Synthetic cell–based materials extract positional information from morphogen gradients

Abstract

Biomaterials composed of synthetic cells have the potential to adapt and differentiate guided by physicochemical environmental cues. Inspired by biological systems in development, which extract positional information (PI) from morphogen gradients in the presence of uncertainties, we here investigate how well synthetic cells can determine their position within a multicellular structure. To calculate PI, we created and analyzed a large number of synthetic cellular assemblies composed of emulsion droplets connected via lipid bilayer membranes. These droplets contained cell-free feedback gene circuits that responded to gradients of a genetic inducer acting as a morphogen. PI is found to be limited by gene expression noise and affected by the temporal evolution of the morphogen gradient and the cell-free expression system itself. The generation of PI can be rationalized by computational modeling of the system. We scale our approach using three-dimensional printing and demonstrate morphogen-based differentiation in larger tissue-like assemblies.

Synthetic cells use positional information to determine their position when exposed to a synthetic morphogen gradient.

INTRODUCTION

Biological development—the generation of a complex, differentiated organism starting from a single cell—is a notable example of self-organization in biology that has inspired chemists, materials scientists, molecular programmers, and synthetic biologists alike to envision autonomously developing, self-differentiating, and self-sustaining biomimetic systems (1–12). Newly available techniques such as three-dimensional (3D) printing of soft materials have opened up the possibility to automate and standardize the assembly of materials, where properties are defined across scales by combining top-down specification via additive manufacturing with bottom-up pattern formation via molecular self-organization. In this context, researchers have recently begun to create artificial multicellular structures (13–15), which may form the basis of biomaterials capable of differentiating into functionally distinct regions, based on external chemical and physical cues.

A common mechanism for biological patterning uses the information supplied by morphogen gradients that are interpreted by gene regulatory circuits to infer the position of cells within the developing organism (16). In a similar way, synthetic morphogen gradients might be used in the context of synthetic cell–based materials that host engineered gene circuits for pattern formation. To reproducibly manufacture these materials, it will be important to understand the potential and limitations of morphogen-based self-organization in these systems (17). As position determines the fate of the synthetic cells and the future organization of the biomaterial—together with its desired functionality-developmental processes have to take place robustly in the presence of stochastic variations in both external and internal parameters, e.g., the size of the artificial tissue, the gradient profile, or gene expression noise (18).

The ability of a genetic circuit to determine position within a system, in the presence of noise, can be precisely quantified by calculating the “positional information” (PI) based on the “mutual information” between gene expression levels and position within the organism (19, 20). PI is a global measure of the information contained within the gene expression spatial profiles of an organism. PI has been thoroughly analyzed in the context of the gap gene network that is involved in the development of the Drosophila early embryo. It was found that the gap gene expression pattern allows specifying the position along the embryo’s anterior/posterior axis with a remarkable accuracy of 1% (19, 20). The concept has also been successfully applied to the decoding of PI provided by opposing morphogen gradients in the developing neural tube (18). In both cases, it can be argued that the gene networks interpret the underlying morphogen gradients in an “optimal” way that minimizes patterning errors (18, 21).

In the present work, we apply the PI concept in a synthetic context by characterizing the response of synthetic multicellular systems to the presence of a morphogen gradient formed by a diffusible genetic inducer. To this end, permeable tissues of synthetic cells are equipped with different kinds of cell-free gene circuits—composed of different combinations of genetic repressors—that, depending on the circuit topology, respond to this gradient in different ways. Backed up by numerical modeling, we find that the extracted PI depends on the circuit’s response function relative to the morphogen gradient, the temporal evolution, and lifetime of the cell-free gene expression reactions in the presence of gene expression noise. Quantitation of PI is thus shown to provide a rational approach for the characterization and engineering of developmental processes in synthetic cell–based biomaterials. To explore the route toward the automated and standardized manufacturing of differentiated synthetic tissues, we also apply our results obtained from 1D differentiation studies to investigate the evolution of a developmental circuit within a synthetic multicellular structure fabricated with a custom-made multipurpose bioprinting platform.

RESULTS

A summary of our approach is shown in Fig. 1. Our experimental system consists of linear assemblies of water-in-oil droplets, serving as prototypical synthetic cellular compartments. Multicellular systems are formed by bringing lipid monolayer–enclosed compartments into contact with each other using a micromanipulator, which creates a permeable lipid bilayer between adjacent cells as previously described (Fig. 1A) (22–24). Using this technique, we generated assemblies of six droplets each, in which one of the terminal cells contained a genetic inducer [isopropyl-β-d-thiogalactopyranoside (IPTG)] acting as the morphogen, and the other cells contained a cell-free expression system and a genetic circuit responding to the morphogen. IPTG was chosen over other inducers because of its favorable membrane permeability and diffusion properties in droplet assemblies, which we had characterized earlier (22). Diffusion of the inducer from the “organizer” or “sender” cell into the array creates a morphogen gradient across the “receiver” cells that elicit a position-dependent gene expression response (Fig. 1, A to C, and movie S1).

Fig. 1. Investigation of morphogen-based differentiation in synthetic cell assemblies.

The response of gene networks to morphogen gradients is used to quantify PI and PE. (A) Artificial cell assemblies consist of nanoliter-sized water-in-oil droplets connected by lipid bilayer interfaces. Assemblies consist of a source droplet containing a morphogen (the inducer IPTG in our case) and identical receivers containing the gene network. The morphogen diffuses from its source and forms a dynamic gradient along the main axis of the system. Induction of genes in the morphogen gradient results in differentiation of the artificial cells (microscopy image obtained for network topology A: Red and blue represent two fluorescent reporters of gene activity; cf. movie S1 for a time lapse). (B) Three gene network topologies investigated in this work involving transcriptional repressors LacI (coexpressed with RFP) and TetR (coexpressed with YFP). Topology A, mutual repression with degradation of one of the repressors; topology B, mutual repression without degradation; topology C, repression of YFP by LacI-RFP with degradation of the repressor. (C) Simulated morphogen gradient for 1 mM IPTG in the sender droplet and varying droplet volumes at t = 8 hours. (D) Diffusion of IPTG through droplet interface bilayer (DIB) networks is membrane limited, resulting in a dynamic morphogen gradient in a discrete space. (E) To estimate the PE and PI, the expression of the tagged repressors is measured in each droplet with high accuracy for a large collection of droplet assemblies, resulting in position-dependent distributions of gene expression levels (fig. S8). (F) The capability of a circuit to differentiate distinct regions in the presence of noise can be measured by the PI. (G) The local uncertainty of position based on a measurement of the gene expression levels can be quantified by the PE σ_x and the deduced probability that a position estimate is correct.

We investigated three simple gene circuit topologies (A to C) (Fig. 1B) for the readout of the morphogen gradient (Fig. 1C). Circuits A and B comprised two transcriptional repressors (LacI and TetR) mutually repressing each other’s expression, a circuit motif often found also in biological developmental circuits (25). The repressors were transcriptionally fused to fluorescent proteins [mScarlet-I, a red fluorescent protein (RFP) variant, and yellow fluorescent protein (YFP), respectively] for readout. Furthermore, in feedback circuit A, LacI was destabilized using a degradation tag (26). Circuit C, where LacI-RFP with degradation tag simply represses the expression of YFP, serves as a control without feedback via a second repressor.

In a noise-free system, each position within the assembly would be entirely defined by its local morphogen concentration and corresponding gene expression. Because of variabilities during assembly of the array, environmental fluctuations, and variations in gene expression, both morphogen gradient and gene expression levels differ from assembly to assembly. The PI I then is used as a global measure of the precision of patterning within an assembly: The number of differentiated regions in presence of these uncertainties is 2^I. A system with a total PI of 1 bit has two distinct regions, 2 bits correspond to four distinct regions, etc. We systematically calculated the PI, which is defined as the mutual information I({g_j}; x) between a set of gene expression levels {g_j}, j = 1, …, J∫, and the spatial position x, i.e.,(19, 20)

$$I(\{g_j\};x)=\int \mathit{dx} p_x(x)\int d^J\mathbf{g} p(\{g_i\}\mid x){\text{log}}_2\frac{p(\{g_i\}\mid x)}{p_g(\{g_i\})}$$

Here, p({g_j} ∣ x) denotes the probability distribution of the gene expression levels for each position x, while p_g({g_j}) and p_x(x) are the corresponding marginal distributions, and d^Jg = dg₁…dg_J. In our experiments, J = 2, g₁~[TetR − YFP], and g₂~[LacI − RFP]. Mutual information measures how much information is gained about one random variable (here, x) from knowing another (g₁ and g₂). When the variables are independent (p({g_i}∣ x) = p({g_i}), this expression is zero, and one cannot obtain any information about position. Intuitively, PI measures the base 2 logarithm of the number of regions in the system that can be differentiated (Fig. 1F).

We also evaluated how well the position can be determined at a specific point by quantifying the positional error (PE) σ_x(x). This is a local measure of the precision of patterning at each point within the assembly. PE can be estimated using the Fisher information $\mathcal{J}$(x) = ∫ d^Jg p({g_j}∣x) · (∂_x log p({g_j}∣x))², which provides a lower bound for the PE via the Cramér-Rao inequality${\mathrm{\sigma }}_x^2 (x)\ge 1/\mathcal{J}(x)$. When p({g_j} ∣ x) is Gaussian, PE can be estimated from the gradients in the mean and variance of the gene expression levels as

$$\mathcal{J}(x)=\frac{{({\mathrm{\partial }}_x \bar{g}(x))}^2}{{\mathrm{\sigma }}_g^2(x)}+2 \frac{{({\mathrm{\partial }}_x {\mathrm{\sigma }}_g(x))}^2}{{\mathrm{\sigma }}_g^2(x)}$$

Because PE diverges in regions with flat gene expression profiles (fig. S10), we instead display the probability with which the position of a droplet within the array can be inferred correctly P_corr(σ_x (x)) ∈ [0,1] (Fig. 1G and fig. S10).

To apply these concepts to our experimental data, we hence have to infer probability distributions p({g_j} ∣ x) for each position x in the assembly (Fig. 1E) and marginalize this distribution over x to obtain p_g({g_j}). p_x(x) = 1/5 in our system is uniform (section S1.3 and fig. S8).

A detailed description of our data analysis pipeline to estimate p({g_j}∣x) is given in section S1.3. Briefly, we analyzed large numbers (N = 9 to 37; table S3) of nominally identical linear arrays of synthetic cells for each of our three circuit topologies and different inducer concentrations. To ensure that the measured variability allows statements about the positional variability of gene expression, we developed an optimized image processing routine to correct for imaging and segmentation artifacts and normalized the fluorescence signals with a coencapsulated reference dye to reduce the experimental variability of the fluorescence measurements sufficiently (coefficient of variation CV < 3%, compared to 20 to 30% in gene expression profiles).

Next, we tracked the positions of the cells over time to obtain fluorescence traces for the YFP and RFP channels [as proxies for the gene expression levels $g_1^{(n)}(x,t)$ and $g_2^{(n)}(x,t)$] for each assembly (n = 1, …, N) and at each receiver position (x = 1, …,5) (Fig. 2, A to C). This resulted in experimental probability distributions for the gene expression levels at each position, i.e., p(g₁∣x, t) and p(g₂∣x, t), and the joint distribution p({g₁, g₂}∣x, t) (fig. S8). We then corrected for finite sampling and binning bias as described in detail in the Supplementary Materials.

Fig. 2. Experimental observation of gene expression gradients and determination of PI.

(A) Kymograph of an overlay of two fluorescence channels and an inverted brightfield image showing the evolution of the two genes expressed in a single assembly for topology A at 1 mM IPTG. The IPTG sender droplet is on the left. (B) Sample images for fully developed assemblies (after 7.5 hours) for varying morphogen concentrations (topology A). (C) Temporal evolution of normalized fluorescence intensity of the two genes (g₁, TetR-YFP: blue, top; g₂, LacI-RFP: red, bottom) for the full dataset as in (A) grouped by droplet position relative to the sender droplet. Solid lines represent the mean, and shaded area represents the SD for N = 27 samples. (D) Corresponding gene expression gradients after 7.5 hours. a.u., arbitrary units. (E) Probability to correctly predict the position of a droplet based on measuring the concentration of the genes for the data in (D) after 7.5 hours. (F and G) Temporal evolution of the estimated PI in (F) the TetR-YFP and (G) the LacI-RFP gradient at different morphogen concentrations (colors: from light to dark, 0.1 to 100 mM IPTG, topology A). The corresponding simulation (H) reproduces the experimental observations that (i) the onset of PI evolution in the RFP gradient is delayed by about 1 hour and (ii) that there is an optimum morphogen concentration above which PI in the YFP gradient is lost after an initial transient increase [colors correspond to (F) and (G)]. (I) Comparison of experimental and simulated PI values after 7.5 hours. Error bars and shaded areas in (E) to (G) and (I) are statistical uncertainties of the PI and PE estimates as described in sections S1.3.6 and S1.3.7.

Our key experimental observations are presented in Fig. 2, which shows a typical kymograph for the optimized topology A at an optimal morphogen concentration of 1 mM (Fig. 2A). When the morphogen-containing compartment is connected to the assembly, a resulting morphogen gradient initially establishes rapidly in the first droplets while increasing more slowly in the remote droplets before assuming a relatively steady profile (fig. S19). TetR-YFP expression (blue) is switched on in the nearest droplets, whereas LacI-RFP (red) expression dominates in the more remote droplets.

Whether a synthetic cell can reliably “infer” its position within the array will depend on the width of the distribution p({g_j} ∣ x, t) (fig. S8) and how it compares to the distribution of the neighboring cells. From the average time traces of the full dataset shown in Fig. 2C, it is apparent that YFP fluorescence levels differ substantially depending on the position, and the relatively small width of the distributions may allow to distinguish between several different positions. By contrast, the spatial variation of the mean RFP levels is less pronounced. Repression of LacI-RFP close to the morphogen source requires production of TetR-YFP, and LacI-RFP produced in the initial phase has to be degraded. At the same time, components of the cell-free expression system are continuously depleted. As a result, the variability in LacI-RFP for each droplet position is considerable, providing less information about the position of the compartments.

To quantify this impression, we first calculated P_corr (x) to measure the local positional accuracy. P_corr (x) for the first three droplets is relatively high, indicating that these droplets can, in principle, very well determine their position with respect to the organizer droplet (Fig. 2E). On the contrary, P_corr (x) for the two remote droplets is very low. Thus, the local P_corr(x) measure indicates that the circuits are performing well for the first three droplets, but the uncertainty in the determination of the two remote droplets does not contribute to the global PI measure. In addition, we observe that P_corr (x) is generally lower for the RFP gradient than for the YFP gradient and that the joint information about both gradients does not substantially improve on the information compared to the YFP gradient alone.

We next analyzed data for different inducer concentrations (0, 0.1, 1, 10, and 100 mM) (Fig. 2B) and calculated the temporal evolution of PI contained in the YFP and RFP levels (Fig. 2, F and G). As expected, the system has zero PI initially, but then PI-YFP rises to its maximum value (1.08 to 1.15 bit in the best cases across all topologies) within ≈2 hours (Fig. 2F), indicating that a distinction of more than two regions within the five compartments is possible. For our optimum inducer concentration [IPTG] = 1 mM, the PI-YFP stays constant after its initial rise, whereas, for higher inducer concentrations, generation of PI-YFP is transient, peaking at around 1 hour and then decreasing again. This phenomenon can be attributed to the transient nature of the diffusing IPTG gradient, which initially only induces the first droplets but then floods the whole system.

The PI contained in the RFP expression levels rises with a delay of ≈1 hour and is generally less than in the YFP levels (Fig. 2G). The same delay is also observed in the temporal evolution of P_corr (x). The delay in PI-RFP is caused by the cascaded dynamics of LacI-RFP in the circuit: To reduce the LacI-RFP level in the droplets close to the IPTG source, TetR-YFP has to be produced first, LacI-RFP production has to be stopped, and already present LacI-RFP has to be degraded (which only occurs in topology A). PI calculated from the joint probability distributions for both TetR-YFP and LacI-RFP gave only a slight improvement over the PI contained in the YFP levels alone (fig. S9). Together, these results support the hypothesis that PI is generated from TetR-YFP and then transferred to LacI-RFP (where it is therefore lower and delayed), rather than generated jointly.

We attempted to rationalize these results by computationally modeling the circuits’ responses to morphogen gradients (section S2). Our model qualitatively correctly predicts the initial rise of the PI YFP, followed by a 1-hour delay in PI RFP (Fig. 2H). It also results in a lower PI in the RFP level for 0.1 and 100 mM IPTG than for 1 and 10 mM IPTG. The model captures the transient maximum PI for the 10 and 100 mM IPTG concentrations and an earlier peak of PI YFP for higher inducer concentrations. The trend of PI dependency on IPTG concentrations is well predicted by our model (Fig. 2I, topology A). In contrast to our experiments, the PI in the RFP and YFP expression levels is comparable, indicating that our model predicts a stronger correlation between YFP and RFP expression than observed experimentally. Accordingly, the model predicts larger PI values for RFP expression than obtained in the experiment, whereas it shows better agreement with YFP expression (Fig. 2I). We attribute the numerical discrepancy between simulated and experimental PI values to the sensitivity of the PI with respect to some of the experimentally determined circuit parameters such as induction thresholds and expression strengths, as discussed below and characterized in fig. S20.

We used the model to assess the influence of key parameters on the PI such as circuit dynamics, induction thresholds, and different types of noise. As diffusion of the morphogen through our assemblies is limited by its permeation through the lipid bilayers (Fig. 3C and figs. S13 and S18), each compartment can be regarded homogeneous, and positions can thus be considered discrete. In our model, we therefore only considered slow permeation of the morphogen through the interface bilayers and calculated the circuit responses in each droplet by solving the corresponding ordinary differential equations (section S2).

Fig. 3. Bulk response and noise sources.

(A and B) Bulk titrations and simulated dose-response curves for the three circuit topologies for (A) the YFP readout and (B) the RFP readout (normalized intensities, t = 10 hours). Simulations were performed with the same set of parameters obtained from bulk titrations of the individual nodes (fig. S13). Hence, the change in the apparent circuit K_d can be purely attributed to the differences in circuit topology. (C and D) Using model simulation, two sources of noise are considered to explain the observed variability in the gene expression gradients (t = 8 hours). First, geometrical noise, as caused, for instance, by variations in droplet volumes (C) and consequently bilayer areas, leads to variability in the morphogen gradient but does not strongly propagate to a variability in the gene expression profiles. On the contrary, variability in gene expression strength (D) does not affect the morphogen gradient but leads to a variability of protein profiles closely reproducing the observed variability in the gene expression profiles. All error bars are SDs from 500 simulations, where the droplet volumes or gene expression strengths were drawn from a normal distribution with CVs of 35 and 20%, respectively (section S3.4).

Relevant model parameters were measured experimentally by characterizing the circuit responses in bulk experiments, in which we varied the concentration of the inducer morphogen IPTG (Fig. 3, A and B). With increasing amounts of IPTG, TetR and YFP production is activated in all circuits as expected. In addition, for the feedback circuits (A and B), LacI and RFP production is reduced for high [IPTG], whereas in the absence of feedback (topology C), the RFP level is unaffected by IPTG. The transfer functions of the three topologies differ as predicted by the model: the feedback circuits resulted in steeper regulation/transfer functions than the simple repression circuit (Hill coefficients of n = 2.3 and 1.4, as opposed to n = 0.76). The presence of a degradation tag (topology A) rendered the circuit responsive to lower concentrations of IPTG (Hill K_d = 1.51 μM, as opposed to Hill K_d = 26.2 μM for topology B; fig. S16). The degradation of LacI produced in the initial phase of the system leads to a greater sensitivity of TetR-YFP induction to low IPTG concentrations in topology A. Topology C presents a simpler architecture than topologies A and B, which differ from each other in their sensitivity to IPTG. The steepness and threshold of these transfer functions affect how the circuit interprets the morphogen gradients and how much PI can be extracted.

We next used a Monte Carlo approach to identify relevant noise sources and quantify their effect on the PI. We considered two principal noise sources: the variation of droplet sizes together with their spatial arrangement and gene expression noise. Other parameters, such as the volume of the morphogen-containing compartment, changes in interfacial tension, or leaky protein expression did not significantly affect the system’s response (figs. S14 and S20).

The overall variability of droplet volumes in the experiments is about 30 to 40%, and although we balanced the osmolarity of the contents of the droplets to avoid osmotic swelling or shrinking, droplets still changed size and sometimes rearranged over time (fig. S11). In the model, we systematically varied the volume of all droplets within and between assemblies. This resulted in some variation in the inducer concentrations in the individual droplets (Fig. 3D) but had only a minor effect on the final expression levels (Fig. 3E), and the resulting PI values were well above those measured experimentally (fig. S19). The model does not consider the impact of initial conditions such as the arrangement of the droplets (see fig. S11), as we consider the diffusion mechanism similar to “hopping” from one droplet to the next.

By contrast, variations in gene expression strength (with a constant inducer gradient) (Fig. 3E) were found to have a comparatively large impact on the variability of the expression levels (Fig. 3G) and the predicted PI values (figs. S19 and S20), which are typically larger than those obtained from the experiments. The apparent noise in gene expression strength is consistent with previous observations (22, 27) and could have various sources: time of manufacture, temperature variations, and partitioning effects, which have been observed even for large droplet volumes (28).

The experimental values obtained for the PI and its temporal evolution can be well understood through simulations with our model (Fig. 4). Both experimentally and in the model, we find a strong dependence of the PI on the organizer morphogen concentration, with a maximum PI for YFP of above 1 for topology A at [IPTG] = 1 mM. As expected, topology C—in which RFP expression is not regulated–has a PI of ≈0 bit for RFP.

Fig. 4. Simulated circuit sensitivity and reaction kinetics.

(A and B) Simulated PI in the YFP (A) and RFP (B) gradient, respectively, for varying sender morphogen concentration and circuit K_d. PI is maximal when the circuit K_d matches the morphogen gradient and the maximum PI increases with increasing sensitivity. (C to E) Effect of circuit induction threshold, cell extract activity, and diffusion profile simulated with topology A. (C) Simulated circuit activity (topology A, YFP) against inducer morphogen concentration, indicating three regions: circuit off (below 5% activity), circuit on (above 95% activity), and the region where the circuit induction can be differentiated (between 5 and 95% activity; shaded area). For the other topologies, the gray transition region shifts with the K_d. (D) Simulated temporal evolution of PI overlaid with the presumed reaction activity. Cell extract activity (75%) is lost after 2 hours. (E) Diffusion of the morphogen (source: 1 mM IPTG) into a five receiver droplet array. The time interval when the IPTG concentration in each droplet induces differentiated protein expression is indicated by thicker lines. Dashed line: 75% cell extract activity lost. (F) Diffusion of the morphogen for three source concentrations [0.1 mM (left), 1 mM (center), and 10 mM (right)] creates a time window during which differentiated induction of the circuit can occur. Maximizing this time window for each receiver with respect to the finite reaction lifetime allows to generate higher PI, as is the case for 1 mM IPTG and topology A. (G) Effect of topology on the time window for differentiated induction (10 mM source concentration): Topology B (left) has a higher K_d than topology A, making the time window optimal for higher inducer concentrations. Topology C (right) has a similar K_d to topology A but a less steep transfer function, leading to a longer time window where the cell extract is inactive.

Our computational model further suggests that PI is optimal for an inducer gradient matching the threshold of induction of the genetic circuit and that higher PI can be reached for more sensitive circuits induced with correspondingly lower morphogen concentrations (Fig. 4, A and B, and fig. S21). Differentiation of the protein expression between compartments is optimal when the morphogen profile spans the response region of the circuit, determined by the threshold and steepness of the transfer function (Fig. 4, C to E). When the morphogen concentration is too low or too high (e.g., [IPTG] = 10 mM), all compartments are similarly induced and the PI is low (Fig. 4F, right). The morphogen profile also explains the transient peak of PI for high inducer concentrations: initially, gene expression is only induced in the first droplets, and the system is more differentiated; however, soon all droplets are fully induced, and the total PI of the system decreases.

Crucially, the cell-free expression reaction only has a finite lifetime on the order of a few hours, which we phenomenologically account for in the model with an exponential decay function (section S2.2.3). Whether a protein gradient is established depends on whether the IPTG concentration rises above the induction threshold within the lifetime of the cell-free expression system and how much activity is left at this point (Fig. 4D). When the morphogen profile reaches the circuit’s threshold too late (e.g., [IPTG] = 0.1 mM), most of the expression activity is lost, and differentiated gene expression no longer occurs (Fig. 4F, left). When the morphogen diffusion profile maps the dynamic range of the circuit topology within the lifetime of the cell extract, PI is maximized [Fig. 4, F (center) and G].

We lastly studied the dynamics of the circuit in the context of more complex, 3D printed assemblies of synthetic cells (Fig. 5). To this end, we developed a custom multipurpose bioprinting platform (Fig. 5, A and B, and section S1.2), which could be used to deposit simple, well-defined assemblies of emulsion droplets (Fig. 5C) or more complex, tissue-like assemblies (Fig. 5, D and E), extending in three dimensions (for a detailed description of the bioprinter, see section S1.2).

Fig. 5. 3D printing of assemblies and circuit implementation.

(A) Automated assembly of the networks is implemented with a custom-built bioprinting platform. (B) Experiment chamber and printing nozzle. (C) Well-defined but small 3D structures can be reproducibly printed, such as a pyramid with a seven droplets base and close packing of the droplets. Scale bar, 100 μm. (D and E) Printing of larger tissue-like assemblies. Scale bars, 100 μm. (F) The two-node feedback gene circuit is implemented in a larger printed 2D assembly. Overlay of inverted brightfield image and fluorescence images at 6 hours (blue, TetR-GFP; red, LacI-RFP; sender droplet containing 1 mM IPTG at the top of the assembly is marked with a red dye). Scale bar, 100 μm. (G) Distance from the sender (S) groups receiver droplets 1 to 10 into layers indicated by shades of the same color. Scale bar, 100 μm. (H and I) Fluorescence images of GFP (H) and RFP (I) reporters of the assembly in (F) at 0, 1, 3, and 6 hours. Scale bars, 100 μm. Uneven background in RFP is due to illumination inhomogeneity and relatively low total fluorescence compared to GFP. (J) Simulated IPTG concentration at 6 hours in the assembly’s geometry. (K and L) GFP and RFP fluorescence at 6 hours in the assembly. Technical mean and SD from data extraction are indicated by circles and error bars. FI, fluorescence intensity.

As shown in Fig. 5F, an “organizer cell” is initially loaded with IPTG as for the linear assemblies discussed above. Upon diffusion into the assembly, green fluorescent protein (GFP) (used as an alternative reporter for TetR) expression is activated in the proximal droplets (Fig. 5, G and J), while RFP is generated in the distal droplets (Fig. 5, H and K), clearly generating a division into two regions.

As shown in Fig. 5 (I to K), an additional structure appears to emerge in the 3D assembly, which is caused by the sphere packing geometry of the droplets. Gene expression levels vary in “shells” around the organizer cell, within which the receiver droplets approximately have the same distance from the source. This is consistent with the morphogen levels predicted by our model in each droplet at 6 hours.

As it was challenging to generate a large number of identical 3D assemblies with our current setup, a systematic analysis of the PI in this context could not be carried out. Nevertheless, the step-like change in expression levels in the shells seen in Fig. 5J suggests that even more PI could be extracted in the 3D context than in our 1D chains.

DISCUSSION

We have shown that the concepts of PI and PE—originally used for the analysis of developmental processes in biology—can be fruitfully applied in the artificial context of synthetic cellular assemblies, which is motivated by the vision of dynamic, “living” biomaterials composed of synthetic cells that interact with their environment and are capable of context-dependent cellular specialization or differentiation. Efficient use of PI will be important in cases where the materials have to autonomously make decisions in the presence of uncertainties generated during their production and self-assembly.

In the specific case considered here, we analyzed three simple gene circuit topologies based on a standard feedback motif containing two mutually repressing transcriptional repressors, which were encapsulated in linear assemblies of five cell-like compartments connected by permeable lipid bilayer membranes. We found that the circuits responded to externally generated “morphogen” gradients, which were created by genetic inducers emanating from an organizer cell. From this gradient, in the best case, the circuits could derive a PI of ≈1.2 bits, which allows distinction of two to three regions within the five-cell assembly. To infer the position of all five cells, a correspondingly higher PI of log₂ 5= 2.3 bits would be required. The use of the PI and PE concept also allowed us to precisely quantify which of the circuits could best transfer information from one gene expression layer to the next (from TetR to LacI), which otherwise would have been based on rather vague visual impressions.

Several factors nonetheless limit the extraction of PI from the gradient—next to the inherent variability in gene expression itself, the temporal evolution of the gradient and of the cell-free expression system itself play a role. In our closed system containing a finite reservoir of inducer molecules acting as morphogens, the gradient steadily evolves during the “differentiation” process (fig. S19). Our computational model shows how the interplay of circuit response (characterized by the induction threshold K_d) and diffusion dynamics affects the total PI (Fig. 4, topology A, and fig. S21, other topologies). If the concentration is too high (Fig. 4F), then the inducers quickly rise above the induction threshold in all droplets, preventing any spatial differentiation. If it is too low, then the concentrations are not sufficient to elicit any response. The spatiotemporal evolution of the morphogen is then sampled by the circuits for a finite amount of time. Cell extract activity decays exponentially over time (Fig. 4E), and after 2 hours, 75% of the protein expression activity is lost. Thus, if diffusion is too slow, then the inducers will reach some of the droplets too late (i.e., after their “death”; Fig. 4F, leftmost). Our experimental observations, together with the insights drawn from our model, provide insights into the rational engineering of these systems. To maximize PI, the inducer concentration in all droplets should span the sensitive transition region of the circuit response function for long periods of time, allowing for a differentiated induction of the response in each droplet (Fig. 4F, center).

The lifetime of the cell-free system and relatively slow gene expression dynamics also affect the transfer of PI from one transcription factor to another (i.e., from TetR to LacI in our case). Our system is not able to complete a full cycle of the feedback circuit used, and therefore, the gradient information extracted from the IPTG gradient by TetR-YFP cannot be transferred to the LacI expression level, which it influences.

This situation is not unlike that of developing organisms, where cell fate must be determined in the time period during which morphogen gradients are stable and provide high PI. In the case of the vertebrate neural tube, for example, the combined antiparallel gradients of morphogenetic proteins can only allow precise patterning during 10 hours before they diverge (18). Layers of patterning circuits, wherein a morphogen gradient induces the differentiated expression of a protein that itself becomes a morphogen for other proteins, allow for robust, stepwise patterning of an organism. Contrary to our system, production-diffusion-degradation mechanisms often stabilize morphogen gradients in living systems. In the case of Drosophila, in the first 90 min of embryonic development, a roughly exponential gradient of Bcd/Bcd mRNA is established along the anterior-posterior axis, which stays stable for ≈1 hour (between cell cycles 10 and 14), during which the spatial differentiation of the next layer of morphogens (caudal and hunchback) is achieved (17). The stability of this gradient has been recognized as one of the key factors for the astonishingly high PI extracted in this biological system.

In addition to a stabilized morphogen gradient and potentially the use of two opposing inducer gradients (18), the PI contained in the gradient would be more efficiently used in a cell-free expression system with an extended lifetime. To this end, replenishment of its resources via some sort of external supply system would be necessary, possibly coupled to metabolic activity [such as adenosine 5′-triphosphate (ATP) production/regeneration or even self-regeneration]. The finite time window generated by gradient stability and lifetime of the expression system could be used more efficiently by speeding up the regulatory processes involved in the differentiation process. Realization of these improvements could be quite challenging in the context of the closed emulsion-based compartments studied here. Open bioreactors (e.g., permeable structures immersed in “broth” or combined with microfluidic supplies) could thus be promising for “self-differentiating” biomaterials, in which multiple layers of developmental genes would carry out a synthetic morphogenetic program. Further improvements in 3D printing technologies will also facilitate the automated generation of extended, tissue-like structures with an artificial “vasculature,” which would help to keep these living biomaterials out of equilibrium over extended periods of time. The initial anterior-posterior differentiation with ~1-bit PI demonstrated here could be transferred to subsequent gene circuit layers, with the help of the quantification tools and models developed here, to realize stepwise patterning, similarly to developing organisms.

MATERIALS AND METHODS

Materials

The following chemicals were purchased from Sigma-Aldrich (Germany): IPTG (#I6758), hexadecane (#296317), silicone oil AR 20 (#10836), α-hemolysin (#H9395), anhydrotetracycline (#37919), Atto488 (#41051), and lysozyme (#L6876). The following chemicals were purchased from Carl Roth (Germany): LB medium (#X968), glycerol (#3783), nuclease-free water (#T143), chloroform (#3313), and ethanol (#P076). The following chemicals were purchased from Avanti Polar Lipids (USA): diphytanoylphosphocholine (DPhPC) (4ME 16:0 PC) (#850356), dioleoylphosphatidylcholine (DOPC) [18:1 (Δ9-Cis) PC] (#850375), dioleoylphosphatidylglycerol (DOPG) [18:1 (Δ9-Cis) PG] (#840475), and cholesterol (20α-hydroxycholesterol) (#700156). For DNA, single-stranded oligos were purchased from Biomers (Germany) or Eurofins (Germany), and double-stranded gBlocks were purchased from Integrated DNA Technologies (USA). LacI, TetR, and mTurquoise2 were purified in our laboratory according to standard His tag nickel purification protocols [with the following specific buffers for LacI (29) and TetR(30)]. For mTurquoise2, the following buffers were used: lysis and wash buffer [50 mM tris, 500 mM NaCl, 25 mM imidazole, and 1 mM dithiothreitol (DTT) (pH 8.0)], elution buffer [50 mM tris, 500 mM NaCl, 250 mM imidazole, and 1 mM DTT (pH 8.0)], and storage buffer [50 mM tris, 100 mM NaCl, 2% (v/v) dimethyl sulfoxide, 15% glycerol, and 1 mM DTT (pH 7.5)].

Methods

Plasmid cloning and purification

All plasmids were cloned using standard strategies and enzymes from New England Biolabs (NEB; USA). We alternatively used digestion/ligation, Golden Gate assembly (31), or polymerase chain reaction with 5′-phosphated primers, followed by ligation. The plasmids were transformed into the Escherichia coli bacterial strain Turbo (NEB, USA, #C2984I). Constructs were cloned in the plasmid backbones pSB1A3 and pSB1C3. Bacteria were stored in glycerol stocks: An overnight culture in LB medium was mixed with glycerol to a final concentration of 25% (v/v) glycerol and kept at −80°C. To ensure that the glycerol stocks contained a monoclonal population with the correct plasmid, an overnight culture was grown in LB medium from the glycerol stock, mini-prepped (QIAprep Spin Miniprep Kit, QIAGEN, the Netherlands), and sequenced (Sanger sequencing, LightRun, GATC Biotech, Germany). Plasmids were purified before use in cell extract by Midiprep (NucleoBond Xtra Midi, Macherey-Nagel, Germany).

Cell extract preparation

The E. coli cell extract was prepared according to the protocol by Sun et al. (32). Briefly, a mid-log phase culture of BL21(DE3) Rosetta2 was spun, washed, resuspended at 1 g/ml, and incubated with lysozyme (1 mg/ml) on ice for 30 min. It was then lysed by sonication in 4 ml of aliquots at 30 kHz, 10% amplitude, 20 cycles, and 10 s per cycle. The extract was incubated at 37°C for 80 min to allow the digestion of genomic DNA and was then dialyzed for 3 hours at 4°C with a cutoff of 10 kDa (Slide-A-Lyzer Dialysis Cassettes, Thermo Fisher Scientific, USA). Protein concentration was estimated to be 30 mg/ml with a bicinchoninic acid assay (Thermo Fisher Scientific, USA, #23225). In the buffer, instead of 3-phosphoglyceric acid, phosphoenolpyruvate was used as an energy source (33). The buffer was composed of 50 mM Hepes (pH 8), 1.5 mM ATP and guanosine 5′-triphosphate, 0.9 mM cytidine 5′-triphosphate and uridine 5′-triphosphate, tRNA (0.2 mg/ml), 0.26 mM coenzyme A, 0.33 mM nicotinamide adenine dinucleotide (NAD), 0.75 mM adenosine 3′,5′-monophosphate, 68 μM folinic acid, 1 mM spermidine, 30 mM phosphoenolpyruvate, 1.25 mM leucine, 1.5 mM other amino acids, 1.5 mM DTT, 3.5% polyethylene glycol, molecular weight 800, 80 mM K-glutamate, and 4 mM Mg-glutamate. Buffer and extract were flash-frozen in liquid nitrogen, stored at −80°C, and thawed on ice before usage. A cell-free reaction was prepared by mixing 33% (v/v) cell extract with 42% (v/v) buffer and 25% (v/v) DNA, inducers, and other additives. Reactions were conducted at 29°C.

Bulk experiments

Fluorescence measurements in bulk were conducted at 29°C in a plate reader (FLUOstar Omega or CLARIOstar, BMG Labtech, Germany). Fifteen microliters of samples were pipetted in a 384-well plate (pureGrade, BRAND, #781622), and the plate was sealed with an optically transparent film (Microseal “B”; Bio-Rad, Germany) and centrifuged at 700 relative centrifugal force (rcf) for 30 s.

Manual droplet assembly

Droplet experiments were carried out as described by Dupin and Simmel (22). Briefly, water-in-oil emulsions were created with a pressure pump and a micromanipulator. The lipid-oil mixture consisted of 0.25 mM cholesterol, 0.25 mM DOPG, 4 mM DOPC, and 0.5 mM DPhPC in 1:1 hexadecane:AR 20. The lipid and cholesterol powders were dissolved in chloroform, mixed in a glass vial, evaporated under a nitrogen stream, and dried under vacuum, after which the lipid film was resuspended with the oil mix and vortexed. The chambers consisted of rubber O-rings glued with epoxy glue onto glass slides. After being washed with soap, rinsed with ethanol and double-distilled water, and dried at 90°C, the chamber was filled with 65 μl of the lipid-oil mixture. Solutions were pipetted into heat-pulled glass capillaries, which were then fixed onto a homebuilt micromanipulator and connected to a microinjector pump. Pressure injections were applied to create droplets of around 130 μm in diameter, between 0.5 and 1 nl of volume. Droplets were incubated in the oil for 15 min on average to allow for a monolayer of lipids to assemble around them and were moved together with the micromanipulator so that they spontaneously formed bilayers. The chamber was closed with a glass slide to limit evaporation of the droplets.

Automated droplet assembly

In comparison to the manually created circuits using the micromanipulator system, the 2D and 3D arrays (Fig. 5 and fig. S1) were generated using a self-developed modular bioprinting platform (fig. S2). Solutions in cell extract, lipid-oil mixture, and experiment chambers were prepared as for manual assembly experiments. The experiment chamber was filled with 65 μl of lipid-oil equilibrated to room temperature (22°C), and the print head fitted with a Micron-S nozzle (VIEWEG, Germany), with an inner diameter of 60 μm. Pneumatic extrusion was realized using the Flow EZ precision pressure pump (Fluigent SA, France), which was actuated by the printer software. In case of an extrusion event, the printer signals to the TTL receiver (LineUp LINK, Fluigent SA) controlling the pump, and the signal is then interpreted by the Microfluidic Automation Tool (Fluigent SA, France) using a custom code for pump actuation, allowing the adjustment of pulse pressure and duration. Immediately before printing, the nozzle was filled manually with cell extract using a pipette. The nozzle was positioned on the x and y axes at 100 μm in the lipid reservoir, and a drop of cell extract was extruded with a pneumatic pulse. The droplet was released by raising the nozzle from the lipid reservoir. The procedure of calibrating the nozzle tip position and droplet size, the process of extruding and releasing droplets, and exemplary G-code used for 3D printing are described in more details in section S1.2.

Image acquisition

The fluorescence of the networks was recorded with an inverted fluorescence microscope Eclipse Ti2 (Nikon, Japan) and equipped with a SOLA light engine (Lumencor, USA) for excitation, camera Neo 5.5 (Andor, Northern Ireland, UK), a 10× CFI P-Apo objective (numerical aperture, 0.45; Nikon, Japan), temperature-controlled incubation chamber (Okolab, Italy), and acquisition software NIS-Elements Advanced Research from Nikon (Japan). The images were further analyzed with ImageJ and MATLAB_R2015b. The cyan fluorescent protein channel was acquired with an exposure time of 1 s, with an excitation filter of 416 to 440 nm, a dichroic mirror of 458 nm, and an emission filter of 467 to 499 nm. The YFP channel was acquired with an exposure time of 500 ms, with an excitation filter of 479 to 495 nm, a dichroic mirror of 515 nm, and an emission filter of 510 to 540 nm. The RFP channel was acquired with an exposure time of 1 s, with an excitation filter of 542 to 576 nm, a dichroic mirror of 585 nm, and an emission filter of 617 to 633 nm. For figs. S17 and S18, the fluorescence of the assemblies was recorded with an inverted fluorescence microscope IX-71 (Olympus, Japan), with excitation light-emitting diodes (LEDs), filters, and dichroic mirrors from Thorlabs (USA); camera LucaEM from Andor (Northern Ireland, UK); objectives from Olympus (Japan); heating plate from Tokai Hit (Japan); and acquisition software Micro-Manager 1.4.16. A 10× objective was used and a bin of 2; the GFP channel was acquired with an exposure time of 1 s, with an LED of 470 nm, an excitation filter of 450 to 490 nm, a dichroic mirror of 510 nm, and an emission filter of 518 to 545 nm; and the RFP channel was acquired with an exposure time of 3 s, with an LED of 530 nm, an excitation filter of 530 to 550 nm, a dichroic mirror of 576 nm, and, for emission, a long pass filter above 590 nm.

Data analysis

Multichannel fluorescence and brightfield video data were analyzed as described in detail in section S1.3. All automated image processing routines and schemes for calculation of PE and PI were implemented in Fiji or MATLAB. Briefly, we first segmented the images and track the fluorescence in individual droplets. To minimize the measurement uncertainty, we used a calibration dataset to develop a custom image processing routine that includes a normalization to a reference dye and the correction of illumination and segmentation uncertainties. We then used the fluorescence time traces of N = 9 to 37 samples for each dataset to estimate pdfs for each gradient and time point and computed PE and PI measures, as described in (19, 20). Briefly, we corrected the naïve estimates obtained by inserting Gaussian approximations of the experimental probability density functions (pdfs) into the corresponding equations for the finite sample size bias by generating subsamples and extrapolating the naïve estimates to infinite sample size. To verify the PI estimates, we additionally computed the PI directly from binned experimental pdfs and again extrapolated to infinite bin number. The estimates obtained through Gaussian approximation and the direct method generally agree well (fig. S9), except for datasets with an insufficient sample size to apply extrapolation to infinite bin numbers in the direct method (34, 35). We hence generally used the Gaussian approximation method. Error bars for PI estimates are the statistical uncertainties obtained through the extrapolation, whereas error bars for measures derived from PE estimates were obtained with a bootstrapping method and Gaussian error propagation.

Simulation

All simulations were conducted with MATLAB. The models used in the simulations are described in more details in section S2. Noise was modeled using a Monte Carlo method. For each potential noise source, a Gaussian distribution of the corresponding model parameter was determined. For example, droplet volume was estimated for experimental data to follow a Gaussian distribution with a mean of 1.2 nl and an SD of 0.42 nl (fig. S11). The distribution of the biochemical species was determined by running a given number of simulations (typically 500), where the noise parameter was randomly sampled from the Gaussian distribution. Note that we do not consider stochastic effects due to the large number of molecules in one droplet (1 nM · 1 nl · N_A ≈ 10⁶).

Supplementary Materials

This PDF file includes:

Sections S1 to S4

Figs. S1 to S22

Tables S1 and S2

References

Other Supplementary Material for this manuscript includes the following:

Data S1

Movie S1

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