## Abstract

Five point mutations in a particular β-lactamase allele jointly increase bacterial resistance to a clinically important antibiotic by a factor of ∼100,000. In principle, evolution to this high-resistance β-lactamase might follow any of the 120 mutational trajectories linking these alleles. However, we demonstrate that 102 trajectories are inaccessible to Darwinian selection and that many of the remaining trajectories have negligible probabilities of realization, because four of these five mutations fail to increase drug resistance in some combinations. Pervasive biophysical pleiotropy within the β-lactamase seems to be responsible, and because such pleiotropy appears to be a general property of missense mutations, we conclude that much protein evolution will be similarly constrained. This implies that the protein tape of life may be largely reproducible and even predictable.

Resistance to β-lactam antibiotics (e.g., penicillin) is commonly mediated by a bacterial β-lactamase, which hydrolytically inactivates these drugs (*1*). Bacterial resistance to novel β-lactams first arises by point mutations in the β-lactamase gene (*2*, *3*). Five point mutations in an allele of this gene that we designate *TEM ^{wt}* (the reference sequence of the TEM family of β-lactamases) (

*4*,

*5*) jointly increase resistance by a factor of ∼100,000 against cefotaxime (

*6*,

*7*), a third-generation cephalosporin β-lactam. These consist of four missense mutations [A42G, E104K, M182T, and G238S; numbering as in (

*8*)] at clinically important residues (

*3*,

*9*) and one 5′ noncoding mutation [g4205a; numbering as in (

*4*)], and we denote this high-resistance quintuple mutant

*TEM*.*Thus, five mutations must occur for

*TEM**to evolve from

*TEM*, and because these can in principle occur in any order, there are 5! = 120 mutational trajectories linking these alleles. However, natural selection for heightened cefotaxime resistance may not regard all trajectories equivalently (

^{wt}*10*). Here, we determine the prevalence with which these mutations only conditionally increase drug resistance, a form of interaction previously designated sign epistasis (

*10*). Sign epistasis is both necessary and sufficient for one or more trajectories to

*TEM**to be selectively inaccessible (

*10*).

To characterize the effect on drug resistance of each mutation on all allelic backgrounds, we first constructed the 32 combinations of these five mutations (*11*, *12*). We next determined their resistance to cefotaxime (*12*) in *Escherichia coli* strain DH5α (Table 1); because the sign of the mutational effect on drug resistance determines the selective accessibility of each trajectory (*10*), we also report the rank order of drug resistance values exhibited by all alleles. *TEM** exhibits the highest resistance and, because at least one mutation increases resistance in all other alleles, the fitness landscape is single-peaked (*13*). Thus, in the case of cefotaxime resistance evolution, populations cannot become trapped (*13*) at suboptimal alleles between *TEM ^{wt}* and

*TEM**, as was recently also shown for isopropylmalate dehydrogenase (IMDH) evolution from a nicotinamide adenine dinucleotide phosphate (NADP)–dependent form to a nicotinamide adenine dinucleotide (NAD)–dependent form (

*14*).

Missense mutations | Without g4205a mutation | With g4205a mutation | ||||||
---|---|---|---|---|---|---|---|---|

A42G | E104K | M182T | G238S | Clinical designationView inline | MIC | Rank | MIC | Rank |

- | - | - | - | TEM-1 | 0.088View inline | 13View inline | 0.088 | 13 |

- | - | - | + | TEM-19 | 1.4 | 9 | 1.4 | 9 |

- | - | + | - | TEM-135 | 0.063View inlineView inline | 14 | 0.088View inline | 13 |

- | - | + | + | TEM-20 | 32 | 6 | 3.6 × 10^{2} | 5 |

- | + | - | - | TEM-17 | 0.13View inline | 12 | 0.18 | 11 |

- | + | - | + | TEM-15 | 3.6 × 10^{2} | 5 | 3.6 × 10^{2} | 5 |

- | + | + | - | TEM-106 | 0.18View inline | 11 | 0.18 | 11 |

- | + | + | + | TEM-52 | 3.6 × 10^{2} | 5 | 2.1 × 10^{3} | 3 |

+ | - | - | - | None | 0.088 | 13 | 0.088 | 13 |

+ | - | - | + | None | 23 | 7 | 3.6 × 10^{2} | 5 |

+ | - | + | - | None | 1.4 | 9 | 0.088 | 13 |

+ | - | + | + | None | 3.6 × 10^{2} | 5 | 3.6 × 10^{2} | 5 |

+ | + | - | - | None | 1.4 | 9 | 2.0 | 8 |

+ | + | - | + | None | 2.1 × 10^{3}View inline | 3 | 1.5 × 10^{3}View inline | 4 |

+ | + | + | - | None | 0.80 | 10 | 1.4 | 9 |

+ | + | + | + | None | 2.9 × 10^{3} | 2 | 4.1 × 10^{3} | 1View inline |

View inline* Of protein sequence; from (*3*).

View inline† These two values not significantly different after Bonferroni correction.

View inline‡ This allele here designated *TEM ^{wt}*.

View inline§ These two values not significantly different after Bonferroni correction.

View inline∥ These two values not significantly different after Bonferroni correction.

View inline¶ These two values not significantly different after Bonferroni correction.

View inline# This allele here designated *TEM**.

To estimate the relative probabilities with which evolution by natural selection for heightened cefotaxime resistance will realize each of the 120 possible mutational trajectories from *TEM ^{wt}* to

*TEM**, we assumed that the time to fixation or loss of individual mutations is far less than the time between mutations [the “strong selection/weak mutation” model of (

*15*)]. Thus, the relative probability of realizing any particular mutational trajectory is the product of the relative probabilities of its constituent mutations, because under our assumption the choice of each subsequent fixation is statistically independent of all previous fixations (

*12*). Next, for each allele we partitioned all possible mutations into those that are beneficial, deleterious, or neutral with respect to cefotaxime resistance. The probability of fixation for a beneficial mutation far exceeds that for deleterious or neutral mutations (

*12*,

*15*) and, because all alleles have one or more beneficial mutations (Table 1), we approximated the probability of fixation for all other mutations by zero.

Applying this population genetic reasoning (*12*) to the data in Table 1 reveals that 102 of the 120 mutational trajectories from *TEM ^{wt}* to

*TEM**are selectively inaccessible. Although these five mutations were chosen for their large joint phenotypic effect, this result is necessarily (

*10*) a consequence of the fact that some of the mutations do not increase cefotaxime resistance on all allelic backgrounds. Rather, four mutations have negligible or even negative effects on drug resistance in some combinations. Under our model, the probability of fixation for such mutations on such backgrounds—and hence of those trajectories on which they occur—is zero. The number of alleles on which each mutation has a positive, negative, or negligible effect, together with the mean proportional increase in cefotaxime resistance of each, is reported in Table 2. This illustrates the incidence of sign epistasis in our data set: mutations that only conditionally increase phenotype [(

*10*) and supporting online text].

Mutation | Number of TEM alleles on which mean mutational effect is | MeanView inlineproportional increase | ||
---|---|---|---|---|

PositiveView inline | NegativeView inline | Negligible | ||

g4205a | 8View inline | 2View inline | 6 | 1.4 |

A42G | 12 | 0 | 4 | 5.9 |

E104K | 15 | 1 | 0 | 9.7 |

M182T | 8View inline | 3View inline | 5 | 2.8 |

G238S | 16 | 0 | 0 | 1.0 × 10^{3} |

View inline* Differences in mean MIC values are significant at *P* < 0.05.

View inline† Of MIC (*12*); geometric mean across all 16 alleles.

View inline‡ One of these comparisons loses significance after Bonferroni correction.

The relative probabilities of realization among the 18 selectively accessible trajectories reflect the probabilities of fixation of their constituent (beneficial) mutations, which in turn depend on the ecological circumstances in which drug resistance evolves (*12*). The simplest model assumes that all available beneficial mutations fix with equal probability [see (*12*) for ecological interpretation]. A biologically more realistic picture assumes that the relative probability of fixation of beneficial mutations is positively correlated with magnitude of effect (*12*), and we employed extreme value theory (*12*, *15*, *16*) to provide intuition into the evolutionary consequences of such a correlation. Extreme value theory provides estimates of these relative probabilities largely independent of the underlying distribution of fitness effects (*16*).

The mean cumulative probabilities of the 18 selectively accessible trajectories under the equal and correlated fixation models are shown in Fig. 1; individual probabilities are presented in table S2. The sharp skew to the left indicates that only a few trajectories capture most of the probability density. For example, half of all evolutionary realizations will follow just four and two trajectories, respectively, under the equal and correlated fixation probability models. Because some correlation between a mutation's effect on resistance and its probability of fixation is likely (*17*), the biologically relevant number is probably closer to the lower value. Note that the results illustrated in Fig. 1 are largely robust to small, undetected differences in drug resistance (see supporting online text). Figure 2 illustrates the source of this bias at the level of the constituent beneficial mutations defining the 10 most probable trajectories, which represent, respectively, ∼90% and ∼99% of the probability density under the equal and correlated fixation probability models.

The skew in probabilities of realization among trajectories under the equal fixation probability model (Fig. 1) is by definition (*12*) entirely due to the structure of sign epistasis in Table 1. For example, mutations along the most likely trajectory under this model occur in the order G238S, E104K, A42G, M182T, g4205a. Reversing the order of the second and third mutations (G238S, A42G, E104K, M182T, g4205a) defines a second trajectory whose probability of realization under this model is reduced by a factor of three (table S2). This is because after the initial two fixations in the first trajectory, only one beneficial alternative exists, whereas three alternatives exist at that juncture in the second (Fig. 2), reducing the probability of each by one-third (eq. S5a). This effect differs from that due to unequal probabilities of fixation among alternative beneficial mutations (*18*), which gives rise to the modest difference between curves in Fig. 1.

Biochemical and biophysical considerations of β-lactamase offer some insight into the mechanistic origin of the sign epistasis underlying our results. For example, G238S on the *TEM ^{wt}* background is known to enhance cefotaxime hydrolysis (

*19*–

*21*) but simultaneously to increase aggregation (

*19*) and reduce thermodynamic stability of the enzyme (

*20*,

*22*). Conversely, M182T alone modestly reduces hydrolysis (

*20*) while reducing aggregation (

*19*) and increasing thermodynamic stability (

*20*). Thus, intramolecular pleiotropy of M182T and G238S accounts for the fact that M182T exhibits sign epistasis: On

*TEM*it reduces (or at least has negligible effect on) cefotaxime resistance, but together with G238S it increases resistance (Table 1), because the double mutant enjoys increased hydrolysis (

^{wt}*20*) without loss of thermodynamic stability (

*23*). The 5′ noncoding mutation g4205a also exhibits sign epistasis. Although it increases gene expression by a factor of ∼2.5 (

*6*,

*7*), the mean effect on resistance of this mutation is much smaller, and it significantly increases resistance in at most 8 of 16 alleles (Table 2). The explanation may involve aggregation of β-lactamase (

*23*,

*24*): Because the fraction of molecules aggregated rises with protein concentration (

*25*), missense mutations that reduce aggregation [e.g., (M182T)] (

*19*) may be necessary to render g4205a beneficial. (Compare the effects of g4205a on A42G/E104K/G238S with that on A42G/E104K/M182T/G238S in Table 1.) Thus, here again, pleiotropy represents the mechanistic basis of sign epistasis.

Seen as an analysis of clinical cefotaxime resistance evolution, our treatment makes several simplifying assumptions about the mutational and selective processes. For example, we have disregarded horizontal gene transfer and have limited attention to only five mutations. Furthermore we have assumed that selection acts only to increase resistance to cefotaxime, whereas microbes are exposed to a spatial and temporal diversity of antibiotic compounds in nature as well as in clinical settings (*1*). The implications of relaxing these assumptions are explored in the supporting online text.

However, this work was intended to answer a more fundamental evolutionary question: Given a set of point mutations known jointly to increase organismal fitness, how does Darwinian selection regard the many mutational trajectories available? The foregoing limitations notwithstanding, the implications of our study for this broader question are clear: When selection acts on *TEM ^{wt}* to increase cefotaxime resistance, only a very small fraction of trajectories to

*TEM**are likely to be realized, owing to sign epistasis mediated by intramolecular pleiotropic effects. Moreover, inasmuch as intramolecular pleiotropy (

*11*,

*25*) and concomitant sign epistasis are characteristic of many missense mutations (

*25*), constraints on the selective choice of trajectories like those seen here are likely to apply to the evolution of other proteins. For example, application of our population genetic model to the fitness landscape between an engineered NADP- and the wild-type NAD-dependent forms of IMDH (

*12*,

*14*,

*26*) reveals that at most 29% of all mutational trajectories are selectively accessible (supporting online text). Our conclusion is also consistent with results from prospective experimental evolution studies, in which replicate evolutionary realizations have been observed to follow largely identical mutational trajectories (

*27*). However, the retrospective, combinatorial strategy employed here (

*11*) substantially enriches our understanding of the process of molecular evolution because it enables us to characterize all mutational trajectories, including those with a vanishingly small probability of realization [which is otherwise impractical (

*27*)]. This is important because it draws attention to the mechanistic basis of selective inaccessibility. It now appears that intramolecular interactions render many mutational trajectories selectively inaccessible, which implies that replaying the protein tape of life (

*28*) might be surprisingly repetitive. It remains to be seen whether intermolecular interactions similarly constrain Darwinian evolution at larger scales of biological organization.

**Supporting Online Material**

www.sciencemag.org/cgi/content/full/312/5770/111/DC1

Materials and Methods

SOM Text

Fig. S1

Tables S1 and S2

References and Notes