Circadian clock in synthetic cells reveals timekeeping principles

Materials

We purchased Gold Seal™ 60 mm × 22 mm glass coverslips, Fisherbrand ^TM Premium Plain Glass Microscope Slides (75 mm × 25 mm), CELLSTAR® black clear bottom 96 well plates (Greiner), Coplin glass staining jars (DWK Life Sciences), Corning® 15 mm diameter regenerated cellulose syringe filters (0.2 µm pore size), and MilliporeSigma^TM Ultrafree^TM-MC centrifugal filter devices (0.22 µm pore size) from Thermo Fisher Scientific (Waltham, MA). We purchased artist grade tracing paper (Jack Richeson & Co., Inc.), circular hole punches (EK Tools Circle Punch, 3/8 in.), square hollow punch cutters (Amon Tech) from Amazon Inc. (Seattle, WA).

Chemicals

We purchased sucrose (BioXtra grade, purity ≥99.5%), glucose (BioXtra grade, purity ≥99.5%), bovine albumin-fluorescein isothiocyanate conjugate (FITC-BSA) (albumin from bovine, ≥7 mol FITC/mol albumin), sodium chloride (NaCl) (ACS grade, VWR International), magnesium chloride hexahydrate (MgCl₂·6H₂O) (ReagentPlus grade, purity ≥99%, Sigma-Aldrich), and ethylenediaminetetraacetic acid (EDTA) (BioReagent grade, purity ≥98.5%) from Sigma-Aldrich (St. Louis, MO). We purchased chloroform (ACS grade, purity ≥99.8%, with 0.75% ethanol as preservative), 1 N potassium hydroxide (KOH) (Certified grade, 0.995 to 1.005 N, Fisher Chemical), 3-aminopropyl trimethoxysilane (APTES) (purity ≥98.5%, ACROS Organics), glacial acetic acid (ACS grade, purity ≥99.7%, Fisher Chemical), methanol (ACS grade, purity ≥99.8%, Fisher Chemical), adenosine 5′-triphosphate (ATP solution) (Tris-buffered, purity >99% via HPLC, Thermo Scientific) from Thermo Fisher Scientific (Waltham, MA). We obtained 18.2 MΩ·cm Type I ultrapure water from an ELGA Pure-lab Ultra water purification system (Woodridge, IL).We purchased 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-(methoxy(polyethylene glycol)-2000) (PEG2000-DSPE), 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-(biotinyl(polyethylene glycol)-2000) (PEG2000-DSPE-Biotin), and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhodamine B sulfonyl) (Rhod-DOPE) from Avanti Polar Lipids, Inc. (Alabaster, AL). We purchased NHS-ester polyethylene glycol (PEG) (5 kDa) and biotinylated NHS-ester PEG (biotin-PEG) (5 kDa) from Laysan Bio, Inc. (Arab, AL).

Kai clock protein expression, purification, and labeling

Freshly transformed cells harboring the expression construct (seKaiA-1-284, seKaiB-1-102-FLAG, sekaiB-1-102-K25C-FLAG, FLAG-seKaiC-1-519) were used for the inoculation of a starter culture in lysogeny broth (LB) medium with 50 mg/mL kanamycin sulfate and incubated in a shaker at 37 °C and 220 rpm for 6.5 h¹⁴. We then transferred 5 mL of the starter culture to 1 L of M9 medium with 0.2% D-glucose, 2 mM MgSO₄, 0.1 mM CaCl₂, and 50 µg/mL kanamycin sulfate. The cells grew at 37 °C and 220 rpm until an optical density of 0.6 at 600 nm was reached. We induced protein expression by introducing 0.2 mM isopropyl β-d-1-thiogalactopyranoside to the cells and further incubated at 30 °C in the shaker for 12 h.

We harvested the cells and used an Avestin C3 Emulsiflex homogenizer to lyse the cells. The cell lysate was spun down by centrifugation at 27,000 × g for 45 min at 4 °C. We then performed affinity purification with Ni-NTA columns at 4 °C using lysis buffer (50 mM NaH₂PO₄, 500 mM NaCl, pH 8.0), wash buffer (50 mM NaH₂PO₄, 500 mM NaCl, 20 mM imidazole, pH 8.0), and elution buffer (50 mM NaH₂PO₄, 500 mM NaCl, 250 mM imidazole, pH 8.0). Then we added ULP1 for the cleavage of the 6×His-SUMO fusion protein at 4 °C for 15 h. We loaded the cleaved protein on a Ni-NTA column again to remove the 6×His-SUMO. We concentrated the flow-through with a 10 kDa molecular weight cut-off (MWCO) membrane filter in an Amicon^TM stir-cell concentrator at 4 °C, then further purified the recovered protein by gel-filtration chromatography¹⁴.

For fluorescent labeling of KaiB, we mixed the purified KaiB-K25C with 80 µL of 12.5 mg/mL 6-(Iodoacetamido)fluorescein (6-IAF) suspended in methanol and incubated at 4 °C for 15 h. The sample was then concentrated to 2 mL with a 10 kDa MWCO membrane filter in an Amicon stirred cell concentrator, then further purified by gel-filtration chromatography to separate labeled protein from free fluorophore¹⁴.

Preparation of biotin-PEG functionalized glass

Biotin-PEG functionalized glass allows vesicles to be bound to the glass surface through streptavidin-biotin interactions, effectively preventing lateral and axial diffusion of the vesicles during imaging. The lipid mixture used to assemble vesicles must contain a biotinylated lipid for this methodology to work. The procedure to prepare the functionalized slides outlined below is primarily based on procedures reported in ref. ³⁷ with some modifications.

First, we scratched ten 60 × 22 mm glass coverslips and ten 75 × 25 mm glass slides with a small line in the top right corner using a diamond-tipped scriber. The line allowed identification of which surface is functionalized. Otherwise, both the functionalized and non-functionalized surfaces appear identical. Working in a chemical safety hood, we placed the ten marked glass coverslips and ten marked glass slides together into a Coplin glass staining jar with each of the five slots containing one glass coverslip and one glass slide. The glass slides and coverslips were placed so that the marked surfaces to be functionalized were facing away from one another. The jar containing the glass was filled with 50 mL of ultrapure water, swirled, and then emptied.

These steps were repeated two more times. The jar was filled with 50 mL of acetone and placed in a bath sonicator in a chemical safety hood for 20 min. We then discarded the acetone and rinsed the jar with ultrapure water three times. The jar was next filled with 50 mL of 1 N KOH and placed in a bath sonicator for 30 minutes. We then left the jar in the chemical safety hood overnight to allow KOH to etch the surface layer of the glass.

The next day, we prepared a 50 mL “silanization mixture” of 3-aminopropyl trimethoxysilane (APTES) and acetic acid at 10 v/v% and 5 v/v% in methanol, respectively. We then discarded the KOH and rinsed the jar with ultrapure water three times. The silanization mixture was then added to the jar and incubated for 30 min. After 30 min, we discarded the silanization mixture in an appropriate waste container and rinsed the jar with 50 mL of neat methanol 3 times. Then, we dried the coverslips using a stream of ultrapure nitrogen gas from a nitrogen gun.

We filled empty 10–100 µL or 100–1000 µL plastic pipette tip boxes, with the insert included, with 20 mL of ultrapure water to act as humidity chambers (Supplementary Fig. 3A). We prepared a mixture of NHS-PEG (5 kDa) and biotinylated NHS-ester PEG (5 kDa) at a concentration of 125 mg/mL and 3.1 mg/mL, respectively, in 0.1 M sodium bicarbonate buffer (pH 8.5). 64 μL of this mixture was sandwiched between two sets of marked surfaces of the coverslips or slides. The surfaces were placed into the humidity chamber, propped up by pipette tips (Supplementary Fig. 3B). Any air bubbles between the glass surfaces were removed by applying gentle pressure. We closed the lid of the pipette tip boxes and placed the box in a benchtop cabinet that was cool and protected from light. Functionalization was allowed to continue overnight. The next day, we carefully took the glass sandwiches apart and rinsed the surfaces with ultrapure water. We then dried the slides using a stream of ultrapure nitrogen gas from a nitrogen gun. Each pair of glass slides and coverslips was stored in a 50 mL Falcon^TM conical centrifuge tube in a −20 °C freezer such that the functionalized sides were not in contact with each other or the walls of the centrifuge tubes.

Buffers

10× clock buffer consisted of 200 mM Tris, 1500 mM NaCl, 50 mM MgCl₂, 10 mM ATP, and 5 mM EDTA, and was based on the buffer optimized for cyanobacterial circadian clock proteins when diluted to 1×¹⁴. The initial budding buffer consisted of 119 mM sucrose. The final buffer composition after GUV assembly consisted of 1× clock buffer and 100 mM sucrose. The sedimentation buffer was equimolar with the budding buffer, consisting of 100 mM glucose and 1× clock buffer. All buffers and solutions were filtered through a 0.2 μm regenerated cellulose syringe filter.

Phospholipid mixtures

The standard phospholipid mixture used in studies with GUVs consisted of a 1 mg/mL solution of DOPC:PEG2000-DSPE:PEG2000-DSPE-Biotin:Rhod-DOPE at 94.4:5.0:0.5:0.1 mol% in chloroform. Here, DOPC (94.4 mol %) was the primary bilayer forming phospholipid. PEG2000-DSPE (5.0 mol %) is a PEG functionalized lipid that provides steric repulsion and has the primary role of inhibiting aggregation of vesicles in the salty clock buffer. PEG2000-DSPE-Biotin (0.5 mol %) is a PEG functionalized lipid with a terminal biotin moiety that allows streptavidin-biotin binding interactions used to immobilize GUVs to the biotinylated glass surfaces. Rhod-DOPE is a rhodamine functionalized lipid that allows the visualization of bilayer membranes.

Protein solutions

Protein solutions were prepared at 15× the intended final concentrations in 1× clock buffer and filtered through a 0.2 μm regenerated cellulose syringe filter. FITC-BSA was used as the model protein for investigating encapsulation statistics. 1.0× PTO reactions contained 1.2 µM KaiA, 1.75 µM KaiB, 1.75 µM KaiB-6IAF, and 3.5 µM KaiC. We scaled the other PTO concentrations accordingly.

Assembly of giant vesicles using PAPYRUS with diffusive loading (PAPYRUS-wdL)

We deposited 10 μL of a 1 mg/mL lipid solution onto a 9.5 mm diameter circular cutout of tracing paper using a Hamilton glass syringe^15,16. The lipid was dispensed slowly, nearly parallel to the paper, while simultaneously using the long edge of the syringe tip to evenly spread the lipid across the tracing paper as the chloroform evaporated. During this process, the tracing paper was held by clean metal tweezers and not placed down until the chloroform had completely evaporated. We then placed the lipid-coated tracing paper into a standard laboratory vacuum chamber for 1 h to remove traces of residual chloroform.

Diffusive loading allows the assembly of GUVs in salty solutions by first allowing budding to occur in low salt solutions (Supplementary Fig. 4A). After the formation of buds, salt and then proteins are introduced into the lumens of the surface-attached GUV buds via diffusion (Supplementary Fig. 4B). For these experiments, the assembly and loading steps were done at room temperature.

We first affixed a polydimethylsiloxane (PDMS) gasket (12 mm Ø_ID × 1 mm height) onto a clean glass slide to form an assembly chamber. We then removed the lipid-coated tracing paper from the vacuum chamber and placed it into the assembly chamber. Next, we added 126 μL of a solution of 119 mM sucrose into the assembly chamber. After three minutes, we added 14 μL of 10× clock buffer underneath the paper. Adding the solution underneath the paper protects the buds that are assembling on the surface of the paper. The concentration gradient equilibrates via diffusion and the components of the clock buffer enter the lumens of the surface-attached buds. Seven minutes later, 10 μL of 15× protein solution was added directly to the external phase, above the paper substrate, and given an additional 110 min for the protein to diffuse into the surface-attached buds (Supplementary Fig. 4C). Supplementary Table 1 summarizes the buffer and protein addition steps for the PAPYRUS-wDL method.

After the incubation, we aspirated the solution in the chamber with a 100–1000 μL pipette set at a volume displacement of 100 μL. We aspirated a total of six times over different locations on the paper. This action detached the buds from the surface of the paper, which self-closed to form GUVs (Supplementary Fig. 4D). The fully-formed GUVs trapped the protein and salts in their interior.

Sample preparation and imaging

A custom chamber was used for imaging the GUVs. To make this chamber, we broke a PEG-biotin functionalized glass coverslip into two equal parts (~30 mm × 22 mm) by first scoring the surface with a diamond-tipped scriber. We then affixed a circular PDMS gasket (Ø_OD = 10 mm) with an internal 6 mm × 6 × mm × 1 mm square chamber to one-half of the PEG-biotin functionalized glass coverslip. The PDMS gasket and the glass adhere reversibly through van der Waals interactions if both are clean and free from dust. Next, we added 20 μL of 0.1 mg/mL streptavidin to the chamber and allowed the solution to incubate for 15 min. We then removed and discarded the streptavidin solution and washed the coverslip five times with 60 µL of the sedimentation buffer to remove unbound streptavidin.

We prepared concentration-matched sedimentation buffers by mixing 1260 μL of a solution of 119 mM glucose with 140 μL of the concentrated 10× clock buffer and 100 μL of 15× protein solution in a 1.5 mL Eppendorf tube, to match the concentrations used in the assembly and loading of the GUVs. We added 30 μL of the GUV containing suspension to the chamber and then added 30 μL of the concentration-matched sedimentation buffer. The chamber was sealed with a 22 × 22 mm square coverslip. We waited 3 h for the GUVs to sediment to the bottom of the chamber and bind to the streptavidin-coated glass through biotin-streptavidin interactions.

Prior to imaging, the chamber was flipped upside down, so that the bound GUVs were at the top surface. Flipping allowed us to image using high NA low-working distance objectives on the upright microscope. We used a Zeiss upright microscope (LSM 880, Axio Imager.Z2m, Zeiss, Germany), with a 63× 1.4 NA Oil Plan-Apochromat objective to image the samples. The “red” channel which imaged the Rhod-DOPE lipids was configured with 2.5% power for the 561 nm diode-pumped solid-state (DPSS) laser and a detector gain of 700 A.U. for the confocal photomultiplier tube detector. The “green” channel which imaged the FITC-BSA was configured with 2% power for the 488 nm argon laser and a detector gain of 650 A.U. for the gallium arsenide phosphide (GaAsP) detector. The pinhole diameter was set to 1 A.U., corresponding to a 0.7 μm thick imaging slice. A 7 × 7 tile scan, consisting of 49 images covering a region of 135 × 135 μm per image, was taken using reflection-based autofocusing with an offset of 3 μm into the sample from the glass surface. The image resolution was set to 1584 × 1584 pixels with 4× line averaging. Supplementary Fig. 5 shows a schematic of the imaging geometry.

Field flatness correction

Although a Plan-Apochromat objective provides good field flatness, there was still noticeable dimming near the edges of the images (Supplementary Fig. 6A). We corrected this dimming by flattening the field. We created a background mask using the red channel and used it on the green channel to obtain the background intensity. We fit this background image with a 2D polynomial, \(f(x,y)={a}_{0}+{a}_{1}x+{a}_{2}y+{a}_{3}{x}^{2}+{a}_{4}{y}^{2}+{a}_{5}{xy}\). We multiplied the green channel with the flatness correction factor \(\left(\frac{{z}_{\max }}{f\left(x,y\right)}\right)\). Here z_max is the global maximum value of the function \(f(x,y)\). An example of the effect of each step of the algorithm on an image is shown in Supplementary Fig. 6B-D.

Selection using the coefficient of variation (CV) of pixel intensities

GUVs are the target of interest but lipid aggregates, multilamellar vesicles (MLVs), and multivesicular vesicles (MVVs) can also be present in the sample (Supplementary Fig. 7A). We use a selection algorithm that distinguishes GUVs from other objects by their coefficient of variation (CV) of pixel intensities. The CV is the standard deviation of the pixel intensities, \(\sigma\) divided by the mean of the pixel intensities, \(\mu\), of an object, \({{{\rm{CV}}}}=\frac{\sigma }{\mu }\). The CV was calculated using the intensity of all pixels located within each object in the red channel. The large contrast between the high pixel values of the bright fluorescent membranes and the low pixel values of the dark lumens results in a high CV value. Aggregates, MLVs, or MVVs have lower CV values than GUVs since the interior of these objects contains membranes that are imaged as bright pixels. Gating for objects with a CV > 0.75 selects mainly GUVs while excluding other objects (Supplementary Fig. 7B). We then examined the images manually and excluded any non-GUV objects that may have been selected. For negative controls where no FITC-BSA was encapsulated in the lumen but was present in the exterior solution, we performed a second automated selection based on the CV of the objects in the green channel to exclude GUVs with invaginations in the membrane.

Imaging geometry of the lumen

A slice thickness of 0.7 μm with 3 μm offset from the coverslip places the imaging plane within the lumen of GUVs ≥ 4 μm in diameter. Thus, only GUVs with diameters ≥4 μm were considered in our analysis. We measured the intensity of FITC-BSA within a concentric circular region of interest (ROI) at the center of each GUV. The diameter of the ROI is 30% of the GUV diameter, \({D}_{{ROI}}=0.3{D}_{{GUV}}\).

Determination of empty GUVs

We expect that the hydrodynamic perturbation of adding the buffers with salts or proteins to the chamber will cause some of the buds to detach prematurely and close to form GUVs (Supplementary Fig. 4) Buds that detach from the lipid film and close to form GUVs early in the process of diffusive loading are expected to remain empty or have very low amounts of encapsulated protein since the GUV membranes are impermeable to the protein. Histograms of the intensities of the lumen of the GUVs show two distinct peaks, one at a lower intensity and the other at an intensity corresponding to the loading concentration (Supplementary Fig. 8A). In comparison, histograms of GUVs that are prepared without any protein show a single low-intensity peak (Supplementary Fig. 8B). We found the location of the peak(s) and the full width at half maximum (FWHM) using the findpeaks function for both histograms. The peak position and the right boundary of GUVs not loaded with protein corresponded to the lower peak in the histogram of the samples loaded with protein. The fraction of GUVs within this peak ranged from 18 to 20% of the samples loaded with protein. The fraction did not depend on the loading concentration of the protein [F(3,8) = 0.46, p = 0.72]. We exclude the bottom 20% of the histogram of all samples prepared with protein as coming from GUVs devoid of protein.

Bulk measurements of fluorescence intensity of clock reactions

We deposited 50 µL of the reactions into wells of a black clear-bottom 96-well plate. To minimize evaporation during the multiday experiments, we filled empty wells with ultrapure water. We use a SpectraMax® M2e plate reader to measure the mean fluorescence intensity every 30 min for a total of 96 h using the bottom read mode. The chamber temperature was set to 30 °C, fluorescence was excited at 485 nm, and emission was collected between 530 and 538 nm. Measurements were taken with high detector sensitivity and each data point was an average of 6 reads.

Fluorescence quenching measurements of KaiB-6IAF

To obtain a readout on the state of the PTO using fluorescence measurements, 50 mol% of the KaiB molecules were labeled using 6-(Iodoacetamido)fluorescein (6IAF) to form the fluorescently labeled KaiB-6IAF. KaiB-6IAF is quenched when it forms KaiBC and KaiABC complexes resulting in a drop in the mean fluorescence intensity. When KaiB-6IAF complexes disassociate, they become unquenched, and fluorescence intensity is restored. This allows real-time readout of the state of the clock using measurements of fluorescence intensity. The quenching occurs due to the presence of tryptophan residues near the KaiB-binding site on the CI domain of KaiC³⁸. Tryptophan residues quench the fluorescence intensity of many fluorophores, such as the conjugated fluorescein on KaiB-6IAF³⁹.

We add 25 µL of 50:50 mixture of KaiB:KaiB-6IAF at a concentration of 7 µM to 25 µL of serially diluted KaiC in a black clear bottom 96-well plate. Since KaiB binds slowly to fully phosphorylated KaiC, we obtain kinetic plots of the mean intensity of KaiB-6IAF for 22 h. Note that the formation of the KaiBC complex can occur even without the presence of KaiA because KaiC is initially hyperphosphorylated due to its preparation and storage at low temperatures^27,40,41. The results in Supplementary Fig. 1A demonstrate the decrease in KaiB-6IAF fluorescence intensity with time for various KaiC concentrations. Supplementary Fig. 1B shows that the decrease in KaiB-6IAF fluorescence intensity is linearly related to KaiC concentration (\(y=0.12\left[{{{\rm{KaiC}}}}\right]+1,\,{R}^{2}=0.97\)) (5). The fluorescence intensity decreased by ~60% at 3.5 μM KaiC. Further increasing the concentration of KaiC to 7.0 µM did not result in additional quenching, indicating that the maximal quenching of KaiB-6IAF is ~40 %. This value is consistent with the 42% value reported in the literature for fluorescein-peptide-tryptophan quenching³⁹. We thus conclude that at 3.5 µM of KaiC, all available KaiB is bound to KaiC. Indeed, at this concentration, KaiB and KaiC monomer concentrations were equal (3.5 μM KaiB and 3.5 μM KaiC), consistent with reports that KaiBC complexes have a 6:6 monomer ratio^10,42.

Protein-loading solutions for PTO encapsulation in GUVs

We prepared protein-loading solutions at 15× the intended final protein concentration in 30 µL of 1× clock buffer. The solution was filtered using MilliporeSigma™ Ultrafree™ -MC centrifugal filters in a microcentrifuge at 13,900 × g for 3 min to remove protein aggregates. PTO-GUVs were prepared following the PAPYRUS-wDL protocol.

Sample preparation for imaging of PTO-GUVs

We followed the sample preparation protocol for GUVs encapsulating FITC-BSA with the following modifications. We did not place a coverslip on the chamber during sedimentation. Instead, we placed the chamber in a lab-built humidity chamber that consisted of two folded Kimwipes saturated with ultrapure water in a 100 mm diameter Petri dish. We find that the use of this ad hoc humidity chamber was sufficient to minimize evaporation of the solution during the 3 h of sedimentation. After three hours, we exchanged the sedimentation buffer with vesicle- and protein-free hydration buffer. Then, we gently removed 30 µL of the supernatant from the sample and added 30 µL of fresh vesicle- and protein-free hydration buffer. This process was repeated five times. Then, the imaging chamber was sealed with a circular glass coverslip (diameter = 12 mm), which produced a 1 mm overhang around the imaging chamber. The overhang was filled with Loctite^® Instant Mix Epoxy and allowed to set for at least 15 min before imaging. Sealing with epoxy minimizes evaporation from the chamber over multiple days of imaging.

Imaging PTO-GUVs

The PTO-GUVs was imaged using dual-channel imaging using a Zeiss LSM 700 upright microscope with a 20× 0.8 NA Plan-Apochromat objective. The sample chamber was flipped so that the immobilized GUVs were close to the objective on the upright stand. We used a Peltier stage to keep the sample at 30 °C. The red channel was configured to image the Rhod-DOPE in the PTO-GUV membranes, and the green channel was configured to image the KaiB-6IAF. The Rhod-DOPE was excited with a 555 nm laser and the KaiB-6IAF was excited with a 488 nm laser. Time-lapse imaging consisted of 10 positions (328 × 328 µm per position) imaged every 2 hours over the course of 100 hours (~4 days). We selected positions that had many PTO-GUVs with polydisperse distributions of diameters. The plane of optimal focus was determined manually at the beginning of the acquisition and a reflection-based autofocus was used to maintain focus over the time-lapse. Images had a resolution of 2048 × 2048 pixels with 4× line averaging. The pinhole was set to the maximum size which is 13.6 Airy Units (AU). The voxel size was 0.16 × 0.16 × 26.7 µm (Supplementary Fig. 9). The pinhole was opened to the maximum since it allowed us to use low laser power to reduce photobleaching over the course of the 4-day experiment.

PTO time series preprocessing

The raw native.czi time-series images were preprocessed using the MultiStackReg plugin with the “Translation” algorithm in ImageJ to align the images. The alignment corrected for drift in the images that occur at each acquisition time point. The red channel images, which showed the PTO-GUVs, were segmented from the background using a custom MATLAB routine. Then objects that had mean intensities within ± one full width at half maximum (FWHM) of the global peak in the mean intensity histogram were selected as potential GUVs. We select objects with diameters of 2 ± 0.5, 3 ± 0.5, 4 ± 0.5, 6 ± 0.5, 8 ± 0.5, and 10 ± 0.5 µm for analysis. The selected objects were manually inspected and objects that did not resemble GUVs (defined as spherical objects with uniform intensities) were removed from the analysis. We then used the pixel locations of the PTO-GUVs obtained from the red channel to calculate the mean intensity of KaiB-6IAF within the lumens of the PTO-GUVs in the green channel. Empty GUVs were identified as GUVs with mean intensities <20% of the encapsulated mean intensity and were not used for analysis.

Time traces of fluorescence intensity

Time traces of the intensities of KaiB-6IAF from each PTO-GUV were obtained using the regionprops MATLAB function. The time trace of the intensity of the background was subtracted from the signal from the PTO-GUVs. The signals were normalized using the intensity at t* = 0. Here t* = 0 represents the time point of the first frame of the time-lapse, which is 7 h after the clock reaction was started by mixing the Kai proteins for loading into the GUVs. The normalized KaiB-6IAF time traces of each PTO-GUV was fit to a two-term exponential decay equation (\(y={a}{e}^{{bt}}+c{e}^{{dt}}\)). The fitted line was then subtracted from the normalized time traces to correct for photobleaching⁴³.

Fast Fourier Transform (FFT) analysis of PTOs

To identify oscillating PTO-GUVs, we performed a fast Fourier transform (FFT) with 1000 point zero-padding on each of the time traces and obtained a single-sided amplitude spectrum. Then, we used the findpeaks function to find peaks in the spectrum. We then filtered the spectra to identify spectra with a single global peak that i) had a height > 0.04, ii) was 30 % higher than any other peak, and iii) had a center within a frequency range of 1.39 × 10^-5Hz (16 h) to 1.07 × 10^-5Hz (30 h). The frequency corresponding to the center of the global peak is converted into the characteristic period of oscillation. Spectra that do not satisfy these criteria are classified as not oscillating. This filtering criteria resulted in ≤2% of the negative control being falsely identified as oscillating. Clock fidelity is the sum of PTO-GUVs that oscillate divided by the total number of PTO-GUVs in the group. A clock fidelity of zero would mean no PTO-GUVs oscillate, and one would mean all PTO-GUVs oscillate.

Assignment rules for Kai proteins in modeled PTO-GUVs

Kai proteins form complexes during the process of diffusive loading. Approximately 13% of KaiC are expected to be in a KaiABC protein complex (Supplementary Fig. 1A). The KaiABC complex consists of KaiA, KaiB, and KaiC monomers in a 12:6:6 molar ratio^10,42. KaiA was assigned as dimers, KaiB as tetramers, and KaiC as hexamers. We assigned concentrations in 5000 simulated vesicles by using the gamrnd function with the shape parameter \(k\) and scale parameter \(\theta\). The parameter values were determined assuming a CV of 0.31 and a mean concentration, \(\mu,\) corresponding to the loading concentration of the protein. Then the parameters were calculated using \(k=1/{{{\rm{C}}}}{{{{\rm{V}}}}}^{2}\) and \(\theta=\mu {{{\rm{C}}}}{{{{\rm{V}}}}}^{2}\). After assignment to each vesicle, the concentration of the constituent components of the KaiABC complexes was redistributed as monomeric KaiA, KaiB, and KaiC.

We assume that KaiB binds to the membrane resulting in a reduction of the free concentration of KaiB in the lumen. We use Eq. (1) with b = 650 KaiB monomers per µm² to calculate the concentration of free KaiB (\({C}_{{free},{KaiB}}\)) in a vesicle of radius, \({r}_{i}\).

In this equation, \({C}_{i,{KaiB}}\) is the nominal concentration of KaiB obtained from the gamma distribution and \({N}_{A}\) is Avogadro’s number.

Limiting concentration and ratio rules for modeled PTO-GUVs

Limiting concentrations (\({C}_{L,[X]}\)) and ratios were obtained from our bulk plate reader experiments. The stoichiometric ratios were obtained from values in the literature. The PTO failed in the bulk experiments when the concentration of the PTO proteins was 0.5×, that is when the concentration of KaiA <0.6 µM, KaiB <1.75 µM, and KaiC <1.75 µM. Following convention in the field, all concentrations are reported as monomeric concentrations. This result was consistent with previous bulk measurements^8,19,22. The limiting stoichiometric ratios of KaiA and KaiB were measured relative to fixed KaiC concentrations^8,19,22. The limiting ratio of KaiA to KaiC 0.17 ≤ \({R}_{L,[{KaiA}:C]}\) ≤ 1.02 and KaiB to KaiC \({R}_{L,[{KaiB}:C]}\,\)≥ 0.5. There appears to be no upper limit of stoichiometric ratios for KaiB to KaiC^8,22.

Calculation of fidelity

A vesicle was considered to oscillate only if (i) all the protein stoichiometries are at or above the limiting ratio and at or below the maximum ratios, and (ii) the concentration of free proteins is at or above the minimum concentration for all protein species. A measure of clock fidelity was determined by taking the sum of vesicles that oscillate divided by the total number of vesicles in the group (5000 simulated vesicles).

Calculation of periods and amplitude

The period and amplitude of the PTO depend on the concentrations and stoichiometric ratios of the Kai proteins⁸. The concentration of KaiA, KaiB, and KaiC and their ratio varies from vesicle to vesicle. We hypothesized that linear addition to the periods and amplitudes that we measured in our bulk experiment can be used to predict the properties of the PTO in the vesicles. We use Eq. (2), and Eq. (3) and calculate the periods, \({T}_{i}\) and amplitude \({A}_{i}\) of the encapsulated PTO in vesicle \(i\).

\({T}_{\left[C\right]}\) and \({A}_{\left[C\right]}\) are the period and amplitude measured from our bulk experiments with concentrations varying from 0.75× to 2.5×, and with the in vitro WT stoichiometry of 0.34:1:1 of monomeric KaiA:KaiB:KaiC. \(\varDelta {T}_{\left[A\right]:\left[C\right]}\), \(\Delta {A}_{\left[A\right]:\left[C\right]}\) and \(\varDelta {T}_{\left[B\right]:\left[C\right]\,}\), \(\varDelta {A}_{\left[B\right]:\left[C\right]}\) are the changes in the period and amplitude due to varying KaiA-to-KaiC and KaiB-to-KaiC stoichiometric ratios respectively. \(\varDelta {T}_{\left[A\right]:\left[C\right]}\), \(\varDelta {T}_{\left[B\right]:\left[C\right]\,}\), and \(\Delta {A}_{\left[A\right]:\left[C\right]}\) were calculated from the data reported in ref. ⁸. \(\varDelta {A}_{\left[B\right]:\left[C\right]}\) was obtained from the data reported in Supplementary Fig. 1B. Values between the data points were obtained by linear interpolation. The relationships between the concentration and ratios with the amplitude and period shown in Supplementary Fig. 10.

PTO in cyanobacteria-mimicking simulations

Cyanobacteria, unlike GUVs, have internal thylakoid membranes^19,44,45. It is known that approximately 50 % of the KaiB is associated with membrane fractions in cyanobacteria²³. To simulate the effect of protein variation, we assign the Kai proteins according to the gamma distribution with a mean concentration of KaiA= 2.70 µM, KaiB = 10.80 µM, KaiC = 7.26 µM into 5000 “bacteria” which corresponds to 2.1× the in vitro WT KaiC PTO concentration⁴. The other concentrations were changed accordingly by multiplication. Note the in vivo stoichiometry does not correspond exactly to the in vitro PTO stoichiometry that is commonly used for bulk experiments. We use a CV value of 0.25¹⁷. Then the KaiB concentration was reduced by 50% before the fidelity, the period, and the amplitude of oscillations were calculated.

For the conditions with SasA and CikA support, we ease the limiting concentration, KaiA <0.3 µM, KaiB <0.9 µM. The limiting ratio of KaiA to KaiC becomes 0.09 ≤ \({R}_{L,\left[A\right]:\left[C\right]}\) ≤ 1.02 and KaiB to KaiC becomes \({R}_{L,\left[B\right]:\left[C\right]}\) ≥ 0.25. These numbers were obtained from⁸ where CikA and SasA were added to the PTO mixture and ratios and concentration of the Kai proteins were varied.

Calculation of traces for the “No memory” scenario

We select from the gamma distribution 17 times to reflect 17 cycles. We calculate the period, \({T}_{i}\), and expected amplitude, \({A}_{i}\), for vesicle \({i}\) for each of the \(j=1-17\) cycles. We then obtain the time trace for each cycle using \({F}_{i,j}={A}_{i}\sin \left(\frac{2\pi }{{T}_{i}}t\right)\), and concatenate the trace for each cycle to obtain the time trace for the simulated cyanobacteria. \(t=0:0.01:{T}_{i}\). \({t}\) and \({T}_{i}\) are measured in hours. The simulation was repeated 5 times, and the mean and standard deviation of the parameters were used to plot the data in Fig. 7.

Calculation of traces for the “Perfect memory” scenario

We retain the initial concentration obtained from the gamma distribution for each of the 17 cycles. We calculate the period, \({T}_{i}\), and expected amplitude, \({A}_{i}\), for vesicle \({i}\) for each of the \(j=1-17\) cycles. We then obtain the time trace for each cycle using \({F}_{i,j}={A}_{i}\sin \left(\frac{2\pi }{{T}_{i}}t\right)\), and concatenate the trace for each cycle to obtain the time trace for the simulated cyanobacteria. \(t=0:0.01:{T}_{i}\). \({t}\) and \({T}_{i}\) are measured in hours. The simulation was repeated 5 times, and the mean and standard deviation of the parameters were used to plot the data in Fig. 7.

Calculation of traces for the “No memory + TTFL” scenario

To simulate the effect of the TTFL, we assume that the stoichiometry is corrected so that at the end of each cycle, the simulated cyanobacteria will have a period and amplitude equal to the WT average. We averaged the period and amplitude calculated from the concentration and stoichiometry of the protein at the beginning of each cycle with the WT period and used the averaged value for \({A}_{i}\) and \({T}_{i}\).

Calculation of phase shifts

The time traces of each individual vesicle are averaged. Then a sinusoid, \(f\left(t\right)=\,B\,{{{\rm{sin}}}}\left(\frac{2\pi }{{t}_{0}}t-\phi \right)\) was fit to the curve to obtain the characteristic period, \({t}_{0}\). In this equation, \(B\) is the amplitude and \(\phi\) is the phase shift. The use of a sine simply shifts the phases by \(\frac{\pi }{2}\) relative to the cosine which was used in refs. ^3,8,11. Then, each signal is windowed to a 24-hour cycle. The windowed signal for each simulated cyanobacteria is fitted with the sine function with \({t}_{0}\) as a fixed parameter to obtain the phase shift, ϕ, and the amplitude, \(B\). For the polar plots in Fig. 7, the reference period and amplitude are calculated using the mean clock protein concentration and stoichiometric ratios. We randomly chose 500 simulated cyanobacteria from the 5000 to plot the polar plots.

Calculation of the synchronization index

To characterize the synchronization of the signals, we used the synchronization index as described in refs. ^11,31. The synchronization index (SI) is based on the Shannon entropy of the phase distribution, defined as \({SI}=({S}_{\max }-S)/\,{S}_{\max }\). Here \({S}_{\max }={{\mathrm{ln}}}N\), where \(N\) is the number of bins and \({p}_{k}\) is the probability of the data occurrence in each bin. The entropy of the distribution is defined as \(S=\,-{\sum }_{k=1}^{N}{p}_{k}{{\mathrm{ln}}}{p}_{k}\). Following¹¹, we used N = 8 bins for the phase distributions as a function of time. The phase shifts were wrapped to be between 0 and 2π. The SI was calculated for the signal for each 24-hour window. The SI is set up where a value of 1 corresponds to perfect synchronization (Dirac-like distribution) and a value of 0 corresponds to no synchronization (uniform distribution)³¹.

Statistics and reproducibility

Sample sizes and the number of repeats are reported in the legends and the main text. Statistical tests were performed using MATLAB 2023b (version 23.2). A p level of >0.05 was considered significant.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.