Mechanistic origin of drug interactions between translation-inhibiting antibiotics

Antibiotics that interfere with translation, when combined, interact in diverse and difficult-to-predict ways. Here, we demonstrate that these interactions can be accounted for by “translation bottlenecks”: points in the translation cycle where antibiotics block ribosomal progression. To elucidate the underlying mechanisms of drug interactions between translation inhibitors, we generated translation bottlenecks genetically using inducible control of translation factors that regulate well-defined translation cycle steps. These perturbations accurately mimicked antibiotic action and their interactions, supporting that the interplay of different translation bottlenecks causes these interactions. We further showed that the kinetics of drug uptake and binding together with growth laws allows direct prediction of a large fraction of observed interactions, yet fails for suppression. Simultaneously varying two translation bottlenecks in the same cell revealed how the dense traffic of ribosomes and competition for translation factors results in previously unexplained suppression. This result highlights the importance of “continuous epistasis” in bacterial physiology.


23
Inhibiting translation is one of the most common antibiotic modes of action, crucial for restraining 24 pathogenic bacteria [Walsh, 2003]. Antibiotics targeting translation interfere with either the assem- 25 bly or the processing of the ribosome, or with the proper utilization of charged tRNAs and trans-26 lation factors (Fig. 1A,B; Table 1) [Wilson, 2014]. Still, the exact modes of action and physiolog-27 ical responses to many such translation inhibitors are less clear, and responses to drug combina-28 tions are even harder to understand, even though they offer effective ways of fighting antibiotic re-29 sistance [Yeh et al., 2009]. Recently, mechanism-independent mathematical approaches to predict the 30 responses to multi-drug combinations were proposed [Zimmer et al., 2016;Wood et al., 2012], yet 31 these approaches rely on prior knowledge of pairwise drug interactions, which are diverse and have 32 notoriously resisted prediction. They include synergism (inhibition is stronger than predicted), antag-33 onism (inhibition is weaker), and suppression (one of the drugs loses potency) [Bollenbach, 2015;34 Mitosch and Bollenbach, 2014] (Fig. 1C). To design optimized treatments, the ability to predict or alter 35 drug interactions is crucial -a challenge that would be facilitated by understanding their underlying 36 mechanisms [Chevereau and Bollenbach, 2015]. 37 Apart from their clinical relevance, antibiotic combinations provide powerful, quantitative and con-38 trolled means of studying perturbations of cell physiology [Falconer et al., 2011] -conceptually similar 39 to studies of epistasis between double gene knockouts [Yeh et al., 2006;Segre et al., 2005]. Trans-40 lation inhibitors are particularly suited for this purpose since translation is a fundamental, yet complex 41 multi-step process that still lacks a comprehensive quantitative description. Part of any such descrip-42 tion are "growth laws," which quantitatively capture the compensatory upregulation of the translational 43 machinery in response to perturbations of translation [Scott et al., 2010]. Growth laws have enabled 44 a model that elegantly explains the growth-dependent bacterial susceptibility to individual translation 45 inhibitors [Greulich et al., 2015]. Finally, well defined translation steps cannot only be perturbed chemi- 46 cally [Blanchard et al., 2010;Wilson, 2014], but also genetically, as these steps are regulated by trans-47 1 and that they can be predicted solely from known responses to the individual drugs. To establish this 61 result, we used a combination of precise growth measurements, quantitative genetic perturbations of 62 the translation machinery, and theoretical modeling.  Table 1). (C) Examples of growth curves obtained by luminescence assay (left column) in the presence of different antibiotics and their combinations and response surfaces corresponding to different interaction types (right column) (Methods).
Symbols on the growth curves indicate the condition used: no symbol, triangle, square and a circle correspond to no drug, CHLonly, second drug only (see vertical axis), and the combination of both, respectively. The growth curves were shifted in time so as to originate from the same point at time 0. Drug interactions are determined based on the shape of lines of equal growth (isoboles). If the addition of the second drug has the same effect as increasing the concentration of the first, the isoboles are straight lines [Loewe and Muischnek, 1926]. Deviations from this additive expectation reveal synergism (the combined effect is stronger and isoboles curve towards the origin), antagonism (the effect is weaker and isoboles curve away from the origin), or suppression (at least one of the drugs loses potency due to the other). (D) The drug-interaction network of translation inhibitors.
Color-code is as in (C); dashed gray lines denote additivity.

Antibiotic
Abbreviation IC 50 [µg/mL] Mode of action, notes Chloramphenicol CHL 1.55 ± 0.01 Binds in the vicinity of the peptidyl-transferase centre (PTC) on the 50S subunit; partially overlaps with the acceptor stem of tRNA on the A-site [Wilson, 2014].
Capreomycin CRY 23.6 ± 0.1 Inhibits translocation by binding to the interface between subunits and stabilization of the ribosome in the pretranslocation state of the ribosome.
It only binds the fully assembled ribosome [Stanley et al., 2010].  lation inhibitors. Third, we identified a previously unreported synergy between CRY and CHL. Some of 82 the observed general trends in the drug interaction network, in particular the prevalence of antagonism, 83 may be explained by a general physiological response to translation inhibition. 84 A number of the interactions we measured confirm previous reports. For example, synergy between 85 erythromycin (ERM) and tetracycline (TET) was observed before [Yeh et al., 2006;Russ and Kishony, 86 2018]. Additivity between CHL and TET was also reported; moreover, this interaction proved to be 87 highly robust to genetic perturbations [Chevereau and Bollenbach, 2015]. Globally,antagonism and 88 suppression are more common in the translation inhibitor interaction network than synergy, consistent 89 with a general prevalence of antagonistic interactions between antibiotics [Brochado et al., 2018]. differential equations taking into account passive antibiotic transport into the cell, binding to the ribo-97 some ( Fig. 2A,B), dilution of all molecular species due to cell growth, and the physiological response of 98 the cell to the perturbation (Fig. 2C). The latter is described by ribosomal growth laws [Scott et al., 2010;99 Greulich et al., 2015], which quantitatively connect the growth rate to the total abundance of ribosomes 100 when growth rate is varied by the nutrient quality of media or by translation inhibitors. All parameters of 101 the model can be inferred from the dose-response curves of individual drugs (Fig. 2D). 102 When two different antibiotics are present simultaneously, separate variables are needed to describe 103 ribosomes that are bound by either of the antibiotics individually or simultaneously by both ( Fig. 2A). 104 In the absence of knowledge about direct molecular interactions on the ribosome (as for the pairs 105 of lankamycin and lankacidin or of dalfopristin and quinupristin [Harms et al., 2004;Belousoff et al., 106 2011]), we assumed that the antibiotic binding and unbinding rates are independent of any previously 107 bound antibiotic (Fig. 2B). The resulting model makes direct predictions for drug interactions between 108 translation inhibitors using only parameters that are inferred from the individual drug dose-response 109 curves. 110 Using this model, we calculated the predicted response surfaces for all translation inhibitor pairs 111 and compared them to the experimentally measured surfaces (Methods, Fig. 2E). Certain drug interac-   Gordon, 1970;Blumenthal et al., 1976;Furano and Wittel, 1975], limiting the expression of a single 145 translation factor imposes a highly specific bottleneck as all other components get upregulated. Fur-146 thermore, any global feedback regulation is left intact as we removed the factor from its native operon.

147
These synthetic strains thus offer precise control over artificial translation bottlenecks that determine 148 the rates of different translation steps. 149 We next used these strains to assess the impact of bottlenecks on antibiotic efficacy. Accordingly, 150 we measured growth rates over a two-dimensional matrix of concentrations of inducer and antibiotic 151 for each of the six strains ( Fig. 3C; Methods). To address if the action of the antibiotic is independent 152 of the translation bottleneck, we analyzed these experiments using a multiplicative null expectation. 153 Note that additivity as used for antibiotics ( Fig. 1C)   introduced to control the expression of a translation factor x, which creates an artificial bottleneck in translation at a well-defined stage; lacI codes for the Lac repressor, which represses the P LlacO-1 -promoter (Methods, [Lutz and Bujard, 1997] 1D) originates in the diversity of 169 translation steps targeted by the drugs (Fig. 1A). 170 The bottleneck dependency vector of a given antibiotic provides a quantitative, functional summary 171 of its interaction with the translation cycle. In this sense, it is a characteristic "fingerprint" of the antibiotic. and membrane permeabilization [Davis, 1987]. Some of these processes, in particular the production 207 of dysfunctional proteins, overlap with those of NIT [Bandow et al., 2003], offering an explanation for the 208 observed similarity of these seemingly unrelated drugs. antibiotics can be directly explained and predicted. In practice, this is done by remapping the antibiotic-242 translation factor response surfaces as described above (Fig. 5A,B). The resulting prediction will be 243 faithful if the drug interaction originates exclusively from the combination of two bottlenecks in the trans-244 lation cycle. Drug interactions predicted using this procedure were often highly accurate (Fig. 5C). In 245 particular, some of the most striking cases of antagonistic and suppressive interactions were correctly 246 predicted. For example, the suppressive interaction of CHL with FUS was correctly predicted, including 247 its direction: FUS loses potency when exposed to CHL ( is lowered (smaller factor symbol), the rate of step 1 decreases (thinner arrows) and ribosomes queue in front of the bottleneck.
Bottom: the same rate is reduced by an antibiotic. The effects of factor deprivation and antibiotic action on growth are equivalent. that the action of CHL is largely equivalent to inhibiting tRNA delivery. As CHL binding interferes with a 261 distal end of tRNA on the A-site [Wilson, 2014], this suggests that perturbation of tRNA dynamics is at 262 the heart of the drug interaction between TET and CHL. KSG and ERM constitute another antibiotic pair 263 that interacted additively and was clustered together. Remapping correctly predicted additivity between 264 KSG-ERM (SI); however, ERM does not directly inhibit initiation as does KSG (Table 1). Yet, it is likely 265 that the inability of ERM to inhibit translation when the nascent peptide chain is extended beyond a 266 certain length effectively leads to a functional equivalence, which results in additivity and co-clustering 267 of ERM and KSG. 268 For certain antibiotic pairs, the predictions based on equivalent translation bottlenecks failed to ex-269 plain the observed drug interactions (e.g., for LCY-CRY and CHL-CRY; SI), indicating that these in- 270 teractions have origins outside of the translation cycle. We expect that these cases are often due 271 to idiosyncrasies of the drugs, which will require separate in depth characterization in each case. In What is the underlying mechanism of the suppressive interaction between initiation and transloca-313 tion inhibitors? We hypothesized that this suppression results from alleviating ribosome "traffic jams" 314 that occur during translation of transcripts when the translocation rate is low (Fig. 6D). The traf-315 fic of translating ribosomes that move along mRNAs can be dense [Mitarai et al., 2008] and when 316 a ribosome gets stuck (e.g., due to a low translocation rate), it blocks the translocation of subse-317 quent ribosomes. The resulting situation is similar to a traffic jam of cars on a road. Traffic jams 318 form due to asynchronous movement and stochastic progression of particles in discrete jumps, which 319 is a good approximation for the molecular dynamics of a translating ribosome. If particle progres-320 sion were deterministic and synchronous, no traffic jams would form. A classic model of queued 321 traffic progression, which can be applied to protein translation [MacDonald et al., 1968;MacDonald 322 and Gibbs, 1969], is the Totally Asymmetric Simple Exclusion Process (TASEP) [Shaw et al., 2003;323 Zia et al., 2011]. 324 We developed a variant of the TASEP that describes the traffic of translating ribosomes on mRNAs 325 and takes into account the laws of bacterial cell physiology. There are several differences between the 326 classic TASEP and translating ribosomes moving along a transcript. First, a ribosome does not merely 327 occupy a single site (codon), but rather extends over 16 codons [Kang and Cantor, 1985]. Second, the 328 total number of ribosomes in the cell is finite and varies as dictated by bacterial growth laws [Scott et al., The factor titration platform and the repressor operon were Sanger-sequenced at the integration junc-626 tions using PCR primers or a primer binding into the kan R promoter region (which is upstream of the 627 P LlacO-1 promoter prior the resolution). The final genotype for the strains bearing the factor titration 628 platforms is HG105 ∆galK::frt-P LlacO-1 -x ∆x::frt ∆intS::frt-P LlacO-1 -lacI, where x denotes the chosen 629 factor. These strains contained no plasmids and no antibiotic resistance cassettes but had a single 630 copy of a translation factor under inducible control.

631
To generate the strain with independently regulated initiation and translocation factors, we started 632 with a strain carrying a single infB copy driven by P LlacO-1 . Then, the negatively autoregulated tetR  Growth rate assay and two-dimensional concentration matrices 643 Rich lysogeny broth (LB) medium, which at 37 • C supports a growth rate of 2.0 ± 0.1 h -1 , was used.

644
LB medium was prepared from Sigma Aldrich LB broth powder (L3022), pH-adjusted by adding NaOH 645 or HCl to 7.0 and autoclaved. Antibiotic stock solutions were prepared from powder stocks (for catalog 646 numbers, see Table S1) To quantify the drug interaction between a pair of antibiotics, we defined the Loewe interaction score as 692 LI = log g(x 1 , x 2 )dx 1 dx 2 g(x 1 , x 2 ) add dx 1 dx 2 , where g(x 1 , x 2 ) and g add (x 1 , x 2 ) are the measured and the predicted additive dose-response surfaces 693 over a 2D concentration field (x 1 , x 2 ), respectively. The score LI is a log-transformed ratio of volumes 694 underneath the dose-response surfaces. It is positive for antagonistic and suppressive interactions, 0 695 for perfectly additive, and negative for synergistic interactions. To avoid imposing arbitrary bounds for 696 classifying a measured interaction as synergistic or antagonistic/suppressive (rather than additive), we 697 performed smooth bootstrapping on a set of ideal additive response surfaces to establish a distribution of 698 interaction indices expected for perfectly additive but noisy surfaces. To achieve this, we generated ad-699 ditive dose-response surfaces for drugs with Hill steepness parameter n between 1.8 and 6.6 (obtained 700 as 10% and 90% percentiles of the steepnesses distribution for measured dose-response curves). We response curves (Fig. S3). Mathematically, this means that r x = y (c) and r y = g(in) for antibiotic 716 and inducer, respectively. In response space, the null-expectation is independence, i.e. the expected 717 response is a product of individual responses. Thus, we define the BD score as 718 BD = log r (r x , r y )dr x dr y r x r y dr x dr y . (2) This score is zero when the two perturbations (bottleneck and antibiotic) are independent; it is pos-719 itive or negative for alleviation and aggravation, respectively. As for the LI score, we evaluated the 720 independence interval of BD scores by bootstrapping the BD score for independent surfaces at given antibiotic binding and transport as well as physiological constraints. We briefly summarize the results 728 for a single antibiotic and its main ingredients. The growth laws are given as and where r u , r b and r tot are concentrations of unbound, bound and total ribosomes. The constants κ t = 0.06 µM -1 h -1 , r min = 19.3 µM, r max = 65.8 µM and ∆r = r max -r min = 46.5 µM were experimentally determined in Refs. [Scott et al., 2010;Greulich et al., 2015]. Transport of antibiotic is captured by the average flux as J(a ex , a) = p in a ex -p out a, where p in and p out are influx and efflux rates, respectively, and a and a ex are the intracellular and external antibiotic concentration, respectively. The kinetics of binding of the antibiotic to the ribosome is given as f (r u , r b , a) = -k on a(r u -r min ) + k off r b , where k on and k off are binding and unbinding rates, respectively, and K D = k off /k on . The fraction of inactive ribosomes r min is assumed not to bind antibiotics [Greulich et al., 2015]. The following system of ordinary differential equations (ODEs) describes the kinetics of the system In Eqs. (5) the terms -λX (with X = a, r b , r tot ) describe effective dilution due to growth and s(λ) = λr tot is 731 the ribosome synthesis rate. In balanced exponential growth all time derivatives in Eqs.

738
Pair of antibiotics When a pair of antibiotics is considered, additional ODEs are added to describe the binding of individual antibiotics to ribosomes (first binding step) as well as the simultaneous binding of two antibiotics to the already bound ribosome (second binding step): In the system of Eqs. (9) Here, ψ ij is 1 if the i-th and j-th data points are either inside or outside of the same cluster and zero 765 otherwise; the denominator is the total number of unique pairs between N elements. We generated 10 4 766 reshuffled datasets, evaluated RI for each dataset and calculated the cumulative distribution function. 767 We evaluated an empirical p-value as which is an estimate of the probability for obtaining the observed clustering of median BD vectors by 769 chance. The cluster areas shown in Fig. 3 were obtained by smooth bootstrapping of median BD as c = y -1 (g(in)) at a given α, which can be arbitrarily chosen for the idealized antibiotic. When 781 α < α crit , the dose-response curve is bistable and has a region in which more than one response 782 will yield the same concentration -in these cases we consider only the concentration corresponding 783 to the highest stable growth rate as the other solutions are either unstable or will be outcompeted. Hill functions with Hill exponents n WT and n t for WT and factor-titrating strain, respectively. Then, by 793 equating the responses captured by these Hill functions, we calculated the rescaled relative (with respect to IC 50 ) antibiotic concentrations as c a,t = c n t /n WT a,WT . We refer to this conversion as the "power-law 795 transform". Such regularized surface was then used in remapping. antibiotic grid and sampling, and inherent noisiness of growth rate determination. We first restricted 804 the dataset to data points with relative growth equal to 0 or above 0.1 with growth rate coefficient of 805 determination R 2 > 0.8. In each round of bootstrapping, the following steps are carried out:

806
• drawing of a remapping parameter α from a normal distribution, centered at the best-fit-value and 807 with standard deviation estimated from fitting, and remapping, 808 • drawing of a random sample from remapped data points that is of random size (between 75% and 809 100% of the data set), 810 • addition of Gaussian noise to the growth rates (estimated from the growth rate fit),

811
• calculation of the ideal additive surface at a given α for comparison, and 812 • calculation of LI score. 813 This procedure was repeated 100 times for each bottleneck-antibiotic pair and yielded a set of distri-814 butions. Each LI distribution was then statistically evaluated for being inside the additive interval. We 815 obtained the cumulative distribution function (CDF) for each distribution and we calculated its value on 816 both ends of additive interval (Fig. S1). If either 1 -CDF (b lower ) or CDF b upper is below p = 0.05, the 817 pair is considered inequivalent -this is the case in which the remapped surface is unlikely to be additive. 818 For each antibiotic, more than one of the bottlenecks could be statistically equivalent -we thus deemed 819 the bottleneck-antibiotic pair with the highest correlation between average remapped and ideal additive 820 growth rates to be the primary candidate for equivalence of perturbations. surface segments further away from individual axes. We thus sought an applicable metric that would 826 identify systematic deviations from predicted isoboles. 827 We developed an "isobole sliding" method in which we determine a mean deviation of points close 828 to some predicted growth rate from measured values. It provides a concise quantitative description of 829 differences between predicted and measured isoboles and identifies the most discrepant areas of the 830 surfaces. For that we systematically move along the (ordered) predicted growth values g i and select 831 S = 20 consecutive points and average their deviations from measured values of growth rate h i . This 832 yields a deviation trajectory t(ĝ) of a mean deviation as a function of average predicted growth rate Keeping the number of points S in the window fixed allows the comparison between different subsets of 834 the data. 835 To assess the probability of observing such deviation by chance, we created a benchmark dataset by Doing so, we observed that twenty-one out of twenty-eight (75%) surfaces act as statistically significant 852 predictions for one another. This serves as an approximate upper bound for how many predictions-853 measured pairs can be at most expected to match at the given experimental variability.

854
Assessment of predictive power 855 At this point we can assess the consistency of predictions. Using the method described above, we eval-856 uated both independent and competitive binding schemes for their congruence with measured surfaces.

857
The scheme that led to the distribution with the smallest mean maximal deviation, was considered as 858 best-match. However, both schemes can yield a good match -by asking how many of the schemes 859 yield a match in both replicates, we obtain an estimate for a fraction of correct predictions (Fig. S2). By 860 counting in how many cases at least one of the schemes yields a match between replicates, we find 861 that sixteen out of twenty-eight interactions can be accounted for by a biophysical model. 862 Applying isobole sliding to the prediction of remapping shows that even small quantitative deviations 863 will lead to discarding of the prediction (Fig. S5) and J tran (ζ, γ) = γ where ζ and γ are initiation and translocation attempt-rates, respectively. The ribosome (coverage) 884 density ρ reads: and ρ tran (ζ, γ) = ρ max = 1 The elongation velocity u depends both on the current and the ribosome density ρ r = ρ/L via u = Js/ρ r , 886 where s is the step size (1 aa). This in turn yields 887 u init (ζ, γ) = s(γζ) and u tran (ζ, γ) = s

Distribution of ribosomes across different classes
The total ribosome concentration r tot is 888 r tot = r i + r tr + r min , where r i and r tr are the concentrations of non-initiated and translating ribosomes, respectively. Trans-889 lating ribosomes are distributed across numerous mRNA transcripts in the cell and their concentration 890 can be written as: where D p and ρ r ,p are the length and ribosome density of the p-th transcript, respectively, M is the 892 total number of transcripts and V the cell volume (Ξ = M/V is the concentration of transcripts). The 893 density of ribosomes ρ r = ρ/L is a TASEP-derived quantity and depends on the initiation attempt rate 894 α and translocation attempt rate γ. In the last step, we assumed for simplicity that the density of 895 ribosomes across the transcripts does not vary significantly between transcripts. However, if transcripts 896 do differ in their ribosomes densities, the ones with higher densities will enter the translocation limiting 897 regime (in which traffic jams form) already at a smaller decrease in translocation attempt rate. If those 898 transcripts code for essential genes, this will correspondingly lead to a decrease in growth rate already 899 at such smaller decreases in translocation attempt rate. Such traffic jams would still be relieved by Michaelis-Menten function for the translation rate, we obtain u max ≈ 18 aa/s. Thus, the growth rate is 914 given as 915 λ = κ t r tr min u(ζ, γ) u max , 1 .
However, the growth rate feeds back into the total ribosome concentration via the growth law as 916 r tot = r i + r tr + r min = r max -λ∆r We can estimate Ξ at λ 0 as Factor-dependent translocation attempt rate The ribosome will perform a specific step only when the associated factor is bound to it: the step-attempt rate is proportional to the probability P b of the ribosome being bound by a factor. This probability can be calculated by assuming a population of elongation factors with concentration c ef = c ef,b + c ef,n and translating ribosomes r tr = r tr,b + r tr,n , where the indices b and n denote the factor-bound and unbound subpopulations, respectively. Binding is described by dr tr,b dt = k on c ef,n r tr,n -k off r tr,b , (21a) dc ef,b dt = k on c ef,n r tr,n -k off c ef,b .
Solving for steady state, noting that r tr,b = c ef,b and defining K D = k off /k on we obtain the probability for a 918 ribosome to be bound as 919 P b = r tr -r tr,n r tr = 1 -(r tr -K D -c ef ) + 4K d r tr + (r tr -K D -c ef ) 2 2r tr .
The binding constant of EF-G to the ribosome complex I (pre-translocation analog with N-Ac-dipeptidyl-920 tRNA at the A-site and deacylated-tRNA in the P-site) [Yu et al., 2009]  The estimated ribosome density is ρ r ≈ 0.042, which is lower than the maximal attainable ribosome 946 density of ρ r,max = ρ max /L = 1/(L + √ L)| L=16 = 0.05. Thus, translation in the WT is likely in the initiation-947 limited regime. Thus, the equations for ribosomal density and elongation velocity for the initiation limiting 948 regime are used to estimate the apparent initiation and translocation attempt rates: 949 ρ r (ζ) = ζ γ + ζ(L -1) ≈ 0.042 and u = (γζ)s ≈ 18 aa/s.
The apparent rates are γ ≈ 20.    all 28 antibiotic pairs. Due to small, but systematic variability in concentrations between replicates done on different days, we rescaled concentration axes with respect to the IC 50 . Dose-response surfaces were smoothed using LOESS (Methods). Black and gray dots denote measured points from different experiments. Isoboles from duplicates are in high agreement; small deviations are caused by occasional outliers that skew the isoboles. As the dose-response surface was measured over a 12×16 grid, the duplicates change the drug axes (12×16→16×12) on different days to check for effects coming from spreading the measurements over different plates. (B) An example of growth curves over a 12×16 grid. Note, that here the concentrations change between wells in a geometric manner, i.e. the ratio between concentrations in neighboring wells is fixed. (C) Exemplary growth curve and details of the fitting procedure. The growth rate is determined by fitting a line in the regime of exponential growth. The determination of this regime in the growth curve is carried out automatically; procedure: (i) check if the maximum value of luminescence is above the lower bound of the fitting interval lum min = 10 3 cps and take points before the maximum, (ii) take points that are the latest to rise over lum min , (iii) determine the upper limit (bnd) of the fitting interval to be either ten-fold above the lum min (guaranteeing log 2 10 ≈ 3.3 doublings of fitting interval) or eight-times less than the track maximum (three doublings away from saturation) and (iv) fit a line to the log-transformed values of the luminescence signal if there are at least three data points. If lum min is not exceeded, the well is counted as having no growth; if any of the other criteria is not fulfilled, growth is characterized as  on root-mean-square error (with respect to the experimental data). Parameters are required for forward time integration. Rootmean-square error was normalized with respect to the maximal error in the scanned interval. Effective dissociation constant K D exhibits roughly two orders of magnitude wide plateau (double-headed arrow; minimum is denoted by a circle). First order binding rate constant kon does not exhibit a plateau but rather flattens out -consistently with the requirement that kon κ t . (C) All predictions for replicated measurements. Predicted surface is show in full; overlaid thick and dashed purple isobole denote 20% and 50% isobole, respectively, of the measured surface. Each prediction is evaluated for goodness of prediction as described in Methods. Check-mark and cross denote a match and mismatch, respectively. Inset text denotes the best-matching binding Green check marks denote that LI did not fall outside of the additivity interval; in these cases, the rounded correlation ρ is reported. A good agreement with the additive expectation suggests equivalency of antibiotic and genetic perturbation. (B) Examples of histograms of LI for CRY in combination with a translocation and recycling bottleneck [see matching pentagon and star in (A)], respectively. (C) Color-coded sequential evaluation of equivalence between bottleneck and translation inhibitor. Red and yellow denote that LI was outside or inside of the additive interval, respectively. From the cases in which the LI is statistically inside the additive interval, the case with highest correlation was chosen as the putative primary mode of action (green). This approach correctly identified the mode of action for all cases in which it is known from literature (CRY, FUS, STR, KSG and TET). Each prediction is evaluated for goodness of prediction as described in Methods. Check-mark and cross denote a match and mismatch, respectively. isoboles from the prediction assuming a constant pool of mRNA are shown in purple. Both results are qualitatively equivalent.