Difference between revisions of "Part:BBa K4619010"

Line 61: Line 61:
 
<p> We simulated T=1000 for each inducer strength, and for each inducer strength we set the repressor strength to be 5-10. It means we simulated <mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="10.81ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 4778 748" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.186ex;"><defs><path id="MJX-1-TEX-N-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path id="MJX-1-TEX-N-2217" d="M229 286Q216 420 216 436Q216 454 240 464Q241 464 245 464T251 465Q263 464 273 456T283 436Q283 419 277 356T270 286L328 328Q384 369 389 372T399 375Q412 375 423 365T435 338Q435 325 425 315Q420 312 357 282T289 250L355 219L425 184Q434 175 434 161Q434 146 425 136T401 125Q393 125 383 131T328 171L270 213Q283 79 283 63Q283 53 276 44T250 35Q231 35 224 44T216 63Q216 80 222 143T229 213L171 171Q115 130 110 127Q106 124 100 124Q87 124 76 134T64 161Q64 166 64 169T67 175T72 181T81 188T94 195T113 204T138 215T170 230T210 250L74 315Q65 324 65 338Q65 353 74 363T98 374Q106 374 116 368T171 328L229 286Z"></path><path id="MJX-1-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-1-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-1-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><use data-c="35" xlink:href="#MJX-1-TEX-N-35"></use></g><g data-mml-node="mo" transform="translate(722.2,0)"><use data-c="2217" xlink:href="#MJX-1-TEX-N-2217"></use></g><g data-mml-node="mn" transform="translate(1444.4,0)"><use data-c="31" xlink:href="#MJX-1-TEX-N-31"></use><use data-c="30" xlink:href="#MJX-1-TEX-N-30" transform="translate(500,0)"></use></g><g data-mml-node="mo" transform="translate(2722.2,0)"><use data-c="3D" xlink:href="#MJX-1-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(3778,0)"><use data-c="31" xlink:href="#MJX-1-TEX-N-31"></use><use data-c="30" xlink:href="#MJX-1-TEX-N-30" transform="translate(500,0)"></use></g></g></g></svg></mjx-container><script type="math/tex">5* 10=10</script> times to get 50 points of stable status. We plot a scatter plot to display. And according to the plot we find the threshold to be roughly 0.6 -0.8. As is shown in the following figure.</p>
 
<p> We simulated T=1000 for each inducer strength, and for each inducer strength we set the repressor strength to be 5-10. It means we simulated <mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="10.81ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 4778 748" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.186ex;"><defs><path id="MJX-1-TEX-N-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path id="MJX-1-TEX-N-2217" d="M229 286Q216 420 216 436Q216 454 240 464Q241 464 245 464T251 465Q263 464 273 456T283 436Q283 419 277 356T270 286L328 328Q384 369 389 372T399 375Q412 375 423 365T435 338Q435 325 425 315Q420 312 357 282T289 250L355 219L425 184Q434 175 434 161Q434 146 425 136T401 125Q393 125 383 131T328 171L270 213Q283 79 283 63Q283 53 276 44T250 35Q231 35 224 44T216 63Q216 80 222 143T229 213L171 171Q115 130 110 127Q106 124 100 124Q87 124 76 134T64 161Q64 166 64 169T67 175T72 181T81 188T94 195T113 204T138 215T170 230T210 250L74 315Q65 324 65 338Q65 353 74 363T98 374Q106 374 116 368T171 328L229 286Z"></path><path id="MJX-1-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-1-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-1-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><use data-c="35" xlink:href="#MJX-1-TEX-N-35"></use></g><g data-mml-node="mo" transform="translate(722.2,0)"><use data-c="2217" xlink:href="#MJX-1-TEX-N-2217"></use></g><g data-mml-node="mn" transform="translate(1444.4,0)"><use data-c="31" xlink:href="#MJX-1-TEX-N-31"></use><use data-c="30" xlink:href="#MJX-1-TEX-N-30" transform="translate(500,0)"></use></g><g data-mml-node="mo" transform="translate(2722.2,0)"><use data-c="3D" xlink:href="#MJX-1-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(3778,0)"><use data-c="31" xlink:href="#MJX-1-TEX-N-31"></use><use data-c="30" xlink:href="#MJX-1-TEX-N-30" transform="translate(500,0)"></use></g></g></g></svg></mjx-container><script type="math/tex">5* 10=10</script> times to get 50 points of stable status. We plot a scatter plot to display. And according to the plot we find the threshold to be roughly 0.6 -0.8. As is shown in the following figure.</p>
 
<p><img src="https://static.igem.wiki/teams/4619/wiki/modelling/main/modelling-rafit.png" referrerpolicy="no-referrer" title="Simulation Data" width="600px" height="400px"></p>
 
<p><img src="https://static.igem.wiki/teams/4619/wiki/modelling/main/modelling-rafit.png" referrerpolicy="no-referrer" title="Simulation Data" width="600px" height="400px"></p>
<p><center>&emsp;&emsp;&emsp;&emsp;<b>Simulation Data</b></center></p>
+
<p><center><b>Simulation Data</b></center></p>
 
<p>To unify, we processed the data, took the logarithm of the experimental data to the relative intensity interval, and used the function to fit the data to obtain the fitting curve. Then we find that the true threshold is roughly 680 <mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="7.669ex" height="2.059ex" role="img" focusable="false" viewBox="0 -694 3389.7 910" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.489ex;"><defs><path id="MJX-9-TEX-I-1D707" d="M58 -216Q44 -216 34 -208T23 -186Q23 -176 96 116T173 414Q186 442 219 442Q231 441 239 435T249 423T251 413Q251 401 220 279T187 142Q185 131 185 107V99Q185 26 252 26Q261 26 270 27T287 31T302 38T315 45T327 55T338 65T348 77T356 88T365 100L372 110L408 253Q444 395 448 404Q461 431 491 431Q504 431 512 424T523 412T525 402L449 84Q448 79 448 68Q448 43 455 35T476 26Q485 27 496 35Q517 55 537 131Q543 151 547 152Q549 153 557 153H561Q580 153 580 144Q580 138 575 117T555 63T523 13Q510 0 491 -8Q483 -10 467 -10Q446 -10 429 -4T402 11T385 29T376 44T374 51L368 45Q362 39 350 30T324 12T288 -4T246 -11Q199 -11 153 12L129 -85Q108 -167 104 -180T92 -202Q76 -216 58 -216Z"></path><path id="MJX-9-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-9-TEX-I-1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path><path id="MJX-9-TEX-I-1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path><path id="MJX-9-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-9-TEX-I-1D43F" d="M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D707" xlink:href="#MJX-9-TEX-I-1D707"></use></g><g data-mml-node="mi" transform="translate(603,0)"><use data-c="1D45A" xlink:href="#MJX-9-TEX-I-1D45A"></use></g><g data-mml-node="mi" transform="translate(1481,0)"><use data-c="1D45C" xlink:href="#MJX-9-TEX-I-1D45C"></use></g><g data-mml-node="mi" transform="translate(1966,0)"><use data-c="1D459" xlink:href="#MJX-9-TEX-I-1D459"></use></g><g data-mml-node="mo" transform="translate(2264,0)"><use data-c="2E" xlink:href="#MJX-9-TEX-N-2E"></use></g><g data-mml-node="mi" transform="translate(2708.7,0)"><use data-c="1D43F" xlink:href="#MJX-9-TEX-I-1D43F"></use></g></g></g></svg></mjx-container><script type="math/tex">\mu mol.L</script>. Note that we calculate the threshold at which the desired concentration reaches the turn-on threshold, which is <mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="15.193ex" height="2.52ex" role="img" focusable="false" viewBox="0 -864 6715.1 1114" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-19-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-19-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-19-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-19-TEX-I-1D707" d="M58 -216Q44 -216 34 -208T23 -186Q23 -176 96 116T173 414Q186 442 219 442Q231 441 239 435T249 423T251 413Q251 401 220 279T187 142Q185 131 185 107V99Q185 26 252 26Q261 26 270 27T287 31T302 38T315 45T327 55T338 65T348 77T356 88T365 100L372 110L408 253Q444 395 448 404Q461 431 491 431Q504 431 512 424T523 412T525 402L449 84Q448 79 448 68Q448 43 455 35T476 26Q485 27 496 35Q517 55 537 131Q543 151 547 152Q549 153 557 153H561Q580 153 580 144Q580 138 575 117T555 63T523 13Q510 0 491 -8Q483 -10 467 -10Q446 -10 429 -4T402 11T385 29T376 44T374 51L368 45Q362 39 350 30T324 12T288 -4T246 -11Q199 -11 153 12L129 -85Q108 -167 104 -180T92 -202Q76 -216 58 -216Z"></path><path id="MJX-19-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-19-TEX-I-1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path><path id="MJX-19-TEX-I-1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path><path id="MJX-19-TEX-N-2F" d="M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z"></path><path id="MJX-19-TEX-I-1D43F" d="M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msup"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-19-TEX-N-31"></use><use data-c="30" xlink:href="#MJX-19-TEX-N-30" transform="translate(500,0)"></use></g><g data-mml-node="mn" transform="translate(1033,393.1) scale(0.707)"><use data-c="30" xlink:href="#MJX-19-TEX-N-30"></use></g></g><g data-mml-node="mo" transform="translate(1714.3,0)"><use data-c="3D" xlink:href="#MJX-19-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(2770.1,0)"><use data-c="31" xlink:href="#MJX-19-TEX-N-31"></use></g><g data-mml-node="mi" transform="translate(3270.1,0)"><use data-c="1D707" xlink:href="#MJX-19-TEX-I-1D707"></use></g><g data-mml-node="mi" transform="translate(3873.1,0)"><use data-c="1D45A" xlink:href="#MJX-19-TEX-I-1D45A"></use></g><g data-mml-node="mi" transform="translate(4751.1,0)"><use data-c="1D45C" xlink:href="#MJX-19-TEX-I-1D45C"></use></g><g data-mml-node="mi" transform="translate(5236.1,0)"><use data-c="1D459" xlink:href="#MJX-19-TEX-I-1D459"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(5534.1,0)"><g data-mml-node="mo"><use data-c="2F" xlink:href="#MJX-19-TEX-N-2F"></use></g></g><g data-mml-node="mi" transform="translate(6034.1,0)"><use data-c="1D43F" xlink:href="#MJX-19-TEX-I-1D43F"></use></g></g></g></svg></mjx-container><script type="math/tex">10^0 = 1\mu mol/L</script>. While at the point where the slope is greatest, that is, <mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="17.347ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 7667.4 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-29-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-29-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-29-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-29-TEX-N-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path id="MJX-29-TEX-I-1D707" d="M58 -216Q44 -216 34 -208T23 -186Q23 -176 96 116T173 414Q186 442 219 442Q231 441 239 435T249 423T251 413Q251 401 220 279T187 142Q185 131 185 107V99Q185 26 252 26Q261 26 270 27T287 31T302 38T315 45T327 55T338 65T348 77T356 88T365 100L372 110L408 253Q444 395 448 404Q461 431 491 431Q504 431 512 424T523 412T525 402L449 84Q448 79 448 68Q448 43 455 35T476 26Q485 27 496 35Q517 55 537 131Q543 151 547 152Q549 153 557 153H561Q580 153 580 144Q580 138 575 117T555 63T523 13Q510 0 491 -8Q483 -10 467 -10Q446 -10 429 -4T402 11T385 29T376 44T374 51L368 45Q362 39 350 30T324 12T288 -4T246 -11Q199 -11 153 12L129 -85Q108 -167 104 -180T92 -202Q76 -216 58 -216Z"></path><path id="MJX-29-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-29-TEX-I-1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path><path id="MJX-29-TEX-I-1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path><path id="MJX-29-TEX-N-2F" d="M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z"></path><path id="MJX-29-TEX-I-1D43F" d="M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-29-TEX-N-31"></use><use data-c="30" xlink:href="#MJX-29-TEX-N-30" transform="translate(500,0)"></use><use data-c="30" xlink:href="#MJX-29-TEX-N-30" transform="translate(1000,0)"></use></g><g data-mml-node="mo" transform="translate(1722.2,0)"><use data-c="2212" xlink:href="#MJX-29-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(2722.4,0)"><use data-c="31" xlink:href="#MJX-29-TEX-N-31"></use><use data-c="35" xlink:href="#MJX-29-TEX-N-35" transform="translate(500,0)"></use><use data-c="30" xlink:href="#MJX-29-TEX-N-30" transform="translate(1000,0)"></use></g><g data-mml-node="mi" transform="translate(4222.4,0)"><use data-c="1D707" xlink:href="#MJX-29-TEX-I-1D707"></use></g><g data-mml-node="mi" transform="translate(4825.4,0)"><use data-c="1D45A" xlink:href="#MJX-29-TEX-I-1D45A"></use></g><g data-mml-node="mi" transform="translate(5703.4,0)"><use data-c="1D45C" xlink:href="#MJX-29-TEX-I-1D45C"></use></g><g data-mml-node="mi" transform="translate(6188.4,0)"><use data-c="1D459" xlink:href="#MJX-29-TEX-I-1D459"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(6486.4,0)"><g data-mml-node="mo"><use data-c="2F" xlink:href="#MJX-29-TEX-N-2F"></use></g></g><g data-mml-node="mi" transform="translate(6986.4,0)"><use data-c="1D43F" xlink:href="#MJX-29-TEX-I-1D43F"></use></g></g></g></svg></mjx-container><script type="math/tex">100-150\mu mol/L</script>, is the threshold our wet lab uses. The repressor strength is more than 10 in terms of the strength interval we divided. Finally, the fitting curve is drawn together with our simulation data through the interval maximum scaling, and it is found that the data fitting is very good. </p>
 
<p>To unify, we processed the data, took the logarithm of the experimental data to the relative intensity interval, and used the function to fit the data to obtain the fitting curve. Then we find that the true threshold is roughly 680 <mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="7.669ex" height="2.059ex" role="img" focusable="false" viewBox="0 -694 3389.7 910" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.489ex;"><defs><path id="MJX-9-TEX-I-1D707" d="M58 -216Q44 -216 34 -208T23 -186Q23 -176 96 116T173 414Q186 442 219 442Q231 441 239 435T249 423T251 413Q251 401 220 279T187 142Q185 131 185 107V99Q185 26 252 26Q261 26 270 27T287 31T302 38T315 45T327 55T338 65T348 77T356 88T365 100L372 110L408 253Q444 395 448 404Q461 431 491 431Q504 431 512 424T523 412T525 402L449 84Q448 79 448 68Q448 43 455 35T476 26Q485 27 496 35Q517 55 537 131Q543 151 547 152Q549 153 557 153H561Q580 153 580 144Q580 138 575 117T555 63T523 13Q510 0 491 -8Q483 -10 467 -10Q446 -10 429 -4T402 11T385 29T376 44T374 51L368 45Q362 39 350 30T324 12T288 -4T246 -11Q199 -11 153 12L129 -85Q108 -167 104 -180T92 -202Q76 -216 58 -216Z"></path><path id="MJX-9-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-9-TEX-I-1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path><path id="MJX-9-TEX-I-1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path><path id="MJX-9-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-9-TEX-I-1D43F" d="M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D707" xlink:href="#MJX-9-TEX-I-1D707"></use></g><g data-mml-node="mi" transform="translate(603,0)"><use data-c="1D45A" xlink:href="#MJX-9-TEX-I-1D45A"></use></g><g data-mml-node="mi" transform="translate(1481,0)"><use data-c="1D45C" xlink:href="#MJX-9-TEX-I-1D45C"></use></g><g data-mml-node="mi" transform="translate(1966,0)"><use data-c="1D459" xlink:href="#MJX-9-TEX-I-1D459"></use></g><g data-mml-node="mo" transform="translate(2264,0)"><use data-c="2E" xlink:href="#MJX-9-TEX-N-2E"></use></g><g data-mml-node="mi" transform="translate(2708.7,0)"><use data-c="1D43F" xlink:href="#MJX-9-TEX-I-1D43F"></use></g></g></g></svg></mjx-container><script type="math/tex">\mu mol.L</script>. Note that we calculate the threshold at which the desired concentration reaches the turn-on threshold, which is <mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="15.193ex" height="2.52ex" role="img" focusable="false" viewBox="0 -864 6715.1 1114" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-19-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-19-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-19-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-19-TEX-I-1D707" d="M58 -216Q44 -216 34 -208T23 -186Q23 -176 96 116T173 414Q186 442 219 442Q231 441 239 435T249 423T251 413Q251 401 220 279T187 142Q185 131 185 107V99Q185 26 252 26Q261 26 270 27T287 31T302 38T315 45T327 55T338 65T348 77T356 88T365 100L372 110L408 253Q444 395 448 404Q461 431 491 431Q504 431 512 424T523 412T525 402L449 84Q448 79 448 68Q448 43 455 35T476 26Q485 27 496 35Q517 55 537 131Q543 151 547 152Q549 153 557 153H561Q580 153 580 144Q580 138 575 117T555 63T523 13Q510 0 491 -8Q483 -10 467 -10Q446 -10 429 -4T402 11T385 29T376 44T374 51L368 45Q362 39 350 30T324 12T288 -4T246 -11Q199 -11 153 12L129 -85Q108 -167 104 -180T92 -202Q76 -216 58 -216Z"></path><path id="MJX-19-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-19-TEX-I-1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path><path id="MJX-19-TEX-I-1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path><path id="MJX-19-TEX-N-2F" d="M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z"></path><path id="MJX-19-TEX-I-1D43F" d="M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msup"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-19-TEX-N-31"></use><use data-c="30" xlink:href="#MJX-19-TEX-N-30" transform="translate(500,0)"></use></g><g data-mml-node="mn" transform="translate(1033,393.1) scale(0.707)"><use data-c="30" xlink:href="#MJX-19-TEX-N-30"></use></g></g><g data-mml-node="mo" transform="translate(1714.3,0)"><use data-c="3D" xlink:href="#MJX-19-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(2770.1,0)"><use data-c="31" xlink:href="#MJX-19-TEX-N-31"></use></g><g data-mml-node="mi" transform="translate(3270.1,0)"><use data-c="1D707" xlink:href="#MJX-19-TEX-I-1D707"></use></g><g data-mml-node="mi" transform="translate(3873.1,0)"><use data-c="1D45A" xlink:href="#MJX-19-TEX-I-1D45A"></use></g><g data-mml-node="mi" transform="translate(4751.1,0)"><use data-c="1D45C" xlink:href="#MJX-19-TEX-I-1D45C"></use></g><g data-mml-node="mi" transform="translate(5236.1,0)"><use data-c="1D459" xlink:href="#MJX-19-TEX-I-1D459"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(5534.1,0)"><g data-mml-node="mo"><use data-c="2F" xlink:href="#MJX-19-TEX-N-2F"></use></g></g><g data-mml-node="mi" transform="translate(6034.1,0)"><use data-c="1D43F" xlink:href="#MJX-19-TEX-I-1D43F"></use></g></g></g></svg></mjx-container><script type="math/tex">10^0 = 1\mu mol/L</script>. While at the point where the slope is greatest, that is, <mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="17.347ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 7667.4 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-29-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-29-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-29-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-29-TEX-N-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path id="MJX-29-TEX-I-1D707" d="M58 -216Q44 -216 34 -208T23 -186Q23 -176 96 116T173 414Q186 442 219 442Q231 441 239 435T249 423T251 413Q251 401 220 279T187 142Q185 131 185 107V99Q185 26 252 26Q261 26 270 27T287 31T302 38T315 45T327 55T338 65T348 77T356 88T365 100L372 110L408 253Q444 395 448 404Q461 431 491 431Q504 431 512 424T523 412T525 402L449 84Q448 79 448 68Q448 43 455 35T476 26Q485 27 496 35Q517 55 537 131Q543 151 547 152Q549 153 557 153H561Q580 153 580 144Q580 138 575 117T555 63T523 13Q510 0 491 -8Q483 -10 467 -10Q446 -10 429 -4T402 11T385 29T376 44T374 51L368 45Q362 39 350 30T324 12T288 -4T246 -11Q199 -11 153 12L129 -85Q108 -167 104 -180T92 -202Q76 -216 58 -216Z"></path><path id="MJX-29-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-29-TEX-I-1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path><path id="MJX-29-TEX-I-1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path><path id="MJX-29-TEX-N-2F" d="M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z"></path><path id="MJX-29-TEX-I-1D43F" d="M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-29-TEX-N-31"></use><use data-c="30" xlink:href="#MJX-29-TEX-N-30" transform="translate(500,0)"></use><use data-c="30" xlink:href="#MJX-29-TEX-N-30" transform="translate(1000,0)"></use></g><g data-mml-node="mo" transform="translate(1722.2,0)"><use data-c="2212" xlink:href="#MJX-29-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(2722.4,0)"><use data-c="31" xlink:href="#MJX-29-TEX-N-31"></use><use data-c="35" xlink:href="#MJX-29-TEX-N-35" transform="translate(500,0)"></use><use data-c="30" xlink:href="#MJX-29-TEX-N-30" transform="translate(1000,0)"></use></g><g data-mml-node="mi" transform="translate(4222.4,0)"><use data-c="1D707" xlink:href="#MJX-29-TEX-I-1D707"></use></g><g data-mml-node="mi" transform="translate(4825.4,0)"><use data-c="1D45A" xlink:href="#MJX-29-TEX-I-1D45A"></use></g><g data-mml-node="mi" transform="translate(5703.4,0)"><use data-c="1D45C" xlink:href="#MJX-29-TEX-I-1D45C"></use></g><g data-mml-node="mi" transform="translate(6188.4,0)"><use data-c="1D459" xlink:href="#MJX-29-TEX-I-1D459"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(6486.4,0)"><g data-mml-node="mo"><use data-c="2F" xlink:href="#MJX-29-TEX-N-2F"></use></g></g><g data-mml-node="mi" transform="translate(6986.4,0)"><use data-c="1D43F" xlink:href="#MJX-29-TEX-I-1D43F"></use></g></g></g></svg></mjx-container><script type="math/tex">100-150\mu mol/L</script>, is the threshold our wet lab uses. The repressor strength is more than 10 in terms of the strength interval we divided. Finally, the fitting curve is drawn together with our simulation data through the interval maximum scaling, and it is found that the data fitting is very good. </p>
 
<p><img src="https://static.igem.wiki/teams/4619/wiki/modelling/main/modelling-switchcurve.png" referrerpolicy="no-referrer" title="Experiment Data Fitting" width="600px" height="400px"></p>
 
<p><img src="https://static.igem.wiki/teams/4619/wiki/modelling/main/modelling-switchcurve.png" referrerpolicy="no-referrer" title="Experiment Data Fitting" width="600px" height="400px"></p>

Revision as of 14:19, 12 October 2023


PobR-Threshold Guard Switch

Sequence and Features


Assembly Compatibility:
  • 10
    COMPATIBLE WITH RFC[10]
  • 12
    COMPATIBLE WITH RFC[12]
  • 21
    COMPATIBLE WITH RFC[21]
  • 23
    COMPATIBLE WITH RFC[23]
  • 25
    INCOMPATIBLE WITH RFC[25]
    Illegal NgoMIV site found at 462
    Illegal AgeI site found at 154
    Illegal AgeI site found at 675
  • 1000
    INCOMPATIBLE WITH RFC[1000]
    Illegal BsaI.rc site found at 595
    Illegal SapI.rc site found at 1573

Description

This composite part consists of four main components: the pobR, the pobR RBS, the pobR operator, the pobA/R dual-directional promoter, and the digitizer.

pobR


The gene pobR creates a transcriptional activator that attaches to the pobR operator on the dsDNA before combining with 4-HBA. Once 4-HBA is introduced to the solution, PobR binds with it and triggers the transcription of the dual pobA/R promoter on the side of pobA.

One of the advantages of this protein is its sensitivity and low leakage properties. Even tiny amounts of 4-HBA, at the micromolar level, can trigger transcription. This characteristic is crucial in creating a high-quality digitizer with a sharp response between two stable states[1].

Additionally, research indicates that most analogs of 4-HBA, such as p-aminobenzoate, can impede the activation of PobR, ensuring precise detection of 4-HBA.

Moreover, the combination of the non-activated PobR and pobR operator will inhibit the transcription of pobR when there is no 4-HBA stimulus, reducing the pressure on our bacteria.

Threshold Guard Switch

The promoters we utilize are controlled by signal-sensitive receptors, which typically demonstrate different relationships between inputs and outputs when exposed to specific inducers.

However, it's important to highlight that a more thorough transcription halt allows for tighter signaling control, which is undoubtedly vital for trace chemical detection. Therefore, We placed the original threshold guard switch (first developed by Ángel & Víctor[2]) downstream of our detection fragment. Here are the critical components of this post-transcriptional control circuit:


Given PobR's excellent properties, we create a chimeric switch by combining it with a portion of the original threshold guard switch.


For more descriptive information, please visit our wiki

Experiment & Result

1)The Threshold Guard Switch

As described by Ángel and Víctor, the “Digitalizer module” they built has a clearly defined on-and-off status. As mentioned in Design, we used it as a threshold guard switch that only allowed a specific inducer of a specific concentration to open our promoter. To verify the functionality and the minimum threshold of this switch, we conducted a series of gradient concentration tests using classical inducers of the Xyls/Pm system: Benzoic acid and 3MBz.

Inducer: Benzoic acid

Initially, a wide range of 2000µM to 0µM benzoic acid was added to E. coli BL21(DE3) (initial OD value = 0.688) that had the switch sequence (BBa_K3202045). msfGFP fluorescence was measured by a synergy HTX microplate reader with excitation at 485 nm (±20 nm) and emission at 520 nm (±20 nm). Fluorescence was normalized to the OD after the background fluorescence value was subtracted from all RFU data. Continually Measuring every 2 minutes for 12 hours, we surprisingly found that the turning-on threshold of this lay at a low level—between 150 μM and 100 μM.(shown in the figure below)


Besides, the time that this switch needed to turn on was collected when the relative fluorescent units (RFU) reached above 200, providing strong evidence that when the concentration of benzoic acid was above 150μM can be regarded as a line separating the on-and-off status of this switch. However, the response time might not be as promising as we thought. The minimum time our switch cost to reach the on-status was 74.33 minutes at 2000μM Benz. Acid.(shown in the figure below)


Being curious about what happened when benzoic acid concentration changed from 100μM to 150μM, we performed a detailed threshold test around this range (80μM~150μM). Using the same bacteria (initial OD value = 0.480) and following the same protocol, we obtained the detailed situation shown in the figure below. Although the absolute value of RFU might be different from the previous test due to the initial growth status, we still found it distinguishable between the on (above 100 μM) and off (below 100 μM) models of this switch. (shown in the figure below)


Inducer: 3MBz

In order to ensure the on-and-off status that happened on our threshold guard switch is non-specific to benzoic acid, we used 3MBz as another inducer. The result shown below also provided an on-and-off threshold line at 10μM and aligned with the work done by Ángel and Víctor[2].


Model Result

We simulated T=1000 for each inducer strength, and for each inducer strength we set the repressor strength to be 5-10. It means we simulated times to get 50 points of stable status. We plot a scatter plot to display. And according to the plot we find the threshold to be roughly 0.6 -0.8. As is shown in the following figure.

Simulation Data

To unify, we processed the data, took the logarithm of the experimental data to the relative intensity interval, and used the function to fit the data to obtain the fitting curve. Then we find that the true threshold is roughly 680 . Note that we calculate the threshold at which the desired concentration reaches the turn-on threshold, which is . While at the point where the slope is greatest, that is, , is the threshold our wet lab uses. The repressor strength is more than 10 in terms of the strength interval we divided. Finally, the fitting curve is drawn together with our simulation data through the interval maximum scaling, and it is found that the data fitting is very good.

      Experiment Data Fitting

     Simulated Date with Experiment Data

 

2)Pobr

Threshold Test


The diagram above shows the changes in GFP fluorescence levels over time for varying concentrations of 4-HBA.

We grew E. coli (Fast-T1) with a chimeric PobR threshold guard switch (GFP version) and measured the quantity of GFP expression over time at different concentrations of 4-HBA using a microplate reader.

After removing the control group and dividing it by OD600, we obtained the following results from our analysis. We observed that concentrations above 0.25mM efficiently activate the switch, leading to a normalized fluorescence intensity more significant than 140 after a certain period. Conversely, intensities below 140 are considered non-activated, as 140 represents the asymptote of the curve with a concentration of 0.25mM, and the proteins produced at that concentration are just enough. Therefore, we conclude that the detection threshold falls between 0.25 and 0.5mM, indicating that it is a trace amount.

We observed negative intensities of normalized fluorescence in some cases. Our analysis indicates that the decrease in bacterial concentration is due to the antibacterial effect of 4-HBA, combined with low GFP production at low concentrations of 4-HBA, resulting in negative intensity.

We believe the detection threshold can be lowered by replacing GFP with *luxI* in the final work. LuxI produces VAI, activating the downstream Quorum sensing system as a signal amplifier.

In addition, We need to analyze how long it takes to open the switch successfully. We define it as open when the intensity level reaches 140.

Time limit


The diagram above shows the time needed to open the switch at different concentrations.

By analyzing the data in the figure, we can observe that a concentration ranging from 0.5mM to 10mM requires approximately 120 minutes. Despite this duration being slightly longer than our initial estimates, it should have minimal impact on the final products because only a tiny quantity of LuxI is required to initiate the quorum sensing system.



References

  1. [1]Na D, Yoo SM, Chung H, Park H, Park JH, Lee SY (2013) Metabolic engineering of Escherichia coli using synthetic small regulatory RNAs. Nat Biotech 31: 170 – 174
  2. [2]Calles B , Goni-Moreno A , Lorenzo V D .Digitalizing heterologous gene expression in Gram-negative bacteria with a portable on/off module[J]. 2019.DOI:10.1101/783506.