A Rapid Method to Rank Proteins of Widely Varying Stability: Application to Paramyxovirus Foot Domains

Abstract

The foot domains of polymerases from the Paramyxoviridae family mediate attachment of the viral polymerases to their nucleocapsid templates during viral RNA synthesis. Detailed structural and biophysical characterization of these foot domains reveals that they share a common structure, but when not bound to the nucleocapsid they may exist as intrinsically unstructured chains, molten globules, or highly stable folded domains. With hundreds of paramyxovirus sequences now known, the diverse family of foot domains provides a valuable system to investigate the physical and evolutionary processes that dictate protein stability. To enable rapid and robust evaluation of the relative stability of these domains, we tested the applicability of the split β‐lactamase assay. This assay couples β‐lactamase activity to the folding of a protein inserted into a loop on the enzyme, with antibiotic resistance being conferred in proportion to the stability of the insert. In this work, five foot domains of broadly varying stability were tested with this assay. We constructed a bespoke vector to facilitate the use of this assay, and we introduced a novel statistical approach that generates a probability‐based ranking of relative stability from the experimental data. We find that this assay reproduces the order of stabilities obtained through biophysical approaches. Though classical definitions of stability, evaluated using traditional biophysical techniques, are ill‐defined for proteins of low intrinsic stability, this work finds that the split β‐lactamase assay can be fruitfully adapted in such cases, and can be made more convenient and interpreted more rigorously through the innovations we describe. © 2026 The Author(s). Current Protocols published by Wiley Periodicals LLC.

Basic Protocol 1: Preparation of screening vector suBLA for ligation‐independent cloning

Basic Protocol 2: Ligation‐independent cloning of inserts into screening vector suBLA

Basic Protocol 3: Use of PCR to check for inserts

Basic Protocol 4: Dilution series assay

Basic Protocol 5: Scoring of dilution assay

Basic Protocol 6: Statistical analysis of dilution assay

INTRODUCTION

Paramyxoviral polymerases share a common structure that enables them to efficiently transcribe and replicate the viral genome. The RNA genome is packaged by the viral N protein, forming a ribonucleoprotein complex (nucleocapsid) that protects and organizes the genome. The catalytic L subunit of the polymerase carries out transcription and replication of the RNA genome. However, the interaction between the polymerase and the nucleocapsid is mediated by the P protein, an accessory subunit of the polymerase (Kingston, Baase, et al., 2004; Kingston, Hamel, et al., 2004; Kingston et al., 2008). These interactions must be transiently maintained to facilitate processive movement of the polymerase along the nucleocapsid. Central to these interactions are small domains at the C‐terminus of the P protein, which can bind both N and L, referred to here as foot domains (Yegambaram & Kingston, 2010). Foot domains have a very simple structure, forming a parallel 3‐helix bundle of ∼50 residues, and appear to be close to the minimum size of a self‐organizing domain (Fig. 1A).

Figure 1.

Structural basis of split β‐lactamase assay. (A) Ribbon diagrams representing the crystal structures of the measles (green) and mumps (yellow) foot domains. The overlay at center (1.1 Angstroms rmsd) illustrates that although these foot domains manifest dramatically different solution behavior, their folded structures are highly similar (Kingston, Hamel, et al., 2004, Kingston et al., 2008). (B) Structure of β‐lactamase fusion constructs. At left, diagram of TEM‐1 β‐lactamase structure (Jelsch et al., 1993), with the N‐terminal fragment colored gray and C‐terminal fragment colored black. The loop with the insertion site between amino acids 196 and 197 is indicated with a red arrow. For the split β‐lactamase assay, an exogenous domain, illustrated here as the measles foot domain, is inserted at this location by short linkers (dashed lines). (C) Model for assay mechanism, where the state of the inserted domain controls the activity of the β‐lactamase. When folded, the inserted domain stabilizes an active conformation of the β‐lactamase, conferring antibiotic resistance. When unfolded, the inserted domain renders the β‐lactamase inactive. Strains harboring fusion constructs with stable inserts are therefore able to grow more robustly in the presence of lactam antibiotics than strains harboring fusions with unstable inserts.

A comparison of the relative degree of structure formed by the foot domains from the polymerases of selected paramyxoviruses (subfamily Rubulavirinae) revealed a spectrum of conformational stability (Yegambaram et al., 2013). The foot domain from Mapuera virus appears to be largely unstructured under most conditions, while the domains from simian virus 5 (SV5) and mumps are best described as molten globules, forming secondary structure but lacking persistent tertiary structure (Kingston et al., 2008). In contrast, the foot domain from human parainfluenza virus type 4 (HPIV‐4b) virus is a stable cooperatively folding domain. Related studies of the foot domain from measles virus (subfamily Orthoparamyxovirinae) established that this domain was also stable and folded (Kingston, Baase, et al., 2004; Kingston, Hamel, et al., 2004).

The functional role of the foot domains as mediators of transient protein‐protein interactions may be tuned through modulation of intrinsic stability (Curran & Kolakofsky, 1999; Sourimant et al., 2020; Troilo et al., 2018). Therefore, measurement of foot domain stability is of direct functional relevance. Biophysical characterization of purified domains remains the gold standard for determination of stability but is costly and laborious. Here we aimed to develop a faster and cheaper, yet highly informative method, to survey the properties of these domains.

Our approach rests upon a genetic selection for protein stability, devised by the Radford and Bardwell laboratories, which employs a split version of the TEM‐1 β‐lactamase (hereafter β‐lactamase) (Foit et al., 2009). The enzyme has a surface‐exposed loop between residues 196 and 197, between which an entire protein domain may be inserted (Fig. 1B). Folding of the insert brings the two parts of the β‐lactamase together, enabling enzyme function. This tripartite fusion construct thereby confers antibiotic resistance to the strain in proportion to the stability of the insert (Fig. 1C). Serial dilution of cultures containing the fusion constructs provides a means to measure their relative growth, making it possible to compare the stability of protein variants in vivo.

In this work the split β‐lactamase assay has been applied in a comparative study of the Paramyxoviral foot domains as a test of its utility in studying proteins of low intrinsic stability. The set of five domains described above (from Mapuera, SV5, mumps, HPIV‐4b, and measles viruses) has been well characterized by biophysical and structural methods and were utilized as the test subjects.

To facilitate the assay, we constructed a custom vector that incorporates features simplifying cloning, expression, and screening. In addition, we introduce a novel probabilistic approach for interpretation of dilution series data based on ranking the relative growth of constructs. By focusing on relative rather than absolute growth, it is possible to determine quantitatively the degree of confidence in the assigned order. Overall, we find that the split β‐lactamase assay reproduces the relative ordering of stability as determined through physical techniques, extending the applicability of this genetic assay to marginally folded proteins. Additionally, our statistical approach assigns a degree of confidence to each possible ranking of the proteins under study.

Protocols for the procedures used in this work are provided below. Basic Protocols 1 and 2 describe preparation of the vector and insert for cloning, and Basic Protocol 3 describes a convenient method for checking the results of the cloning procedure. Basic Protocol 4 details the procedure for the split β‐lactamase assay itself. Basic Protocol 5 describes the scoring of the assay results, and Basic Protocol 6 describes the statistical analysis of the assay data.

STRATEGIC PLANNING

Materials and Methods

Development of custom vector suBLA

To implement the assay, we developed a custom expression vector, suBLA. The overall motivation was to devise a vector that would facilitate the genetic screen enabled by the split β‐lactamase approach but also included elements to simplify purification and detection of expressed constructs if desired. A schematic diagram of the gene coding for the β‐lactamase fusion construct is shown in Figure 2A. The vector confers kanamycin resistance for propagation of constructs in the absence of selection for β‐lactamase activity, and utilizes a β‐d‐thiogalactoside (IPTG)‐inducible T5 promoter for expression of the β‐lactamase fusion protein incorporating inserts (Gentz & Bujard, 1985; Lanzer & Bujard, 1988). The T5 promoter enables expression in most Escherichia coli lab strains, making it unnecessary to transfer the plasmid after cloning into a specialized expression strain. The vector employs a ligation‐independent cloning (LIC) site (Aslanidis & de Jong, 1990) (see next section) simplifying placement of sequences into the insertion site in the β‐lactamase gene. The regions of the β‐lactamase sequence that encode the N‐ and C‐termini of the protein construct have also been modified to facilitate purification and detection of the expressed protein. To direct trafficking of the protein to the periplasm, the vector employs the periplasmic localization sequence (PLS) from the β‐lactamase sequence at the N‐terminus. Following the PLS is a 6‐histidine purification tag at the N‐terminus of the SUMO protein (Weeks et al., 2007). To enable specific detection of the fusion construct, a lanthanide‐binding tag (LBT) sequence (YIDTNNDGWYEGDELLA) was placed at the C‐terminus. This tag generates luminescence in the presence of terbium ions (Franz et al., 2003; Nitz et al., 2003, 2004).

Figure 2.

Ligation‐independent cloning scheme. (A) Schematic diagram of the gene coding for the fusion construct on the vector suBLA. (B) LIC site with BseR1 recognition site indicated in bold and cut site indicated with triangles. Proximal cytosine is indicated in red. (C) Cleavage of vector by BseR1 disrupts stop codon. (D) Treatment of cleaved vector with T4 polymerase in presence of dCTP degrades 3’ ends at the cut site back to proximal cytosines, generating large overhangs. (E) PCR product of insert with LIC handles. Proximal guanine is shown in red. (F) Treatment of PCR product with T4 polymerase in presence of dGTP degrades 3’ ends back to proximal guanine, generating overhangs complementary to those on vector. (G) Insert annealed into vector. Successful insertion converts the stop codon at the BseR1 cut site to TCT, coding for serine.

Design of a ligation‐independent cloning site for in‐frame insertion into the β‐lactamase sequence

The design of the cloning site in the vector is similar to that in pLIC‐SGC1 (Burgess‐Brown, 2013) and petHSUL (Weeks et al., 2007) with modifications to incorporate in‐frame insertion with linkers to the adjacent β‐lactamase sequence. The ligation‐independent cloning site is illustrated in Figure 2B‐G. The cloning procedure uses the type IIS restriction endonuclease BseR1, which recognizes asymmetric sequences and cleaves 8 bases in the 5’ direction from its recognition site. In suBLA, this cut site coincides with a stop codon (Fig. 2B). On the coding strand, the closest cytosine in the 5’ direction is located 16 bases from the site of cleavage of BseR1, and on the noncoding strand, the closest cytosine in the 5’ direction is located 18 bases from the site of cleavage (Fig. 2C). After BseR1 cleavage, treatment of the digested vector with T4 DNA polymerase in the presence of cytosine results in degradation of the exposed 3’ ends until these proximal cytosines are reached, generating a 15‐base overhang on the coding strand and a 13‐base overhang on the noncoding strand (Fig. 2D).

Each sequence for insertion was amplified with appropriate primers incorporating additional sequences 5’−ggtagtaatagttct−3’ on the coding strand and 5’−agaggagttggtttgcgc–3’ (LIC handles) on the noncoding strand (Fig. 2E). During PCR, the complementary sequences to these handles incorporated guanine 16 bases from the 3’ end on the coding strand and 14 bases from the 3’ end on the noncoding strand opposite the cytosines. Treatment of the resulting PCR product with T4 polymerase in the presence of dGTP resulted in degradation in the 3’ to 5’ direction until these proximal guanines were exposed, creating overhangs complementary to those on the vector (Fig. 2F). The treated insert and vector were mixed to form a nicked circular plasmid that was transformed directly into a bacterial host, where the endogenous ligase activity sealed the nicks. The insertion is fused in‐frame with the β‐lactamase between residues 196 and 197, with a 6‐residue linker GGSNSS on the N‐terminal side and a 7‐residue linker AQTNSSG on the C‐terminal side (Fig. 2G).

The vector was constructed such that overhangs are asymmetric, precluding cloning of inserts in the wrong orientation or closure of the vector upon transformation. The empty vector itself has a stop codon at the cleavage site intended to suppress growth on media containing antibiotics, whereas successful cloning allows translation of the insert and the C‐terminal region of the β‐lactamase.

Ligation‐independent cloning

All plasmids were propagated in E. coli strain DH5α by overnight culture in LB broth supplemented with 100 µg/ml kanamycin.

Vector was prepared for ligation‐independent cloning by digesting 4 µg of suBLA with 4 U of BseR1 and 4 U of calf alkaline phosphatase (New England Biolabs) for 1 hr at 37°C. The digested vector was gel‐purified, then treated with T4 DNA polymerase in the presence of 1 mM dCTP for 1 hr at 25°C. After heating at 75°C for 20 min the prepared vector was stored at –20°C.

The mumps and measles virus foot domain sequences were obtained as synthetic genes from ATUM Bio. The HPIV‐4b, SV5, and Mapuera virus foot domain sequences were amplified from plasmids pKY303, pKY330, and pKY331 (Yegambaram et al., 2013). E. coli cytochrome b562, previously shown to confer antibiotic resistance when used with the split β‐lactamase system (Foit et al., 2009), was used as a positive control for comparison with the foot domain sequences. The gene for cytochrome b562 (cb562 hereafter) was amplified from the E. coli DH5α chromosome. PCR products were gel‐purified and treated with T4 DNA polymerase (New England Biolabs) in the presence of 1 mM dGTP for 1 hr, followed by heating to 75°C for 20 min. Prepared inserts were stored at –20°C. In addition, the SUBLA‐TEV construct that contains the short peptide linker GENLYFQGA was created by directly cloning oligonucleotides 5’‐ggtagtaatagttCTGGCGAAAACCTGTATTTCCAGGGCGCG‐3’ and 5’‐agaggagttggtttggcCGCGCCTGGAAATACAGGTTTTCGCC‐3’, where the lower‐case portions comprise the LIC handles and the upper‐case portions encode the cleavage site sequence. Sequences for each construct are detailed in Table 1.

Table 1.

Sequences of Constructs Used in This Work

Construct name	Accession	Insert sequence
Mapuera	GenBank NC009489	SDGTRIMILQMIKESVSDPLEQSRFETKLSSCTTEDQGKAIKMEILRRATY
SV5	GenBank NC006430	TGLKITLEQLAKDSISKPKMREEYLLKINQASSEAQLIDLKKAIIRSAI
Mumps	SWISS‐PROT F8V2V0	AGRKVMITKMITDCVANPQMKQAFEQRLAKASTEDALNDIKRDIIRSAI
Measles	SWISS‐PROT P35974	ASRSVIRSIIKSSRLEEDRKRYLMTLLDDIKGANDLAKFHQMLMKIIMK
HPIV‐4b	GenBank AB543337	GVRIDALKITVSEMIRDLFGDSDKSRKLLESINMATTEQDINSIKTNALRSITY
cb562	SWISS‐PROT P0ABE7	ADLEDNMETLNDNLKVIEKADNAAQVKDALTKMRAAALDAQKATPPKLEDKSPDSPEMKDFRHGFDILVGQIDDALKLANEGKVKEAQAAAEQLKTTRNAYHQKYR
suBLA‐TEV		GENLYFQGA

For ligation‐independent cloning, 1 µl of the prepared vector was mixed with 1 µl of the insert PCR products. In the case of the TEV site oligonucleotides, 1 µl each at 100 mM was used. Insert samples were spun down, annealed by incubation at 70°C for 2 min followed by incubation at 25°C for 5 min, and transformed into DH5α with selection on kanamycin plates. Select colonies obtained were screened by culturing for 4 to 6 hr in LB + kanamycin followed by PCR using the primers 5’‐cgttgcgcaaactattaactgg‐3’ and 5’‐gccgctaccagaggagttgg‐3’ to identify colonies bearing plasmids with inserts. These primers amplify a 200 bp product from the empty vector, whereas vectors bearing inserts will yield a larger product. The identity of the inserts detected were confirmed by DNA sequencing.

Detailed procedures for the ligation‐independent cloning process are provided in Basic Protocols 1 and 2, and Basic Protocol 3 describes the use of PCR to check for inserts.

Detection of expression

To test the expression of the constructs in DH5α, overnight cultures in LB with 100 µg/ml kanamycin were grown and used to inoculate 25 ml cultures in the same media. These were induced with IPTG when optical density at 600 nm (OD600) reached 0.5. Cultures were harvested 4 hr after induction, then frozen at –20°C. To determine the solubility of the constructs, samples were resuspended in 50 mM Tris pH 8.0 with 300 mM NaCl, lysed by sonication, and then centrifuged to separate soluble and insoluble fractions. Samples were then analyzed on SDS‐PAGE gels.

For lanthanide staining, gels were rinsed briefly with distilled water, then incubated with gentle shaking in 10 mM HEPES pH 7.0, 100 mM NaCl (buffer A) and then buffer A with 1 µM terbium chloride for 10 min each, followed by destaining the gel through two further washes in fresh buffer A for 10 min each. Gels were imaged on a Bio‐Rad gel imager with illumination at 280 nm. After terbium staining, gels were stained with Coomassie blue for comparison.

Dilution assay

To test the ability of inserts to confer growth, 5 ml samples were grown overnight in LB + 100 µg/ml kanamycin at 37°C then induced with 1 mM IPTG for 1 hr. The cultures were first diluted with medium to achieve OD600 = 1, and 10‐fold serial dilutions up to 10⁷‐fold of each culture subsequently prepared in 96‐well plates. All bacterial dilution series were plated in 3‐µl drops onto LB agar plates prepared containing 1 mM IPTG, with differing concentrations of ampicillin. Plates were incubated at temperatures of 22°, 30°, 37°, and 42°C for 24 and 48 hr. Plates were scored by recording the highest dilution that permitted growth for each construct on each plate. In cases where ≥2 constructs showed growth at equal dilutions, they were given equal rankings. Complete lack of growth was scored as –1. Basic Protocol 4 provides a detailed procedure for the dilution assay.

Interpretation of assay results

The design of the plate assay is that, as far as is possible, the same number of bacteria are present in each sample at a given dilution, but that different numbers of the plated bacteria from different constructs survive depending on the level of antibiotic resistance conferred by each construct. However, due to the sampling process, there will be variability in the number of bacteria that are present in different samples of the same volume. We developed a statistical measure that takes into account this intrinsic variability, deriving the probability distribution of possible population sizes that could give rise to an observed difference in the plate‐based survival assay. See Supporting Information Appendix PDF file, where part A describes this statistical measure of the original population size and of the degree of confidence that can be placed in this estimate. To summarize, the relative likelihood of the possible populations b from which a single observed plate assay result could arise is given by:

$$P\left(b\right)=\left(1-e^{-\frac{bv{d}^{k-1}}{V}}\right)e^{-\frac{bv{d}^k}{V}}$$ (1)

where V is the volume from which the sample is drawn, v is the volume aliquot placed on the plate, d is the dilution factor, and k is the dilution where failure to grow is first observed. The maximum likelihood estimate for the original population b from which a sample is drawn is:

$$b_{best}=\frac{V}{v{d}^{k-1}}ln\left(1+\frac{1}{d}\right)$$ (2)

However, this direct estimate of population size is both imprecise and biased toward overestimation (see Supporting Information Appendix PDF file, part A).

An alternative to a direct estimate of populations as a means of comparison is to determine the relative rather than absolute population size. See Supporting Information Appendix PDF file, part B, which describes the derivation of a statistical measure of the probability that one population is greater than another based on comparison of the two using a dilution assay. If a plate assay using dilution factors d shows a difference where one sample survives to a given dilution, while a second sample survives only at the n^th lower dilution, the intuitive expectation is that the first sample was drawn from a larger population. The quantity p_true represents the probability that the intuitive expectation is correct, considering the intrinsic variability of the sampling process.

$$p_{true}(d,n)=\frac{d+d^2+d^n+3d^{n+1}+3d^{n+2}}{(1+d^n)(1+d+d^{n+1})(d+d^n+d^{n+1})}$$ (3)

For the 10‐fold dilutions used in this work (d = 0.1) and for a difference of one dilution (n = 1), the degree of confidence measure p_true is ∼95%.

Experimentally, the plate assay is carried out by aliquoting a fixed volume from samples having approximately the same starting concentration of bacteria. When plated on selective media, fewer bacteria survive and form colonies than on permissive media. In this work, the population estimates P(b) and b_best obtained from a dilution series on selective medium, are considered as the effective populations which give rise to the plate assay results, providing a means to compare the growth of different constructs under a given set of conditions. Although the effective populations vary with the stringency of selection, the primary focus in this work is to determine the rank order of growth for the samples tested. For this purpose, it is unnecessary to make direct reference to these populations themselves, as only the relative growth is considered through the measure p_true .

Using our statistical framework, we develop procedures for establishing the rank order of constructs under study. Doing so establishes the relative stability of the constructs tested. We describe our approach to determination of this ordering in Supporting Information Appendix PDF file, part C. Making use of the pairwise measures p_true for each pair of constructs, we additionally derive several composite statistical measures describing the rank order. These are the probability of each possible rank ordering (P(R_k )), the probabilities of each construct m taking each place ℓ within the rank ordering [P_place (m, ℓ)], and the probability that construct m₁ ranks higher than another m₂ without regard for the particular place these occupy in a ranking [P_order (m₁, m₂ )].

Basic Protocol 1. PREPARATION OF SCREENING VECTOR suBLA FOR LIGATION‐INDEPENDENT CLONING

This protocol describes the procedure for preparing the suBLA vector for ligation‐independent cloning (LIC). The vector is first cleaved with a restriction enzyme and then treated to generate overhangs which are complementary to those on the insert. When combined with Basic Protocol 2, a successful outcome generates bacterial strains suitable for screening using Basic Protocol 5.

Materials

• suBLA vector miniprep (see Strategic Planning)

• 10× restriction enzyme buffer (e.g., rCutSmart Buffer, New England Biolabs, cat. no. B6004S, supplied with BSER1)

• H₂O, RNase‐free

• BseR1 restriction enzyme (e.g., New England Biolabs, cat. no. R0581S)

• Alkaline phosphatase, calf or shrimp (e.g., New England Biolabs, cat. nos. M0525S or M0371S)

• 10× T4 polymerase buffer containing bovine serum albumin (BSA) (e.g., New England Biolabs, cat. no. B6002S, supplied with polymerase)

• 100 mM dCTP solution (e.g., Thermo Fisher Scientific, cat. no. FERR0151)

• T4 DNA polymerase (e.g., New England Biolabs, cat. no. M0203S)

• Spectrophotometer

• Heat blocks, 37° and 75°C, or PCR machine

• Additional reagents and equipment for agarose gel electrophoresis and agarose gel‐purification

• 1Prepare suBLA vector via miniprep and elute the purified vector with RNase‐free water. Determine concentration via spectrophotometry.
• 2
  Set up BseR1 digestion:

  1. Add 5 µl of 10× restriction enzyme buffer, 4 µg of suBLA vector, and RNase‐free water to 50 µl.
  2. Mix by gentle pipetting and reserve 1 µl as pre‐digest sample.
  3. Add 1 µl alkaline phosphatase and 1 µl BseR1 restriction enzyme to the digest mixture.
• 3Mix by gentle pipetting and incubate at 37°C for 30 min.
• 4Inactivate enzymes by heat treatment at 75°C for 20 min. Reserve 1 µl as post‐digest sample.
• 5Run digest on agarose gel and gel‐purify the digested vector. Elute from gel‐purification column in 48 µl of RNase‐free water. Reserve 4 µl as post‐purification sample.
• 6Run agarose gel with size standards, pre‐digest sample, post‐digest sample, and post‐purification sample.

  The purpose of running this gel is to confirm recovery of digested vector. If the post digest sample contains a single band, digest has run to completion. The yield from gel‐purification can vary but if the post‐purification sample is clearly visible, the yield is likely to be sufficient.

• 7
  Generate complementary ends on vector. To the 44 µl of gel‐purified vector, add:

  • 5 µl T4 DNA polymerase buffer
  • 0.5 µl of 100 mM dCTP
  • 5 µl T4 DNA polymerase.
• 8Mix by gentle pipetting and incubate at 25°C for 60 min.
• 9Inactivate polymerase by heat treatment at 75°C for 20 min.
• 10Dispense LIC‐ready suBLA vector into 10 µl aliquots and freeze at –20°C until needed.

Basic Protocol 2. LIGATION‐INDEPENDENT CLONING OF INSERTS INTO SCREENING VECTOR suBLA

This protocol describes the procedure for cloning PCR products in‐frame into the split β‐lactamase construct. PCR products of a gene of interest are treated to generate ends complementary to the insert site, mixed with the vector, and transformed into the bacterial host strain. The result will be bacterial strains harboring the fusion construct.

NOTE: Before starting the protocol, run a 50 µl PCR reaction to amplify the gene of interest with primers that incorporate the LIC handles 5’−ggtagtaatagttct–3’ on the coding strand and 5’−agaggagttggtttgcgc–3’ on the noncoding strand. This starting PCR reaction may be run ahead of time and stored frozen at –20°C until needed.

Materials

• PCR reaction (see NOTE above)

• H₂O, RNase‐free

• 100 mM dGTP solution (e.g. Thermo Fisher Scientific, cat. no. FERR0161)

• T4 DNA polymerase (e.g., New England Biolabs, cat. no. M0203S)

• 10× T4 DNA polymerase buffer containing BSA (e.g., New England Biolabs NEBuffer r2.1, cat. no. B6002S, supplied with polymerase)

• LIC‐ready suBLA vector (from Basic Protocol 1)

• Competent cells of desired strain (e.g., E. coli DH5α, Invitrogen, cat. no. 18265017), thawed and placed on ice

• LB agar plates containing kanamycin (see recipe; replace ampicillin with 100 µg/ml kanamycin, Gold Bio, cat. no. K‐120‐25)

• Heat blocks, 70° and 75°C, or PCR machine

• 0.2‐ml tube

• Microcentrifuge

• Incubator, 37°C

• Additional reagents and equipment for agarose gel electrophoresis and agarose gel‐purification

• 1From PCR reaction, reserve 1 µl of amplification reaction as pre‐purification sample.
• 2Gel‐purify amplification reaction following the instruction from the gel‐purification kit. Elute product from gel‐purification column in 44 µl of RNase‐free water.

  Note that spin‐purification of PCR products may result in retention of incomplete DNA fragments which can interfere with cloning; therefore, we recommend gel‐purification at this stage.

• 3Reserve 4 µl from elution as post‐purification sample.
• 4Run agarose gel with pre‐ and post‐purification samples to check recovery yield.
• 5
  Generate complementary ends on insert. To gel‐purified insert, add:

  • 5 µl T4 DNA polymerase buffer
  • 0.5 µl of 100 mM dGTP
  • 1 µl T4 DNA polymerase
• 6Mix by gentle pipetting and incubate at 25°C for 60 min.
• 7Inactivate polymerase by heat treatment at 75°C for 20 min.
• 8At this point the LIC‐ready inserts may be frozen at –20°C if desired.
• 9To clone the inserts, add 1 µl of LIC‐ready suBLA vector and 1 µl of LIC‐ready insert to a 0.2‐ml tube and pulse in centrifuge for 5 s at 14,000 × g, room temperature.
• 10Incubate the mixture at 70°C for 2 min, then at 25°C for 5 min.
• 11Add 50 µl of competent cells, mix by gentle pipetting.
• 12To 50 µl of competent cells, add 1 µl of LIC‐ready insert as insert‐only control.
• 13To 50 µl of competent cells, add 1 µl of LIC‐ready vector as vector‐only control.
• 14Proceed with transformation. Plate transformed cells on LB/kanamycin agar plates and incubate at 37°C overnight.
• 15Check colonies for inserts by PCR (Basic Protocol 3) or by sequencing.

Basic Protocol 3. USE OF PCR TO CHECK FOR INSERTS

This protocol described the procedure for screening potential clones. Individual colonies are cultured and screened by PCR for the presence of inserts. Cultures containing inserts of the correct size are saved as glycerol stocks and sequenced. When the desired sequence has been confirmed, strains are ready for the dilution assay (Basic Protocol 4).

Materials

• LB plates with bacterial colonies (from Basic Protocol 2)

• LB broth (see recipe) supplemented with 100 µg/ml kanamycin (Gold Bio, cat. no. K‐120‐25)

• PCR reagents:

  • Polymerase (e.g., New England Biolabs Q5 Hot Start Polymerase, cat. no. M0493S)

  • 10 mM dNTPs (e.g., Invitrogen, cat. no. 18427013)

  • 5× buffer (e.g., New England Biolabs Q5 Buffer, cat. no. B9027S)

• H₂O, RNase‐free

• 10 µM insert check primer 1: 5’‐ cgttgcgcaaactattaactgg‐3’

• 10 µM insert check primer 2: 5’‐gccgctaccagaggagttgg‐3’

• 100 bp ladder (e.g., Gold Bio, cat. no. D001‐500)

• 50% glycerol (e.g., Sigma‐Aldrich, cat. no. G5516)

• Sterile test tubes

• Shaking incubator set to 37°C

• Sterile 8‐strip PCR tubes

• Sterile microcentrifuge tube

• PCR machine

• Additional reagents and equipment for agarose gel electrophoresis, agarose gel‐purification, and mini‐preps

• 1Label test tubes with strain and colony numbers (e.g., label the tube for strain 4, colony 2 as “4.2.”).

  Testing 2 or 3 colonies for each strain is usually sufficient.

• 2Add 5 ml LB broth with kanamycin to each tube and inoculate with a single colony.
• 3Incubate tubes at 37°C with shaking for 2 to 3 hr.
• 4Label PCR strip tubes with strain and colony numbers.
• 5
  Prepare PCR reaction pool in a 1.5‐ml microcentrifuge tube. Recipes for 20‐µl test reactions (1, 8, 16, or 24) are below. To analyze a different number of colonies, multiply the single reaction volumes by the desired number.

  Component	8 Reactions (µl)	16 Reactions (µl)	24 Reactions (µl)	1 Reaction (µl)
  5× PCR buffer	32	64	96	4
  RNase‐free water	99.2	198.4	297.6	12.4
  dNTPs (10 mM)	3.2	6.4	9.6	0.4
  Primer 1 (10 µM)	8	16	24	1
  Primer 2 (10 µM)	8	16	24	1
  Polymerase	1.6	3.2	4.8	0.2

• 6Mix pool thoroughly by gentle pipetting.
• 7Aliquot 19 µl of PCR pool into PCR strips.
• 8Add 1 µl of the cultures from step 3 as template.
• 9
  Place tubes in PCR machine and run the program as follows.

  1. Lysis/Denaturation: 98°C for 30 s.
  2. Denaturation: 98°C for 10 s.
  3. Annealing: 65°C for 10 s.
  4. Extension: 72°C for 10 s.
  5. Repeat b to d (denaturation, annealing, extension) 25 times.
  6. Final extension: 72°C for 120 s.
  7. Hold: 4°C until needed.

  We used Q5 Hot Start Polymerase (New England Biolabs). Adjust extension times, temperatures, and volumes as appropriate for other polymerases.

• 10Run all reactions on agarose gel. Be sure to include 100 bp ladder. Optionally, include lanes with purified inserts from Basic Protocol 2, step 8, for use as a size standard.

  The insert check primers are complementary to locations 100 bp upstream and downstream of the LIC site on suBLA and so will produce a 200 bp amplification product from the empty vector. Successful incorporation of inserts will result in an amplified product the size of the desired insert plus 200 bp. Therefore, appearance of a 200 bp product indicates that the cloning was unsuccessful, whereas the larger product indicates that the cloning succeeded.

• 11Discard cultures which gave rise to a 200 bp amplification product.
• 12Make glycerol stocks from cultures which gave rise to amplification products with the correct size (insert size + 200 bp).
• 13Allow the insert‐containing cultures to grow overnight.
• 14Miniprep cultures and sequence resulting plasmids using primer 1, or both primers 1 and 2 for long inserts.

  Sequencing is sufficiently inexpensive and rapid that it may be more convenient or efficient to forgo this analysis step and simply sequence the plasmid produced from selected colonies to identify clones; however, if problems are encountered, checking the inserts may be helpful for troubleshooting.

Basic Protocol 4. DILUTION SERIES ASSAY

This protocol describes the procedure for carrying out the dilution assay. Overnight cultures are diluted to OD600 = 1 and a dilution series for each sample is prepared in a 96‐well plate. Samples from the 96‐well plate are then transferred to a set of agar plates containing a range of ampicillin concentrations and incubated over a range of temperatures. The result will be plates on which growth of strains to higher dilutions allows comparison of the stability of the corresponding inserts.

Materials

• Glycerol stocks of strains harboring suBLA with inserts (see Basic Protocol 3)

• LB broth (see recipe) supplemented with 100 µg/ml kanamycin (e.g., Gold Bio, cat. no. K‐120‐25)

• Labeled LB agar plates with 1 mM IPTG and varying concentrations of ampicillin (see recipe)

• Incubator, 37°C

• Spectrophotometer

• Sterile 100‐mm Petri dish or pipetting reservoir

• Sterile pipette

• Sterile 96‐well plate

• 8‐channel pipettors capable of dispensing 3, 30, and 270 µl

• Camera

NOTE: An important aspect of the assay is the number and variety of plates needed. In this work we described two formats for the assay: the wide range assay and the narrow range assay. Other choices may be more appropriate for different constructs. The wide‐range assay was used initially to identify the most informative conditions and employed antibiotic concentrations over a wider range. It consisted of two replica plates (A and B) at each of four antibiotic concentrations (2, 4, 8, and 16 µg/ml) and three temperatures (22°, 30°, and 37°C). This required 6 plates for each antibiotic concentration for a total of 24 plates. The narrow range assay, used subsequently, employed 2 replica plates (A and B) at 5 antibiotic concentrations (4, 6, 8, 10, and 12 µg/ml) and 2 temperatures (30° and 37°C). There were 4 plates for each antibiotic concentration for a total of 20 plates.

• 1Inoculate 5 ml cultures of each strain in LB/kanamycin and grow overnight at 37°C.
• 2Measure OD600 of each sample using a spectrophotometer and assign numbers 1 through 8 to samples. These numbers will correspond to the rows of the 96‐well plate. Ensure that each is OD600 >1.
• 3
  Calculate quantity of culture and medium needed for 300 µl of culture diluted to OD600 = 1 as follows:

  1. Amount of culture in µl = 300/OD600.
  2. Amount of medium in µl = 300 – 300/OD600.
• 4Add 20 ml of LB + kanamycin medium to Petri dish or reservoir using sterile pipette.
• 5To wells of columns 2 to 8 of a 96‐well plate, transfer 270 µl of medium from reservoir using multichannel pipettor. Cover plate with lid between additions to reduce chance of contamination.
• 6To wells of column 1 of the 96‐well plate, add quantity of culture and medium determined in step 3 and mix by gently pipetting up and down 10 times. Place sample 1 in row 1 of the 96‐well plate, sample 2 in row 2, etc.
• 7Using multichannel pipettor, transfer 30 µl of contents of wells in column 1 to column 2 of 96‐well plate and mix by gently pipetting up and down. Column 2 will therefore contain a 10‐fold dilution of column 1.
• 8Repeat process in step 7 for columns 2 to 8 to create dilution series of all strains. The different strains are arrayed in the rows, and the successive dilutions of each strain are arrayed in the columns.
• 9Line up the group of agar plates containing the first antibiotic concentration adjacent to the 96‐well plate with covers on.

  We recommend dispensing drops on small groups of 4 to 6 plates to reduce the chance of losing track.

• 10Using a multichannel pipettor, dispense 3‐µl drops from 96‐well plate onto agar plates.

  We recommend dispensing column wise, as drops aligned vertically will facilitate comparison between strains at a given dilution. Use the grid markings on the agar plates as references to maintain alignment and spacing of drops. To minimize chances of contamination, remove lid from 96‐well plate only while removing samples, and remove lids from agar plates only while dispensing samples. While dispensing drops, refrain from moving plates.

• 11Repeat steps 9 and 10 for the next group of plates until all plates are complete.
• 12After dispensing drops onto plates, avoid moving plates until drops are fully absorbed into surface of agar and no liquid remains on the surface of the agar.

  Typically, 20 min is sufficient.

• 13Incubate plates at desired temperatures (e.g., 30° and 37°C) for 24 hr.
• 14Record status of growth by photographing plates using a camera. Ensure each image contains label with ampicillin concentration, incubation temperature, and time of incubation, e.g., by simply including a Post‐it note containing this information.

Basic Protocol 5. SCORING OF DILUTION ASSAY

This protocol describes the procedure for interpreting the results of the dilution assay in a form suitable for rank order analysis (Basic Protocol 6).

Materials

• Images of dilution assay plates (from Basic Protocol 4)

• 1Create a CSV‐format spreadsheet with columns headed with date, ampicillin concentration, incubation temperature, replicate, and strains 1 to 8. Each line in the spreadsheet will correspond to a single plate.
• 2For each plate, enter the date, ampicillin concentration, incubation temperature, and replicate in the appropriate columns.
• 3For each strain, record the highest dilution where growth can be discerned in the corresponding column.

  For example, if growth can be observed for a given strain at the 10³‐fold dilution but not in the 10⁴‐fold dilution, record a 3 for that strain.

• 4Record a score of –1 for samples with no visible growth.
• 5Repeat steps 2 to 4 for each plate.

Basic Protocol 6. STATISTICAL ANALYSIS OF DILUTION ASSAY

This protocol describes the procedure for carrying out the statistical analyses described in the text. Three Jupyter notebooks containing python scripts to carry out examples of the statistical analyses are provided in the Supporting Information. Pseudocode for these calculations is provided below.

Necessary Resources

Hardware

Computer with internet access

Software

Spreadsheet in CSV format containing scores (from Basic Protocol 5)

Environment for running Jupyter notebooks (e.g., Anaconda Navigator)

Web browser

Files (see Supporting Information)

cpz170479‐sup‐0001‐SuppMat.ipynb

• This script reads the raw data and calculates the statistical weights w_k and the probability P(R_k) for all rankings R_k. It also generates a graphic for visualization of the ranking probabilities.

cpz170479‐sup‐0002‐SuppMat.ipynb

• This script first calculates the ranking weights w_k and probabilities P(R_k) and then and then uses them to calculate the ranking statistic P_place from them. It also generates a graphic for visualization of the values of P_place .

cpz170479‐sup‐0003‐SuppMat.ipynb

• This script first calculates the ranking weights w_k and probabilities P(R_k) and then uses them to calculate the ranking statistic P_order from them. It produces the values of P_order arrayed in a matrix as shown in the Commentary section.

cpz170479‐sup‐0005‐SuppMat.csv (sample data file for wide range assay)

cpz170479‐sup‐0006‐SuppMat.csv (sample data file for narrow range assay)

• 1Place scripts and CSV files into same directory.
• 2Open desired script with Jupyter notebooks, which will open a tab in your web browser application. The scripts are organized into a minimal number of cells containing groups of commands.
• 3Change the line defining the string data_name_str in cell 3 to reflect the name of the CSV file containing desired data.
• 4Run all cells in the notebook by selecting the “Run all cells” command from the “Run” pulldown menu.
• 5Results will appear below the final cell when the calculations are complete.

Pseudocode

• 1Read data stored in csv.
• 2Select strains to include in analysis.
• 3Create list of dilution scores for each plate.
• 4Create list of permutations.
• 5Create sortable list to store statistical weight for each ranking.
• 6Initialize Z (sum of statistical weights) to zero.
• 7
  Calculate Z. For each ranking:

  • 7.1 Initialize statistical weight w_k for current ranking to zero.
  • 7.2 Calculate contribution to statistical weight from all plates for current ranking. For each plate:
    • 7.2.1 Calculate p_true values for all pairwise combinations of strains on current plate.
    • 7.2.2 Combine pairwise probabilities into statistical weight for current plate.
    • 7.2.3 Add statistical weight for current plate to statistical weight for current ranking.
    • 7.2.4 Repeat 7.2.1 to 7.2.3 for all plates.
  • 7.3 Store statistical weight and current ranking in sortable list.
  • 7.4 Add statistical weight for current ranking to Z.
  • 7.5 Repeat 7.1 to 7.4 for all rankings.
• 8Divide statistical weights in sortable list by Z to convert them into probabilities.
• 9Sort the rankings in sortable list by probability.

Script B: Calculation of P_place(m, ℓ)

Steps 1 to 7 are identical to those in script A, and the following steps are simply concatenated onto it.

• 8
  Calculate P_place (m, ℓ).

  • 8.1 Create matrix Pplace_mat to store values.
  • 8.2 Loop through list of weights. For each ranking:
    • 8.2.1 Divide corresponding weight by Z to convert to probability of current ranking.
    • 8.2.2 Loop through places in current ranking. Add probability of current ranking to location corresponding to (strain, place) in Pplace_mat.

Script C: Calculation of P_order(m, ℓ)

Steps 1 to 7 are identical to those in script A. There is no step 8 in this script. If desired step 9 may be concatenated with script B. The numbering is intended to avoid confusion with step 8 in script B.

• 9
  Calculate P_order .

  • 9.1 Create matrix to store P_order values.
  • 9.2 Create matrices of rows and columns of strain indices.
  • 9.3 Fill matrix with P_order values. For each pairwise combination of strains:
    • 9.3.1 Calculate P_order for current pair. For each ranking:
    • 9.3.1.1 Divide weight for current ranking by Z to convert to probability.
    • 9.3.1.2 Add probability for current ranking to P_order value for current pair of strains.

REAGENTS AND SOLUTIONS

Ampicillin, 100 mg/ml

Weigh 1 g of ampicillin sodium salt and dissolve in 10 ml of deionized distilled water. Sterilize with 0.22‐micron syringe filter into a 15‐ml tube. Store up to 1 week at −20°C.

IPTG, 1 M

Weigh 2.383 g of isopropyl β‐d‐thiogalactoside (IPTG) (Gold Bio, cat. no. 12481C5) and dissolve in 10 ml of deionized distilled water. Sterilize with 0.22‐micron syringe filter into a 15‐ml tube. Store up to 1 week at −20°C.

LB broth and LB agar plates

For LB broth:

To prepare plates with 2, 4, or 6 antibiotic concentrations, first make 1, 2, or 3 L of LB broth, respectively. To a 4‐L beaker, add:

Ingredient	For 1 L	For 2 L	For 3 L
Tryptone (Thermo Fisher Scientific, cat. no. 211705)	10 g	20 g	30 g
Yeast extract (Thermo Fisher Scientific, cat. no. 212750)	5 g	10 g	15 g
NaCl (Thermo Fisher Scientific, cat. no. J21618.A7)	10 g	20 g	30 g
ddH2O	To 1 L	To 2 L	To 3 L

Add a stir bar and stir until all components are dissolved. Add 1 M NaOH (Current Protocols, 2006) to adjust to pH 7.0.

• For LB agar:

For each antibiotic concentration needed, prepare 500 ml LB agar. To a 1‐L Pyrex bottle, add 7.5 g agar (Thermo Fisher Scientific, cat. no. LP0011T) and a small Teflon‐coated autoclavable stir bar. Add 500 ml LB broth to each bottle, stir briefly on stir plate to break up solid clumps, and sterilize by autoclaving. After autoclaving, place bottles in a 60°C water bath and allow to equilibrate. Arrange plates from 1 sleeve on clean surface sterilized with 70% isopropanol. Label side of plate with desired antibiotic concentration. Take bottle containing liquid LB agar from water bath and add appropriate amount of 100 mg/ml ampicillin (see recipe) to achieve desired concentration:

Concentration (µg/ml)	2	4	6	8	10	12	14	16	18	20
Volume per 500 ml (µl)	10	20	30	40	50	60	70	80	90	100

Add 500 µl of 1 M IPTG (see recipe) to the bottle. Stir on stir plate to mix in antibiotic and IPTG. Avoid introducing bubbles. Remove lid from each plate, pour ∼25 ml of agar into plate, and replace lid slightly offset to allow moisture to escape. Repeat the LB agar recipe for each antibiotic concentration needed. Discard unused agar.

Use sterile 100 × 100–mm square gridded Petri plates. We recommend preparing plates containing a single antibiotic concentration in batches of 20 (typically one sleeve), each of which requires 500 ml of agar. We found it helpful to prepare the plates 2 days ahead of the actual assay to allow time for the plates to dry thoroughly. Alternatively, premixed LB agar can be used.

COMMENTARY

Results

Cloning and expression

The ligation‐independent cloning site enabled convenient construction of the constructs used in the assay. The T5 promoter functioned in DH5α as evidenced by expression detected on sodium dodecyl sulfate–polyacrylamide gel electrophoresis (SDS‐PAGE), and expression of the fusion constructs was confirmed by terbium staining (Fig. 3).

Figure 3.

Detection of split β‐lactamase construct expression in DH5α. Top: Coomassie‐stained SDS‐PAGE gel of insoluble (P) and soluble (S) fractions of bacterial cell lysate. Bottom: Terbium‐stain of same gel. Yellow arrows at left indicate expected positions of fusion constructs (∼55 kDa). Fusion proteins can be detected in the insoluble fractions but little to none is detected in the soluble fractions.

Split β‐lactamase assays

In an initial broad range assay, the serial dilutions of construct‐containing strains were spread onto plates with 2, 4, 8, and 16 µg/ml antibiotic concentrations and incubated at 25°, 30°, 37°, and 42°C. The assay was performed with 2‐fold technical replication and results observed at 24 and 48 hr. At 25°C, little or no growth was observed at 24 hr, but growth was observed at 48 hr. At the intermediate temperatures of 30° and 37°C, clear differences in the growth of the constructs became apparent. Negligible growth was seen at 42°C for all constructs, even after 48 hr, so the 42°C condition was eliminated from subsequent experiments. Figure 4 details the scoring scheme employed for a single plate.

Figure 4.

Scoring of dilution assay plate. Serial 10‐fold dilutions of samples are arrayed from left to right for each construct. The dilution factor (top) is the factor by which the original sample (first adjusted to OD600 = 1) has been diluted, e.g., the original OD600 = 1 sample is in the 10⁰ column, while in the 10²‐dilution column, the samples have been diluted 100‐fold. The score for each strain is the highest dilution (bottom) at which growth is observed. The Mapuera, SV5, and mumps strains show growth at the 10¹‐fold dilution, and so are given a score of 1. Under these conditions the suBLA vector control shows no growth and so is scored at –1. The scores are: suBLA = –1; Mapuera = 1; SV5 = 1; mumps = 1; measles = 2; HPIV‐4b = 3; and cb562 = 3. For this plate, the antibiotic concentration was 8 µg/ml, and the plate was incubated at 30°C.

To assess the reproducibility of the assay, three successive replicates (1, 2, and 3) of the broad range assay using antibiotic concentrations of 2, 4, 8, and 16 µg/ml incubated at 22°, 30°, and 37°C were carried out, again using two replicate plates (A and B) with reads at 24 and 48 hr. Results are shown in Figure 5. In general, higher temperatures and higher antibiotic concentrations result in more stringent selection, as expected. Comparison of the relative growth at these conditions reveals that the strain harboring the cb562 construct shows the most robust growth, followed by the foot domain‐containing constructs HPIV‐4b, measles, mumps, SV5, and Mapuera. The weakest growth is shown by the strain with the suBLA vector without an insert (i.e., the empty vector, which serves as the negative control).

Figure 5.

Broad range assay: Survival curves. Plots show the mean and standard deviation of the highest dilution with growth at 22° (left panels), 30° (middle panels), and 37°C (right panels) after 24 (top panels) and 48 hr (bottom panels). Constructs are identified by color key. The data are the mean of 6 measurements for each condition (3 separate experiments with 2‐fold technical replication). Qualitatively, the mean of the growth curves appears generally consistent with the known order of stability of the isolated domains under most conditions. However, different conditions do suggest slightly different orderings. For example, the measles strain appears to outgrow the HPIV‐4b strain under a subset of the conditions tested, while under the majority of conditions, the HPIV‐4b strain survives under more stringent selection. Interpretation by visual inspection is rendered more difficult as the uncertainty in the data appears to exceed the differences between strains.

Results of the split β‐lactamase assay appear consistent with the order of stability of the inserted foot domains as determined through biophysical approaches (Yegambaram et al., 2013). However, there are examples where apparently contradictory results from replicate plates are recorded, as expected from the sampling process (see Supporting Information Appendix PDF file, part B). In addition to these statistical fluctuations arising from the sampling process, there is also experimental variation in the measurements of growth which can be seen through comparison of separate replicates, i.e., identical experiments carried out at different times (Fig. 5). Each technical replicate entailed measurement of the highest dilution where growth appeared for 7 constructs at 4 antibiotic concentrations, 3 temperatures, and 2 time points, or 168 conditions. Correlation of the 504 measurements of growth between the A and B plates from all assays (which compares measurements within a single replicate) gives a correlation coefficient of 0.97. In contrast, pairwise correlation coefficients between replicates 1, 2, and 3 (which compare measurements between separate replicates) gave correlations of 0.75, 0.83, and 0.87.

A measure of the discriminatory power of each condition is the range of dilutions over which the strains containing the different constructs survive. In general, the most informative conditions, those where there is the greatest difference in growth between the different constructs, were 4 and 8 µg/ml antibiotic at 30° and 37°C. In a second round “narrow range” assays, a finer sampling of antibiotic concentrations at 4, 6, 8, 10, and 12 µg/ml was used at 30° and 37°C. Figure 6 shows a comparison of plates over this concentration range at the two temperatures tested, and Figure 7 shows the survival curves for one technical replicate.

Figure 6.

Narrow range assay: Comparison of growth. In general, ranking the relative growth of constructs requires comparison across multiple conditions. Comparison of the SV5, mumps, and measles constructs at 30°C shows that the SV5 construct has weaker growth at 8 µg/ml. The mumps and measles constructs have similar behavior, but the measles construct appears to grow weakly at a 10²‐fold dilution at 10 µg/ml where the mumps construct does not (red arrow). In contrast, at 37°C and 10 µg/ml antibiotic, the mumps construct appears to have weak growth where the measles construct does not (blue arrow). In this second group of assays, an additional construct suBLA‐TEV is used, in which a short peptide linker was placed at the insertion site.

Figure 7.

Narrow range assay. Survival curves for one replicate of the narrow range assay (5 antibiotic concentrations, with plates incubated at 2 temperatures). The number of ties is greatly reduced compared to the broad range assay, and where ties do occur the relative growth of strains may be resolved by comparison between different conditions. For example, while the growth of the HPIV‐4b strain (cyan) and suBLA‐TEV strains (purple) are identical at 30°C, a difference in their relative growth becomes apparent at 37°C.

Critical Parameters

Basic Protocols 1 to 3

These protocols detail the preparation and analysis of the strains needed for the split β‐lactamase assay and consist of routine molecular biology techniques (plasmid construction, enzymatic treatment, PCR, and bacterial cell culture) for which many resources exist. The PCR amplification reactions will need to be modified to take into account different sized inserts. For ligation‐independent cloning, note that in preparation of the vector (Basic Protocol 1), the T4 polymerase treatment requires dGTP, while in the preparation of the inserts (Basic Protocol 2), dCTP is used.

Basic Protocol 4

The main task in the split β‐lactamase assay itself is to adjust the stringency of selection to reveal differences in the growth of strains. Lower antibiotic concentrations and lower temperatures reduce the stringency, while higher antibiotic concentrations increase the stringency. We found it helpful to first carry out assays over a wide range of antibiotic concentrations and temperatures (the wide range assay), using 2, 4, 8, and 16 µg/ml antibiotic, and 25°, 30°, 37°, and 42°C to identify the most informative conditions. For the inserts used here, these proved to be an antibiotic concentration of 8 µg/ml and temperatures of 30° and 37°C. We then carried out a second set of assays at these temperatures centered around the 8 µg/ml antibiotic concentration (the narrow range assay) to resolve differences more finely between the strains.

While finer sampling of the antibiotic concentration or temperatures has the potential to reveal subtle differences between the growth of strains, it also necessitates the use of larger numbers of plates. The combinatorial possibilities can quickly become an organizational and experimental challenge. Moreover, assays with similar conditions tend to yield redundant results, and may not prove very informative. Conditions where ties are minimized are the most useful. Therefore, there is a balance to be achieved in selecting a sufficiently wide range of conditions to document the differences between strains, while keeping the number of plates to a convenient size. Some experimentation may be necessary to determine the appropriate conditions.

A mild technical challenge when dispensing the dilution series onto the plates is that drops may run together, making it impossible to compare conditions. This occurrence may be avoided by first ensuring that the surfaces of the agar plates are quite dry, which facilitates absorption. If the agar surface appears shiny, it is likely too moist, and drops will run when placed upon it. Another potential problem is that movement of the plates before the drops have been fully absorbed will likely cause the drops to run into one another.

We found that 100 × 100–mm square Petri plates accommodated 8 strains dispensed from a standard 8‐channel multichannel pipettor using 3‐µl drops. The statistical analysis can accommodate any number of strains, but as a practical matter it would require a different experimental format to compare >8 strains directly.

Troubleshooting

See Table 2 and Table 3 for troubleshooting guides for ligation‐independent cloning and for the split β‐lactamase assay, respectively.

Table 2.

Troubleshooting Guide for Ligation‐Independent Cloning

Problem	Possible cause	Solution
No colonies	Failure of insert and vector to anneal	Remake LIC‐ready insert and vector; be sure to use dCTP for T4 polymerase treatment of vector, and dGTP for treatment of insert
Many colonies: few or no inserts	Incomplete or failed digestion of vector with BseR1, or contamination of linearized vector with circular vector	Repeat LIC‐ready vector preparation; be sure to separate linearized vector from circular vector by gel‐purification
Colonies present from vector‐only control	Incomplete or failed digestion of vector with BseR1, or contamination of linearized vector with circular vector	Repeat LIC‐ready vector preparation; be sure to separate linearized vector from circular vector by gel‐purification
Colonies present from insert‐only control	Failure to separate template and amplification product	Repeat LIC‐ready insert preparation; be sure to separate amplified insert from template by gel‐purification

Table 3.

Troubleshooting Guide for Split β‐Lactamase Assay

Problem	Possible cause	Solution
Smeared or uneven‐shaped spots on dilution assay	Drops ran or moved	Be sure to dry plates sufficiently before dispensing drops; avoid bumping plates while dispensing drops; allow drops to be absorbed into agar before moving to incubator
Few differences in growth between plates	Plate growth conditions are too similar	Increase difference in stringency of selection between plates by using larger antibiotic concentration differences or larger temperature differences

Statistical Analysis

The survival curves in Figure 5 provide a qualitative view of the relative growth of the different strains; however, a quantitative approach to interpretation of such data has been lacking. To address this need, we developed a probability‐based rank ordering scheme which provides a way to quantify the results of these experiments and determine the relative domain stabilities. The theoretical basis of the method is developed in the Appendix PDF file in Supporting Information. In our rankings the constructs conferring the greatest antibiotic resistance are ranked first.

The most obvious approach to comparison of the constructs is to determine the ranking with the highest probability P(R_k ) (Supporting Information Appendix PDF file, Equation C.3). However, the major issue with this approach is that there are many alternative rankings with almost equal probabilities. Figure 8 shows the 10 rankings with the highest probability. For the data set illustrated in Figure 5, the ranking with the highest P(R_k ) is cb562 > measles > HPIV‐4b > mumps > SV5 > Mapuera > suBLA. However, there is little separation in probabilities between this and the next most probable rankings, so in this case the absolute ranking may not be particularly informative. It should be noted that because these are rankings of 7 constructs, there are 7! = 5040 possible rankings, hence the absolute probability of even the most likely is rather small. Among the top 10 rankings, the cb562 construct clearly confers the greatest growth, while the suBLA and Mapuera constructs confer the weakest growth. However, as these top 10 together account for only ∼5% of the aggregate probability of all rankings, the examination of individual rankings does not seem to provide a path for making definitive inferences.

Figure 8.

Top 10 rankings: Wide range assay. Rankings with the 10 highest values of P(R_k ) are illustrated using the color coding for the strains at left. For example, the highest probability ranking corresponds to the ordering cb562 > measles > HPIV‐4b > mumps > SV5 > Mapuera > suBLA. The corresponding probabilities P(R_k ) are shown at right.

Consequently, instead of making conclusions from just the top ranking, or even the top 10 rankings, we employ the more rigorous approach of constructing a statistic that takes into account the probability of all rankings. The quantity P_place (m, ℓ) (Supporting Information Appendix PDF file, Equation C.6) gives the probability for each construct m that it will fall in the ℓ^th place in the ranking, as determined by the weighted average over all possible rankings. Figure 9 shows P_place (m, ℓ) for all constructs, calculated from the narrow range assay data (Fig. 7). In calculating these P_place (m, ℓ) using the data from these 8 constructs, the weights from all 40,320 possible rankings were used. The probability for each construct is distributed over the 8 places. From this analysis, it is clear that the controls cb652 and suBLA‐TEV are the most robust constructs overall, and the empty vector suBLA is the weakest, with the paramyxoviral foot domains in the mid rank positions.

Figure 9.

Comparison of all constructs. Comparison of P_place (m, l), where m delineates the constructs (labeled at top) and l indicates their place in each ranking. Each bar indicates the sum of weights w_k for the rankings R_k in which the indicated construct m occupies the place l. At left, all 8 constructs were used in the calculation of P_place , and at right, only the five foot domain inserts were used. Data is from the narrow range assay.

While the controls are valuable in assessing the effectiveness of the assay, including them in the ranking has the effect of distributing the probability for the foot domains over 8 places, because the foot domain constructs are compared against all tested constructs. For the purposes of comparing the foot domains among themselves, more resolution between them can be obtained by recalculating P_place (m, ℓ) using only the data for the constructs of interest. The outcome of this calculation is shown in Figure 9. From these data, there is a strong basis for concluding that HPIV‐4b ranks first and that Mapuera ranks last. The analysis ranks measles, mumps, and SV5 as second, third, and fourth, respectively, although the separation between these is less pronounced.

A complementary approach, facilitating pairwise comparison of constructs, is to compute the quantity P_order (m ₁ , m ₂), which is the probability that construct m ₁ ranks ahead of m ₂, averaged over all rankings. Table 4 gives the value of P_order for the five foot domains, as calculated from the narrow range assay. This statistic finds it to be 83% likely that the HPIV‐4b construct ranks ahead of the measles construct. The calculation also yields the estimates that it is ∼56% likely that the measles construct outranks the mumps and SV5 constructs, but that there is little basis for ranking the mumps construct ahead of the SV5 construct, as P_order is very close to 50% for this pair. While the different statistical measures differ in some particulars, both P_place and P_order are consistent with the order suggested by biophysical analysis of foot domain stability (Yegambaram et al., 2013).

Table 4.

P_order (m ₁ , m ₂) Matrix ^a

Construct	HPIV‐4b	Measles	Mumps	SV5	Mapuera
HPIV‐4b		0.1334	0.13068	0.1434	0.0527
Measles	0.8666		0.4428	0.4424	0.1680
Mumps	0.8694	0.5572		0.4996	0.2018
SV5	0.8566	0.5576	0.5004		0.1463
Mapuera	0.9473	0.8320	0.7982	0.8537

^a Pairwise Probability that constructs m ₁ (top) are ranked higher than constructs m ₂ (left) as determined by sum of weights for rankings where construct m ₁ precedes construct m ₂.

Understanding Results

Applicability of split β‐lactamase assay to low stability proteins

Foit et al. (2009) showed that growth in the split β‐lactamase assay correlated strongly with thermodynamic stability for both stabilized and destabilized variants of 4 proteins of varying size, structure, and properties with a range of stabilities. Indeed, the method showed promise for general applicability irrespective of the structure or properties of the target protein. The proteins tested in these experiments were those for which stability measurements could be readily made, i.e., structured globular proteins which fold in a 2‐state manner. The motivation for the current work was to examine whether the assay could be applied even more widely to proteins existing at the lower edge of the protein stability spectrum. Here we have applied it to a group of polypeptides which can realize the same folded state but may exist natively in the molten globule or even largely unstructured state. While a quantitative measure of stability for proteins in this regime may not be well‐defined, it proved possible to resolve differences between these constructs.

Experimentally, the methods described here are inexpensive and accessible to most laboratories. The assay, as implemented here, requires only basic equipment for molecular biology. It allows the cloning and screening of constructs to be performed within a single bacterial strain, with no need to transfer plasmids into a specialized expression strain. Staining with terbium allows specific detection of expressed constructs to confirm expression without resorting to western blots, requiring only a UV transilluminator.

Conceptually, the assay provides an empirical but experimentally based metric that for stable proteins relates to thermodynamic stability as formally understood. This can be seen by comparing results for the cb562 and the HPIV‐4b constructs (Fig. 9). For these two constructs, the standard Gibbs energies of unfolding have been reported [cb562, ∆G_unf = 47.3 kJ/mol (Kamiya et al., 2001; Robinson et al., 1997); HPIV‐4b, ∆G_unf = 13.5 kJ/mol (Yegambaram et al., 2013)] and the results of the plate assay are consistent with those data.

However, we have shown here that the assay is also applicable to unstable proteins that lack a well‐defined stability measure. Some of the foot domains are conditionally disordered, appearing partially (mumps, SV5) or even entirely (Mapuera) unstructured when studied in isolation. Nevertheless, these proteins can realize a specific folded state, dependent on biological context or physiochemical environment (Hausrath & Kingston, 2017). While the stability of these kinds of proteins cannot be interpreted within a 2‐state framework, the assay shows the capacity to resolve subtle differences in structure formation. The rank ordering of stability suggested by analysis of the assay data (Fig. 9) is consistent with what is known about extent of structure within the mumps, SV5, and Mapuera virus foot domains (Yegambaram et al., 2013).

The molecular basis by which an insert confers the ability to grow deserves some consideration. The relatively strong growth shown by the suBLA‐TEV construct, which bears a simple peptide linker, approaches that shown by the cb562 construct. This observation is consistent with the interpretation that the assay reports on the relative ability of inserts to draw the two parts of the β‐lactamase together. This might control the activity of the β‐lactamase directly, as depicted in Figure 1C, but could also act through alternative mechanisms, such as differential susceptibility to proteolysis or relative expression level. In the case of an insert which consists of an entire protein, the stability of that insert, or equivalently, the extent to which the protein folds to a compact structure confers the ability to grow. But such growth is dependent on enzyme activity, which seems unlikely to exceed that of the native β‐lactamase. This predicts that if increasingly stable inserts are placed into the β‐lactamase, eventually no difference in growth would be discernable. In the case of a short peptide linker, the two parts of the β‐lactamase cannot be physically distant (even at elevated temperatures) and confers the ability to grow, although by a different mechanism.

With this picture in mind, the assay would seem to be well‐suited for comparison of constructs at the opposite end of the stability spectrum, where no such limit exists. But appropriate growth conditions (lower temperatures and reduced antibiotic concentrations) must be employed for constructs in this regime. Experimentally, lower temperatures generally were more permissive than higher temperatures. However, because E. coli grows more slowly at temperatures below its optimal growth temperature of 37°C, it is important to avoid conflating slow growth due to temperature and weak growth due to the instability of an insert. In this work we took the empirical approach of comparing growth at fixed times but over variable temperatures and antibiotic concentrations. The interplay between these factors underscores the need for both a positive control (e.g., the robust grower cb562, or the suBLA‐TEV construct) to reveal the temperature range which supports growth, and a negative control (e.g., the empty vector) to reveal the antibiotic concentration required to prevent growth without additional stability conferred by the insert.

Reproducibility and internal consistency of assay results

The reproducibility of results for replicates measured on the same day is very good (97% correlation). However, there is significantly greater variation between the results of measurements made on different days (75% to 85% correlation). We interpret this difference as arising from distinct sources of variability.

The nature of the dilution assay is that by necessity, small numbers of surviving colonies are present in dilutions near the boundary between growth and lack of growth. Ultimately, the objective of the dilution assay is to estimate the point where there is a similar probability of finding a colony or not finding a colony. Determination of this point is intrinsically subject to the fluctuations attendant on measurements of small numbers and cannot be eliminated. The measurements from within an individual replicate must necessarily reflect this property of the dilution assay.

Comparison of the results between distinct replicates are subject to this intrinsic variability, but in addition, to other common sources of experimental error. For example, small variations between replicates in incubation temperature or humidity could affect the growth on the assay plates. If a small difference of this type allowed all the plates of a given replicate to grow slightly better, the resulting scores might differ from those derived from a prior replicate. But although growth of the whole replicate might be slightly greater, the more relevant information for comparison of strains is the relative growth of strains on a given plate rather than the absolute conditions of growth.

Examination of the raw data (see Fig. 6) illustrates that it is difficult to find a single condition that makes a clear distinction between all constructs, but that the relative growth can be revealed through comparison of growth under different conditions. For this reason, we made use of multiple temperatures to identify differences in the growth of strains, and a consequence is that the particular antibiotic concentration where growth ceased varies with temperature. Experimental protocols of this nature interfere with determination of a Minimal Inhibitory Concentration (MIC) of antibiotic, which was the strain growth measure used by Foit et al. (2009).

The difficulty of reproducibly measuring MIC, and the need to draw a distinction between relative growth of strains as observed on single plates (as contrasted with differences in growth due to different culture conditions) led us to develop a statistical measure that can combine data from different conditions. Our solution to this problem builds on the sampling statistics of the dilution assay, which furnishes an estimate of an original population, the most probable number, based on analysis from dilution series measurements in liquid culture. The use of the most probable number has a venerable history in microbiology (Cochran, 1950; McCrady, 1915) where the focus is on determination of the density of microorganisms in a sample. Numerous variants and procedures for its estimation have been developed and are widely used. In contrast, in this work, the focus is on comparison of the relative size of populations of distinct strains rather than determination of the population of a particular strain.

Statistical description of assay results

The approach we have developed generates probabilistic statements about the relative size of populations (their rank order), rather than attempting to determine their absolute size. The analog to the most probable number in our approach is the quantity b_best , which is the maximum likelihood estimate of an original population b which gives rise to a result on one single dilution assay. We find that, although b_best may be the best single estimate for the population available, it is neither precise nor accurate. The foundation on which our approach rests is the pairwise comparator p_true , which is the probability that one population b ₁ exceeds another b ₂, as determined by comparison of the results of dilution assays performed with the two strains. Our analysis shows that the probability that one population exceeds another can be inferred with a high level of confidence from the data, even when only very rough estimates of the actual sizes can be made. Therefore, while determination of the relative sizes of two populations may be a weaker characterization than determination of their absolute sizes, it can be made with much greater confidence. This is the central innovation of our statistical description.

The approach was constructed to address several aspects of the data described above. First, the variation between assays carried out at different times does not affect the derived statistical measures because the quantity p_true , from which all other measures are obtained, is generated from the experimental results within a single condition. In effect, subsequent comparisons between differing conditions are accomplished by combining probabilities rather than averaging over experimental measurements as is done in in Figure 5. Second, the presence of apparently contradictory outcomes (see Fig. 6) can be understood not as noise in the measurement, but as an expected and predictable feature arising from the sampling of small numbers, which is intrinsic to the assay. Third, and most importantly, the method allows combination of experimental outcomes across an entire data set, such that every individual condition contributes to the overall interpretation. Analysis of data measured under individual conditions is often ambiguous and unable to resolve differences between strains. These ambiguities can be resolved by appropriately combining the data measured under different conditions.

While p_true is a pairwise measure suitable for comparison of two strains, alternative measures are needed for application to larger numbers of strains. From the pairwise probability measure p_true , we derived an additional statistical measure to enable comparison of any desired number of populations, enabling the construction of rankings R_k of these populations, and assign to each ranking an associated probability P(R_k ). For small numbers of samples, this measure may suffice to represent the relationships between the different samples. For larger numbers of strains, this statistic becomes less useful because of the large number of possible but very similar rankings. In such cases the composite statistics P_place and P_order may be more informative about the relationship of individual samples to the group.

Summary

In this work we have shown that relative stabilities of proteins can be determined with the split β‐lactamase assay and extended its applicability to examples that lack stable tertiary structure. The statistical framework we have developed allows the probability of a stability difference to be determined from data obtained under varying conditions, and despite inherent limits to the experimental precision. Our work demonstrates that this assay can be broadly applied to proteins of diverse stability in a quick, accessible, and inexpensive manner.

Time Considerations

Basic Protocol 1 requires ∼4 hr. Basic Protocol 2 requires ∼3 hr, not including time for the PCR reaction to amplify the insert itself. Basic Protocol 3 requires ∼4 hr on the first day, but much of the time is for the growth of the test cultures; ∼1 hr is needed on the second day. Basic Protocol 4 requires ∼30 min. Basic Protocol 5 requires only a few minutes.

Author Contributions

Andrew Hausrath: Conceptualization; formal analysis; investigation; writing—original draft; writing—review and editing. Richard Kingston: Conceptualization; resources; writing—review and editing. Megan McEvoy: Conceptualization; resources; writing—review and editing.

Conflict of Interest

The authors declare no conflicts of interest.

Supporting information

Jupyter notebook script for calculating the ranking weights w_k and probabilities P(R_k).

Jupyter notebook script for calculating the P_place statistic.

Jupyter notebook script for calculating the P_order statistic.

This file contains the appendices detailing the derivation of the statistical quantities used in this work.

Data for wide range assay.

Data for narrow range assay.

Hausrath, A. C. , Kingston, R. L. , & McEvoy, M. M. (2026). A rapid method to rank proteins of widely varying stability: Application to paramyxovirus foot domains. Current Protocols, 6, e70479. doi: 10.1002/cpz1.70479

Data Availability Statement

The data that support this protocol are available in the Supporting Information of this article.