2023.11.18.567649v1.full-html.html

TITLE

Design and Mathematical Analysis of Synthetic Inhibitory Circuits that Program Self-Organizing

Multicellular Structures

AUTHOR

Calvin Lam

1,2

ORCID

0000-0003-2768-4230

CORRESPONDENCE

calvin.lam.k@gmail.com

AFFILIATIONS

Independent Investigator

Present Address: Department of Biochemistry and Molecular Biology,

University of Nebraska Medical

Center, Omaha, NE, 68198, USA

ABSTRACT

Bottom-up approaches are becoming increasingly popular for studying multicellular self-

organization and development. In contrast to the classic top-down approach, where parts of the

organization/developmental process are broken to understand the process, the goal is to build the process

to understand it. For example, synthetic circuits have been built to understand how cell-cell

communication and differential adhesion can drive multicellular development. The majority of current

bottom-up efforts focus on using activatory circuits to engineer and understand development, but efforts

with inhibitory circuits have been minimal. Yet, inhibitory circuits are ubiquitous and vital to native

developmental processes. Thus, inhibitory circuits are a crucial yet poorly studied facet of bottom-up

multicellular development. To demonstrate the potential of inhibitory circuits for building and developing

multicellular structures, I designed several synthetic inhibitory circuits that combine engineered cell-cell

communication and differential adhesion. Using a previously validated in silico framework, I examine the

capability of these circuits for synthetic development. I show that the designed inhibitory circuits can

build a variety of patterned, self-organized structures and even morphological oscillations. These results

support that inhibitory circuits can be powerful tools for building, studying, and understanding

developmental processes.

KEYWORDS

Synthetic biology, computational biology, synthetic development, synthetic receptors, amplifiers, tissue

engineering, self-organization, morphogenesis

INTRODUCTION

The development of multicellular organisms is an intricate, highly coordinated dance that has

fascinated scientists for centuries

1–9

. With minimal external control, individual units communicate with

one another, alter their behavior accordingly, and self-organize into ornately patterned, functional

structures

10–17

. Understanding these developmental processes is a longstanding goal of biology; it not

only provides insight into multicellular life, but also insight for clinical applications such as tissue

engineering and regenerative medicine

10,11,13–28

However, understanding these multicellular developmental processes is notoriously difficult. The

classic top-down “break-it-to-understand-it” approach focuses on breaking a part of the process to

understand the process, but breaking a part can affect the subsequent and parallel parts

15,16,29

. This

approach informs of the necessity of the part, but not necessarily the function(s) of the part

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In recent years, a complementary strategy has emerged through the field of synthetic biology. The

field’s modular tools allow programming and controlling cells, enabling a bottom-up “build-it-to-

understand-it” approach. In contrast to the top-down approach, the bottom-up approach seeks to join

together parts that can construct/build the process, thereby providing understanding of the process

10,11,13,14,16–23,25–27,29,30

. Though nascent, this approach has proven powerful thus far

10,31

. Using synthetic

juxtacrine receptors as parts to control cell-cell signaling processes, Morsut et al. demonstrated that such

processes can build complex multicellular multi-layered patterns

. Adding differential adhesion as a part

illustrated that processes combining juxtacrine signaling with differential adhesion can build a variety of

3D multicellular patterned structures

. These constructed processes provide insight into how basic

components such as cell signaling and adhesion expression can direct complex self-organization.

Moreover, these synthetic processes have features such as regeneration, cell fate divergence, and

symmetry breaking, providing insight into how these features occur in native multicellular developmental

processes

10,31

The majority of these bottom-up, synthetic development efforts emphasize activation. For

instance, the above works used a synthetic juxtacrine receptor to activate expression of a target gene

(Fig.1A)

10,31

. With different fluorescent reporter and adhesion cadherin genes as the target gene, these

activatory circuits, when programmed into cells, yield developmental processes that can build a variety of

patterned, multicellular self-organizing structures (Fig.1A)

10,31

To date, inhibitory circuits, despite being integral to native multicellular developmental

processes, have been much less used in synthetic development (Fig.1B). Nonetheless, the few current

results support that inhibitory circuits could be a powerful strategy for building and understanding

multicellular development. For instance, using inhibitory circuits to build morphogen gradients revealed

that double negative signaling logic coupled with negative feedback improves gradient pattern formation

in the Sonic Hedgehog pathway

. Using inhibitory circuits to inhibit morphogen activity allows the

formation of sharp gradient boundaries

. Inhibitory circuits coupled with differential adhesion can drive

the formation of at least one type of patterned 3D structure

To investigate the potential of inhibitory circuits for bottom-up multicellular development, I

designed several generalizable synthetic inhibitory circuits. These circuits are driven by the synthetic

Notch (synNotch) receptor, a powerful, fully modular receptor that is capable of both activating and

inhibiting gene expression

31,32

. Upon binding the juxtacrine cognate ligand, this receptor releases a

transcription factor controlling the gene of choice (Fig.1C)

31,32

. For gene activation, an activating

transcription factor is released to drive target gene expression. For gene inhibition, the receptor can either

directly repress gene expression by releasing an inhibitory transcription factor

or indirectly by driving

expression of an inhibitory transcription factor that then represses target gene expression

. The

flexibility of the synNotch receptor allowed me to design inhibitory circuits with varying temporal

dynamics for building and developing multicellular structures (Fig.1D-F)

. In the published

accompanying study, I showed how activatory circuits with varying spatiotemporal control can be used

for bottom-up multicellular development

Moreover, use of the synNotch receptor allowed me to employ a previously validated

computational strategy. This enabled me to thoroughly explore the developmental capabilities of these

inhibitory circuits

18,19

. In a previous work, my colleagues and I developed a mathematical and in silico

approach for modelling synNotch circuits that drive self-organization

. The Generalized Juxtacrine

Signaling Model (GJSM) set of equations allows simple and intuitive modeling of synNotch circuits.

SynNotch circuits are first converted to GJSM equations and then implemented into in silico cells (via a

framework such as the cellular Potts model

33–35

). This computational approach can successfully predict

the developmental structures that result from programming in vitro cells with synNotch circuits

. This

computational approach is ideal for exploring these circuits’ capabilities for bottom-up multicellular

development; I can rapidly and systematically investigate circuit behavior across different parameters

Here, I show that the designed inhibitory circuits are capable of their intended behavior. More

100

importantly, when these circuits are combined with differential adhesion and implemented into in silico

101

cells, these inhibitory circuits give rise to a variety of patterned multicellular structures. Of the structures

102

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obtained, the model predicts the only known in vitro patterned structure (expected as this was

103

demonstrated in the original study

), but the model also predicts that this only known structure is but a

104

fraction of the morphologies possible. Further examination of the various structures indicated that one

105

circuit is capable of morphological oscillations, but these oscillations dampen quickly, suggesting that

106

further temporal regulation is required. Incorporating activating transcriptional amplifiers to additionally

107

modulate temporal control revealed that the amplifiers can not only improve, but even rescue oscillations.

108

These results support that inhibitory circuits can be powerful tools for bottom-up synthetic development.

109

110

RESULTS

111

Design of the synthetic inhibitory circuits.

112

The direct inhibition circuit is the simplest of the designed inhibitory circuits, using a synNotch

113

receptor that, upon binding its juxtacrine cognate ligand, releases a transcriptional repressor inhibiting

114

expression of the target gene (Fig.1D)

. Because repression is directly mediated by the synNotch

115

receptor, this circuit is highly dependent on the presence of cognate ligand to maintain gene repression;

116

loss of the signaling ligand should quickly result in decrease of gene repression

18,31,32

. Thus, this design

117

offers basic spatial control with minimal temporal control

31,32

118

To demonstrate how inhibitory circuits can be used for bottom-up multicellular development, it

119

would be ideal to also test other inhibitory circuits with additional levels of temporal control. I therefore

120

designed two additional circuits: the temporary inhibition circuit and 2-transcription factor (2-TF)

121

permanent inhibition circuit.

122

In the temporary inhibition circuit, I take advantage of the synNotch receptor’s modularity to also

123

activate gene expression

10,31,32

. The synNotch receptor drives expression of an inhibitory transcription

124

factor (ITF) that then inhibits target gene expression (Fig.1E)

. Repression is now dependent on the ITF

125

level, rather than the synNotch signal, and thus gene repression should continue even when synNotch

126

signaling is lost, as long as the ITF remains elevated enough to continue repression. Compared to the

127

direct inhibition circuit, this circuit should enable temporarily prolonging gene repression.

128

In the 2-transcription factor (2-TF) permanent inhibition circuit, the synNotch receptor activates

129

expression of both an activating transcription factor (ATF) and an inhibitory transcription factor (ITF)

130

(Fig.1F). An example gene cassette would be the ATF and ITF genes linked by an internal ribosomal

131

entry site or ribosomal skipping site, and expression controlled by a promoter activated by the synNotch

132

receptor. The ATF drives itself and the ITF, providing a positive feedback loop for permanent ITF

133

expression and thus should result in permanent gene repression

18,36–38

134

135

Circuits inhibit gene expression with temporal control over repression as designed.

136

With the circuits designed, I converted them into GJSM equations and implemented them into in

137

silico cells using the CompuCell3D cellular Potts framework

33,34

. This combination was previously tested

138

for modeling synNotch circuits for bottom-up multicellular development

18,19

. See prior works

18,19

and the

139

Methods section for more details. I then tested these circuits for their temporal control over gene

140

repression. Blue cells, blue as they constitutively express blue reporter, were programmed to express a

141

synNotch receptor that responds to orange ligand on orange cells (Fig.2A). In the direct inhibition circuit,

142

the synNotch receptor directly inhibits blue reporter expression (Fig.2A). In the temporary inhibition

143

circuit, the synNotch receptor drives an ITF that then inhibits blue reporter expression (Fig.2A). In the 2-

144

TF permanent inhibition circuit, the synNotch receptor drives both an ATF and ITF. The ATF acts as a

145

permanent amplifier of ITF expression and ITF inhibits blue reporter expression (Fig.2A)

. I then tested

146

these cells for their temporal control over gene repression using a simple cell-cell signaling setup from the

147

accompanying study that examines activatory circuits

148

A blue cell, imbued with one of the inhibitory circuits, is seeded with 3 orange sender cells. Cells

149

are cubic and frozen (i.e. locked in shape, volume, and surface area) to maintain consistent synNotch

150

signaling (Fig.2B). At 25000 timesteps, orange senders are deleted to test how ligand and synNotch

151

signaling loss affects repression (Fig.2B). This setup allows controlling the exact level of synNotch

152

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signaling at a given time, thus enabling simultaneous testing of the circuit’s ability to inhibit reporter

153

expression and temporality of repression

154

In GJSM equations for synNotch circuits, gene expression and repression are modelled by several

155

parameters. For gene activation or gene expression,

β models gene expression difficulty while for

156

inhibition or gene repression,

β models gene repression difficulty. Higher values of β model higher

157

expression/repression difficulties while lower values model lower expression/repression difficulties.

158

Lower

β values, however, do increase the risk of background gene expression/repression

18,19

κ models

159

protein product degradation rate/saturation levels. See the accompanying study

, the original study

160

the Methods section for further details.

161

I therefore first checked the circuits for background gene inhibition. At reporter repression

162

difficulties (

β reporter) ≥1000, there was no background repression in all designed circuits (SFig.1A). I

163

then tested the circuits at higher repression difficulties and found that all circuits were able to yield

164

reporter repression (Fig.2C). The direct inhibition circuit was able to inhibit reporter expression up to

165

reporter=3000 and as predicted, had high spatial but minimal temporal control. Loss of synNotch

166

signaling via loss of orange neighbors at 25000 timesteps resulted in immediate loss of blue reporter

167

repression (Fig.2C). This temporal dynamic is consistent with reported synNotch signaling dynamics in

168

vitro

18,31,32

169

In contrast, the temporary inhibition circuit repressed reporter expression up to

β reporter=12000

170

and maintained inhibition for some time even after loss of orange neighbors (Fig.2C). Reporter levels

171

eventually increased once again (Fig.2C) due to the ITF’s reliance on synNotch signaling to remain

172

elevated (SFig.1B), confirming the design as a temporary inhibition circuit. The 2-TF permanent

173

inhibition circuit repressed reporter expression up to

β reporter=18000 and maintained permanent blue

174

reporter repression even after loss of the orange neighbors (Fig.2C). This is due to the ATF’s positive

175

feedback loop allowing permanent ITF expression and thus permanent reporter repression, confirming the

176

circuit’s design as a permanent inhibition circuit (SFig.1B).

177

Similar results were obtained with 1 and 6 orange sender neighbors (data not shown). While all

178

the inhibition circuits operate as designed, it is important to note that they fail at some parameter sets.

179

Thus, circuit behavior is not solely defined by circuit design, but by its parameters as well

180

181

Temporary inhibition circuit can build a variety of patterned multicellular structures.

182

With data supporting that the inhibitory circuits function as designed, I then tested the circuits’

183

for their ability to build and develop multicellular structures. A version of the temporary inhibition circuit,

184

the lateral inhibition circuit, has been shown capable of driving bottom-up synthetic development in vitro

185

. In this circuit, cells signal to one another via a CD19 synNotch interaction to drive expression of the

186

transcriptional repressor tTs and the adhesion protein E-cadherin (gene is ECAD) (Fig.3A). tTs repressor

187

then inhibits expression of the CD19 ligand. L929 mouse fibroblasts programmed with this circuit

188

reliably form only one type of patterned structure, a 2-layered structure with CD19

E-cadherin

green

189

cells and CD19

E-cadherin

yellow cells in the center (Fig.3B). CD19

E-cadherin

red cells form the

190

peripheral ring (Fig.3B).

191

The robust formation of the 2-layered structure is likely due to the lateral inhibition circuit being

192

partially calibrated

, thereby limiting the structures buildable. However, systematically investigating the

193

generalized version of the lateral inhibition circuit, the temporary inhibition circuit, revealed that this

194

circuit design can form a wealth of patterned structures (Fig.3E and SFig.2A). The circuit was

195

implemented in in silico L929 (ISL929) cells

18,19

to parallel the in vitro implementation. I tested a wide

196

range of expression difficulties for ITF/ECAD (ITF is generic representation of tTS, gene representation

197

is ITF) and repression difficulties for blue ligand (blue ligand is generic representation of CD19, gene is

198

BLUE-L). A cell color guide is given in Fig.3D. Scanned parameters are in SFig.2A.

199

Several structure types were formed, ranging from types 1 and 6 of highly homogenous E-

200

cadherin

spheroids to 3, 4, 5, and 7 for 2-layered structures to 2 for mixed E-cadherin

spheroids

201

(Fig.3E). Representative structure types are shown and additional structures, organized by the parameters

202

that generated them, are given in SFig.2A. Out of all the structure types obtained, only one (type 5 of

203

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Fig.3E), was the 2-layered structure built by the lateral inhibition circuit (Fig.3B). These results indicate

204

that the temporary inhibition circuit can build a variety of patterned, multicellular structures. The only

205

known in vitro example is but a fraction of the structures possible.

206

207

Direct inhibition circuit and 2-TF permanent inhibition circuit can also build a variety of patterned

208

multicellular structures.

209

Testing the direct inhibition circuit and 2-TF permanent inhibition circuit revealed that both

210

circuits can also generate a variety of patterned structures. The direct inhibition circuit built structure

211

types ranging from types 1 and 3 of heterogenous E-cadherin

spheroids to 4, 6, and 7 for 2-layered

212

structures to 2 and 5 for E-cadherin

spheroids (Fig.4A). The full gallery of structures, organized by the

213

parameters that generated them, is given in SFig.2B.

214

Likewise, the 2-TF permanent inhibition circuit also proved capable of building various patterned

215

structures. Structure types ranged from 1 and 4 for highly homogenous E-cadherin

spheroids to 2, 3, and

216

5 for 2-layered structures (Fig.4B). Interestingly, this circuit yields less structure types compared to the

217

other two, possibly due to its permanency in gene repression. The full gallery of structures, organized by

218

the parameters that generated them, is given in SFig.2C.

219

Altogether, these results (Figs.3-4, SFig.2) demonstrate that inhibitory circuits can be powerful

220

tools for building multicellular structures.

221

222

Temporary inhibition circuit can build oscillatory structures.

223

Of the diverse structures built by the inhibitory circuits, the homogenous spheroids of the

224

temporary inhibition circuit (structures of types 1 and 6 of Fig.3E) were of notable interest. During the

225

development of these structures, cells were highly uniform in the expression state of ITF/E-cadherin and

226

blue ligand (i.e. all cells were ITF/E-cadherin

blue ligand

or ITF/E-cadherin

blue ligand

etc, see

227

Fig.3D for all possible expression states and cell color for each state). Cells then synchronously

228

transitioned from one expression state to another expression state (i.e. cells transitioned from one color to

229

another color at a similar time). An example development with these features is shown in Fig.5A. These

230

features are strikingly similar to those observed with oscillations in development

6,35,39,40

. Because

231

temporary gene repression is known to drive oscillation

6,35,39–43

, I hypothesized that the temporary

232

inhibition circuit can build morphological oscillators (Fig.5B).

233

Extending the simulation time to 100000 timesteps for the pink outlined structures of SFig.2A

234

revealed that the temporary inhibition circuit can indeed build morphological oscillators (Fig.5C-D,

235

SFig.3). An initial structure of blue cells sharply transitions to cyan before transitioning to red and then

236

gray before repeating the cycle (Fig.5C). Testing the circuit with a higher blue ligand repression difficulty

237

β BLUE-L=11000 built a morphological oscillator that skipped the gray and blue phases, yielding a cyan

238

red oscillator (Fig.5D). Oscillators with the remaining parameters (

β BLUE-L=16000, 21000) are given in

239

SFig.3. All these oscillations were highly reproducible and consistent (n=3 each).

β BLUE-L=1000 was a

240

notably poor oscillator (SFig.3C). With the same parameters, the direct inhibition circuit and 2-TF

241

permanent inhibition circuit did not yield oscillatory structures, confirming that temporary gene

242

repression is the driver of oscillation (SFig.4)

6,35,39–43

243

244

Additional temporal control via activating amplifiers improves oscillation quality.

245

In addition to being able to build multicellular structures, inhibitory circuits can also generate

246

morphological oscillations, demonstrating their potential for bottom-up synthetic development. It would

247

be even more powerful, however, if the oscillations could be further modified and improved. The

248

morphological oscillations generated by the temporary inhibition circuit dampened quickly (Fig.5C-D).

249

These results were confirmed by running the simulations for longer (SFig.5A,C).

250

In the accompanying study

, I showed how activatory circuits, through activating transcriptional

251

amplifiers, can be used to enact spatiotemporal control over gene expression in bottom-up multicellular

252

development. As temporary gene repression is what drives oscillation, I reasoned that using an activating

253

amplifier to control the temporary gene repression of the temporary inhibition circuit could improve

254

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oscillation (Fig.6A). The circuit design (Fig.6B) is a simple modification of the temporary inhibition

255

circuit; it uses an activating amplifier to control the inhibitory circuit of Fig.3C. The synNotch receptor

256

now drives an activating amplifier consisting of an activating transcription factor (ATF) (Fig.6B). The

257

ATF then drives expression of E-cadherin and ITF (Fig.6B). ITF then inhibits blue ligand expression as in

258

the original circuit (Fig.6B).

259

Using the same parameters as the temporary inhibition circuit oscillator of Fig.5C and SFig.5A,

260

the amplified oscillator improved morphological oscillation (Fig.6C). I compared oscillation quality

261

between circuits using the number of cyan phases completed before half amplitude (ring-down method in

262

signal analysis)

. I chose the cyan phase for quantification as it is present in all oscillators (i.e. cyan red

263

oscillators lack gray and blue phases (Fig.5D)) and does not have constant drift (i.e. see SFig.7B).

264

Compared to its non-amplified variant (Fig.5C and SFig.5A), the amplified oscillator (Fig.6C) was

265

approximately a 1.5-fold improvement in oscillation quality (3 cyan phases to 2 cyan phases). Due to

266

prolonged inhibition from the activating amplifier

, oscillation took notably longer, requiring almost

267

400000 timesteps for the three cycles (Fig.6C). Dampening was also observed but is notably less

268

prominent. The oscillator of SFig.5A had red cell percentage quickly drift up with each red phase (5% to

269

20% to 50%) (SFig.5A). In contrast, the amplified oscillator had a much lower drift (0% to 5% to 20%)

270

(Fig.6C).

271

Similar results were obtained for the

β ECAD/ITF=1000 β BLUE-L=11000 amplified oscillator

272

(SFig.5B). The amplified oscillator was at least a 1.3-fold improvement in oscillation quality compared to

273

its non-amplified counterpart (SFig.5C) (4 cyan phases to 3 cyan phases). The oscillation occurred over a

274

longer duration due to prolonged inhibition from the activating amplifier as expected (SFig.5B).

275

Dampening was observed but the amplified oscillator only had red percentage drift from 5% to 10% to

276

20% in the observed red phases (SFig.5B) while in the equivalent red phases of the oscillator, drift was

277

from 0% to 40% to 70% (SFig.5C).

278

To confirm that oscillations are not limited to

β ECAD/ITF=1000 circuits, I tested if β

279

ECAD/ITF=6000 circuits could also generate oscillatory structures. Oscillators with

β ECAD/ITF=6000

280

and

β BLUE-L=1000 or 6000 generated no oscillations (SFig.6A and SFig.7A). However, the amplified

281

oscillator circuits were able to oscillate (SFig.6B and SFig.7B). These results indicate that incorporating

282

activating amplifiers can not only improve, but even rescue oscillations.

283

These results, in conjunction with those of Fig.5 and SFig.3, indicate that inhibitory circuits are

284

powerful tools for achieving morphological oscillations. These circuits can be flexibly modified with

285

additional circuits to alter their oscillatory behavior, supporting their utility for bottom-up synthetic

286

development.

287

288

DISCUSSION

289

The bottom-up approach is an emerging but powerful strategy for studying multicellular

290

development. Most bottom-up efforts focus on activatory circuits to drive synthetic development, but in

291

this study, I show that inhibitory circuits can also be powerful tools for driving development. Via an in

292

silico approach, I show that the designed inhibitory circuits can build a variety of patterned multicellular

293

structures. A systematic parameter scan reveals that the only known inhibitory structure to date is but a

294

fraction of the structures possible with inhibitory circuits. Further examination of one circuit revealed that

295

it is capable of morphological oscillations and that these oscillations could be improved by using

296

activatory circuits from the accompanying study. Altogether, these results support that inhibitory circuits

297

can be powerful tools for building and studying developmental processes.

298

To demonstrate how inhibitory circuits can be used to build multicellular structures, I employed a

299

previously tested computational approach

18,19

. By combining the GJSM with a cellular Potts framework, I

300

was able to test the circuits across a variety of parameter combinations and show the numerous different

301

morphologies buildable from these circuits (Fig.3-4, SFig.2)

18,19,34

. This computational setup has been

302

validated for modelling and predicting the self-organizing structures that arise from synNotch circuits

303

driving differential adhesion

. Nonetheless, I recognize that a key limitation of computational studies is

304

experimentational validation. Unfortunately, as an independent investigator, I lack all the fundings and

305

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resources to perform any of the analogous biological experiments. With this limitation in mind, at the

306

inception of this study, I deliberately designed and chose to test the direct inhibition circuit and temporary

307

inhibition circuit as specific biological versions of these circuits exist

10,31

. The specific version of the

308

direct inhibition circuit uses Gal4-KRAB as the inhibitory transcription factor

. Its inhibition and

309

temporal dynamics are consistent with the results obtained for the direct inhibition circuit in Fig.2C. The

310

specific version of the temporary inhibition circuit, the lateral inhibition circuit (Fig.3A), served as an

311

additional check for my strategy. The lateral inhibition circuit’s only known structure was predicted by

312

the in silico approach (Fig.3E), confirming the results of the previous study

and supporting the validity

313

of the computational approach. The in silico approach additionally predicted a variety of other structures

314

yet to be obtained in vitro (Fig.3E), but this reflects a difference in methodology. The in vitro lateral

315

inhibition circuit was partially calibrated

, thereby limiting the types of structures buildable, while the in

316

silico temporary inhibition circuit was systematically examined across numerous different parameters.

317

In addition, the in silico model also predicts that the temporary inhibition circuit is capable of

318

morphological oscillations (Fig.5, SFig.3). Temporary repression is well-known to drive oscillations in

319

single cells, but it has yet to be shown how oscillations in multiple cells can drive synthetic multicellular

320

development

41–43,45,46

. This result would be particularly interesting to test biologically, as it could

321

demonstrate that inhibitory circuits can build dynamic structures as well. Such results would indicate that

322

inhibitory circuits are indispensable tools for bottom-up synthetic development.

323

As in the accompanying study

, I designed the circuits generically to accommodate the rapidly

324

increasing toolkit of synthetic biology

31,38,47–62

. I leave the component choice to the user so that future

325

components can be incorporated and tested. For example, typical transcription factors (TFs) at the time of

326

the lateral inhibition circuit included the ATFs Gal4-VP64, LexA-VP64, tTa and ITF Gal4-KRAB

327

31,32,38,63–65

. Since then, however, new TFs have emerged with improved compatibility and modularity

47–

328

49,66

329

These TF development efforts, like most bottom-up efforts, notably focus on gene activation. For

330

bottom-up approaches to advance, there needs to be efforts towards developing new and improved ITFs

331

as well. As an example, the direct inhibition circuit that builds multicellular structures (Fig.4A) requires a

332

bifunctional transcription factor that can both inhibit and activate gene expression. Such a transcription

333

factor has yet to be engineered and used for multicellular synthetic development, but natural bifunctional

334

transcription factors do exist and could be a viable starting point for this component

67–70

335

Though the circuits here are relatively basic in design, they can build a wealth of patterned

336

multicellular structures and even morphological oscillations. They even have features of native

337

developmental processes such as cell fate divergence, self-organization, and synchronized oscillation.

338

“Build-it-to-understand-it” efforts with inhibitory circuits could advance our understanding of native

339

multicellular developmental processes. Beyond multicellular development, inhibitory circuits, like

340

activatory circuits, could potentially be used for therapeutic purposes as well such as regenerative

341

medicine and synthetic organ development

18,21,23,24

. This work supports future research on inhibitory

342

circuits, and I hope it will promote the use of inhibitory circuits in multicellular synthetic biology.

343

344

ACKNOWLEDGEMENTS

345

I would like to thank UNMC for access to and aid in printing research articles. I am thankful to the three

346

anonymous reviewers of my previous article

as their suggestions have also helped improve this

347

manuscript.

348

349

AUTHOR CONTRIBUTIONS

350

C.L. conceived, designed, performed, analyzed, and wrote the entire study.

351

352

DECLARATION OF INTERESTS

353

I declare no competing or financial interests.

354

355

FUNDING

356

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available under a

(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made

The copyright holder for this preprint

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;

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This work was not funded by any private or public agency. This work was solely funded by the author.

357

358

METHODS

359

Key Resource Table

360

SOFTWARE AND ALGORITHMS

SOURCE

IDENTIFIER

CompuCell3D (CC3D) v3.7.8

RRID:SCR_003052

Mathematica v12.0.0.0

Wolfram Research

RRID:SCR_014448

Excel v2310

Microsoft

RRID:SCR_016137

General Juxtacrine Signaling Model (GJSM)

N/A

Activating Transcriptional Amplifiers in GJSM

N/A

361

Lead Contact

362

Requests for

information and code

should be directed to

Calvin Lam (

calvin.lam.k@gmail

363

364

In silico cell line ISL929.

365

ISL929 is an in silico cell line developed in

to model the in vitro L929 cell line used for

366

building multicellular structures with the synNotch receptor

. This line was developed in the

367

CompuCell3D cellular Potts framework

and has been used with the Generalized Juxtacrine Signaling

368

Model (GJSM) to successfully predict how synNotch circuits can drive multicellular development

369

Because the lateral inhibition circuit was implemented in L929 cells

, ISL929 served as the ideal in

370

silico cells for this study. It would allow me to check the previous study’s results

while also providing a

371

biological experiment start point such as testing the inhibitory circuits from this study in L929 cells. A

372

brief description of ISL929 is given in the accompanying study

and a complete description is in the

373

original study

374

375

Overview of the Generalized Juxtacrine Signaling Model.

376

The Generalized Juxtracine Signaling Model (GJSM) was developed to model synthetic

377

juxtacrine receptor (i.e. synNotch

10,31

, SNIPR

) regulation of gene expression

. When parameterized,

378

the model can capture synthetic juxtacrine receptor signaling dynamics and has successfully predicted the

379

developmental structures that arise from synNotch-based differential adhesion circuits

. A brief

380

description of the relevant model features is given below. Full descriptions can be found in

18,19

381

Gene expression by a synthetic juxtacrine receptor such as synNotch can be described by the

382

general equation

383

The change in the expressed gene’s protein level R at a given timestep t is a function of both

384

production (first term) and degradation (second term). In the production term, signal S models receptor or

385

activating transcription factor (ATF) signaling driving gene expression.

β models gene expression

386

difficulty and encompasses the biological processes that affect gene to functional protein product such as

387

such as promoter, transcription, translation, trafficking inefficiencies, and expression delay, etc

18,19

388

Degradation (second term) is modelled by the standard linear decay model. Protein product level

389

R decays proportional to itself and inverse to decay constant

κ. As a result, κ controls not only decay rate

390

but saturation level as well.

391

The logistic form was chosen for GJSM over the Hill form for several reasons as described in the

392

original study

and accompanying study

. First, the logistic form has simple and intuitive parameter

393

interpretations that allow a user new to modeling to easily start. Weighing S against

β allows a user to

394

quickly understand how expression difficulty and signal affects expression. If S largely exceeds

395

expression difficulty, then expression is easy. If expression difficulty largely exceeds S, then expression is

396

difficult. Second, because the logistic form is mathematically equivalent to the Hill form, a more

397

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advanced user can convert the logistic equations to Hill equations to obtain more biologically relevant

398

parameters if desired

18,71,72

399

Because the logistic function is equivalent to the Hill function, GJSM is also capable of modeling

400

gene repression. This was shown in the original study

. Gene repression in GJSM can be described by

401

the equation

402

This form is mathematically obtained by transforming the expression equation with S to -S and

403

to –

. Signal S now models receptor or inhibitory transcription factor (ITF) signaling inhibiting gene

404

expression.

β now models gene repression difficulty and still encompasses the processes of gene to

405

functional protein product as in the expression equation. Intuitive interpretations remain and degradation

406

modelling remains the same as in the expression equation.

407

408

Inhibitory circuits as modelled by GJSM.

409

With the general equations described, equation sets for the inhibitory circuits can now be defined.

410

411

Direct Inhibition Circuit

412

In the direct inhibition circuit, the synNotch receptor directly inhibits target gene expression

413

(Fig.1D). Then, the circuit equation is

414

415

ௌ௃ோ

416

SJR

is the number of activated synNotch receptors at a given timestep, with activated meaning

417

bound to cognate ligand and released its transcription factor. Parameters are as described above for

418

inhibitory circuits. How S

SJR

is calculated is in a below section.

419

In the direct inhibition circuit for building multicellular structures (Fig.4A), the synNotch

420

receptor also drives expression of the adhesion protein E-cadherin. E-cadherin levels are described by

421

422

ௌ௃ோ

423

SJR

is the number of activated synNotch receptors at a given timestep. Parameters are as

424

described above for activatory circuits. How S

SJR

is calculated is in a below section.

425

426

Temporary Inhibition Circuit/Oscillator Circuit

427

In the temporary inhibition circuit/oscillator circuit, the synNotch receptor indirectly inhibits gene

428

expression by driving expression of an inhibitory transcription factor (ITF) that then inhibits target gene

429

expression (Fig.1E). ITF levels are described by

430

431

ௌ௃ோ

432

Parameters are as described above for activatory circuits. Target gene product level R is then

433

described by the inhibitory equation

434

435

ூ்ி

436

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ITF

is the ITF level at a given timestep from solving the first equation in the circuit. Parameters

437

are as described above for inhibitory circuits.

438

In the temporary inhibition circuit for building multicellular structures (Fig.3) or oscillators

439

(Fig.5), the synNotch receptor, in addition to driving the ITF, also drives expression of E-cadherin. To

440

simplify the number of parameters and equations used per circuit, E-cadherin levels are described by the

441

ITF equation.

442

443

ௌ௃ோ

444

However, if desired, E-cadherin can be defined separately from ITF with its own parameters

445

governing expression difficulty and decay.

446

447

2-Transcription Factor (2-TF) Permanent Inhibition Circuit

448

In the 2-TF permanent inhibition circuit, the synNotch receptor drives expression of the activating

449

transcription factor (ATF) and ITF (Fig.1F). The ATF is also able to drive expression of the ATF and ITF

450

(Fig.1F). Then, ATF levels are described by

451

452

ௌ௃ோ

஺்ி

453

ATF

is the ATF level from solving this equation at a given timestep. Parameters are as described

454

above for activatory circuits.

455

To simplify parameters and equations used and because the ITF is linked to ATF expression, the

456

ITF is assigned the same equation

457

458

ௌ௃ோ

஺்ி

459

The ITF then inhibits target gene expression as in the temporary inhibition circuit. Thus, the

460

equation is

461

ூ்ி

462

In the 2-TF permanent inhibition circuit for building multicellular structures (Fig.4B), in order to

463

avoid the use of hybrid combinatorial promoters, which are not tested with GJSM

, E-cadherin must be

464

controlled by the same type of promoter as the ATF/ITF. Because ATF is able to drive expression of itself

465

through this promoter, E-cadherin must also be driven by the ATF. E-cadherin is also driven by the

466

synNotch receptor. Then, to simplify the number of parameters and equations used per circuit, E-cadherin

467

levels are described by the ATF/ITF equation

468

469

ௌ௃ோ

஺்ி

470

As in the temporary inhibition circuit, E-cadherin can be defined separately from ATF/ITF with

471

its own parameters if desired.

472

473

Amplified Oscillator Circuit (Temporarily Amplified Activation Circuit Controlling Temporary Inhibition

474

Circuit)

475

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In the amplified oscillator circuit, a temporarily amplified activation circuit controls the

476

temporary inhibition circuit (Fig.6B). The synNotch receptor drives expression of an ATF that then

477

controls the temporary inhibition circuit.

478

The ATF equation is as in the published accompanying study

479

480

ௌ௃ோ

481

This ATF then drives expression of ITF and E-cadherin, replacing the role of the synNotch

482

receptor in the temporary inhibition circuit. Then, the equations are

483

484

஺்ி

485

஺்ி

486

Finally, the ITF then inhibits target gene expression as in the temporary inhibition circuit. Thus,

487

the equation is

488

ூ்ி

489

For the equations of each circuit, parameters that do not change between equations are denoted

490

with the same variable (i.e.

β1 is the same across all equations in the same circuit). However, it is

491

important to note that parameters can be set differently between equations if desired. This confers

492

additional flexibility in modeling, but increases the parameters used for a circuit. Parameters are given in

493

Supplementary Table 1.

494

495

Programming ISL929 cells with circuits and receptors.

496

Having defined the equations for each circuit, I then implemented them into ISL929 cells. See

497

SFig.1A of the accompanying study for a graphical depiction of this process

. I then added the

498

appropriate constitutive ligands into the appropriate cells (i.e. orange ligand on orange cells). I also added

499

synNotch to the appropriate cells as well. To simplify calculations, I assumed synNotch to be in excess

500

and non-limiting as in the reference and accompanying studies

10,18,19

. If desired, the complete GJSM

501

framework can be used to model receptor limiting cases. See the original study

for the receptor limiting

502

formulation of GJSM. With these rules defined, it is now possible to calculate the signal S

SJR

from

503

synNotch signaling in the circuit equations. The relevant calculations are given here. The complete

504

description and generalized formula can be found in the original study

505

SynNotch functions in a 1:1 stoichiometry; one activated receptor releases one transcription

506

factor regulating the target gene

18,19,31,32,62

. Because I assume synNotch to be in excess, S

SJR

can be

507

calculated from the amount of cognate ligand a focal cell is exposed to at the given timestep. Then, S

SJR

508

for a focal cell

σ can be calculated using the equation

509

510

ௌ௃ோ

! ! # $ #%&%' ( )

! ! (

ௌே

511

This formula is from the original GJSM study

. For a focal cell

σ, it receives SJR signal S

SJR

512

calculated from the total number of cognate ligand it is exposed at a given timestep. For each signaling

513

neighbor (SN) with the cognate ligand, L is the amount of cognate ligand on its surface. Dividing L by the

514

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SN’s surface area yields the ligand density. Multiplying this density by the shared surface area between

515

the focal cell and SN gives the amount of ligand the focal cell sees from that single SN. Summing over all

516

SNs then gives the total number of cognate ligand the focal cell is exposed to at a given timestep and

517

yields S

SJR

518

L is a constant value for a constitutive ligand like orange ligand, but for a ligand that is inhibited

519

by the signaling circuit (i.e. blue ligand), L is defined by R in the circuit equations. Parameters are given

520

in Supplementary Table 1.

521

522

Linking expression and repression to behavior.

523

I linked expression and repression to intended behavior using a discrete transition model as in the

524

original and accompanying study

18,19

. Cells with protein product level exceeding the threshold (7000 for

525

all simulations in this study) gained the feature of the protein product. For example, exceeding 7000 for

526

E-cadherin levels allows cells to be adhesive to other E-cadherin expressing cells. Falling under this

527

threshold results in cells losing the feature. For example, E-cadherin levels falling under 7000 reverts

528

cells to non-adhesive.

529

530

General simulation conditions.

531

Cells were initialized as a 5x5x5 pixel cube in a 100x100x100 lattice. For the cell-cell signaling

532

setup, initial configuration is specified in the results section. For the building multicellular structure

533

experiments, cells were seeded as a spherical blob at the center of the lattice. The seeded number of cells

534

in each blob is given per experiment. Data was collected every 100 timesteps for analysis. Simulation

535

runtime is given per experiment.

536

537

Cell-cell signaling assay.

538

Assay was performed as described in the results section and in the accompanying study

539

Parameters are given in Supplementary Table 1.

540

541

Structure images.

542

Representative cross sections of the structures are shown as in the reference in vitro experiment

543

. Scalebar is 17.5 pixels to 100 um as determined in the original study

544

545

Cell percentage quantification.

546

Cell percentage was calculated by dividing the number of cells of the focal type over total

547

number of cells in the simulation at that timestep.

548

549

Mitosis removal.

550

I removed cell growth and mitosis in oscillation simulations with runtime >100000 timesteps.

551

The longer runtime required for observing oscillation along with its termination would otherwise result in

552

cells completely filling the lattice and slowing the simulation significantly. I validated that growth and

553

mitosis removal did not affect oscillation (compare Fig.5C to SFig.5A, Fig.5D to SFig.5C). Cells sharply

554

transitioned at the same timepoints and transitioned to the correct phase independent of growth and

555

mitosis.

556

557

Comparing oscillation quality.

558

To roughly compare oscillation quality between circuits, I calculated the quality factor Q for each

559

oscillation using the ring-down method

. Q, the quality of the oscillation, can be defined proportionate to

560

the number of oscillations before the oscillation decays to 50% of its maximum amplitude. I used 100%

561

as the maximum amplitude and chose to calculate Q off the cyan phase of the oscillation as it is present in

562

all oscillators and does not have constant drift. Q was then compared between circuits to calculate the fold

563

improvement.

564

565

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Statistical analysis.

566

Sample size is given in the text, figures, or captions. Plots are mean±SEM.

567

568

FIGURE LEGENDS

569

Figure 1. Design of the synthetic inhibitory circuits for bottom-up multicellular development.

570

A) The majority of bottom-up “build-it-to-understand-it” approaches for multicellular development use

571

activatory circuits. A target gene is activated to drive development. Such circuits are capable of building

572

multitudes of structures. B) Inhibitory circuits, in contrast, are rarely used in the bottom-up approach. Are

573

they also capable of building various multicellular structures? C) The synthetic Notch (synNotch)

574

receptor is a synthetic receptor modular in both ligand binding and intracellular domain. Ligand binding

575

domain allows sensing a ligand of choice and intracellular domain allows releasing an activating or

576

inhibitory transcription factor of choice. D) The direct inhibition circuit has the synNotch receptor release

577

an inhibitory transcription factor to directly repress target gene expression

. E) The temporary inhibition

578

circuit has the synNotch receptor first drive an inhibitory transcription factor (ITF) that then represses

579

target gene expression. This circuit should result in temporarily prolonging gene repression. F) The 2-TF

580

permanent inhibition circuit has the synNotch receptor drive a transgene cassette with an activating

581

transcription factor (ATF) and ITF. ATF drives itself and the ITF, permanently expressing ITF to

582

permanently repress gene expression.

583

584

Figure 2. Inhibitory circuits inhibit gene expression as designed. A) Signaling schematic for testing if

585

the inhibitory circuits operate as designed. Blue cells are programmed with an anti-orange ligand

586

synNotch that triggers one of the inhibitory circuits to repress blue reporter expression. B) Cell-cell

587

signaling test setup, where a blue cell is seeded with 3 orange neighbor cells and orange cells are deleted

588

at 25000 timesteps to determine how orange ligand-synNotch signaling loss affects blue reporter

589

repression. C) Blue reporter traces from the signaling test setup at different blue reporter repression

590

difficulties (

β reporter). Cells with the direct inhibition circuit lost gene repression immediately after

591

orange neighbor loss, consistent with the circuit’s minimal temporal control design. These results are

592

consistent with in vitro direct synNotch signaling dynamics

18,31,32

. In contrast, the temporary inhibition

593

circuit repressed at even higher repression difficulties and maintained repression for some time despite

594

synNotch signaling loss. The 2-TF permanent inhibition circuit repressed at even further higher repression

595

difficulties and maintained permanent blue reporter repression even after signaling loss. These results

596

confirm that the circuits operate as designed. One trace shown per condition. Simulations run for 100000

597

timesteps.

598

599

Figure 3. Temporary inhibition circuit can build a variety of multicellular structures. A) One

600

version of the temporary inhibition circuit, the lateral inhibition circuit

. In this version, anti-CD19

601

synNotch drives E-cadherin (ECAD) and tet transcriptional repressor (tTS) that represses CD19

602

expression. B) Mixing ~100 cells programmed with this circuit results in a 2-layered structure with CD19

603

E-cadherin

green cells and CD19

E-cadherin

yellow cells in the center with CD19

E-cadherin

red

604

cells on the periphery. Micrograph reproduced from Toda et al, 2018

with permission from AAAS. C)

605

The temporary inhibition circuit is the generalized version of the lateral inhibition circuit. ECAD is E-

606

cadherin. ITF is generic representation for tTs. BLUE-L (blue ligand) is generic representation for CD19.

607

D) A cell state color key is given to match expression state to cell color in the subsequent images. E)

608

Mixing 93 blue cells programmed with the temporary inhibition circuit results in multitudes of patterned

609

structures. A representative set of structures is given, showcasing the variety of patterned structures that

610

can form from the temporary inhibition circuit. Each structure resulted from a different parameter set of

611

expression difficulties for ITF/ECAD and repression difficulties for blue ligand. The full gallery of

612

structures, along with the parameters that generated them, is given in SFig.2A. As expected, and

613

previously shown, the model predicts the known in vitro structure

. These results indicate that the only

614

known structure to date is a small subset of structures possible with this circuit. N=3 for each structure.

615

Simulations run for 50000 timesteps.

616

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Figure 4. Designed inhibitory circuits can build multitudes of multicellular structures. A) The direct

617

inhibition circuit can also build various patterned structures. 93 blue cells with this circuit results in 7

618

different types of patterned structures. One representative structure for each pattern type is shown. Full

619

gallery of structures is given in SFig.2B. B) The 2-TF permanent inhibition circuit can also build various

620

patterned structures. 93 blue cells with this circuit results in 5 different types of patterned structures. One

621

representative structure for each pattern type is shown. Full gallery of structures is given in SFig.2C. N=3

622

for each structure. Simulations run for 50000 timesteps.

623

624

Figure 5. Temporary inhibition circuit can build oscillatory structures. A) Homogenous spheroids

625

built by the temporary inhibition circuit had cells synchronized in expression state (color) with sharp

626

transition to the next expression state. An example developmental trajectory with these synchronous and

627

sharp transitions is shown. Cell expression state is given below each image. B) This led me to hypothesize

628

that the temporary inhibition circuit can build oscillatory structures. Hypothesized oscillation is shown

629

along with cell expression state for each phase in the oscillation. C) 57 blue cells programmed with the

630

temporary inhibition circuit and ECAD/ITF expression difficulty=1000 (

β ECAD/ITF=1000) with blue

631

ligand repression difficulty=6000 (

β BLUE-L=6000) generated morphological oscillation. Cells

632

synchronously transitioned from blue to cyan to red to gray before repeating the oscillation.

633

Developmental trajectory shown is of images at the transition time. Plot of cell percentage is given as

634

well. D) 57 blue cells programmed with the temporary inhibition circuit but

β ECAD/ITF=1000 and β

635

BLUE-L=11000. Oscillation differed from that of C, skipping the blue and gray phase. Developmental

636

trajectory is shown along with plot of cell percentage. Additional oscillations with different parameters

637

are given in SFig.3. A representative developmental trajectory is given per oscillation. N=3 for each

638

oscillation. Simulations run for 100000 timesteps.

639

640

Figure 6. Using activating amplifiers to control the temporary inhibition circuit can improve

641

oscillation quality. A) I recently showed that activating amplifiers can modulate temporal dynamics in

642

synthetic circuits

. I therefore tested if prolonging repression with an activating amplifier could improve

643

oscillation quality. B) Temporarily amplified activation circuit controlling temporary inhibition circuit.

644

The temporary inhibition circuit is rewired such that the synNotch receptor now drives the activating

645

amplifier (activating transcription factor, ATF). The activating amplifier then drives the inhibitory circuit

646

that then represses target gene expression. C) Mixing 93 blue cells programmed with this circuit builds an

647

oscillator with improved oscillation quality compared to its non-amplified variant (SFig.5A). Mitosis was

648

removed due to computational limitations, but this does not affect timing or quality of oscillation

649

(compare Fig.5C to SFig.5A, Fig.5D to SFig.5C). Developmental trajectory is shown along with plot of

650

cell percentage. Additional oscillations with different parameters are given in SFig.5-7. A representative

651

developmental trajectory is given per oscillation. N=3 for each oscillation. Simulations run for 400000

652

timesteps.

653

654

SUPPLEMENTARY FIGURES

655

Supplementary Figure 1. Inhibitory circuits operate as designed, related to figure 2. A) Uses the

656

cell-cell signaling setup of Fig.2B, but blue cells are seeded without orange neighbors to determine

657

background reporter repression. Reporter repression difficulties

≥1000 do not have leaky repression (β

658

reporter must be at least 1000 in simulations). B) Inhibitory transcription factor (ITF) traces from the blue

659

reporter traces of Fig.2C. One trace shown per condition. Simulations run for 100000 timesteps.

660

661

Supplementary Figure 2. Full gallery of multicellular structures from the inhibitory circuits,

662

related to figures 3 And 4. A) Full gallery of the structures built by the temporary inhibition circuit with

663

parameters specified. Number labels correspond to structures shown in Fig.3E. Pink box encloses

664

structures tested for oscillation later in the study. B) Full gallery of the structures built by the direct

665

inhibition circuit with parameters specified. Number labels correspond to structures shown in Fig.4A. C)

666

Full gallery of the structures built by the 2-TF permanent inhibition circuit with parameters specified.

667

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Number labels correspond to structures shown in Fig.4B. Initial mixture is 93 blue cells. One

668

representative structure for each parameter combination is shown. N=3 for each structure. Simulations run

669

for 50000 timesteps.

670

671

Supplementary Figure 3. Additional oscillatory structures built by the temporary inhibition circuit,

672

related to figure 5. A) Oscillator resulting from 57 blue cells programmed with the temporary inhibition

673

circuit and ECAD/ITF expression difficulty=1000 (

β ECAD/ITF=1000) with blue ligand repression

674

difficulty=16000 (

β BLUE-L=16000). Plot of cell percentage is given on the right. B) Same as A but with

675

blue ligand repression difficulty=21000 (

β BLUE-L=21000). C) 93 blue cells programmed with the

676

temporary inhibition circuit and ECAD/ITF expression difficulty=1000 (

β ECAD/ITF=1000) with blue

677

ligand repression difficulty=1000 (

β BLUE-L=1000) yielded poor oscillation. Mitosis was removed so

678

the simulation could be run longer while limiting computational strain. Mitosis does not affect oscillation

679

behavior. See Methods Section for validation. A representative developmental trajectory with images at

680

the transition time is given per oscillation. N=3 for each oscillation. Simulations run for timesteps shown.

681

682

Supplementary Figure 4. Direct inhibition circuit and 2-TF permanent inhibition circuit do not

683

build oscillatory structures, related to figure 5. A) 93 blue cells programmed with the direct inhibition

684

circuit were run with the same parameter combinations tested for oscillation in the temporary inhibition

685

circuit of Fig.5 and SFig.3. There were no oscillations. B) Same as A but with the 2-TF permanent

686

inhibition circuit. Mitosis was removed so the simulation could be run for 200000 timesteps. Plots of cell

687

percentage is given. N=3.

688

689

Supplementary Figure 5. Comparing oscillatory structures built by the amplified oscillator to the

690

oscillator (temporary inhibition circuit) with

β ECAD/ITF=1000, related to figure 6. A) Oscillator

691

resulting from 93 blue cells programmed with the temporary inhibition circuit (oscillator) and ECAD/ITF

692

expression difficulty=1000 (

β ECAD/ITF=1000) with blue ligand repression difficulty=6000 (β BLUE-

693

L=6000). Plot of cell percentage is given on the right. Oscillation is to be compared to oscillation of

694

Fig.6C. B) Oscillator resulting from 93 blue cells programmed with an activating amplifier controlling the

695

temporary inhibition circuit. ECAD/ITF expression difficulty=1000 (

β ECAD/ITF=1000) with blue

696

ligand repression difficulty=11000 (

β BLUE-L=11000). Plot of cell percentage is given on the right.

697

Oscillation is to be compared to oscillation of SFig.5C (below). C) Oscillator resulting from 93 blue cells

698

programmed with the temporary inhibition circuit (oscillator) and ECAD/ITF expression difficulty=1000

699

(

β ECAD/ITF=1000) with blue ligand repression difficulty=11000 (β BLUE-L=11000). Plot of cell

700

percentage is given on the right. Oscillation is to be compared to oscillation of SFig.5B. Mitosis was

701

removed in all simulations shown here. A representative developmental trajectory with images at the

702

transition time is given per oscillation. N=3 for each oscillation. Simulations run for timesteps shown.

703

704

Supplementary Figure 6. Comparing oscillatory structures built by the amplified oscillator to the

705

oscillator (temporary inhibition circuit) with

β ECAD/ITF=6000, β BLUE-L=1000, related to figure

706

6. A) Oscillator resulting from 93 blue cells programmed with the temporary inhibition circuit (oscillator)

707

at given parameters. Oscillation is to be compared to oscillation of SFig.6B. B) Oscillator resulting from

708

93 blue cells programmed with an activating amplifier controlling the temporary inhibition circuit at

709

given parameters. Oscillation is to be compared to oscillation of SFig.6A. Mitosis was removed in all

710

simulations shown here. A representative developmental trajectory with images at the transition time is

711

given per oscillation. N=3 for each oscillation. Simulations run for timesteps shown.

712

713

Supplementary Figure 7. Comparing oscillatory structures built by the amplified oscillator to the

714

oscillator (temporary inhibition circuit) with

β ECAD/ITF=6000, β BLUE-L=6000, related to figure

715

6. A) Oscillator resulting from 93 blue cells programmed with the temporary inhibition circuit (oscillator)

716

at given parameters. Oscillation is to be compared to oscillation of SFig.7B. B) Oscillator resulting from

717

93 blue cells programmed with an activating amplifier controlling the temporary inhibition circuit at

718

CC-BY-NC-ND 4.0 International license

available under a

(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made

The copyright holder for this preprint

this version posted November 18, 2023.

;

https://doi.org/10.1101/2023.11.18.567649

doi:

bioRxiv preprint

given parameters. Oscillation is to be compared to oscillation of SFig.7A. Mitosis was removed in all

719

simulations shown here. A representative developmental trajectory with images at the transition time is

720

given per oscillation. N=3 for each oscillation. Simulations run for timesteps shown.

721

722

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Figure 1

Designed Synthetic Inhibitory Circuits

2-Transcription Factor

(2-TF) Permanent

Inhibition

ATF

Target Gene

ITF

Temporary

Inhibition

Target Gene

ITF

Direct Inhibition

Target Gene

Extracellular Ligand

Binding Domain

Intracellular

Activating Transcription Factor

Inhibitory Transcription Factor

Regulating Gene of Choice

Synthetic Notch (synNotch) Receptor

Build-it-to-understand-it

Inhibitory Circuit

Patterned

Multicellular

Structures Obtainable?

Target Gene

Build-it-to-understand-it

Activatory Circuit

Diverse Variety of Patterned

Multicellular Structures

Synthetic

Receptor

Cognate

Ligand

Target Gene

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Figure 2

Cell-Cell

Signaling

Setup

Delete Orange Senders

at 25000 Timesteps

Neighboring

Orange

Senders

Quantify Reporter

and ITF Levels

Reporter Levels at Different Reporter Repression Difficulties

Reporter (10

)

Timestep (10

)

Direct

Temporary

2-TF Permanent

3000

6000

12000

18000

25000

1000

25 50 75 100

β Reporter

Signaling Schematic

Direct Inhibition

Temporary

Inhibition

2-TF Permanent

Inhibition

Blue Reporter

ITF

Blue Reporter

ATF

ITF

Anti-orange

ligand

synNotch

Orange

ligand

25 50 75 100

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Figure 3

Lateral Inhibition Circuit

Only Known Resulting Structure

Ligand+

E-cadherin-

Cells

Ligand-

E-cadherin+

Cells

Ligand+

E-cadherin+

Cells

Image reproduced from Toda et al, 2018

with permission from AAAS.

ECAD

tTS

CD19

E-cadherin

CD19

Anti-CD19

synNotch

ECAD

tTS

Temporary Inhibition Circuit

t=50

Ligand+

E-cadherin-

Cells

Ligand-

E-cadherin+

Cells

Ligand+

E-cadherin+

Cells

t=50

Various Resulting Structures of the Temporary Inhibition Circuit

ECAD

ITF

BLUE-L

E-cadherin

Blue

ligand

Anti-(Blue ligand)

synNotch

ECAD

ITF

BLUE-L

Cell State Color key

Ecad/ITF+

Blue ligand-

Ecad/ITF-

Blue ligand+

Ecad/ITF+

Blue ligand+

Ecad/ITF-

Blue ligand-

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Figure 4

t=50

Direct Inhibition Circuit and Various Resulting Structures

2-TF Permanent Inhibition Circuit and Various Resulting Structures

t=50

ECAD

BLUE-L

ECAD

BLUE-L

E-cadherin

Blue

ligand

Anti-(Blue ligand)

synNotch

ECAD

ITF

ATF

ITF

ATF

BLUE-L

E-cadherin

Blue

ligand

Anti-(Blue ligand)

synNotch

ECAD

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Figure 5

Oscillator with

β ECAD/ITF

=1000,

β BLUE-L=6000

Cell Percentage

Timesteps (10

mcs)

20 40 60 80 100

100

Timesteps (10

)

74.5 77.5

85.5

100

8.5

Oscillator with

β ECAD/ITF

=1000,

BLUE-L=11000

Timesteps (10

mcs)

20 40 60 80 100

Cell Percentage

100

Timesteps (10

) 0

8.5 46.5

84.5 89.5

100

Development of

Homogenous Spheroid

from

Temporary Inhibtion Circuit

t=39.5

E-cadherin+

blue ligand-

Red Cells

t=0

E-cadherin-

blue ligand+

Blue Cells

t=8.5

E-cadherin+

blue ligand+

Cyan Cells

Hypothesized Oscillation

E-cadherin+

blue ligand-

Red Cells

E-cadherin-

blue ligand+

Blue Cells

E-cadherin+

blue ligand+

Cyan Cells

E-cadherin-

blue ligand-

Gray Cells

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Figure 6

Controlling Inhibitory Circuits with Activating Amplifiers

Step 1

Step 2

Step 3

Amplifier

Target Gene

Temporarily Amplified Activation Circuit Controlling

Temporary Inhibition Circuit

Amplified Oscillator with

β ECAD/ITF

=1000,

β BLUE-L=6000

Timesteps (10

)

158 162.5 168 250.5

262.5 266.5 272 354.5

366

370 375.5 400

9.5

40 146.5

Cell Percentage

Timesteps (10

mcs)

100 200 300 400

100

Inhibitory

Circuit

E-cadherin

Blue

ligand

Anti-(Blue ligand)

synNotch

ECAD

ITF

BLUE-L

ATF

ECAD

ITF

BLUE-L

ATF

ECAD

ITF

ATF

BLUE-L

Activating

Amplifier

Inhibitory

Circuit

Target

Gene

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Supplementary Figure 1

Determining Background Reporter Repression

Quantify Reporter

Levels Over

Experiment

Orange

Senders

Cell-Cell

Signaling

Setup

β Reporter

0 25 50 75 100

1000

Direct

Temporarily

Amplified

2-TF Permanently

Amplified

Level (10

)

Timestep (10

)

ITF

Reporter

ITF Levels at the Tested Reporter Repression Difficulties

β Reporter

Direct

Temporary

2-TF Permanent

3000

1000

6000

12000

18000

25000

25 50 75 100

ITF Levels (10

)

Timestep (10

)

25 50 75 100

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Supplementary Figure 2

Temporary Inhibition

ECAD/ITF Expression Difficulty, β ECAD/ITF (10

)

Blue Ligand Repression Difficulty (10

)

* *

Direct Inhibition

ECAD/ITF Expression Difficulty, β ECAD/ITF (10

)

Blue Ligand Repression Difficulty (10

)

2-TF Permanent Inhibition

ECAD/ITF Expression Difficulty, β ECAD/ITF (10

)

Blue Ligand Repression Difficulty (10

)

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Supplementary Figure 3

Oscillator with

β ECAD/ITF

=1000,

BLUE-L=16000

Timesteps (10

mcs)

20 40 60 80 100

Cell Percentage

100

Timesteps (10

)

100

8.5

57.5

Oscillator with

β ECAD/ITF

=1000,

BLUE-L=21000

Timesteps (10

mcs)

20 40 60 80 100

Cell Percentage

100

82.5

97.5

100

Timesteps (10

)

8.5

Oscillator with

β ECAD/ITF

=1000,

BLUE-L=1000, No Mitosis

Timesteps (10

)

113.5

114.5 134.5

137.5

200

8.5

Timesteps (10

mcs)

50 100 150 200

Cell Percentage

100

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Supplementary Figure 4

Direct Inhibition with

β ECAD/ITF

=1000, No Mitosis, 90 Blue Cells

Timesteps (10

mcs)

1000

6000

11000

16000

21000

50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200

Cell Percentage

100

β BLUE-L->

2-TF Permanent Inhibition with

β ECAD/ITF

=1000, No Mitosis, 90 Blue Cells

β BLUE-L->

Timesteps (10

mcs)

1000

6000

11000

16000

21000

50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200

Cell Percentage

100

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available under a

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Supplementary Figure 5

Oscillator with

β ECAD/ITF

=1000,

β BLUE-L=6000, No Mitosis

Timesteps (10

mcs)

50 100 150 200

Cell Percentage

100

Timesteps (10

)

74.5

77.5

85.5

200

8.5

Oscillator with

β ECAD/ITF

=1000,

BLUE-L=11000, No Mitosis

Timesteps (10

mcs)

50 100 150 200

Cell Percentage

100

Timesteps (10

)

84.5

89.5

200

8.5

46.5

Amplified Oscillator with

β ECAD/ITF

=1000,

β BLUE-L=11000

Timesteps (10

)

169

260

277

367

384

400

9.5

47.5

152.5

Cell Percentage

Timesteps (10

mcs)

100 200 300 400

100

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Supplementary Figure 6

Amplified Oscillator with

β ECAD/ITF=6000 β BLUE-L=1000, No Mitosis

Timesteps (10

mcs)

100 200 300 400

Cell Percentage

100

Timesteps (10

) 0

15.5

99.5

156.5 170.5

176

220.5

277.5

291.5 296.5

342

398.5

400

Oscillator with

β ECAD/ITF

=6000,

β BLUE-L=1000, No Mitosis

Timesteps (10

mcs)

50 100 150 200

Cell Percentage

100

Timesteps (10

)

127

200

8.5

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Supplementary Figure 7

Amplified Oscillator with

β ECAD/ITF=6000 β BLUE-L=6000, No Mitosis

Timesteps (10

mcs)

100 200 300 400

Cell Percentage

100

Timesteps (10

) 0

15.5

107.5

119

129

141.5 193.5

205

213.5

226.5

400

Oscillator with

β ECAD/ITF

=6000,

β BLUE-L=6000, No Mitosis

Timesteps (10

mcs)

50 100 150 200

Cell Percentage

100

Timesteps (10

)

200

8.5

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