Engineering

Engineering Overview

Engineering (DBTL Cycle：Design → Build → Test → Learn)

We engineered GenOMe as a next-generation platform for genome-integrated BioBricks, transforming the idea of “one-time insertion” into a reusable modular system. Guided by the Design–Build–Test–Learn cycle, we started by re-designing ORBIT for dual attB landing sites, then constructed the GenOMe strain, validated stepwise multi-site integrations, and iteratively optimized the workflow. Through this process, we created a platform that is not only robust and scalable, but also simple enough for iGEM teams to use as a genome “LEGO baseplate” for building ambitious genetic designs.

1. Design – We extended ORBIT by introducing dual attB sites, supported by GenOMe Navigator to predict integration feasibility.
2. Build – We installed attB sites, integrated a multifunctional Landing Pad with Bxb1, and constructed the GenOMe strain.
3. Test – We validated the system by inserting a GFP payload and confirmed stable dual-site recombination through fluorescence.
4. Learn – We refined the platform into GenOMe, a modular system using alternating Slot A and Slot B cassettes to assemble multi-gene arrays like a genome LEGO baseplate.

Design

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Why GenOMe?

In iGEM projects, many genetic circuits are initially built on plasmids. However, plasmids face key limitations: restricted cargo capacity, fluctuating copy numbers, and the need for continuous antibiotic selection. For designs that require stability, inheritance, and stepwise scalability, chromosomal integration is the better option.

Traditional methods for genome integration, however, are often cumbersome, low in efficiency, and difficult to expand for multiple successive insertions. The problem is, traditional methods like CRISPR/Cas9 or λ-Red are slow, complex, and costly. Integrating large DNA fragments can take weeks, requires expensive synthesis, and demands extensive colony screening.

This poses a major bottleneck for iGEM teams that want to build stable, inheritable multi-gene arrays. GenOMe was conceived as a platform to make genome editing modular and user-friendly — so that iGEM teams can build chromosomal circuits like stacking LEGO bricks.

Bxb1-Mediated attP–attB Recombination

The GenOMe system is built on Bxb1-mediated site-specific recombination. Bxb1 integrase recognizes the phage attachment site (attP) and the bacterial attachment site (attB), brings them together, and catalyzes recombination into attL and attR. Importantly, attB/P 1–6 sites pair strictly with their cognate partners (1–1, 2–2, 3–3, 5–5, 6–6), enabling accurate and independent integrations without cross-interference.

A defining feature of this mechanism is its directionality. In the absence of a Recombination Directionality Factor (RDF), the forward reaction (attP + attB → attL + attR) is irreversible. Once integrated, DNA fragments remain stably inherited, making Bxb1 particularly valuable for synthetic biology applications requiring long-term stability and predictable circuit behavior.

The phage attachment site (attP) and the bacterial attachment site (attB) are recognized by Bxb1 integrase. The enzyme catalyzes a 180° DNA rotation, producing the hybrid products attL and attR.

ORBIT: Foundation and Limitation (Single attB Integration)

Our starting point for developing GenOMe (Genome-integrated Modular Engineering) was ORBIT (Oligonucleotide Recombineering followed by Bxb1 Integrase Targeting). In E. coli, ORBIT functions by first installing a short attB site into the chromosome using a single-stranded oligonucleotide, and then employing Bxb1 integrase to insert a non-replicating DNA fragment carrying the cognate attP site, which recombines to generate stable attL/attR sites (Saunders & Ahmed, 2024). This provides a powerful method for stable chromosomal integration.

However, ORBIT still faces practical bottlenecks. Beyond being commonly applied to single-site integration, the system requires a complex helper plasmid that provides multiple functions simultaneously: a single-strand annealing protein (SSAP) to promote oligo recombination, a mismatch repair inhibitor (MutL_E32K) to prevent correction of the oligo, and inducible expression of Bxb1 integrase. Together with the targeting oligo and a non-replicating integration plasmid, these components must all be co-delivered and tightly regulated. This multi-component requirement increases system complexity and makes ORBIT less accessible for iterative applications such as iGEM projects.

This limitation naturally raises the question: if we had two attB sites in the chromosome, could we integrate a linear DNA fragment that carries two attP sites, and thereby achieve multi-locus insertion in one step?

By designing a chromosome with two attB sites and a DNA fragment carrying two attP sites, a genetic payload can be integrated into the chromosome at both sites in a single step, simplifying chromosomal insertion

In principle, introducing two attB sites could expand ORBIT beyond single-site applications, but it also raises challenges such as low efficiency, the need for synchronization, and the complexity of helper plasmids. To address these issues, we re-engineered the system into GenOMe, embedding the Bxb1 integration machinery directly into the host genome together with optimized attB sites, thereby creating a simplified and BioBrick-compatible platform for iterative genome integrations.

GenOMe Navigator — Showing That Dual attB Integration Is Feasible

To evaluate whether dual attB integration was feasible, we used GenOMe Navigator — our genome integration decision software — to analyze key factors influencing recombination efficiency. Instead of building abstract equations, the Navigator translated real experimental data into actionable guidance for the wet-lab, identifying the optimal timing and expression balance required for efficient Two-to-Two recombination.

A payload flanked by attP ends is inserted into dual attB sites in the genome by Bxb1 integrase, resulting in stable chromosomal integration through attL/attR recombination.

Drawing from prior literature, systems such as ORBIT typically achieve only ~0.1–1% single-locus efficiency (Saunders & Ahmed, 2024), while λ-Red dsDNA recombineering performs at 10⁻⁵–10⁻³ per cell. Even CRISPR/Cas9 + λ-Red hybrids (Pyne et al., 2015) reached only 39–47% correct clones without CFU normalization. Given these baselines, achieving synchronized dual-site integration in one step was initially considered unrealistic.

However, GenOMe Navigator simulated the Two-to-Two process across three mechanistic layers — protein, DNA, and population — and predicted parameter ranges that could dramatically improve performance. Its recommendations included:

• Extend ssAP induction (~45 min) to maximize attB site installation.
• Limit Bxb1 activity (~30 min) once attB sites are available.
• Use 1–2 kb fragments and include new attB sites for iterative expansion without genome elongation.

Simulation of Bxb1 and SSAP expression levels showing the optimal induction window for synchronized recombination (~200–300 min, 4–8 μM Bxb1).

Following these software-guided adjustments, our wet-lab team achieved reproducible ~80% integration efficiency, transforming what was once thought infeasible into a predictable and repeatable genome integration strategy.
Through this process, GenOMe Navigator demonstrated that even complex dual-site events can be rationally optimized — turning theory into design and computation into real experimental success.

From Prediction to Design: The GenOMe Strain

Guided by GenOMe Navigator — our genome integration decision software, we engineered the GenOMe strain, a redesigned genome chassis that extends the ORBIT concept beyond single-site integration into a scalable and modular engineering platform.
In this chassis, the chromosome is equipped with dual attB sites, functioning as expandable “genomic sockets,” while the Cassette BioBrick carries matching attP “plugs” to deliver genetic payloads. The detailed construction of the strain — including the installation of the Landing Pad with recombination sites, Bxb1 integrase, and selection markers — is described in the Build section below.

Genome engineering in GenOMe is based on two components: a Cassette BioBrick carrying attP sites, and a GenOMe strain with pre-installed attB sites in the chromosome. Together, they form a modular “plug-and-socket” system that enables scalable genome integrations.

Build

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With the design principles established and dual attB integration shown to be feasible in our modeling, the next step was to physically realize GenOMe in E. coli. We therefore set out to construct a working chassis by embedding attB sites and a multifunctional Landing Pad into the chromosome, creating the foundation of the GenOMe system.

Build: Constructing the GenOMe System

To implement this design, we established a stepwise workflow:

1. Installing attB sites by oligonucleotide recombineering.
2. Designing and integrating the Landing Pad with recombination sites, Bxb1 integrase, and a selectable marker.
3. Establishing the GenOMe strain by co-electroporation of all components.

This systematic approach ensured that each component of GenOMe was embedded into the chromosome in a stable and verifiable way.

Part 1. ssDNA Design for Installing attB Sites in the Genome

The first step in constructing GenOMe was to design a single-stranded DNA oligonucleotide (ssDNA) capable of embedding attB1 and attB6 sites into the E. coli chromosome. This was achieved using oligonucleotide recombineering, a method adapted from the ORBIT system (Saunders & Ahmed, 2024).

We targeted the lacZ locus as the integration site, providing a defined chromosomal position and an easy screening phenotype. To achieve this, we designed a 150-nt ssDNA oligonucleotide, TargetingOligo_B1_B5, with homology arms to lacZ that carried two attB cores (attB1 and attB6) separated by a short neutral spacer, enabling their precise installation into the genome.

A synthetic 150-nt ssDNA (TargetingOligo_B1_B5) was designed with lacZ-derived homology arms (blue), attB1 and attB6 cores, and a short spacer (yellow)

The ssDNA anneals to the lagging strand template during DNA replication. Assisted by the SSAP encoded on the helper plasmid, attB1/attB6 are precisely embedded into the chromosome, creating genomic sockets for downstream integration.

Part 2. The Landing Pad Design

The Landing Pad (LandingPad_B3B2B5) is an integrated DNA fragment that equips the GenOMe chassis with modular integration capacity. It is pre-encoded with attP1 and attP6 for recombination with chromosomal attB1/attB6, and contains additional attB3, attB2, and attB5 sites reserved for future insertions. To support stable selection and autonomous recombination, the fragment also carries a kanamycin resistance marker (KanR) and the Bxb1 integrase gene. Together, these elements form a compact platform embedded in the genome, enabling stepwise and expandable integrations.

LandingPad_B3B2B5 includes attP1/attP6 for recombination, additional attB2/attB3/attB5 sites for future integrations, KanR for selection, and the Bxb1 integrase gene for recombination.

Part 3. Establishing the GenOMe Strain

To construct the GenOMe chassis, E. coli MG1655 was first transformed with the ORBIT helper plasmid pHELP_TS_V2_ampR (Addgene plasmid #214467); gift from the Saunders Lab). This plasmid provides expression of the SSAP and Bxb1 integrase upon induction, which are essential for efficient recombineering and integration.

After induction, two elements were co-electroporated:
1. the ssDNA oligonucleotide carrying attB1/attB6, and
2. the Integrated DNA fragment (Landing Pad) containing attP1/attP6, attB2/attB3/attB5, KanR, and bxb1.

The ssDNA introduced attB1/attB6 into the genome, while the Integrated DNA fragment recombined with these sites to form attL/attR junctions. This process generated the GenOMe strain, embedding the Landing Pad into the chromosome as the foundation for modular genome engineering.

Overview of the GenOMe design, showing how attB sites are installed and a Landing Pad fragment integrates into the chromosome, establishing the modular chassis. E. coli MG1655 carrying the helper plasmid pHELP_TS_V2_ampR was induced to express SSAP and Bxb1. A ssDNA (TargetingOligo_B1_B6) and the LandingPad_B3B2B5 fragment were then co-electroporated, resulting in insertion of attB1/attB6 and integration of the Landing Pad into the chromosome.

TEST

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Having designed and built the GenOMe platform, the next step was to evaluate whether our system truly worked as intended. Importantly, our validation showed that GenOMe not only supports modular integration but also achieves high integration efficiency, with test fragments reaching up to ~80%. We divided this evaluation into two stages: first confirming the construction of the GenOMe strain itself, and then functionally validating it with test DNA fragments.”

Part I: Construction of the GenOMe Strain

After designing and building the GenOMe system, our first step was to verify that the chassis had been correctly established. To achieve this, we co-electroporated three elements into E. coli: (i) TargetingOligo_B1B6, a synthetic ssDNA oligo carrying attB sites; (ii) the helper plasmid pHELP_TS_V2_ampR, which provides recombineering proteins (SSAP, Bxb1, and a mismatch repair inhibitor); and (iii) LandingPad_B3B2B5, an integration fragment flanked by attP sites.

Stepwise procedure for building the GenOMe chassis: induction of the helper plasmid, co-electroporation of ssDNA and the Landing Pad, and site-specific recombination forming attL/attR junctions.

Successful construction of the strain was confirmed by blue-white screening and cross-boundary PCR (one primer on the payload and the other on the flanking lacZ gene). The expected PCR band provided direct evidence that the Landing Pad was correctly integrated, marking the completion of the GenOMe strain.

Part II: Functional Validation with Test Fragments

With the GenOMe strain in place, we next evaluated whether it could support modular genome editing. For this purpose, we designed three linear DNA fragments (test fragments), each flanked by attP sites, and introduced them into the chassis through the Two-to-Two mechanism.

• TestVer1 – IntTest_P3_GFP_P2
  A single GFP cassette, serving as a proof-of-concept to demonstrate that the chassis could stably integrate a reporter gene.
• TestVer2 – IntTest_P3_GFP_genR_P2
  A dual module carrying GFP and gentamicin resistance, designed to test whether GenOMe could support simultaneous dual-gene insertion in a single step.
• TestVer3 – IntTest_P3_GFP_genR_P5
  A fragment carrying GFP and gentamicin resistance, which replaced the entire LandingPad_B3B2B5 at attB3/attB5. The integration removed both the kanamycin marker and the Bxb1 cassette, leaving only small attL/attR scars. This result demonstrates that the Landing Pad can be completely replaced, not just supplemented.

Integration Efficiency Assay

To evaluate genome integration efficiency, electroporated cells were plated on both antibiotic-containing LB agar (selection) and plain LB agar (non-selection). Colony counts from the two plates were compared to calculate the proportion of cells in which the test fragment was successfully integrated.

• TestVer2 – IntTest_P3_GFP_genR_P2: 79%
• TestVer3 – IntTest_P3_GFP_genR_P5: 80%

Both dual-gene insertion (TestVer2) and complete Landing Pad replacement (TestVer3) occurred at high efficiency, confirming the robustness of the GenOMe platform.

Validation Methods

Verification of all three test DNA fragments relied on cross-boundary PCR (one primer on the payload and one on the flanking genome), ensuring that only correctly integrated fragments produced the expected band size. In parallel, GFP fluorescence and gentamicin selection provided additional confirmation.

Together, these results demonstrated that GenOMe can perform single-gene integration, dual-gene insertion, and complete Landing Pad replacement at high efficiency, establishing it as a robust and scalable platform for modular genome engineering.

Schematic overview of three test integrations (TestVer1–3) through the Two-to-Two mechanism. Red arrows mark cross-boundary PCR primer sites for verifying correct integration.

Learn

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From our test results, we understood the key factors for reliable recombination: high-quality competent cells, immediate recovery after electroporation, extended SSAP induction (~45 min) for efficient attB installation, and only short Bxb1 expression (~30 min) once attB sites were present. These lessons showed us that the true bottleneck was attB availability rather than integrase activity, and gave us the confidence to scale GenOMe into a modular genome engineering platform.

The refined design of GenOMe works as follows:

Step 1. Pre-installation of genomic slots
Multiple recombination sites (e.g., attP1, attB2, attB3, attP6) are embedded into the E. coli chromosome, serving as expandable slots for later insertions.

Step 2. Alternating insert modules (Slot A/B cassettes)
Two BioBrick cassettes are used in alternation:

• Slot_A_cassette_genR integrates into odd-numbered slots (1, 3, 5 …)
• Slot_B_cassette_kanR integrates into even-numbered slots (2, 4, 6 …)
  The alternating antibiotic markers allow each round of integration to be easily selected and verified.

Step 3. Iterative integration
The cycle proceeds step by step: Slot A inserts one fragment, Slot B the next, then Slot A again, enabling fragments to be added in a stable and reproducible manner.

Step 4. Modular expansion
By repeating this alternation, multiple fragments can be sequentially stacked into long genomic arrays. GenOMe thus functions as a “genome LEGO baseplate,” and any BioBrick flanked with attP/attB sites can directly enter this pipeline. In later replacement cycles, selection cassettes can be swapped out, leaving only minimal att scars.

This iterative framework goes beyond single insertions. It allows iGEM teams to assemble multi-gene constructs directly in the chromosome in a predictable, stepwise manner — free from plasmid instability, size limitations, or antibiotic dependence — and provides the community with a powerful tool to pursue more ambitious and creative projects.

Alternating Slot A (GenR) and Slot B (KanR) cassettes enable stepwise, expandable chromosomal integration, yielding stable genomic arrays

Conclusion of Engineering

By applying the Design–Build–Test–Learn cycle, we transformed the idea of dual attB integration into GenOMe, a fully functional modular genome engineering platform. From GenOMe Navigator simulation to wet-lab validation, we proved that the Two-to-Two mechanism not only works, but also achieves remarkably high integration efficiency (~80%). Along the way, we identified the true bottlenecks and optimized the workflow into a scalable, iterative framework.

The result is a system that is stable, efficient, and easy to use — enabling reliable stepwise genome integrations. With replacement of selection cassettes leaving only minimal att scars, GenOMe delivers a final marker-free genome. This completes our engineering journey, providing iGEM teams with a genome “LEGO baseplate” to build ambitious and creative designs.

References

Ref: Saunders, H. & Ahmed, A. (2024). ORBIT in Escherichia coli: Oligonucleotide recombineering with Bxb1 integrase targeting enables kilobase-scale genome editing. Nucleic Acids Research, 52(5), 227. https://doi.org/10.1093/nar/gkae227

pHelper

Cycle 1

Design

The objective of our design was to enable the host strain to express the single strand annealing protein(ssAP) and bxb-1 integrase. Literature reports indicate that the attB/attP recombination system facilitates the integration of a designed DNA sequence into the host genome, a process that requires the coordinated action of ssAP and bxb-1 integrase. To supply these factors, we introduced a Helper plasmid into the host cells. This plasmid encodes CspRecT, which mediates the expression of ssAP, and bxb-1 Int, which mediates the expression of the bxb-1 integrase.

Build

We selected E. coli MG1655 as the host strain. The Helper plasmid was first isolated from E. coli DH5α using a miniprep procedure and subsequently introduced into MG1655 by electroporation. The rationale for choosing MG1655 as the host will be explained in the Two-to-Two cycle section. The Helper plasmid carries two inducible systems: the xylS system, which is activated by m-toluic acid, and the araC system, which is activated by L-arabinose. The sequence and purpose of using these two induction systems will also be described in the Two-to-Two cycle section.

Fig. 1. Schematic of the Helper plasmid.

Test

Before initiating liquid culture, we performed colony PCR using our designed primers to verify the presence of the plasmid.

Fig. 2. The colony PCR result of the Helper plasmid.

Correct length: 860bp
Lane1, Helper plasmid, 860bp
Lane2, Helper plasmid, 860bp
Lane3, Helper plasmid, 860bp
Lane4, Helper plasmid, 860bp

Plasmids were extracted from the bacterial culture and electrocompetent MG1655 cells were prepared. The Helper plasmid was then introduced into MG1655 via electroporation, after which the cells were plated on selective agar. Colonies appearing on the plates were subsequently verified by colony PCR.

Before initiating liquid culture, we performed colony PCR using our designed primers to verify the presence of the plasmid.

Fig. 3. The colony PCR result of the Helper plasmid.

→ The colony PCR results show we lose the plasmid

Learn

Although colony growth on the selective plates appeared robust, the colony PCR results were negative. Possible explanations include reduced electroporation efficiency due to excessive salt concentration or low plasmid concentration, the emergence of satellite colonies caused by prolonged incubation, and the metabolic burden imposed by the Helper plasmid on the host strain.

Cycle 2

Design

Based on the Cycle 1, we redesigned the protocol for preparing electrocompetent cells by adjusting the number of glycerol washes to more thoroughly remove residual salts. This modification allowed us to increase the concentration of the Helper plasmid used during electroporation. In addition, we freshly prepared LB agar plates to ensure selection efficiency.

Build

Electrocompetent cells were prepared using the revised protocol, and a higher concentration of the Helper plasmid was employed for electroporation.

Test

PCR was performed to confirm that the plasmid stock remained intact.

Fig. 4. The colony PCR result of the Helper plasmid.

Correct length: 860bp
Lane1, Helper plasmid, 860bp
Lane2, Helper plasmid, 860bp
Lane3, Helper plasmid, 860bp
Lane4, Helper plasmid, 860bp

Following electroporation, the transformed strains were plated on selective agar. After overnight incubation, colony PCR was performed to assess whether the transformation was successful.

Fig. 5. The colony PCR result of the Helper plasmid.

→ The colony PCR results show we failed the transformation again.

Learn

The results did not meet our expectations, as PCR yielded negative outcomes. Since the other steps were carried out as intended, we hypothesize that the issue may have arisen during the preparation of electrocompetent cells. Specifically, the bacterial culture may have had an excessively high OD, making it difficult to completely remove residual salts. This could have resulted in arcing during electroporation and subsequently reduced transformation efficiency.

Cycle 3

Design

Based on the insights from Cycle 2, we suspected that the failure of transformation was caused by poor electrocompetent cell quality. Specifically, high OD during culture preparation likely led to incomplete salt removal, which caused arcing during electroporation. To address this, we redesigned the protocol with two main adjustments:

1. Stricter OD control – harvesting MG1655 cells at OD₆₀₀ ≈ 0.6 (mid-log phase).
2. Increased glycerol washes – ensuring more thorough salt removal prior to electroporation.

Build

• Prepared fresh electrocompetent MG1655 cells (OD₆₀₀ ≈ 0.6).
• Washed cells three times with 10% glycerol to minimize salt carryover.
• Mixed 50 µL competent cells with ~100 ng Helper plasmid DNA.
• Cells were recovered in LB broth, plated on LB + Ampicillin, and incubated at 30 °C overnight.

Test

• Colonies appeared after overnight incubation, suggesting improved transformation efficiency compared to Cycle 2.
• To confirm the presence of the Helper plasmid, colony PCR was performed using plasmid-specific primers.
• PCR results showed a clear positive band (~860 bp), confirming that the Helper plasmid was successfully introduced into MG1655.

Fig. 6. The colony PCR result of the Helper plasmid.

→ The result shows we succeed this time.

Learn

By implementing stricter OD control and additional glycerol washes, we successfully addressed the issues identified in Cycle 2. These adjustments led to improved transformation efficiency, with colony PCR confirming the presence of the Helper plasmid in MG1655. This outcome highlights the importance of precise OD monitoring and thorough salt removal during competent cell preparation. With the Helper plasmid now stably maintained in MG1655, the strain is capable of expressing ssAP (CspRecT) and bxb-1 integrase, providing the essential components for subsequent genome integration experiments.

Two to Two

Discover our step-by-step development of the Two-to-Two recombineering system. This design builds on the principle of modular genome engineering, where attP sites act as plugs and attB sites act as sockets. Under the action of Bxb1 integrase, these plugs and sockets snap together like building blocks, enabling precise and repeatable genome modification.

Cycle 1

Design

We constructed the Ex2Ver2 payload, which includes:

• A Kanamycin resistance gene (KanR) for selection
• A Bxb1 integrase gene for autonomous recombination
• attP1 and attP6 sites as integrating site
• attP1, attB2, attB3, attB5 sites as landing pad for future gene insertion

Targeting oligo was designed with the homology arms which can bind on the host genome through the help of ssAP.

• attB1 and attB6 was designed as landing pad for the sites attP1 and attP6 on the Ex2Ver2

Build

To initiate the process, the xylS system was induced with m-toluic acid to drive ssAP expression, after which electrocompetent cells were prepared for co-electroporation. The DNA template (Ex2Ver2) was amplified by PCR, and together with the targeting oligo, was prepared for transformation. Following co-electroporation, the cells were resuspended in LB broth supplemented with L-arabinose, thereby activating the araC regulatory system and enabling the expression of bxb1 integrase.

Test

No colonies survived on the agar plates containing kanamycin for antibiotic selection.

Learn

The absence of surviving colonies on the kanamycin agar plates indicates that the DNA template (Ex2Ver2) was not integrated into the E. coli genome, as the kanamycin resistance gene encoded on Ex2Ver2 would otherwise have conferred survival.

This outcome suggests several possible explanations:

• Low recombination efficiency of the targeting oligo
• Insufficient expression or activity of the bxb1 integrase.

Cycle 2

Design

Increase the amount of targeting oligo & DNA template:

• Targeting oligo from 1 μL of 25 μM → 2 μL of 25 μM
• DNA template from 1 μL of 10 ng/μL → 2 μL of 10 ng/μL

Increase induction time:

• Induction time for the xylS system by m-toluic acid from 30mins → 45mins

The induction time extension is based on the M2 data provided by Dry Lab. It can be seen from the above that the concentration of ssAP in cells approaches the highest point at about 45 mins.

• Induction time for the araC regulatory system by L-arabinose from 1hr → 4hrs

The induction time extension is based on the M2 data provided by Dry Lab. It can be seen from the above that the concentration of bxb1 integrase in cells approaches the highest point at about 4 hrs.

Build

In Cycle 2, the experimental workflow followed the same initial procedure as in Cycle 1, but the amount of targeting oligo and DNA template were increase. Following co-electroporation, the cells were resuspended in LB broth supplemented with L-arabinose. In contrast to Cycle 1, the induction period for the araC system was extended from 1 hr to 4 hrs, thereby aiming to achieve stronger and more sustained expression of the bxb1 integrase.

Test

• Kanamycin plates selected for successful recombinants.
• Colony PCR confirmed integration at the Landing Pad.

A distinct band at 741 bp was observed, matching the expected product size based on our primer design, thereby confirming successful amplification of the target sequence.

Learn

The modifications introduced in Cycle 2 proved effective. By increasing the amounts of DNA template and targeting oligo, we enhanced the likelihood of recombination events. Extending the induction period for the araC system from 1 hour to 4 hours allowed higher levels of bxb1 integrase to accumulate, which was consistent with predictions from Dry Lab modeling. As a result, colonies were able to grow on kanamycin selection plates, and colony PCR confirmed the successful integration of the Ex2Ver2 construct at the landing pad, producing the expected 741 bp fragment.
This cycle demonstrates the critical importance of optimizing both the amount of donor DNA and the timing of integrase induction in order to achieve reliable recombination efficiency. These insights will guide further refinements in subsequent cycles, particularly in balancing integrase expression with cellular growth to maximize transformation outcomes.

Test Version 1

Cycle 1

Design

The objective of Test 1 was to verify whether the GenOMe system could successfully integrate a designed DNA sequence into the E. coli genome. We constructed IntTest_P3_GFP_P2, which contained two engineered attP sites (attP2 and attP3) corresponding to the chromosomal attB2 and attB3 loci in our GenOMe strain. The construct carried a GFP reporter gene, allowing confirmation of successful integration via green fluorescence.

Our rationale was straightforward:

• If integration succeeds, attP sites on IntTest_P3_GFP_P2 recombine with attB2/attB3, producing stable GFP-expressing colonies.
• If integration fails, no GFP expression is observed.

By combining antibiotic selection with GFP fluorescence as a reporter, Test 1 provided a direct validation of the GenOMe system’s site-specific genome integration.

Build

We introduced the IntTest_P3_GFP_P2 sequence into GenOMe strains via electroporation. Since the bxb1 integrase expression cassette had already been placed downstream of the constitutive promoter BBa_J23101, the transformed cells contained abundant bxb1 integrase at the time of DNA entry, thereby enabling efficient genomic integration of the IntTest_P3_GFP_P2 sequence.

Test

After electroporating the IntTest_P3_GFP_P2 sequence into the GenOMe strains, the transformed colonies were observed using an OLYMPUS CKX53 fluorescence microscope. However, no colonies showed green fluorescence, suggesting that the designed integration did not occur under these conditions.

Learn

From the results, it was evident that the integration attempt was unsuccessful. Upon reviewing the experimental process, we identified two major issues:

1. Lack of selectable marker in IntTest_P3_GFP_P2 – Since the construct itself did not carry an antibiotic resistance gene, the transformed cells retained only the kanamycin resistance from the host background. This made it difficult to distinguish true transformants on selection plates. Moreover, without additional selective pressure, the high plating density led to excessive background growth and smear formation.
2. Insufficient recovery step after electroporation – Based on our discussion with Professor Paul P. Lin, we inferred that immediately placing the cells into an incubator for recovery after electroporation is critical. Skipping or postponing this step may have caused degradation of the IntTest_P3_GFP_P2 DNA inside the host, indirectly contributing to the failure of integration.

Cycle 2

Design

To overcome the limitations observed in Cycle 1, we redesigned the experiment with two key improvements:

1. Lack of selectable marker –We aimed to reduce excessive colony density by applying serial dilution. In the subsequent Test Version 2 and Test Version 3 experiments, we planned to introduce gentamicin resistance as an additional selectable marker to facilitate more effective screening.
2. Optimized recovery step – Immediately after electroporation, cells would be incubated in antibiotic-free LB broth at 37 °C for 30 min~1 hr to allow proper recovery and expression of the integration machinery before plating on selective medium.

Our revised rationale:

If integration succeeds under the revised conditions, colonies with stable insertions should be clearly identifiable through fluorescence microscopy, which would show green color.

Build

We repeated the electroporation of IntTest_P3_GFP_P2 into GenOMe strains, this time ensuring:

• Immediate transfer of cells into pre-warmed LB broth and recovery at 37 °C for 30 min
• Before plating on agar, serial dilution was performed to reduce the concentration of E. coli.

Test

Following recovery and plating, colonies were observed using an OLYMPUS CKX53 fluorescence microscope. Colonies were also monitored for background growth reduction compared to Cycle 1.

Learn

The modifications introduced in Cycle 2 proved effective in overcoming the challenges observed in Cycle 1. By incorporating a short recovery phase in antibiotic-free LB broth after electroporation, the host cells had sufficient time to express the integration machinery before being subjected to selection. This significantly improved colony survival and reduced background growth. Additionally, serial dilution effectively lowered colony density, enabling clearer identification of individual colonies for downstream screening.

GFP expression confirmed successful integration of the IntTest_P3_GFP_P2 sequence, validating the robustness of the optimized protocol. These results demonstrate that both recovery optimization and careful control of plating density are critical factors for achieving reliable genome editing outcomes with the GenOMe system.

Test Version 2 & 3

Cycle 1

Design

Building on the success of our initial integration, we next sought to expand the system’s utility by testing both dual-gene integration and gene replacement using specifically designed donor templates.

Test Version 2 (Dual-gene integration):
This construct was designed to introduce GFP under the control of promoter BBa_J23100 and RBS B0034, followed by a gentamicin resistance gene driven by a secondary RBS B0030. By combining a visible marker (GFP fluorescence) with an antibiotic resistance marker (gentamicin), successful integration could be confirmed through two independent selection strategies: fluorescence screening and resistance-based colony growth.

Test Version 3 (Gene replacement):
This construct was designed to replace the GenOMe strain’s original kanamycin resistance cassette with a dual module carrying GFP and gentamicin resistance, driven by the same promoter and RBS architecture as Test Version 2 (IntTest_P3_GFP_P2). This design allowed us to evaluate whether our integration system could not only insert new DNA but also precisely replace existing genomic elements with stable expression.

Both donor designs incorporated attP recombination sites (attP2/attP3in TestVer2 andattP3/attP5 in TestVer3 IntTest_P3_GFP_genR_P5) to mediate integration into the corresponding attB sites in the host genome. Verification was planned through colony phenotype screening (fluorescence and antibiotic resistance).

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We introduced the Test Version 2(IntTest_P3_GFP_P2) and Test Version 3 (IntTest_P3_GFP_genR_P5) sequence into GenOMe cells via electroporation. Since the bxb1 integrase expression cassette was placed downstream of the constitutive promoter BBa_J23101, the transformed cells already contained abundant bxb1 integrase at the time of DNA entry, thereby facilitating efficient genomic integration. To improve transformation outcomes, cells were immediately transferred into pre-warmed LB broth and allowed to recover at 37 °C for 30 min. Prior to plating, serial dilution was performed to reduce colony density and improve downstream screening. Finally, cells were plated on gentamicin-containing agar plates to enable antibiotic selection; under these conditions, only successfully integrated colonies were expected to survive.

Test

Following recovery and plating, colonies were observed using an OLYMPUS CKX53 fluorescence microscope.

Learn

The results of Test Version 2 and Test Version 3 demonstrated that our integration system is both effective and versatile. In Test 2, dual-gene integration was validated by the successful insertion of GFP and gentamicin resistance, confirmed through fluorescence screening, and antibiotic selection. In Test 3, we further established that our method is capable of precise gene replacement, as the kanamycin resistance locus was successfully substituted with GFP and gentamicin resistance, again with high efficiency.

These outcomes highlight several important insights:

1. Robustness of the attB/attP system — Integration was consistently successful across both insertion and replacement contexts, confirming the reliability of bxb1 -mediated recombination.
2. Dual-marker strategy — Combining fluorescence with antibiotic selection provided complementary readouts, which simplified screening and minimized false positives.
3. Scalability of the system — The ability to not only add but also replace genomic elements demonstrates that our platform can be extended to more complex engineering tasks, such as pathway refactoring or functional gene swaps.

Together, these findings validate the feasibility of our GenOMe approach as a generalizable framework for stable, marker-assisted genome editing inE. coli.

Model1: Basic mRNA Dynamics Model

Cycle 1: Basic mRNA Dynamics Model

Design

We constructed a minimal mRNA dynamics model [1][2]: $$ \frac{dm}{dt} = \beta - k_{\mathrm{deg}} m $$ where m(t) denotes the intracellular mRNA concentration, β is the transcription rate, and k_degis the first-order degradation constant. This model does not consider induction windows or gene-specific differences; instead, it serves as the mathematical backbone for subsequent protein-level modeling (M2). The analytical steady state is: $$ m^{*} = \frac{\beta}{k_{\mathrm{deg}}} $$

Build

We implemented the model as an ordinary differential equation (ODE) with the initial condition m(0)=0. Baseline parameters were chosen from literature estimates:

• Transcription rate β=0.20 μMh⁻¹ [3]
• Degradation rate k_deg=0.30 h⁻¹ [4]

Test

We perturbed β and k_deg by ±20% and simulated mRNA concentration profiles over a 16-hour window. Results are shown in Fig. M1-1:

• Transcription rate β (left panel): Increasing β elevated the overall trajectory and raised the steady-state concentration, while decreasing β shifted the curve downward [3].
• Degradation rate k_deg (right panel): Increasing k_deg accelerated the rise but reduced the steady state; decreasing k_deg slowed the rise while increasing the final concentration [4].
• At 12 h, the relative changes aligned precisely with the analytical solution [1].

mRNA concentration profiles under ±5–20% perturbations of transcription rate (β, left) and degradation rate (k_deg, right). The black line denotes the baseline (β=0.20 μMh⁻¹, k_deg=0.30 h⁻¹). Colored curves represent perturbations, with annotated values showing concentrations and relative deviations at 12 h.

This cycle confirmed:

• Mathematical correctness — simulation results converged to the analytical steady state [1].
• Biological interpretability — β controls the output amplitude, while k_deg governs both amplitude and dynamic speed [2][3][4].
• Model positioning — M1 establishes a reliable mRNA backbone; subsequent analyses of induction strength, induction duration, translational delay, and burden effects are carried out at the protein level (M2) [1].

Model2: Translation Dynamics and Protein Accumulation

Cycle 1: Establishing the Protein Dynamics Framework

Design

Building on the mRNA model from M1, we introduced translation and protein degradation to construct the simplest protein-level dynamics [1][2]: $$ \frac{dP}{dt} = k_{\mathrm{tl}} \cdot m(t) - d_{p} \cdot P(t) $$ where P(t) represents protein concentration, ktl is the translation rate constant, and d_p is the protein degradation rate. At this stage, translational delay and cellular burden were not considered; instead, we focused on baseline dynamics of three representative cases: ssAP, Bxb1, and Bxb1 under promoter J23105[3].

Build

We implemented the model using an ODE solver with the following baseline parameters:

• ssAP: k_tl = 0.150 min^-1, d_p = 0.012 min^-1
• Bxb1: k_tl = 0.200 min^-1, d_p = 0.001 min^-1
• Bxb1_J23105: k_tl = 0.050 min^-1, d_p = 0.001 min^-1

The selected k_tl values are within the range of E. coli translation rates [4], and the d_p values are consistent with measured protein turnover times [5].

Test

Simulation results (Fig. M2-C1-1) showed that protein trajectories (thick lines) were smoother and more delayed compared to their corresponding mRNA dynamics (thin lines), demonstrating the “low-pass filtering” effect of protein accumulation [1][2]. ssAP quickly peaked and declined, Bxb1 steadily accumulated and maintained a high level, while Bxb1_J23105 displayed intermediate behavior [3].

We further performed parameter sensitivity analysis for Bxb1 (Fig. M2-C1-2), perturbing k_tl and d_p by ±20%. Results indicated that:

• k_tl modulated the production rate and peak amplitude;
• d_p controlled the steady-state level and decay rate;
• Both 12–16 h mean concentration and 0–16 h AUC varied within reasonable ranges, confirming the robustness of the model to parameter changes [6].

Simulated concentration curves for ssAP, Bxb1, and Bxb1_J23105. Thin lines = mRNA; thick lines = protein. Shaded regions denote induction windows. Distinct dynamics are observed: ssAP declines rapidly, Bxb1 accumulates persistently, and Bxb1_J23105 lies between the two.

Protein concentration trajectories under ±20% perturbations of translation rate (k_tl) and degradation rate (d_p). Left: time courses; upper right: relative change in mean concentration (12–16 h); lower right: relative change in AUC (0–16 h).

Learn

From Cycle 1 we concluded:

1. Protein dynamics exhibit a clear “low-pass filtering” effect, being smoother and more delayed than mRNA [1][2].
2. ssAP and Bxb1 show distinct temporal behaviors, corresponding to their biological roles as short-term support versus long-term supply [6].
3. The model is robust to moderate parameter variation, providing a solid foundation for subsequent incorporation of translational delay, gene-specific properties, and induction duration (Cycles 2 and 3).

Cycle 2: Incorporating Translational Delay and Gene Specificity

Design

To extend the basic protein dynamics framework, we incorporated two biologically realistic factors:

1. Translational delay (τ_tl): mRNA translation into functional protein requires folding and maturation. We modeled an upper-bound delay of ~2 minutes [7][8].
2. Gene-specific differences:
• ssAP: short half-life (~60 min), characterized by rapid accumulation and rapid decay [9].
• Bxb1: long half-life (≫1 h), characterized by slower accumulation but sustained protein levels [10].

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• Implemented translational delay using delay differential equations (DDE) or a simple time-shift approximation [7].
• Assigned distinct degradation rates (d_p) for ssAP and Bxb1, reflecting their different protein stabilities [9][10].

$$ \frac{dp}{dt} = k_{\mathrm{tl}} \cdot m(t - \tau) - d_{p} \, p(t) $$

Test

Simulation results (Fig. M2-C2-1) showed that introducing a 2-minute translational delay shifted the half-max time (t₅₀) by only 1~2 minutes in the first 30 minutes, confirming that delay effects are negligible for induction regimes longer than 1 h [7].

Simulated protein trajectories of ssAP and Bxb1 with (blue) and without (gray dashed) a 2-minute translational delay. Delay shifted the t₅₀ by 1~2 min, confirming negligible influence under practical induction conditions (>1 h).

We next compared protein trajectories of ssAP and Bxb1 (Fig. M2-C2-2):

• ssAP (pre-induced 0–0.5 h) rapidly reached a peak but decayed to nearly zero by 12–16 h [9].
• Bxb1 (induced 0–4 h) accumulated gradually and maintained high concentration even at 12 h and 16 h, ensuring long-term stability [10].

These contrasting behaviors highlight ssAP as a short-term supporter and Bxb1 as the primary long-term supplier [10].

Protein expression profiles of ssAP (orange, short half-life) and Bxb1 (blue, long half-life). Shaded regions mark induction windows (ssAP: 0–0.5 h pre-induction; Bxb1: 0–4 h induction). ssAP peaks early then decays rapidly, while Bxb1 accumulates steadily and sustains high levels, reflecting complementary biological roles.

Learn

To translate these observations into actionable design rules, we quantified time-over-threshold (ToT)—the duration for which protein levels exceed the functional requirement P*. The heatmap in Fig. M2-C2-3 shows ToT as a function of induction length and translation rate (k_tl):

1. Longer inductions and higher translation rates consistently increase ToT [11].
2. The top 10% ToT region (dashed box) corresponds to conditions where Bxb1 remains above threshold for >6 hours, ensuring robust recombination support [11].
3. By contrast, ssAP is effective only within the first ~1 hour post-induction, reinforcing its role as a transient supporter [9].

Heatmap of ToT (hours above threshold P*) as a function of induction length (x-axis) and translation rate k_tl (y-axis). Warmer colors indicate longer ToT. The dashed box highlights the top 10% ToT combinations, revealing that long inductions coupled with strong translation maximize effective protein availability.

Cycle 3: Induction Duration and Cellular Load Effects

Design

After establishing the protein dynamics framework (Cycle 1) and incorporating translational delay and gene specificity (Cycle 2), we focused on two factors most relevant to experimental design:

1. Induction duration: comparing short induction (1 h) versus long induction (4 h) [12].
2. Cellular load effects: when heterologous protein expression becomes excessive, cellular resources are depleted, reducing translational efficiency or increasing degradation. We introduced a parameter γ to represent load strength, tested alongside degradation rate (d_p) [13][14].

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• Adjusted induction windows in the model to simulate protein dynamics under 1 h and 4 h conditions [12].
• Incorporated the load parameter γ into the degradation term to reflect metabolic stress [13]. $$ \frac{dp}{dt} = k_{\mathrm{tl}} \cdot m(t - \tau) - \gamma d_{p} \, p(t) $$
• Defined a functional threshold concentration P* and quantified time-over-threshold (ToT) as the key design metric: the duration for which protein levels exceeded P* [15]. $$ \mathrm{ToT} = \int_{0}^{T} \mathbf{1}_{\{p(t) > P^{*}\}} \, dt $$

Test

1. Comparison of induction duration (Fig. M2-C3-1)
   • ssAP: trajectories under 1 h and 4 h induction were nearly identical, showing that short induction is sufficient [12].
   • Bxb1: protein concentration remained well below P* under 1 h induction but significantly increased and sustained above threshold with 4 h induction [13].

   

   Simulated protein trajectories for ssAP (left) and Bxb1 (right). ssAP shows little difference between 1 h and 4 h induction, while Bxb1 requires ≥4 h induction to exceed threshold P

2. Sensitivity to load versus degradation (Fig. M2-C3-2)
   • Increasing load strength (γ) markedly reduced ToT, even under long induction.
   • In contrast, varying d_p had only modest effects [14].
   • This demonstrates that cellular load is a stronger limiting factor than natural degradation.

   

   Bar plots showing relative changes in ToT under ± perturbations. Stronger load has a much greater negative impact than changes in d_p, highlighting cellular burden as the dominant limiting factor.
3. Design decision plot (Fig. M2-C3-3)
   • ssAP: 1% × 1 h yielded ~2 h of ToT, with minimal benefit from longer induction [12].
   • Bxb1: required at least 1% × 4 h to achieve ~6 h ToT, sufficient for robust recombination support [12][15].
   • This plot directly translates model predictions into intuitive design guidance.

   

   ToT as a function of induction duration under different induction strengths (0.1% vs 1%). ssAP is effective with short induction, while Bxb1 requires ≥4 h induction to achieve functional coverage.

Learn

Cycle 3 provided three major insights:

1. Differentiated induction strategies:
   • ssAP functions optimally with short induction (1 h is sufficient) [12].
   • Bxb1 requires long induction (≥4 h) to sustain functional ToT [12][15].
2. Cellular load is the dominant constraint: metabolic burden limits effective protein levels more strongly than degradation, and excessive induction can be counterproductive [13][14].
3. Design recommendation: the optimal strategy is short pre-induction of ssAP combined with long induction of Bxb1, ensuring early attB support and sustained recombination activity [12][15].

Model3: Single-Cell Stochastic Process of attB Formation

Overview

Across Cycles 1–5, the M3 model progresses from a population-averaged description of attB formation to a stochastic, replication-aware framework.
Successive refinements reveal that oligo uptake heterogeneity, ssAP noise, and replication-fork gating collectively determine integration efficiency—culminating in Cycle 5, where locus distance from oriC emerges as the dominant factor.

Cycle 1 – Initial Binding Kinetics Model

Design

In the initial formulation, we adopted a mass-action kinetics framework, assuming that single-stranded oligonucleotides (Oligo, ssDNA) and the single-strand annealing protein (ssAP, e.g., RecT or CspRecT) reversibly bind in the cytoplasm to form a complex CC (ssDNA:ssAP). This complex subsequently acts on the chromosome to trigger the formation of an attB site.

Key assumptions:

1. Genomes are treated as a high-copy continuous reaction pool, i.e., the number of chromosomal sites is effectively unlimited.
2. Oligo and ssAP concentrations are represented as continuous variables.
3. The rate of attB generation is proportional to the concentration of the complex [C].

This design extends from classical protein–DNA binding models [1].

Build:

The model is represented by a system of three ODEs:

where:

• k_bind: binding rate constant
• k_unbind: dissociation rate constant
• k_{deg, complex}: degradation rate of the complex

Output formulation:

The attB formation rate is assumed proportional to the complex concentration:

$$ \frac{d[\text{attB}]}{dt} \propto [C] $$

Test

Using ssAP dynamics from the M2 model as input, we simulated under varying conditions:

• Different initial Oligo concentrations (low, medium, high).
• Sensitivity analysis with ±20% variation in k_bind, k_unbind, and k_{deg, complex}.

Simulation results showed:

• Complex [C] accumulation increases with higher ssAP and Oligo concentrations.
• attB accumulation is monotonic and nearly linear at high Oligo concentration.
• At low Oligo concentration, the process is delayed and rate-limited.

Learn

Insights from Cycle 1 include:

• Advantages: The model provides a simple, intuitive connection between Oligo and ssAP concentrations and the rate of attB generation.

• Limitations:
  1. Parameter availability: Critical constants k_bind and k_unbind are largely absent in the literature for ssAP proteins [2]. Direct measurements would require techniques such as stopped-flow kinetics or single-molecule FRET, which are experimentally impractical.
  2. Unrealistic assumptions: The bacterial genome is not high-copy; in reality, only 1–2 copies are typically present.
  3. Failure to capture polarization: The “all-or-none” phenomenon—where some cells integrate successfully while most fail—cannot be explained by this continuous model.
  4. No saturation effect: At high Oligo concentrations, the model predicts unlimited rate increases, inconsistent with experimental observations.

For these reasons, Cycle 2 transitioned to a Michaelis–Menten framework, replacing intractable k_bind, k_unbind with effective parameters (V_max, K_m, k_cat) that better capture saturation effects and can be experimentally inferred.

Cycle 2: Michaelis–Menten Saturation Kinetics Refinement

Design

In Cycle 1, we described ssAP–Oligo binding using simple mass-action kinetics. However, two major issues emerged:

1. Parameter gap: The fundamental binding and dissociation constants k_bind, k_unbind are scarcely reported in the literature for ssAP proteins [1].
2. Unrealistic dynamics: At high Oligo concentrations, Cycle 1 predicted an unlimited increase in reaction rate, which is inconsistent with experimental behavior.

Therefore, in Cycle 2, we reformulated the process using Michaelis–Menten saturation kinetics, treating attB formation as an enzyme-like reaction:

• Substrate: Oligo
• Enzyme: ssAP
• Product: attB

In addition, the initial assumption of a reversible two-step binding between ssAP and Oligo (association and dissociation of the complex) was simplified into a single effective step, represented by a Michaelis–Menten form, consistent with enzyme-like kinetics observed in recombineering systems [3][4]

Build

The refined reaction rate is given by:

$$v(t) = \frac{k^{AP}_{cat} [ssAP](t)[Oligo]}{K^{AP}_{m} + [Oligo]}$$

where:

• k_cat^AP: catalytic turnover rate of a single ssAP–Oligo complex
• K_m^AP: half-saturation constant for Oligo

The attB formation rate is then expressed as:

$$\frac{d[attB]}{dt} = v(t)[Genome]$$

When [Oligo] ≫ K_m^AP, this reduces to:

$$\frac{d[attB]}{dt} \approx k^{AP}_{cat}[ssAP](t)[Genome]$$

This formulation naturally accounts for rate saturation at high Oligo levels, overcoming the overestimation problem in Cycle 1.

Test

Simulation setup:

• Input ssAP concentration dynamics from the M2 model.
• Vary initial Oligo concentrations and compare effects on attB accumulation.
• Parameter sweeps across K_m^AP and k_cat^AP.

Results:

1. At low Oligo concentration, attB formation is strongly substrate-limited.
2. Once Oligo exceeds ~5–10× K_m^AP, the rate saturates.
3. attB accumulation curves exhibit sigmoidal-like behavior, contrasting with the linear growth predicted in Cycle 1.

Learn

Cycle 2 brought the following improvements:

• Advantages:
  1. Introduced effective parameters (k_cat, K_m) that can be inferred from experimental data (attB integration efficiency vs Oligo concentration), making them far more tractable than k_bind, k_unbind [2].
  2. Correctly described saturation at high substrate concentration.
  3. Simplified the binding mechanism assumption for Bxb1–attP/attB, making the model more realistic and parsimonious.
• Limitations:
  1. Still based on average concentration dynamics, without capturing stochastic cell-to-cell variation.
  2. Genome copy number is still treated as continuous, not yet accounting for discrete chromosomal sites.

These limitations motivated Cycle 3, where we reframed attB formation as a probabilistic write-in event (“at least one success per cell”) and explicitly introduced genome copy number G.

Cycle 3: Probabilistic Write-In Model (Single-Cell Level)

Design

Although Cycle 2 resolved the issue of rate saturation at high Oligo concentrations, two major limitations remained:

1. Genome copy number: Cycle 2 still treats the genome as a continuous variable, whereas in E. coli cells the genome copy number is only 1–2. This necessitates a discrete-site formulation.
2. Inability to explain polarization: Experimentally, integration outcomes often show strong “all-or-none” behavior, where some cells successfully form attB while most fail completely. This indicates that attB formation is not a mean concentration event but rather a single-cell, binary success process.

Therefore, in Cycle 3, we reframed attB formation as a probabilistic write-in process:

• Each genome site is treated as a trial event.
• If at least one success occurs within a time window, the cell is classified as attB⁺.
• The model output is no longer average concentration but the single-cell probability of success p(t).

Build

The instantaneous success rate at time t is given by:

$$k(t) = \frac{k^{AP}_{cat}[ssAP](t)[Oligo](t)}{K^{AP}_{m} + [Oligo](t)}$$

The probability of attB formation follows:

$$\frac{dp}{dt} = k(t)[1 - p(t)], \quad p(0) = 0$$

with solution:

$$p(t) = 1 - \exp\left(-\int_{0}^{t} k(\tau)\, d\tau\right)$$

If k(t) is approximated as constant:

$$p(t) = 1 - e^{-kt}$$

Here, p(t) represents the probability that a single cell has formed at least one attB site by time t.
For this stage, genome copy number was simplified to G = 1.

Test

• Used ssAP dynamics from the M2 model and varied initial Oligo concentration [O]₀.
• Compared conditions of unstable (rapidly degraded) versus stable Oligo.
• Performed parameter sweeps across k_cat^AP and K_m^AP.

Results showed:

1. With unstable Oligo, p(t) rapidly plateaued, limiting success probability.
2. With stable Oligo, p(t) followed a clear sigmoidal rise and achieved higher plateau values.
3. Key design metrics such as t₁₀, t₅₀, t₉₀(times to 10%, 50%, 90% success) could be defined, guiding optimal induction windows.

Learn

Cycle 3 provided an important conceptual shift:

• Advantages:
  1. Reframed attB formation as a single-cell probabilistic event, producing probability curves rather than concentrations.
  2. Naturally explained the polarization phenomenon: some cells achieve p ≈ 1 early, while most remain at p ≈ 0.
  3. Introduced quantitative design indicators (t₅₀, etc.), offering practical guidance for experimental induction timing.
• Limitations:
  1. Still assumes identical ssAP expression and Oligo uptake across cells.
  2. Genome copy number variability (G∈{1,2,4}) not yet included.
  3. Cell-to-cell stochastic heterogeneity is not captured.

These limitations motivated Cycle 4, where we expanded to a non-homogeneous Poisson process with Monte Carlo simulations, incorporating population-level variability in Oligo uptake, ssAP expression, and genome copy number.

Cycle 4: Non-Homogeneous Poisson Process and Population-Level Simulation

Design

While Cycle 3 reframed attB formation as a single-cell probabilistic event, two key issues remained:

1. Cell-to-cell heterogeneity: Different cells exhibit large variation in Oligo uptake [3] and ssAP expression due to stochastic gene expression noise [4][5].
2. Genome copy number variability: Depending on replication fork position, the number of chromosomal target sites can range from 1–4 [6].
3. Population-level distribution: Cycle 3 only produced an average single-cell probability curve and could not explain the experimentally observed polarization, where a minority of cells succeed while most fail [7].

To address these limitations, Cycle 4 models attB formation as a non-homogeneous Poisson process at the single-cell level and applies Monte Carlo simulations to incorporate distributions of Oligo uptake, ssAP expression, and genome copy number. This yields population-level attB success rates and explains the observed polarization.

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1. Single-cell process
   For cell i, the cumulative hazard function is:

   $$\Lambda_i(t) = \int_0^t k_i(\tau)\, d\tau$$

   with instantaneous rate:

   $$k_i(t) = \frac{k^{AP}_{cat}[ssAP]_i(t)[Oligo]_i(t)}{K^{AP}_{m} + [Oligo]_i(t)} \cdot G_i$$

   where G_i ∈ {1, 2, 4} is the genome copy number [6].

   The probability of at least one successful attB formation in cell i is:

   $$P_i(t \ge 1) = 1 - e^{-\Lambda_i(t)}$$

2. Population output
   Across N cells sampled from distributions of Oligo, ssAP, and genome copy number:

   $$p_{\ge 1}(t) = \frac{1}{N} \sum_{i=1}^{N} P_i(t)$$

3. Implementation
   Monte Carlo simulations (N = 10³ ∼ 10⁴) are used to generate population-level curves, polarization histograms, and sensitivity heatmaps.

Test

Simulation setup:

• Oligo uptake was sampled from a log-normal distribution, consistent with electrotransformation variability [3].
• ssAP expression was converted from M2 concentrations to molecule numbers (1 µM ≈ 602 molecules/cell) and perturbed with stochastic noise [4][5].
• Genome copy number was sampled as discrete values G = 1–4 depending on replication state [6].

Simulation results:

1. Baseline condition analysis (Fig. M3-2A).
   Parameters: g_m,oligo = 300 molecules/cell, k_cat = 0.02 min⁻¹, K_m = 6000 molecules.
   The cumulative curve is S-shaped with three phases:
   • Lag phase (0–15 min): attB formation <10%
   • Rise phase (15–45 min): exponential-like growth, best induction window
   • Plateau phase (≥45 min): saturation at ≈0.33 final fraction

   

   Time landmarks:

   • t₁₀ ≈ 15 min
   • t₅₀ ≈ 30 min
   • t₉₀ ≈ 55 min (limited by plateau)

   The ~33% plateau reflects:

   • Heterogeneity in oligo uptake
   • Ongoing nuclease degradation
   • Variability in ssAP levels

   This agrees with reported 10–30% recombineering efficiency in λ-Red/RecT systems [5].

2. Parameter sensitivity analysis (Figs. M3-2B–C).
   • g_m,oligo × K_m heatmap: Final p≥1 ≥0.95 across most of the 10²–10⁴ × 10³–10⁴ range. Efficiency drops only when g_m ≤10² and K_m ≥10⁴.
     → K_m plays a minor role compared to delivery.
   • g_m,oligo × k_cat heatmap: Low g_m + low k_cat yields <0.9 efficiency. Raising g_m (>10³) or k_cat (>0.05 min⁻¹) pushes final p≥1 >0.95.

     → Parameter priority: gm, oligo > k_cat > K_m.

     

3. Single-cell distributions from Monte Carlo simulations revealed skewed probabilities concentrated around Pi ≈ 0.1–0.3. A dedicated polarization histogram (Fig. M3-2D) highlighted that only under higher Oligo uptake or reduced K_m do a fraction of cells achieve Pi ≈ 1, explaining the experimentally observed “all-or-none” recombineering outcomes [7].

   

   Most cells cluster at low–intermediate probabilities (P_i​≈0.1–0.3); polarization with a fraction reaching P_i≈1 appears only when Oligo uptake is increased or K_m​ is reduced.

4. Locus-dependent efficiency: Experimental validation showed that success rates also vary with genomic position relative to oriC.For example, loci proximal to the origin (metA) integrate more efficiently than mid-replichore (galK) or terminus-proximal loci (leuD).To capture this, we added Fig. M3-2E, showing a declining success probability with increasing distance from oriC. This suggests that replication timing and fork accessibility introduce an additional layer of heterogeneity beyond molecular parameters.

Learn

Advantages:

• Explicitly incorporated cell-to-cell heterogeneity, bridging the gap between average behavior and observed polarization [7].
• Provided population-level indicators, such as the success plateau (~30%) and optimal induction windows.
• Delivered design rules: prioritize improving Oligo uptake and stability, then optimize ssAP expression. Lowering K_m further enhances success when Oligo is limiting (Figs. M3-2B–C).
• Highlighted positional effects: M3-2E revealed that genomic context (oriC-proximal vs distal loci) is a major determinant of recombination success, aligning with experimental observations.

Limitations:

• Assumes cells are independent; population resource competition is not modeled [8].
• Does not capture spatial constraints of Oligo reaching the replication fork [3].
• DNA repair pathways (e.g., mismatch repair) compete with recombination but are not yet modeled [9].
• Does not account for locus-dependent replication timing: The model assumes all chromosomal sites are equally accessible, neglecting that oriC-proximal loci experience earlier and longer replication windows than distal sites (e.g., LacZ), which may explain observed variability in integration efficiency.

While Cycle 4 identified Oligo delivery (g_m) as the dominant determinant, followed by k_cat and then K_m, these molecular factors alone cannot explain why some genomic loci (e.g., leuD, lacZ) remain far below the predicted 30% plateau. This motivated Cycle 5, where locus-dependent replication timing and fork accessibility were explicitly incorporated.

Future Work:

Future work should extend to Gillespie-based stochastic simulations and integrate single-cell measurements for calibration. In addition, locus-specific replication timing and copy number dynamics should be incorporated, extending the non-homogeneous Poisson framework to include oriC–ter gradients. This motivates the subsequent Cycle 5, which explicitly models position- and fork-gated accessibility.

Cycle 5 : Locus Dependence and Replication-Fork Gating

Design

In previous cycles, we formalized the stochastic process of attB formation and initially assumed that two-to-two recombination would be intrinsically less efficient than one-to-one due to steric hindrance.
However, experimental data from Saunders & Ahmed (2024) challenged this assumption:

• hisA, metA, galK, and leuD showed distinct efficiency gradients along the chromosome,
  ranging from ~0.46% (hisA) to ~0.04% (leuD) [10].
• Our lacZ (two-pair) site yielded ~0.0195%, consistent with the same positional trend.

Both datasets confirm that genomic position, rather than site number, dominates integration probability.
Thus, this cycle introduces the locus-dependent replication-timing hypothesis [11][12]:

• Replication-fork gating. Oligo integration occurs efficiently only when the replication fork passes the target locus [11].
• Gene-dosage effect. Loci near oriC are transiently multi-copy during exponential growth, whereas ter-proximal loci remain single-copy [12].
• Steric hindrance as secondary. At high-efficiency ori-proximal sites one-to-one may slightly outperform two-to-two, but at distal loci positional gating dominates.

Build

We extended the Cycle 4 non-homogeneous Poisson framework by adding a locus-specific replication-timing variable [12]:

$$ \lambda_i(x,t)=G_i(x,t),f([O]_i(t),[ssAP]i(t)),\chi{\text{rep}}(x,t) $$

where G_i(x,t) is the locus-specific copy number determined by replication timing, f([O]_i, [ssAP]_i) is the molecular rate from Cycle 4, and (χ_rep) the replication-window indicator. Replication timing was approximated by the Cooper–Helmstetter model [12]; six loci were simulated:

oriC → metA → hisA → lacZ → galK → leuD → (oriC)

Test

(1) Locus-distance effect

Simulations reproduced the gradient measured by Saunders & Ahmed (2024) [10]: integration efficiency declines exponentially with fork distance from oriC, following

$$ P(d)\approx0.6%,e^{-0.0007d} $$

Each additional ~1000 kb causes ≈ 50–70 % loss of success probability.

(2) One-to-one vs Two-to-two

At lacZ (two-pair), efficiency (~0.0195 %) was only ~5–7 % of the one-to-one baseline (metA ~0.35 %),
showing that replication-fork accessibility, not steric hindrance, limits success.

(3) Conceptual replication-timing description

As forks initiate at oriC and travel bidirectionally (oriC → metA → hisA → lacZ → galK → leuD → oriC), early-replicated loci (metA, hisA) exhibit high accessibility; mid-replichore sites (lacZ, galK) moderate;
and terminus-proximal (leuD) the lowest [10][12].

Learn

1. Unified framework.

   By explicitly integrating locus dependence and replication-fork timing, the model provides a quantitative bridge between literature data (leuD, one pair, ~0.0386%) and our experimental lacZ (two pairs, 0.0195%) results [10][12].
   These datasets, together with the ORBIT recombineering map [10], reveal a continuous gradient of integration success along the oriC → terC axis, consistent with the Cooper–Helmstetter replication-timing model [12].
   By embedding these positional variables into the stochastic Poisson formulation, Cycle 5 transforms the abstract single-cell model of Cycle 4 into a chromosome-aware predictive system.

2. Position over site number.

   Contrary to initial expectations, steric hindrance from two-to-two recombination was not the dominant limiting factor.
   Integration probability scales exponentially with locus distance from oriC, while the number of attB/attP pairs contributes only marginally at accessible sites.
   At ter-proximal loci, the replication window is so narrow that additional site pairs do not compensate for the lack of fork overlap.
   This positional dominance clarifies why hisA and metA (ori-proximal) outperform galK, leuD, and lacZ by over an order of magnitude [10].

3. Replication-timing dynamics.
   The model demonstrates that attB installation occurs almost exclusively during replication-fork passage.
   Oligos that arrive too early are degraded before fork exposure, while those arriving too late find double-stranded DNA no longer accessible to recombineering proteins.
   The combination of time-dependent fork accessibility and gene dosage variation defines a probabilistic “window of opportunity,” which quantitatively explains both the 30–35% efficiency plateau seen in Cycle 4 and the locus-specific attenuation observed in Cycle 5.
4. Mechanistic visualization.
   Although Panel B has been replaced by textual explanation, the conceptual mapping remains:
   As replication forks proceed bidirectionally (oriC → metA → hisA → lacZ → galK → leuD → oriC), each locus experiences a distinct temporal window of accessibility and copy number.
   This provides a mechanistic interpretation for the observed exponential decay curve (Fig. M3-2E) and connects chromosomal architecture to stochastic reaction probability.

Although lacZ may be numerically closer to hisA along the genome map, they lie on opposite replichores. Two-to-two recombination requires both ends to be simultaneously exposed within the same replication-fork window; cross-replichore pairs therefore suffer a geometric timing penalty, explaining the particularly low efficiency at lacZ.

Design Rules

1. Target oriC-proximal loci (metA, hisA) to maximize recombination success [10][11][12].
2. For distal loci (lacZ, leuD), extend induction duration or stabilize ssDNA to increase overlap with replication-fork passage [11].
3. Expect a 5–7% yield at ter-proximal sites using two-pair constructs — this represents the empirical positional penalty [10].
4. Time induction to coincide with replication-fork progression: for mid-replichore genes (galK), delayed induction substantially improves success probability.
5. Treat steric hindrance as secondary. It becomes relevant only at high-accessibility loci; positional constraints dominate elsewhere.

Limitations

• Replication timing was modeled theoretically (Cooper–Helmstetter [12]); single-cell visualization of fork passage remains to be validated experimentally.
• DNA mismatch repair and local supercoiling [11, 13] were not incorporated, both of which may alter effective oligo half-life and accessibility.
• Resource competition and transcriptional context effects (e.g., local transcriptional activity near lacZ) remain unquantified.
• Parameter estimation currently assumes homogeneous cell-cycle synchronization, which may not hold in asynchronous populations.

Future Work

• Perform controlled one-to-one vs two-to-two comparisons at oriC-proximal loci to isolate steric hindrance effects under identical accessibility.
• Apply single-cell qPCR or FACS quantification of attB incorporation across loci to empirically calibrate the positional decay constant in Eq. P(d).
• Extend the stochastic framework to include DNA repair dynamics, fork asymmetry, and topological constraints, enhancing predictive power for genome-scale designs.
• Couple Cycle 5 outputs with M4 Cycle 6’s resource-allocation model to evaluate whether positional constraints can be mitigated through dynamic ssAP induction control.

Model4(M4), Model5(M5)

Cycle 1 | Establishing the One-to-One Baseline Model

Design

To provide the theoretical foundation for multi-site recombination modeling, we first constructed a minimal one-to-one model describing recombination between attB and attP mediated by Bxb1 integrase.At this stage, forward recombination and a provisional product inhibition (α) term were included. Subsequent cycles demonstrated that catalytic inhibition requires RDF expression; in its absence, attL/attR only reversibly bind Bxb1 without driving backward conversion. Therefore, α was later removed and replaced by a passive sequestration term in the Bxb1 mass-balance [1][2].

Build

The system was formalized as a set of ordinary differential equations (ODEs) (Fig. M4-C1-1), with key parameters including the binding rate constant (kon), dissociation rate constant (koff), catalytic turnover rate (k_cat), and product inhibition coefficient (α). Numerical simulations were implemented on the Google Colab platform.

System of ODEs describing forward recombination of attB and attP mediated by Bxb1 integrase, including product inhibition. RDF and orthogonal mismatches were excluded in this baseline formulation.

Test

Simulation results (Fig. M4-C1-2) showed a progressive depletion of attB/attP and a concomitant accumulation of attL/attR, consistent with reported ranges of Bxb1 binding affinities (Kd​∼10−8 M) and catalytic efficiencies [3][4]. This agreement confirmed that the baseline parameterization is biophysically reasonable.

Time-resolved trajectories of substrates (attB, attP) and products (attL/attR) generated under baseline parameterization. The model reproduces the expected depletion of substrates and accumulation of products.

Learn

Cycle 1 established that a minimal one-to-one model adequately captures the essential recombination dynamics of Bxb1. This provides a robust foundation for subsequent incorporation of site-specific efficiencies, decoy competition, and dual-end synchronization mechanisms.

Cycle 2｜Bxb1 dynamics and time-over-threshold (ToT)

Design

Following the establishment of the one-to-one baseline model, we next incorporated the dynamic supply of Bxb1 integrase. Since recombination efficiency is determined not only by the peak enzyme concentration but also by the duration for which Bxb1 levels remain above a functional threshold (P*), we introduced time-over-threshold (ToT) as a key design metric [5][6].

Build

Bxb1 trajectories were obtained from transcriptional and translational dynamics (M1/M2) and implemented under three biologically relevant scenarios:

1. Cycle1 – Ideal rise: unlimited accumulation to ~53 μM (~95% of theoretical capacity).
   
2. Cycle2 – Plateau: accumulation capped at ~11.16 μM (~75.8%).
   
3. Cycle3 – Limited supply: restricted accumulation to ~8.53 μM (~68%).
   

Test

Simulation results (Fig. M4-C2-1) demonstrated that these supply profiles yield distinct recombination outcomes. ToT values were directly proportional to recombination efficiency: Cycle1 = 240 min, Cycle2 = 180 min, Cycle3 = 120 min. Importantly, ToT provided a stronger predictive relationship than peak concentration alone, confirming its utility as a design rule [7]. Moreover, short inductions (<1 h) yielded negligible benefits, while longer inductions markedly extended ToT and enhanced recombination probability.

Simulated Bxb1 concentration trajectories under three supply scenarios: (Cycle1) ideal rise to ~53 μM, (Cycle2) plateau at ~11.16 μM, and (Cycle3) limited to ~8.53 μM. The red dashed line denotes the functional threshold (P* = 5.0 μM). Shaded regions above P* define the effective time-over-threshold (ToT) for each scenario, with ToT values: Cycle1 = 240 min, Cycle2 = 180 min, Cycle3 = 120 min.

Learn

Cycle 2 established that Bxb1 supply dynamics critically constrain recombination. By formalizing ToT as a quantitative design principle, we defined an operational guideline: induction strategies must ensure Bxb1 concentrations remain above the functional threshold for a sufficient duration to achieve robust recombination. This kinetic framework provided essential context for subsequent two-to-two modeling in Cycle 3.

Cycle 3｜Initial two-to-two model (conditional on attB formation)

Design

After establishing the one-to-one baseline and defining Bxb1 supply dynamics, we extended the framework to two-to-two recombination, where two pairs of attB/attP sites must recombine simultaneously to yield a successful event. Because our integration sites were designed orthogonally, cross-pairing between non-cognate attB/attP sites was excluded [1]. Under this assumption, the initial success probability was modeled as the product of two independent one-to-one reactions: $$ p_{2\to2}^{\text{ind}} = 1 - (1 - p_1)(1 - p_2) $$

However, experimental trends suggested that this independence assumption consistently overestimated recombination efficiencies. To address this, we introduced a decoy correction factor, denoted as f_free, representing the fraction of free Bxb1 available for productive recombination after accounting for sequestration by additional att sites [8].

Build

The conditional success rate was formulated in an ODE framework. The effective forward rate constants were scaled by $ f_{\text{free}} $, producing a reduced plateau value relative to the independence assumption. Model parameters included $ k_{\text{on}}, k_{\text{off}}, k_{cat}, f_{\text{free}} $, with enzyme input profiles taken from Cycle 2.

Test

At the population level, the independence model predicted a conditional success plateau of ~85%. Incorporating the decoy correction $ f_{\text{free}} = 0.65 $ reduced the plateau to ~58%, in line with the expected trend that non-productive binding events limit recombination efficiency (Fig. M4-C3-1). Importantly, these results describe recombination conditional on attB being present ; overall experimental outcomes (e.g., 0.0195% for M416 vs. 87.5% for M423) additionally depend on the probability of attB formation, which is addressed in Cycle 6.

ODE simulations of conditional success probabilities for two-to-two recombination, assuming attB formation. Blue line: independent assumption $ p_{2\to2}^{\text{ind}} $; Orange line: decoy-corrected model $ f_{\text{free}} = 0.65 $. The decoy-corrected model yields a lower plateau (~58% vs. ~85%), capturing the effect of integrase sequestration. Note: These curves represent conditional successgiven attB presence; overall success rates (e.g., M416 and M423) are analyzed in Cycle 6.

Learn

Cycle 3 demonstrated that two-to-two recombination cannot be treated as the simple product of two independent one-to-one reactions. While orthogonality prevents cross-pairing, enzyme sequestration (decoy effect) significantly reduces the conditional efficiency. This established the foundation for subsequent cycles: Cycle 4 incorporates dynamic enzyme supply, while Cycle 5 introduces synchronization and competing failure pathways.

Cycle 4｜Bxb1 dynamics and synchronization background

Design

In Cycle 3, we established the conditional two-to-two model and demonstrated that the independence assumption overestimates recombination efficiency, while decoy correction provides a more realistic description. However, that framework still assumed static Bxb1 levels. In reality, Bxb1 expression changes dynamically under induction conditions (Cycle 2, described via ToT). Therefore, in Cycle 4 we incorporated dynamic Bxb1 supply trajectories into the two-to-two framework and introduced a synchronization parameter to account for temporal coordination between the two recombination ends. This extension was necessary because decoy correction alone could not fully explain the discrepancies in slope and plateau observed experimentally [10].

Build

• Dynamic Bxb1 input: Plateau-type supply profile from Cycle 2 was used, with reaction rates scaled over time.
  
• Decoy correction: A free fraction of integrase was modeled as (f_free = 0.65), reflecting enzyme sequestration by non-productive binding.
  
• Synchronization parameter (k_half): Defined as the probability of pathway failure when one end completes recombination while the other stalls, capturing the requirement for temporal coupling between the two ends [11].
  

Test

Simulation results are shown in Fig. M4-C4-1:

• Blue curve (independence assumption): Predicted rapid rise and an overestimated plateau (~85%).
• Orange curve (decoy-corrected, (f_free = 0.65)): Reduced the plateau (~58%) but retained an overly steep slope.
• Green curve (decoy + synchronization, (k_half = 0.15)): Simultaneously reduced both slope and plateau, reproducing experimental kinetics.
• Black circles: Experimental data from M423-like conditions (mean ± SEM). Only the synchronization-corrected model accurately matched both trajectory shape and final plateau.

Simulated recombination trajectories under dynamic Bxb1 supply (Cycle 2 plateau profile) with progressive model refinement. Blue curve: independent assumption model, showing rapid rise and overestimated plateau (~85%). Orange curve: decoy-corrected model (f_free = 0.65)), which reduces plateau but retains steep slope. Green curve: decoy + synchronization model (k_half = 0.15)), incorporating temporal coupling between the two recombination sites, which simultaneously reduces both slope and plateau to match experimental kinetics. Black circles with error bars: experimental data from M423-like conditions (n = 3, mean ± SEM). Only the synchronization-corrected model recapitulates both the trajectory shape and final plateau, demonstrating that time-over-threshold (ToT) and inter-site coordination are both necessary for accurate prediction. Note: These data represent conditional success rates(precomb|attB); overall outcomes incorporating (pattB) gating are presented in Cycle 6.

Learn

Cycle 4 demonstrated three key points:

1. Dynamic enzyme supply is essential: High ToT alone is insufficient to explain recombination kinetics.
2. Decoy effects account for plateau reduction, but cannot reproduce curve shape.
3. Synchronization is critical: Only the decoy + synchronization model recapitulated both slope and plateau.

Thus, two-to-two recombination efficiency depends not only on attB availability but also on both Bxb1 temporal dynamics and end-to-end synchronization. This finding motivated Cycle 5, where failure pathways are explicitly modeled and single-cell variability becomes essential.

Cycle 5｜Synchronization mechanisms and failure pathways

Design

While Cycle 4 demonstrated that dynamic enzyme supply and decoy correction improved model performance, experimental data still revealed discrepancies in trajectory shape and final efficiency. In particular, colony-level outcomes exhibited a bimodal pattern—some cells achieved complete two-to-two recombination, while others failed entirely. Such behavior is reminiscent of well-known stochastic phenomena in gene regulation, where single-cell trajectories diverge due to intrinsic noise [12][13]. We therefore hypothesized that synchronization between the two recombination ends is essential, and that failure pathways must be explicitly incorporated into the model. Specifically, if one recombination ends earlier than the other, the system may irreversibly enter a failure state with probability k_half.

Build

We extended the Cycle 4 framework by incorporating:

1. Stochastic simulations (SSA, Gillespie algorithm) to capture cell-to-cell variability.
2. Failure pathway parameterization via k_half, quantifying the probability of pathway collapse under asynchronous end recombination.
3. Cross-batch variability analysis, with repeated simulations used to calculate 50% and 95% confidence intervals of the overall success fraction.
4. Input enzyme profiles taken from Cycle 2’s plateau-type Bxb1 supply (~11.16 μM, ToT ≈ 180 min), chosen because it most realistically reflects experimental induction conditions [7].

Test

• Population-level comparison (Fig. M4-C5-1A): Independent assumption (blue) predicted overly rapid rise and inflated plateau; decoy-corrected model (orange) reduced the plateau but retained a steep slope. Only the decoy + synchronization model (green, (k_half = 0.15)) reproduced both slope and final plateau, consistent with M423-like experimental data.

ODE and stochastic simulations under Cycle-2 plateau enzyme supply. Blue: independent assumption; Orange: decoy-corrected $ f_{free} = 0.65 $; Green: decoy + synchronization $ k_{half} = 0.15 $. Black circles: M423-like experimental data (mean ± SEM). Only the synchronization-corrected model reproduces both slope and plateau.

• Cross-batch variability (Fig. M4-C5-1B): Simulated trajectories across replicate populations yielded a stable plateau with narrow 95% confidence intervals, in line with experimental reproducibility.

Population success fraction simulated with decoy + synchronization. Solid line: mean success; shaded area: 95% binomial CI across replicate populations. This captures aggregate uncertainty and validates reproducibility across experimental replicates.

• Single-cell heterogeneity (expected): Simulations predicted a bimodal outcome: ~60% of cells achieving complete recombination within 120–200 min, while ~40% stalled in incomplete states. This distribution reflects stochastic synchronization failures and aligns with theoretical expectations from single-cell studies [12][13][14].

Stochastic simulations of 200 single cells under Cycle-2 plateau supply. Green: cells achieving complete recombination (~60%); Red: cells stalled in incomplete states (~40%). The bimodal distribution highlights the impact of synchronization failure.

Learn

Cycle 5 established that:

1. Failure pathways are essential: asynchronous recombination leads to permanent loss of productive trajectories.
2. Bimodal single-cell outcomes emerge naturally when synchronization is explicitly modeled, paralleling observations in stochastic gene expression [12–14].
3. Cross-batch variability reproduced experimental reproducibility, strengthening confidence in the model.
4. Connection to Cycle 6: Importantly, Cycle 5 results describe recombination conditional on attB being formed. In Cycle 6, we integrate this conditional probability with the attB gating probability pattB to explain the stark difference between M416 (0.0195%) and M423 (87.5%).

Cycle 6｜attB Gating as the Dominant Bottleneck

Design

Although Cycle 5 established conditional recombination efficiency under enzyme dynamics and synchronization effects, experimental data revealed a dramatic discrepancy between two test cases: M416 exhibited only 0.0195% overall success, whereas M423 reached 87.5%. Such a gap cannot be explained by decoy effects or Bxb1 kinetics alone. We therefore hypothesized that the true bottleneck lies in the probability of attB formation, which gates the downstream recombination process. Conceptually, the overall probability of successful recombination can be factorized as:

$$ p_{overall} = p_{attB} × p_{recomb|attB} $$

where pattB represents the likelihood of oligo integration into the genome to form attB, and precomb|attB denotes the conditional efficiency of Bxb1 recombination once attB exists [1][4].

Build

We extended the Cycle 5 framework into a two-layer hierarchical model:

1. Upstream module (attB gating): defines whether recombination can initiate at all.
2. Downstream module (conditional recombination): corresponds to the Cycle 5 synchronization-corrected model, describing efficiency once attB is present.

Parameters were calibrated to reflect two experimental regimes:

• M416 (with decoy, distant locus): attB formation probability pattB ≪ 1.
• M423 (pre-formed attB): pattB ≈ 1.

Test

• M416 (overall collapse): Simulations reproduced an overall success rate of ~0.0195% (Fig. M4-C6-1B), consistent with experimental colony counts. Despite sufficient enzyme supply, the lack of reliable attB formation prevented downstream recombination.
• M423 (conditional efficiency): In contrast, when attB was pre-formed, the model predicted ~87.5% success (Fig. M4-C6-1A), matching observed GFP readouts. This confirmed that once attB exists, Bxb1 recombination is intrinsically robust, independent of decoy or steric hindrance.
• Comparative analysis: The gating model explained both the dramatic efficiency gap and the conditional consistency of recombination dynamics across replicates, demonstrating that attB availability is the single dominant determinant of success.

Learn

Cycle 6 revealed that:

1. The true bottleneck resides upstream, at attB formation. Without attB, downstream recombination cannot proceed, regardless of enzyme dynamics.
2. The two-layer model is essential. Separating pattB from precomb|attB reconciles M416 vs. M423 outcomes within a unified framework.
3. Experimental consistency is explained. M423 results demonstrate that once attB is established, recombination is highly efficient and reproducible, whereas M416 highlights the catastrophic effect of attB gating failure.
4. Connection to Cycle 7. Having established attB gating as the dominant upstream determinant, Cycle 7 explores secondary sequence-level factors—notably cargo length—that modulate efficiency under conditions where attB is already present.

Spaghetti plot with across-batch confidence bands for conditional recombination precomb|attB. Plateau efficiency reached ~87.5%, consistent with experimental M423 data, demonstrating robust downstream recombination once attB is pre-formed.

Spaghetti plot with across-batch confidence bands for overall recombination efficiency. Plateau collapsed to ~0.0195%, despite similar downstream parameters, highlighting attB gating as the critical upstream bottleneck.