Clocking out: modeling phage-induced lysis of Escherichia coli

Abstract

Phage lambda lyses the host Escherichia coli at a precisely scheduled time after induction. Lysis timing is determined by the action of phage holins, which are small proteins that induce hole formation in the bacterium's cytoplasmic membrane. We present a two-stage nucleation model of lysis timing, with the nucleation of condensed holin rafts on the inner membrane followed by the nucleation of a hole within those rafts. The nucleation of holin rafts accounts for most of the delay of lysis after induction. Our simulations of this model recover the accurate lysis timing seen experimentally and show that the timing accuracy is optimal. An enhanced holin-holin interaction is needed in our model to recover experimental lysis delays after the application of membrane poison, and such early triggering of lysis is possible only after the inner membrane is supersaturated with holin. Antiholin reduces the delay between membrane depolarization and lysis and leads to an earlier time after which triggered lysis is possible.

FIG. 1.

Number of IM holin molecules versus time after phage induction. Four regimens (A to D) of our two-nucleation model are schematically illustrated in the inset and correspond to the times indicated on the graph. At early times (A and B) the number of holin molecules in a dilute phase of small clusters within the membrane (thick solid line) increases as more holin is inserted (IM). After the holin concentration becomes supersaturated on the IM (B), the nucleation of stable condensed rafts of holin (dotted line, including clusters with 20 or more holin) can occur (C). After the raft formation, holes can nucleate within the holin rafts (D). The total number of holin molecules in the IM is indicated by the thin solid line. The leftmost arrow indicates the equilibrium number of holin molecules in the IM; when the total amount of holin exceeds this value, the membrane is supersaturated with holin. After raft nucleation, the supersaturation of the dilute holin phase decreases rapidly towards a steady state at late times. The steady state is elevated with respect to equilibrium due to ongoing holin insertion. The experimental timing of hole nucleation, t_L = 45 min, is indicated by the second arrow (D). This figure represents the average behavior over many bacteria, for the optimal holin interaction strength, Ĵ, as discussed in the text.

FIG. 2.

Lysis timing accuracy, characterized by the fractional width δt_L/t_L versus the holin interaction strength J/k_BT. The filled stars are for an A_c of 40, while the open stars are for an A_c of 20. A significant difference is seen only for the smallest J/k_BT, where large rafts do not nucleate before lysis occurs. All data are weighted across cell sizes.

FIG. 3.

Average time of first raft nucleation t_raft versus the holin interaction strength J/k_BT. Raft nucleation is taken to occur when a raft of 20 or more holin molecules is observed, corresponding to Fig. 1. Similar curves are obtained for other thresholds. Interactions with a J/k_BT of less than 4.6 fail to nucleate large rafts before t_L = 45 min (dotted line). As J/k_BT decreases towards this threshold, the hole nucleation rate R_h must increase to recover lysis at t_L. Vertical bars depict the standard deviation of t_raft over sampled cells, which increases with decreasing J/k_BT. All data are weighted across cell sizes.

FIG. 4.

(A) Fractional width of lysis timing, δt/t_L, versus critical raft size, A_c (measured in number of holins), weighted across cell sizes. The total fractional width (solid line, δt_L/t_L) has contributions from raft formation (dashed line, δt_raft/t_L), hole formation (dash-dotted line, δt_hole/t_L), and cell size variance (dotted line, δt_size/t_L). For an A_c of ≥10 the fractional width is small, approximately constant, and dominated by raft and hole formation dynamics. In this region, cell size variation is small. (B) Calculated hole nucleation rate, R_h, versus critical raft size, A_c, weighted across cell sizes. The hole nucleation rate is only slowly varying for an A_c of ≥10 due to rapid raft growth after raft nucleation. All data are for Ĵ = 4.64.

FIG. 5.

Delay of lysis from time of poison application, (t_L − t_KCN) versus time of poisoning during premature lysis (t_KCN). Without antiholin and with a PMF-independent holin interaction (Ĵ), our model predicts that KCN-triggered lysis (×) will be delayed compared with normal lysis at t_L = 45 min (dotted line). In contrast, experimental delays (open stars, estimated from reference 32) lie below the dotted line, suggesting an enhanced holin interaction in a depolarized membrane (J′ = 5.229) (filled circles, with antiholin; filled squares, without antiholin). Vertical bars depict the standard deviation of lysis timing over sampled cells, and this systematically increases with earlier KCN application. Errors are approximately 5 times smaller than standard deviations. All data are for l = 3.04 μm.