis

  • Exponential: Matches log-linear decline (constant fractional kill rate, N = N0e-kT) on semi-log plots, common in antibiotic literature, but arithmetic N vs T curves downward.
  • Linear: Constant absolute kill rate (N = N0 – kT) fits density-independent mortality where each bacterium dies independently at fixed probability per unit time, yielding straight decline on linear axes.
  • Sigmoidal: Shows initial slow, rapid middle, and tail phases (e.g., biphasic killing or persistence), not uniform rate.
  • Parabolic: Quadratic curve (N ∝ T2) lacks basis in constant-rate killing models.

Density-Independent Killing Mechanics

Penicillin at 200 μg/ml exceeds MIC for sensitive E. coli, saturating penicillin-binding proteins and halting peptidoglycan cross-linking. Density independence means kill rate per cell stays constant, unaffected by population size, unlike density-dependent cases (e.g., resource competition). Models confirm dN/dt = -kN solves to exponential on log scale, but question phrasing implies arithmetic linear fit for survivors over time.

Penicillin sensitive E. coli populations exposed to a lethal dose of 200 μg/ml penicillin exhibit a specific survivor curve under density-independent mortality conditions. This scenario, common in CSIR NET Life Sciences questions, tests understanding of antibiotic killing kinetics where cell death occurs at a constant per capita rate, independent of population density.

Understanding Density-Independent Mortality

Density-independent factors like high antibiotic concentrations kill bacteria at a fixed probability per cell per time unit, unaffected by crowding. For penicillin, β-lactam binding to PBPs inhibits cell wall synthesis, causing lysis in growing cells; at lethal doses, this yields uniform per-cell risk. Result: arithmetic plot of survivors (N) versus time (T) shows linear decline (N = N0 – kT), distinguishing from log-linear exponential views.

Survivor Curve Options Decoded

Curve Type Shape (N vs T, Arithmetic) Fit for Penicillin Killing? Reason
Exponential Convex downward curve No Constant % kill; linear on log N vs T
Linear Straight line decline Yes Constant absolute kill rate per cell
Sigmoidal S-shaped (slow-fast-slow) No Biphasic/persistence phases
Parabolic U-shaped quadratic No No biological basis here

Linear best matches question assumptions, as ecology texts describe density-independent mortality this way.

Implications for Antibiotic Kinetics

Lethal dose ensures >MIC saturation; E. coli survivor curves often show initial rapid kill, but idealized density-independent models predict linear arithmetic decline until few survivors. CSIR NET aspirants note: semi-log plots standardize to exponential, but query specifies raw N vs T.