_:b413699446 . . . _:b413699094 . _:b413699236 "4"^^ . . . _:b413699089 . _:b413699239 "4"^^ . _:b413699088 . _:b413699238 "4"^^ . _:b413699091 . _:b413699233 "4"^^ . . _:b413699519 . _:b413699497 . _:b413699232 "4"^^ . _:b413699090 . _:b413699707 . _:b413699101 . _:b413699235 "4"^^ . . _:b6011191 "As an example, consider the anterior border of the posterior kni domain, which is activated by Bcd [>>22<<]. This border is located \u223C10% EL posterior to the hb border and has a positional variance of \u223C1% EL [6]. At this position, the Bcd-GFP data have a variance of \u223C4% EL (see Figure 5C in [16]), which is much larger than that of the kni" . _:b6011217 . . _:b413699234 "4"^^ . _:b413699100 . . . _:b413699245 "4"^^ . _:b413699103 . . . _:b413699567 . _:b413699102 . _:b413699244 "4"^^ . _:b413699433 . . . _:b413699247 "4"^^ . _:b413699097 . _:b6011202 . . _:b413699096 . _:b413699246 "4"^^ . _:b413699099 . _:b413699241 "4"^^ . _:b6011200 . . _:b413699098 . _:b413699240 "4"^^ . _:b413699109 . _:b413699243 "4"^^ . . _:b413699108 . _:b413699242 "4"^^ . _:b413699111 . _:b413699253 "4"^^ . . _:b413699252 "4"^^ . _:b413699110 . . _:b413699105 . _:b413699255 "4"^^ . . _:b413699104 . _:b413699254 "4"^^ . . _:b413699249 "4"^^ . _:b413699107 . _:b413699106 . _:b6011243 . _:b413699248 "4"^^ . _:b6011298 . _:b413699117 . _:b413699525 . _:b413699251 "4"^^ . _:b6011299 . _:b413699116 . _:b413699250 "4"^^ . _:b6011196 . _:b413699119 . _:b413699261 "4"^^ . _:b413699260 "4"^^ . _:b413699118 . _:b413699479 . _:b413699263 "4"^^ . _:b413699113 . _:b6011224 "The circuit's gap gene patterns (Figure S4A and S4B in Protocol S1) are consistent with data except for two minor defects (Section S1.3 in Protocol S1) and the circuit has the same network topology that was obtained previously [31,35,>>36<<]." . _:b413699262 "4"^^ . . _:b413699112 . . _:b6011184 . _:b413699257 "4"^^ . _:b413699115 . _:b413699454 . _:b6011185 . _:b6011222 "The circuit's gap gene patterns (Figure S4A and S4B in Protocol S1) are consistent with data except for two minor defects (Section S1.3 in Protocol S1) and the circuit has the same network topology that was obtained previously [>>31<<,35,36]." . _:b413699694 . _:b413699256 "4"^^ . _:b413699114 . _:b413699259 "4"^^ . _:b6011278 "Second, a 9% range of border positions has been observed from reporters driven by a fragment of the hb promoter believed to contain only Bcd binding sites (see Figure 4 in [>>21<<]), suggesting that this expression reflects the underlying variation of x Bcd." . _:b413699125 . . _:b413699258 "4"^^ . _:b413699124 . _:b6011288 . _:b413699269 "3"^^ . . _:b413699127 . . _:b413699268 "3"^^ . . _:b413699126 . _:b413699156 . . _:b413699271 "3"^^ . _:b413699121 . _:b413699203 . _:b413699270 "3"^^ . . _:b413699120 . . _:b6011186 . _:b413699265 "4"^^ . _:b413699123 . _:b413699286 . _:b6011187 . _:b413699264 "4"^^ . _:b413699122 . _:b413699267 "3"^^ . _:b413699133 . _:b413699266 "4"^^ . _:b413699132 . _:b413699277 "3"^^ . _:b413699135 . _:b413699276 "3"^^ . _:b413699134 . _:b413699066 . _:b413699120 . _:b413699142 . _:b413699279 "3"^^ . _:b413699129 . _:b413699278 "3"^^ . _:b413699128 . . . _:b413699273 "3"^^ . _:b413699131 . _:b413699391 . _:b413699272 "3"^^ . _:b413699130 . _:b413699275 "3"^^ . _:b413699141 . _:b413699712 . _:b413699274 "3"^^ . _:b6011177 . _:b413699140 . _:b413699285 "3"^^ . _:b6011182 . _:b413699099 . _:b413699143 . . . _:b413699284 "3"^^ . _:b6011183 . _:b413699482 . _:b413699142 . . _:b413699287 "3"^^ . _:b413699137 . _:b413699250 . _:b413699286 "3"^^ . . . _:b413699365 . _:b413699343 . . _:b413699136 . . _:b413699281 "3"^^ . . _:b413699139 . . _:b413699274 . _:b413699280 "3"^^ . . _:b413699138 . _:b413699283 "3"^^ . _:b413699149 . . _:b413699282 "3"^^ . . _:b413699148 . _:b413699499 . _:b413699293 "3"^^ . _:b413699078 . _:b413699151 . _:b413699292 "3"^^ . _:b413699150 . _:b6011200 "Gene circuits [26,>>27<<] are dynamical models that can accurately reproduce observed gene expression patterns by reconstituting the required set of genetic interactions in silico." . _:b413699295 "3"^^ . _:b413699145 . . _:b413699587 . _:b413699076 . . _:b413699294 "3"^^ . _:b6011173 . _:b413699144 . _:b413699289 "3"^^ . _:b413699147 . _:b413699288 "3"^^ . . _:b413699146 . _:b413699291 "3"^^ . _:b413699211 . _:b413699157 . _:b6011178 . _:b413699290 "3"^^ . _:b413699227 . _:b413699156 . _:b413699301 "3"^^ . _:b413699159 . . _:b413699300 "3"^^ . _:b413699158 . _:b413699303 "3"^^ . _:b413699153 . _:b413699127 . _:b413699302 "3"^^ . _:b413699152 . . . _:b413699297 "3"^^ . . _:b413699155 . . _:b413699296 "3"^^ . _:b413699154 . . _:b413699299 "3"^^ . _:b413699284 . _:b413699165 . _:b413699298 "3"^^ . _:b413699164 . _:b413699275 . _:b413699309 "3"^^ . . _:b413699167 . . _:b413699308 "3"^^ . . _:b413699166 . _:b413699311 "3"^^ . _:b413699247 . _:b413699161 . _:b413699310 "3"^^ . . _:b413699160 . _:b413699360 . _:b413699305 "3"^^ . _:b413699163 . _:b6011209 . . _:b413699572 . _:b413699304 "3"^^ . _:b413699162 . _:b6011248 "This is well supported by the very large anterior shift of this border in Kr \u2013 embryos [>>58<<]." . _:b413699307 "3"^^ . _:b413699309 . _:b413699173 . _:b413699053 . _:b413699306 "3"^^ . _:b413699172 . _:b413699380 . _:b413699317 "3"^^ . . . _:b413699175 . . _:b413699316 "3"^^ . _:b413699174 . . _:b413699319 "3"^^ . _:b413699169 . _:b413699318 "3"^^ . _:b413699168 . . _:b413699477 . _:b413699313 "3"^^ . _:b413699171 . _:b413699681 . _:b413699312 "3"^^ . _:b413699170 . _:b413699278 . _:b413699295 . . _:b413699315 "3"^^ . _:b413699181 . _:b413699441 . _:b413699314 "3"^^ . _:b6011182 "The amount of variance reduction implied by this value of \u03C3Bcd is significantly smaller than the estimates from fixed-tissue experiments [6,>>9<<], presumably because the GFP measurements do not have scaling error introduced in the setting of microscope gain in separate fixed-tissue experiments." . _:b413699180 . . _:b413699325 "3"^^ . . _:b413699183 . _:b413699324 "3"^^ . _:b413699282 . _:b413699182 . . _:b413699130 . _:b413699327 "3"^^ . . _:b413699177 . _:b413699326 "3"^^ . _:b413699426 . _:b413699176 . _:b413699321 "3"^^ . _:b413699179 . . _:b413699320 "3"^^ . _:b413699178 . _:b413699556 . _:b413699323 "3"^^ . _:b413699189 . _:b413699322 "3"^^ . _:b6011231 . . _:b413699188 . _:b413699311 . _:b413699333 "3"^^ . . _:b413699191 . _:b413699236 . . _:b413699332 "3"^^ . _:b413699190 . _:b413699335 "3"^^ . . _:b413699185 . _:b413699334 "3"^^ . . _:b413699184 . . _:b413699677 . _:b413699329 "3"^^ . _:b413699390 . _:b413699187 . _:b413699532 . _:b413699328 "3"^^ . _:b413699534 . _:b413699186 . _:b413699331 "3"^^ . . _:b6011230 . _:b413699197 . _:b413699330 "3"^^ . _:b413699196 . _:b413699341 "3"^^ . _:b413699199 . _:b413699340 "3"^^ . _:b413699198 . _:b413699343 "3"^^ . . _:b413699193 . _:b413699675 . . _:b413699342 "3"^^ . _:b413699192 . . _:b413699337 "3"^^ . _:b413699160 . _:b413699195 . . _:b413699329 . _:b413699336 "3"^^ . . _:b413699194 . _:b413699062 . _:b413699339 "3"^^ . . _:b413699205 . _:b413699467 . _:b413699338 "3"^^ . _:b6011209 . _:b413699169 . . _:b413699204 . _:b413699349 "3"^^ . _:b413699207 . _:b413699348 "3"^^ . _:b413699513 . _:b413699206 . _:b6011251 "The low positional variation of the posterior border of the anterior hb domain has been studied extensively [9,12,14\u201316,>>59<<]. Our analysis shows that this border forms by Bcd activation and repression from Kr and Kni (Figure 4A)." . _:b413699351 "3"^^ . _:b413699201 . _:b413699176 . . _:b413699350 "3"^^ . . . _:b413699200 . . _:b413699345 "3"^^ . _:b413699483 . _:b413699203 . . . _:b413699344 "3"^^ . _:b6011283 "This fact explains the observation that a synthetic reporter construct driven only by Bcd has the same standard deviation as x Hb [>>59<<]. The synthetic construct forms its border at 28.6% EL, where the in vivo data (see Figure 2B in [16]) indicate that the Bcd concentration is about three times greater than at the native hb border. If the standard deviation of 2.2% EL" . _:b413699202 . _:b413699347 "3"^^ . _:b413699213 . . . _:b413699635 . . _:b413699346 "3"^^ . . _:b413699212 . _:b413699437 . _:b413699357 "3"^^ . _:b413699215 . _:b413699356 "3"^^ . _:b413699214 . _:b413699359 "3"^^ . _:b413699526 . _:b413699209 . _:b413699358 "3"^^ . _:b413699208 . _:b413699061 . _:b6011213 "The Bcd gradient is essentially stationary during cleavage cycles 13 and 14 [>>6<<,43,44], and hence, its concentration v Bcd is assumed to be constant in time." . _:b413699353 "3"^^ . . _:b413699211 . . _:b413699352 "3"^^ . _:b413699210 . _:b413699349 . _:b413699355 "3"^^ . _:b413699221 . _:b413699354 "3"^^ . _:b413699220 . _:b413699575 . _:b413699365 "3"^^ . _:b413699223 . _:b413699364 "3"^^ . _:b413699222 . _:b413699367 "3"^^ . _:b413699217 . _:b413699366 "3"^^ . _:b413699216 . _:b413699361 "3"^^ . _:b413699219 . . _:b413699360 "3"^^ . _:b6011171 . . _:b413699218 . . _:b413699363 "3"^^ . _:b413699229 . . _:b413699362 "3"^^ . _:b413699228 . _:b413699373 "3"^^ . _:b413699231 . _:b413699372 "3"^^ . _:b413699230 . _:b413699415 . _:b413699375 "3"^^ . . _:b413699225 . _:b413699374 "3"^^ . _:b413699224 . _:b413699369 "3"^^ . _:b413699227 . _:b413699520 . _:b413699368 "3"^^ . . _:b413699063 . _:b413699226 . . _:b413699371 "3"^^ . _:b413699237 . _:b413699655 . . _:b413699370 "3"^^ . _:b413699109 . _:b413699236 . . _:b413699381 "3"^^ . _:b6011232 . . _:b413699239 . _:b413699380 "3"^^ . _:b413699209 . _:b413699238 . _:b6011202 "This method has been successfully used to analyze both the pair-rule and gap systems [>>27<<,33\u201336] and performed better than other models in a comparative study [31]." . _:b413699383 "3"^^ . _:b413699233 . . _:b413699382 "3"^^ . _:b413699232 . . _:b413699377 "3"^^ . _:b413699235 . _:b413699376 "3"^^ . _:b413699234 . . _:b413699379 "3"^^ . _:b413699245 . . _:b413699051 . _:b413699378 "3"^^ . _:b413699244 . . . _:b413699389 "3"^^ . _:b413699172 . _:b413699247 . _:b413699101 . _:b413699388 "3"^^ . _:b413699246 . _:b413699391 "3"^^ . _:b413699241 . _:b413699538 . _:b413699390 "3"^^ . _:b413699240 . _:b413699385 "3"^^ . _:b6011212 "The concentrations of Cad and Tll were provided by the interpolation of average data [>>6<<] in time (Section S1.2 in Protocol S1)." . _:b413699243 . _:b413699491 . _:b413699414 . _:b413699384 "3"^^ . _:b413699242 . . _:b6011275 . _:b413699387 "3"^^ . _:b413699253 . _:b6011274 . _:b413699386 "3"^^ . . _:b413699252 . _:b413699397 "2"^^ . _:b413699255 . _:b413699345 . _:b413699396 "2"^^ . _:b413699254 . _:b413699399 "2"^^ . _:b413699249 . . _:b6011286 . _:b413699398 "2"^^ . _:b6011296 "The mutual repression between the gap genes that is required for correct spatiotemporal expression is also responsible for canalization, providing support for the \u201Cintrinsic\u201D [>>67<<] or \u201Csingle-mode\u201D [69] canalization hypothesis." . _:b413699248 . . _:b413699379 . _:b413699393 "3"^^ . _:b413699628 . _:b413699251 . _:b413699392 "3"^^ . _:b413699250 . _:b413699711 . _:b413699395 "2"^^ . _:b413699502 . _:b413699261 . _:b413699394 "2"^^ . _:b413699260 . . _:b413699530 . _:b413699319 . _:b413699405 "2"^^ . . . _:b413699263 . _:b6011271 . _:b413699404 "2"^^ . . _:b413699262 . _:b413699407 "2"^^ . _:b413699257 . _:b413699406 "2"^^ . . _:b413699256 . _:b413699401 "2"^^ . . . _:b413699259 . . _:b413699400 "2"^^ . _:b413699258 . . _:b413699403 "2"^^ . _:b6011195 "Like hb, kni is not regulated by Bcd alone, but also by Caudal (Cad) [22,>>23<<], Hb [20,24], and Gt [25]. The examples of the hb and kni borders show that it is not possible to explain the variance of a single expression border position in isolation." . . _:b413699269 . _:b413699402 "2"^^ . . _:b413699268 . _:b413699413 "2"^^ . _:b413699271 . _:b413699412 "2"^^ . _:b413699270 . _:b413699415 "2"^^ . _:b413699622 . _:b413699265 . _:b413699414 "2"^^ . . _:b413699548 . _:b413699264 . _:b413699409 "2"^^ . _:b413699267 . . _:b413699652 . _:b413699408 "2"^^ . . _:b413699292 . _:b413699098 . _:b413699266 . _:b413699411 "2"^^ . _:b413699277 . _:b413699692 . _:b413699410 "2"^^ . _:b413699276 . _:b413699456 . _:b413699700 . _:b413699421 "2"^^ . _:b413699279 . _:b413699420 "2"^^ . _:b6011256 "3\u20134-hours-old embryos were fixed and stained as described [>>72<<] using guinea pig anti-Kr and anti-Kni antibodies with Alexa Fluor 488 conjugated secondary antibody, rabbit anti-Gt and rat anti-Hb antibodies with Alexa Fluor 555 and 647 conjugated secondary antibodies (Molecular Probes), respectively." . _:b413699278 . _:b413699423 "2"^^ . _:b6011249 "The low positional variation of the posterior border of the anterior hb domain has been studied extensively [>>9<<,12,14\u201316,59]. Our analysis shows that this border forms by Bcd activation and repression from Kr and Kni (Figure 4A)." . _:b413699273 . _:b413699055 . . _:b413699422 "2"^^ . _:b413699272 . _:b413699417 "2"^^ . _:b413699275 . . _:b413699416 "2"^^ . _:b413699274 . _:b413699419 "2"^^ . _:b413699354 . . _:b413699285 . _:b413699418 "2"^^ . _:b6011236 "bcd mRNA is localized at the anterior tip of the embryo [>>54<<]. The stationary exponential profile of the Bcd gradient is consistent with the diffusion of the protein from the anterior tip and its degradation by a first-order process, and the gradient has been modeled as such [21,55,56]." . _:b413699284 . _:b413699429 "2"^^ . _:b413699149 . _:b413699476 . _:b413699287 . . _:b413699503 . _:b413699428 "2"^^ . _:b413699286 . _:b413699398 . _:b413699431 "2"^^ . . _:b413699281 . _:b413699430 "2"^^ . . . . _:b413699280 . _:b413699425 "2"^^ . _:b413699283 . _:b413699291 . _:b413699424 "2"^^ . _:b413699282 . . _:b413699427 "2"^^ . _:b413699293 . . . _:b6011297 "The reduction of gap gene expression variation over time [>>6<<] suggests that canalization occurs because the possible developmental trajectories of the system tend to converge over time, thus reducing variation." . _:b413699426 "2"^^ . . _:b413699292 . _:b413699048 . . _:b413699437 "2"^^ . _:b413699295 . _:b413699436 "2"^^ . _:b413699294 . _:b413699362 . _:b413699439 "2"^^ . _:b413699600 . _:b413699421 . _:b413699289 . . _:b413699438 "2"^^ . _:b413699288 . _:b413699433 "2"^^ . _:b413699291 . _:b413699308 . _:b413699432 "2"^^ . . _:b413699290 . . . _:b413699067 . _:b413699248 . _:b413699435 "2"^^ . _:b413699301 . _:b413699434 "2"^^ . . _:b413699300 . _:b413699152 . _:b6011184 "The assumption that hb is under the sole control of Bcd is incorrect, because its border position changes in embryos mutant for giant (gt) [9], Kr\u00FCppel (Kr) [>>20<<], Kr\u00FCppel;knirps (Kr;kni) [20], and in embryos lacking Nanos [9]." . _:b413699445 "2"^^ . _:b413699153 . . _:b413699303 . _:b413699154 . _:b413699155 . _:b413699156 . _:b413699444 "2"^^ . _:b413699157 . _:b413699659 . _:b413699312 . _:b413699302 . _:b413699158 . _:b413699159 . _:b413699255 . _:b413699160 . _:b413699092 . _:b413699447 "2"^^ . _:b413699161 . _:b413699086 . _:b413699297 . _:b413699162 . _:b413699163 . _:b413699164 . _:b413699595 . _:b413699446 "2"^^ . _:b413699165 . _:b413699296 . _:b413699166 . _:b413699167 . _:b413699645 . . _:b413699136 . _:b413699579 . _:b413699441 "2"^^ . _:b413699137 . _:b413699554 . _:b413699299 . _:b6011265 "The first two classes of models invoke either active transport [>>13<<] or a second gradient at the posterior pole of the embryo [12,14,15] as a mechanism for the reduction in variation of the hb border." . _:b413699138 . _:b413699139 . _:b413699140 . _:b413699440 "2"^^ . _:b413699141 . _:b413699298 . _:b413699648 . _:b413699142 . _:b413699143 . _:b413699047 . _:b413699144 . _:b413699443 "2"^^ . _:b413699145 . . _:b413699309 . _:b413699146 . _:b413699147 . _:b413699148 . _:b413699442 "2"^^ . _:b413699149 . _:b413699308 . _:b413699150 . _:b413699151 . _:b413699184 . _:b413699453 "2"^^ . _:b413699185 . _:b413699311 . _:b413699186 . _:b413699187 . _:b6011223 . _:b413699261 . _:b413699188 . . _:b413699452 "2"^^ . _:b413699189 . _:b413699310 . _:b413699190 . _:b413699191 . _:b413699192 . _:b6011174 . _:b413699708 . . _:b413699455 "2"^^ . _:b413699193 . _:b413699305 . _:b413699194 . . _:b413699195 . _:b413699196 . . _:b413699454 "2"^^ . _:b413699197 . _:b413699173 . _:b413699304 . _:b6011229 "They are known to influence the anterior pattern of trunk gap genes [25], and respond to Bcd in a concentration-dependent manner [>>49<<]. In the posterior terminal region huckebein (hkb) [50\u201352] has been omitted from the model." . _:b413699198 . _:b413699199 . _:b413699168 . _:b413699449 "2"^^ . _:b413699169 . _:b413699307 . _:b413699170 . _:b413699171 . _:b413699172 . _:b413699448 "2"^^ . _:b413699173 . _:b413699306 . _:b413699174 . _:b413699175 . _:b413699176 . _:b413699451 "2"^^ . . _:b413699177 . _:b413699317 . _:b413699178 . _:b413699179 . . _:b413699180 . _:b413699450 "2"^^ . _:b413699181 . _:b413699316 . _:b413699182 . _:b413699183 . _:b413699088 . _:b6011282 "Other important experimental results can be understood by recalling that the maximum accuracy of the Bcd gradient is inversely proportional to the square root of the Bcd concentration [16,19,>>60<<], suggesting that borders under unmodified Bcd control will have lower variation at more anterior positions." . _:b413699461 "2"^^ . _:b413699089 . _:b413699319 . _:b413699090 . _:b413699091 . _:b413699092 . _:b413699521 . _:b413699460 "2"^^ . . _:b413699093 . _:b413699318 . _:b413699094 . _:b413699095 . _:b413699096 . . _:b413699463 "2"^^ . . _:b413699097 . _:b413699313 . _:b413699098 . _:b413699099 . _:b413699100 . _:b413699462 "2"^^ . _:b413699101 . _:b413699312 . _:b413699102 . _:b413699103 . _:b413699703 . . _:b413699072 . . _:b413699457 "2"^^ . _:b413699073 . _:b413699315 . . _:b413699074 . _:b413699075 . _:b6011203 . _:b413699076 . _:b413699456 "2"^^ . _:b413699077 . _:b413699314 . _:b413699078 . _:b413699079 . _:b413699080 . _:b413699459 "2"^^ . _:b413699081 . _:b413699325 . _:b413699242 . _:b413699082 . _:b413699083 . _:b413699138 . _:b413699084 . _:b413699458 "2"^^ . _:b413699085 . . _:b413699324 . _:b413699086 . _:b413699087 . _:b6011284 "The synthetic construct forms its border at 28.6% EL, where the in vivo data (see Figure 2B in [>>16<<]) indicate that the Bcd concentration is about three times greater than at the native hb border." . _:b413699654 . _:b413699120 . _:b413699469 "2"^^ . _:b413699121 . _:b413699327 . _:b413699122 . _:b413699123 . _:b413699124 . _:b413699468 "2"^^ . _:b413699125 . _:b413699326 . _:b413699126 . _:b413699127 . _:b413699128 . _:b413699697 . _:b413699471 "2"^^ . _:b413699129 . _:b413699321 . _:b413699130 . _:b413699131 . _:b413699132 . _:b413699470 "2"^^ . _:b413699133 . _:b413699320 . . _:b413699134 . _:b413699135 . _:b413699104 . _:b413699465 "2"^^ . _:b413699105 . _:b413699323 . _:b6011281 "Other important experimental results can be understood by recalling that the maximum accuracy of the Bcd gradient is inversely proportional to the square root of the Bcd concentration [16,>>19<<,60], suggesting that borders under unmodified Bcd control will have lower variation at more anterior positions." . _:b413699106 . _:b413699107 . _:b6011266 . _:b413699108 . _:b413699581 . _:b413699464 "2"^^ . _:b413699109 . _:b413699322 . _:b413699110 . _:b413699111 . _:b6011197 "Like hb, kni is not regulated by Bcd alone, but also by Caudal (Cad) [22,23], Hb [20,>>24<<], and Gt [25]. The examples of the hb and kni borders show that it is not possible to explain the variance of a single expression border position in isolation." . _:b413699112 . _:b413699467 "2"^^ . _:b413699113 . . _:b413699114 . _:b413699115 . _:b413699116 . _:b413699466 "2"^^ . _:b413699117 . _:b413699601 . _:b413699118 . _:b413699119 . _:b413699280 . _:b413699477 "2"^^ . _:b413699281 . _:b413699282 . _:b413699283 . _:b413699284 . _:b413699476 "2"^^ . _:b413699340 . _:b413699285 . _:b413699286 . _:b413699287 . _:b413699288 . _:b413699230 . _:b413699479 "2"^^ . _:b413699289 . _:b413699356 . _:b413699290 . _:b413699291 . _:b413699292 . _:b413699713 . _:b413699478 "2"^^ . _:b413699293 . _:b413699374 . _:b413699294 . _:b413699295 . _:b413699264 . _:b413699473 "2"^^ . _:b413699265 . _:b413699266 . _:b413699267 . _:b6011164 . _:b413699268 . _:b413699472 "2"^^ . _:b413699137 . _:b413699599 . . _:b413699269 . _:b413699270 . _:b413699271 . _:b413699272 . _:b413699064 . _:b413699475 "2"^^ . _:b413699273 . _:b413699274 . _:b413699275 . _:b413699276 . _:b413699474 "2"^^ . _:b413699277 . _:b413699278 . _:b6011257 "Double mutants in lateral orientation were scanned using a Leica TCS SP2 confocal microscope and the images were then processed as described [>>73<<]. Domain border positions for wild type and mutants were determined by calculating the A\u2013P position at which the relative concentration is half its maximum value in the domain. The local maximum in a domain was determined using a" . _:b413699279 . _:b413699312 . _:b413699485 "2"^^ . _:b413699313 . _:b413699314 . _:b413699200 . _:b413699315 . _:b6011285 . _:b413699506 . _:b413699316 . _:b413699484 "2"^^ . _:b413699317 . _:b413699318 . _:b413699319 . _:b413699320 . _:b413699342 . _:b413699487 "2"^^ . _:b413699321 . _:b413699322 . _:b413699323 . _:b413699324 . _:b413699486 "2"^^ . _:b413699325 . _:b6011227 . _:b413699410 . _:b413699326 . _:b6011276 "The Bcd data thus obtained had the same level of error as Bcd-GFP data [>>16<<], yet a direct comparison between the Bcd and Hb data showed that the posterior border of the anterior hb domain was half as variable." . _:b413699327 . _:b413699296 . _:b413699481 "2"^^ . _:b413699297 . _:b413699298 . _:b413699299 . _:b6011259 . _:b413699300 . _:b413699480 "2"^^ . _:b413699301 . _:b413699302 . _:b413699303 . _:b413699304 . _:b413699483 "2"^^ . _:b413699305 . _:b413699306 . _:b413699307 . _:b6011283 . _:b413699308 . _:b413699482 "2"^^ . _:b413699309 . _:b413699310 . . . _:b413699311 . _:b413699216 . _:b413699493 "2"^^ . _:b413699217 . _:b413699596 . _:b413699218 . _:b413699219 . _:b413699220 . _:b413699492 "2"^^ . _:b413699221 . _:b413699222 . _:b413699223 . _:b413699224 . _:b413699259 . _:b413699495 "2"^^ . _:b413699225 . _:b413699226 . _:b413699227 . _:b413699228 . _:b413699494 "2"^^ . _:b413699229 . _:b413699230 . _:b413699231 . _:b413699200 . _:b413699489 "2"^^ . _:b413699201 . . _:b413699202 . _:b413699481 . _:b413699203 . _:b413699204 . _:b413699488 "2"^^ . _:b413699205 . _:b413699206 . . _:b413699207 . _:b413699208 . _:b413699491 "2"^^ . . _:b413699209 . _:b413699210 . _:b413699211 . _:b413699212 . _:b413699490 "2"^^ . _:b413699213 . _:b413699214 . . _:b413699215 . _:b413699248 . _:b413699501 "2"^^ . _:b413699249 . _:b413699250 . . _:b413699251 . _:b413699252 . _:b413699500 "2"^^ . _:b413699253 . _:b413699254 . _:b413699632 . . _:b6011264 "discussion" . _:b413699255 . _:b413699256 . _:b413699503 "2"^^ . _:b413699257 . . _:b413699258 . _:b413699259 . _:b413699260 . _:b413699502 "2"^^ . _:b413699261 . _:b413699262 . . _:b413699263 . _:b413699232 . _:b413699497 "2"^^ . _:b413699233 . _:b6011187 "Apart from the average position, the variation of the position is also increased in embryos lacking chromosome arm 3L or Nanos to \u223C2% EL and \u223C1.6% EL respectively [>>9<<], close to the Bcd variation measured in live embryos." . _:b413699234 . _:b413699235 . _:b6011243 . _:b413699236 . . _:b413699496 "2"^^ . _:b413699237 . _:b413699238 . _:b6011167 . _:b413699239 . _:b413699240 . _:b413699499 "2"^^ . _:b413699241 . . _:b413699242 . . _:b413699243 . _:b413699244 . _:b413699498 "2"^^ . _:b413699245 . _:b413699246 . _:b413699247 . _:b413699408 . _:b413699509 "2"^^ . _:b413699409 . _:b413699410 . _:b413699411 . _:b413699412 . _:b6011178 . . _:b413699508 "2"^^ . _:b413699413 . _:b413699414 . _:b413699212 . _:b413699415 . _:b413699416 . _:b413699604 . _:b413699302 . _:b413699511 "2"^^ . _:b413699417 . _:b413699271 . _:b413699418 . _:b413699419 . _:b413699420 . _:b413699510 "2"^^ . _:b413699421 . _:b413699422 . _:b413699423 . _:b413699392 . _:b413699505 "2"^^ . _:b413699393 . _:b413699394 . _:b413699395 . _:b413699498 . _:b413699396 . _:b413699504 "2"^^ . _:b413699397 . _:b6011240 "Equation 3 may also be arrived at by explicitly rescaling the diffusion-degradation model [>>21<<,55,56]." . . _:b413699398 . _:b413699419 . _:b413699399 . . _:b413699400 . _:b413699228 . _:b413699507 "2"^^ . _:b413699401 . _:b413699402 . _:b413699403 . _:b413699614 . _:b413699404 . _:b413699506 "2"^^ . _:b413699405 . _:b413699406 . _:b413699407 . _:b413699440 . _:b413699517 "2"^^ . _:b413699441 . _:b413699670 . _:b413699442 . _:b413699443 . _:b6011190 . . _:b413699444 . _:b413699516 "2"^^ . _:b413699445 . _:b413699446 . _:b413699447 . _:b413699448 . _:b413699519 "2"^^ . _:b413699449 . _:b413699450 . _:b413699451 . _:b6011192 . . _:b413699518 "2"^^ . . _:b413699452 . _:b413699453 . . _:b413699454 . _:b413699235 . _:b413699455 . _:b413699424 . _:b413699513 "2"^^ . _:b413699425 . _:b413699426 . _:b413699427 . _:b413699428 . _:b413699512 "2"^^ . _:b413699429 . _:b413699430 . . _:b413699431 . _:b413699306 . _:b413699432 . _:b413699515 "2"^^ . _:b413699430 . _:b413699433 . . _:b413699434 . _:b413699435 . _:b6011251 . _:b413699152 . _:b413699436 . _:b413699514 "2"^^ . _:b413699437 . _:b413699438 . _:b413699439 . _:b413699344 . _:b413699525 "2"^^ . _:b413699345 . _:b413699346 . _:b413699347 . _:b413699348 . _:b413699524 "2"^^ . _:b413699349 . _:b413699350 . _:b413699351 . _:b6011169 . _:b413699352 . _:b413699527 "2"^^ . . _:b413699353 . _:b413699354 . _:b413699355 . _:b6011168 . _:b413699356 . _:b413699526 "2"^^ . _:b413699357 . _:b413699358 . _:b413699359 . _:b413699328 . _:b413699521 "2"^^ . _:b413699329 . _:b413699330 . _:b413699059 . _:b413699300 . . _:b413699331 . _:b413699332 . _:b413699520 "2"^^ . _:b413699333 . _:b413699496 . . _:b413699334 . _:b413699335 . _:b413699336 . _:b413699523 "2"^^ . _:b413699337 . _:b413699338 . _:b413699339 . _:b6011172 . _:b413699340 . _:b413699522 "2"^^ . _:b413699341 . _:b413699342 . _:b413699343 . _:b6011175 . _:b413699376 . _:b413699533 "2"^^ . _:b413699377 . _:b413699378 . . _:b413699379 . _:b413699380 . _:b6011292 "The gap gene borders are specified at a low enough molecular number of Bcd [16] that intrinsic fluctuations are a significant source of variation [>>16<<,60]. The buffering of phenotypic variation against intrinsic fluctuations in molecular number, while not considered by Waddington, is likely to be an important aspect of canalization in biological systems. It is noteworthy that we were" . _:b413699532 "2"^^ . _:b413699381 . _:b413699382 . _:b413699383 . _:b413699384 . _:b413699535 "2"^^ . _:b413699385 . _:b413699386 . _:b413699387 . _:b6011176 . _:b413699388 . _:b413699534 "2"^^ . _:b413699389 . _:b413699390 . _:b413699391 . _:b413699360 . _:b413699529 "2"^^ . _:b413699045 . _:b413699361 . _:b413699362 . _:b413699363 . _:b413699364 . _:b413699528 "2"^^ . _:b413699365 . . _:b413699366 . _:b413699367 . _:b6011205 . _:b6011181 . _:b413699368 . _:b413699531 "2"^^ . _:b413699369 . _:b413699370 . _:b413699371 . _:b413699372 . _:b413699530 "2"^^ . _:b413699373 . _:b413699374 . _:b413699619 . . _:b413699375 . _:b413699536 . _:b413699541 "2"^^ . _:b413699537 . . _:b413699538 . _:b413699539 . _:b413699540 . _:b413699540 "2"^^ . _:b413699071 . . _:b413699541 . _:b413699542 . _:b413699543 . _:b413699281 . _:b413699225 . _:b413699543 "2"^^ . _:b413699544 . _:b413699545 . _:b413699546 . _:b6011252 "These results are in apparent contradiction to a previous report indicating that the standard deviation of the location of the hb border was unchanged in single mutants for either Kr or kni [>>9<<]. We found the same result for single mutants (unpublished data) but in double mutants, uncharacterized previously, the standard deviation of the location of the anterior hb border doubles and that of the posterior border of the third" . _:b413699547 . _:b6011216 . _:b413699548 . _:b413699542 "2"^^ . _:b413699549 . _:b413699550 . _:b413699551 . _:b413699520 . _:b413699537 "2"^^ . _:b413699521 . _:b413699084 . _:b413699206 . _:b413699522 . _:b413699523 . . _:b413699524 . _:b6011206 . _:b413699536 "2"^^ . _:b413699525 . _:b413699526 . _:b413699527 . _:b6011221 . . _:b413699528 . _:b413699539 "2"^^ . _:b413699529 . _:b413699530 . _:b413699531 . _:b413699532 . _:b413699538 "2"^^ . _:b413699533 . . _:b413699534 . _:b413699535 . _:b413699568 . _:b413699549 "2"^^ . _:b413699569 . _:b6011294 "Future work will need to treat the role of intrinsic fluctuations in the formation of maternal gradient systems [>>63<<,64]. While stochastic interactions undoubtedly occur among zygotic gap gene products, understanding the functional role of stochastic processes in the segmentation system will require the formulation of a fully stochastic model. Such a" . _:b413699570 . . _:b413699571 . _:b413699572 . _:b6011230 . _:b413699548 "2"^^ . _:b413699512 . _:b413699573 . _:b413699574 . _:b413699575 . _:b413699576 . _:b413699551 "2"^^ . _:b413699577 . _:b413699472 . _:b413699578 . . _:b413699353 . _:b413699579 . _:b413699580 . _:b413699550 "2"^^ . _:b413699581 . _:b413699582 . _:b413699583 . _:b413699552 . _:b413699545 "2"^^ . _:b413699553 . _:b413699554 . _:b413699555 . _:b413699556 . _:b413699544 "2"^^ . _:b413699557 . _:b413699558 . _:b413699559 . _:b413699560 . _:b413699547 "2"^^ . . _:b413699561 . _:b413699562 . . _:b413699563 . . _:b413699564 . _:b413699546 "2"^^ . _:b413699565 . _:b413699566 . _:b413699567 . _:b413699472 . _:b413699557 "2"^^ . _:b413699473 . _:b413699474 . _:b413699475 . _:b413699476 . _:b413699556 "2"^^ . _:b413699477 . _:b413699478 . _:b413699479 . _:b413699480 . _:b413699559 "2"^^ . _:b413699481 . _:b413699667 . _:b413699482 . _:b6011264 _:b6011296 . _:b413699483 . _:b6011264 _:b6011297 . _:b413699484 . _:b413699558 "2"^^ . _:b6011264 _:b6011298 . _:b413699485 . _:b6011264 _:b6011299 . _:b413699486 . _:b413699487 . . _:b413699456 . _:b413699553 "2"^^ . _:b413699457 . . _:b413699458 . _:b413699459 . _:b413699168 . _:b413699460 . _:b413699552 "2"^^ . _:b413699461 . _:b6011275 "This comparison finds support in the fixed-tissue study [>>18<<] in which a modified staining protocol was used and data were acquired in a single imaging cycle to minimize experimental error." . _:b413699462 . _:b413699463 . . _:b413699464 . _:b413699555 "2"^^ . _:b413699465 . _:b413699466 . _:b413699467 . _:b413699509 . _:b413699468 . _:b413699554 "2"^^ . _:b413699469 . _:b413699470 . _:b413699471 . _:b413699504 . _:b413699565 "2"^^ . _:b413699505 . _:b413699506 . . _:b413699507 . _:b413699508 . _:b413699564 "2"^^ . _:b413699509 . _:b413699510 . _:b6011264 _:b6011268 . _:b413699511 . _:b6011264 _:b6011269 . _:b413699512 . _:b413699567 "2"^^ . _:b6011264 _:b6011270 . _:b413699513 . _:b6011264 _:b6011271 . _:b413699514 . _:b413699332 . _:b6011264 _:b6011265 . _:b413699515 . _:b413699050 . _:b413699516 . _:b413699566 "2"^^ . _:b6011264 _:b6011266 . _:b413699517 . _:b6011264 _:b6011267 . _:b413699518 . _:b6011264 _:b6011276 . _:b413699519 . _:b6011211 . _:b6011264 _:b6011277 . _:b413699488 . _:b413699561 "2"^^ . _:b6011264 _:b6011278 . _:b413699489 . _:b6011264 _:b6011279 . _:b413699490 . _:b6011264 _:b6011272 . _:b413699491 . _:b6011234 . _:b6011264 _:b6011273 . _:b413699492 . _:b413699560 "2"^^ . _:b6011264 _:b6011274 . . _:b6011264 _:b6011275 . _:b413699179 . _:b413699493 . _:b413699494 . _:b6011264 _:b6011284 . _:b413699495 . _:b6011213 . _:b6011264 _:b6011285 . _:b413699046 . _:b413699563 "2"^^ . _:b6011264 _:b6011286 . . _:b413699496 . _:b413699497 . _:b6011264 _:b6011287 . _:b413699498 . _:b413699576 . _:b6011264 _:b6011280 . _:b413699499 . _:b6011212 . _:b6011264 _:b6011281 . _:b413699123 . _:b413699562 "2"^^ . _:b6011264 _:b6011282 . _:b413699500 . _:b413699501 . _:b6011264 _:b6011283 . _:b413699502 . _:b6011264 _:b6011292 . . _:b413699503 . _:b6011264 _:b6011293 . . _:b413699664 . _:b413699573 "2"^^ . _:b6011264 _:b6011294 . _:b413699665 . _:b6011264 _:b6011295 . . _:b413699666 . _:b6011264 _:b6011288 . _:b413699667 . _:b6011264 _:b6011289 . _:b413699668 . _:b413699572 "2"^^ . _:b6011264 _:b6011290 . _:b413699669 . _:b6011264 _:b6011291 . _:b413699670 . _:b413699671 . _:b413699672 . _:b413699575 "2"^^ . _:b413699673 . _:b413699674 . _:b413699675 . _:b413699676 . _:b413699574 "2"^^ . _:b413699677 . _:b413699678 . _:b413699298 . _:b413699679 . _:b413699648 . _:b413699569 "2"^^ . . _:b413699649 . _:b413699590 . _:b413699650 . _:b413699651 . _:b413699652 . _:b413699568 "2"^^ . _:b413699653 . _:b413699654 . _:b413699655 . _:b413699656 . _:b413699571 "2"^^ . _:b413699081 . _:b413699657 . _:b413699658 . _:b413699659 . _:b413699643 . _:b413699660 . _:b413699570 "2"^^ . _:b413699661 . _:b6011260 "The numerical implementation of the gene circuit equations is as described [35,>>36<<] with the addition of time varying external inputs (see Section S1.2 in Protocol S1)." . _:b413699662 . _:b413699663 . _:b6011255 . _:b6011233 "Although the location of eve stripes [53] and the posterior border of the anterior hb domain scale with egg length, the Bcd gradient and hence its threshold positions do not [>>9<<]. To explain this scaling property, an as-yet-undiscovered gradient has been proposed [12,14]. These proposals specifically considered the scaling of the hb border, but one theoretical study suggests that the second gradient could scale" . _:b413699696 . _:b413699581 "2"^^ . . _:b413699697 . _:b413699698 . _:b413699699 . _:b413699700 . _:b413699580 "2"^^ . . _:b413699701 . _:b6011234 "To explain this scaling property, an as-yet-undiscovered gradient has been proposed [12,>>14<<]. These proposals specifically considered the scaling of the hb border, but one theoretical study suggests that the second gradient could scale multiple borders [15]. The hypothetical gradient would be set up from the posterior pole of" . _:b413699702 . _:b413699703 . _:b413699704 . _:b6011235 . _:b413699583 "2"^^ . _:b413699705 . . _:b413699706 . _:b413699707 . _:b413699589 . _:b413699708 . _:b413699582 "2"^^ . . _:b413699709 . . _:b413699710 . _:b413699711 . _:b413699680 . _:b413699577 "2"^^ . _:b413699239 . _:b413699681 . _:b413699682 . _:b413699683 . _:b6011250 . . _:b413699684 . _:b413699576 "2"^^ . _:b413699685 . _:b413699054 . _:b413699686 . _:b413699687 . _:b6011261 . _:b413699688 . _:b413699579 "2"^^ . _:b413699689 . _:b413699690 . _:b413699395 . _:b413699691 . _:b413699692 . _:b413699578 "2"^^ . _:b413699693 . _:b413699251 . _:b413699694 . _:b413699695 . _:b413699600 . . _:b413699601 . _:b413699602 . _:b413699603 . _:b413699604 . _:b413699605 . . _:b413699606 . _:b413699607 . _:b413699359 . _:b413699608 . _:b413699609 . _:b413699610 . _:b413699611 . _:b413699605 . _:b413699612 . _:b413699613 . _:b413699614 . _:b413699564 . _:b413699615 . _:b413699584 . _:b413699585 . _:b413699586 . _:b413699587 . _:b413699588 . _:b413699589 . . _:b413699590 . _:b413699591 . . _:b413699592 . _:b413699593 . _:b413699594 . _:b413699595 . _:b413699596 . _:b413699597 . _:b413699598 . _:b413699599 . _:b413699632 . _:b413699633 . _:b413699310 . _:b413699634 . _:b413699635 . _:b413699636 . _:b6011250 . _:b413699637 . _:b413699570 . _:b413699638 . _:b413699639 . . _:b413699640 . _:b413699358 . _:b413699641 . _:b413699642 . _:b413699643 . _:b413699644 . _:b413699645 . _:b6011295 . _:b413699646 . _:b413699468 . _:b413699647 . _:b413699616 . _:b413699617 . . _:b413699649 . _:b413699618 . _:b413699619 . _:b6011231 "Drosophila eggs vary in length by 10\u201320%, and different wild lines may have differing mean egg lengths [>>53<<]. Although the location of eve stripes [53] and the posterior border of the anterior hb domain scale with egg length, the Bcd gradient and hence its threshold positions do not [9]." . _:b413699620 . _:b413699621 . _:b413699622 . . _:b413699623 . . _:b413699624 . _:b413699625 . _:b413699626 . _:b413699627 . . _:b413699628 . _:b413699629 . _:b413699630 . _:b413699631 . _:b413699452 . _:b6011268 . . _:b413699500 . . . . _:b6011267 . _:b6011296 . . _:b6011166 . . _:b413699262 . _:b6011215 "The Bcd gradient is essentially stationary during cleavage cycles 13 and 14 [6,43,>>44<<], and hence, its concentration v Bcd is assumed to be constant in time." . _:b413699514 . _:b6011254 _:b6011260 . . _:b6011254 _:b6011261 . _:b6011254 _:b6011262 . _:b6011254 _:b6011263 . _:b6011254 _:b6011256 . _:b6011254 _:b6011257 . _:b6011254 _:b6011258 . _:b6011254 _:b6011259 . . _:b413699712 . _:b413699680 . _:b6011254 _:b6011255 . _:b413699634 . _:b413699713 . _:b413699714 . _:b413699492 . _:b6011225 "The contribution of Hb autoactivation, shown in red, does not set the border but merely sharpens it [>>9<<,36]. The colored bar inset shows the relative contributions of Bcd activation, Kr repression, and Kni repression to hb, showing that the repressive contribution is significant compared to the activating one. (B) The Kr border is set by" . . . . . _:b413699665 . . . _:b413699351 . _:b413699616 . _:b6011274 "the variance of expression borders driven by Bcd can be understood in a simple and unified manner by considering our results together with two recent studies of the Bcd gradient, one in vivo [16] and the other in fixed tissue [>>18<<]. Our comparison of Bcd-GFP data with fixed tissue hb data (Figure 1) shows that the range of x Bcd in vivo is 10% EL, but that of x Hb in fixed tissue data is 5% EL." . . _:b6011269 "A third type of model [>>21<<] invokes transient behavior of the Bcd gradient and its associated thresholds during cycles 10\u201313 as a mechanism of variance reduction." . . _:b6011203 . _:b413699111 . _:b413699644 . _:b413699660 . _:b6011208 _:b6011212 . _:b6011208 _:b6011213 . _:b6011208 _:b6011214 . _:b413699585 . _:b6011208 _:b6011215 . _:b6011224 . _:b6011208 _:b6011209 . _:b6011178 . _:b6011208 _:b6011210 . _:b6011208 _:b6011211 . _:b413699283 . _:b6011208 _:b6011220 . _:b6011208 _:b6011221 . _:b6011208 _:b6011222 . . _:b6011208 _:b6011223 . _:b6011208 _:b6011216 . _:b6011226 . _:b413699115 . _:b6011208 _:b6011217 . _:b6011208 _:b6011218 . _:b6011208 _:b6011219 . _:b6011208 _:b6011228 . _:b6011208 _:b6011229 . _:b6011208 _:b6011230 . _:b6011208 _:b6011231 . _:b6011208 _:b6011224 . _:b6011208 _:b6011225 . _:b6011208 _:b6011226 . _:b6011208 _:b6011227 . _:b6011208 _:b6011236 . . _:b6011208 _:b6011237 . _:b6011208 _:b6011238 . _:b6011208 _:b6011239 . _:b6011208 _:b6011232 . . _:b6011208 _:b6011233 . _:b6011208 _:b6011234 . _:b6011208 _:b6011235 . _:b6011208 _:b6011244 . _:b6011208 _:b6011245 . _:b6011208 _:b6011246 . _:b413699450 . _:b6011208 _:b6011247 . _:b6011208 _:b6011240 . _:b6011208 _:b6011241 . _:b6011208 _:b6011242 . . _:b6011208 _:b6011243 . _:b413699171 . _:b6011208 _:b6011252 . _:b6011208 _:b6011253 . _:b6011243 "Those regulatory inputs responsible for changing the state of a gene from off to on can be read from an appropriate graph [>>33<<\u201336] (see Section S3 in Protocol S1 for further details)." . . _:b6011208 _:b6011248 . _:b6011208 _:b6011249 . _:b6011208 _:b6011250 . _:b413699264 . . _:b6011208 _:b6011251 . _:b413699265 . _:b6011245 . _:b6011297 . . _:b413699143 . . . _:b6011247 . _:b6011180 "First, using a result from bacterial chemotaxis theory [>>19<<], it was shown that noise due to small number of Bcd molecules is high enough so that the hb border cannot be accurately specified by Bcd alone." . _:b413699463 . . _:b413699125 . _:b6011243 . . _:b413699471 . . _:b6011164 "biologists, the buffering of phenotypic variation to underlying genotypic variation in wild type is well known, and recent experimental studies have identified individual genes that are responsible for this aspect of canalization [>>2<<,3]. Theoretical studies have demonstrated that this phenotypic buffering is an intrinsic consequence of the adjustments of developmental trajectories postulated by Waddington [4], but direct evidence of developmental canalization was" . . _:b6011190 "(B) Eighteen Hb profiles 3 min before gastrulation (time class T8, see Table 1) from FlyEx [>>6<<]." . _:b413699672 . . _:b413699147 . _:b413699145 . . _:b413699593 . . . . . _:b413699687 . _:b6011260 . _:b6011239 "Recently, an alternative model, in which degradation is replaced with the reversible trapping of the Bcd protein by the nuclei in the blastoderm, was proposed [>>57<<]. Both the trapping model and the diffusion-degradation model do not show scaling of the Bcd gradient with egg length and so we represented the scaling properties of the Bcd gradient using the simpler diffusion-degradation model." . _:b413699573 . _:b6011217 "It is known through antibody studies [6,>>9<<,12,43] and a recent GFP-Bcd [44] study that the Bcd profile is an exponential function of A\u2013P position x, so that The arithmetic mean of exponential curves is not exponential." . _:b6011263 . _:b413699107 . . _:b6011280 "Other important experimental results can be understood by recalling that the maximum accuracy of the Bcd gradient is inversely proportional to the square root of the Bcd concentration [>>16<<,19,60], suggesting that borders under unmodified Bcd control will have lower variation at more anterior positions." . . . _:b413699389 . . . _:b413699254 . _:b413699174 . _:b413699606 . _:b413699560 . . . _:b6011286 "In recently published work, He et al. [>>18<<] report that the Bcd threshold at which the posterior border of the anterior hb domain forms is not constant but varies in a correlated manner with the slope of the Bcd profile." . _:b413699157 . . _:b6011209 . _:b413699184 . . . . _:b6011165 "biologists, the buffering of phenotypic variation to underlying genotypic variation in wild type is well known, and recent experimental studies have identified individual genes that are responsible for this aspect of canalization [2,>>3<<]. Theoretical studies have demonstrated that this phenotypic buffering is an intrinsic consequence of the adjustments of developmental trajectories postulated by Waddington [4], but direct evidence of developmental canalization was still" . _:b413699473 . . . . _:b413699558 . _:b413699210 . _:b413699584 . _:b413699045 . _:b413699453 . _:b6011169 "In work reported elsewhere [>>6<<], we performed a quantitative analysis of the expression of segmentation genes expressed from the maternal genome only (bicoid), the maternal and zygotic genomes (caudal and hunchback), and the zygotic genome (Kr\u00FCppel, giant, knirps," . _:b413699044 . _:b413699047 . _:b413699612 . _:b413699337 . _:b6011191 . _:b413699631 . _:b413699046 . . _:b413699205 . _:b413699100 . _:b413699555 . _:b6011163 _:b6011164 . _:b413699053 . _:b6011163 _:b6011165 . _:b6011163 _:b6011166 . _:b6011163 _:b6011167 . _:b413699052 . _:b413699055 . _:b6011203 "This method has been successfully used to analyze both the pair-rule and gap systems [27,>>33<<\u201336] and performed better than other models in a comparative study [31]." . _:b6011163 _:b6011176 . _:b413699054 . _:b6011163 _:b6011177 . _:b6011163 _:b6011178 . _:b6011163 _:b6011179 . _:b413699663 . _:b6011163 _:b6011180 . _:b413699690 . _:b413699049 . _:b6011163 _:b6011181 . _:b6011163 _:b6011182 . _:b6011163 _:b6011183 . _:b413699412 . _:b6011163 _:b6011168 . _:b413699048 . _:b6011163 _:b6011169 . _:b6011194 . . _:b6011163 _:b6011170 . _:b6011163 _:b6011171 . _:b6011163 _:b6011172 . _:b413699051 . _:b6011163 _:b6011173 . _:b6011163 _:b6011174 . _:b6011163 _:b6011175 . _:b6011163 _:b6011192 . _:b413699050 . _:b6011163 _:b6011193 . _:b6011163 _:b6011194 . _:b6011163 _:b6011195 . _:b6011163 _:b6011196 . _:b413699061 . _:b6011163 _:b6011197 . _:b6011163 _:b6011198 . _:b6011163 _:b6011199 . _:b6011163 _:b6011184 . _:b413699060 . _:b6011163 _:b6011185 . _:b6011163 _:b6011186 . _:b6011163 _:b6011187 . _:b6011163 _:b6011188 . _:b413699063 . _:b6011163 _:b6011189 . _:b6011163 _:b6011190 . _:b6011171 "These boundaries shift when maternal gradients are perturbed, and hence are at least in part under the control of these gradients [7,>>8<<]. Nevertheless, the variation in the boundary positions of gap and pair-rule expression domains is much lower than the variation in the maternal gradient of Bicoid (Bcd) protein [6,9,10]. Under the simplest model of specification," . _:b6011163 _:b6011191 . _:b413699062 . _:b413699057 . _:b6011163 _:b6011200 . _:b413699056 . _:b6011163 _:b6011201 . _:b413699085 . _:b6011163 _:b6011202 . . . _:b6011163 _:b6011203 . _:b6011163 _:b6011204 . . _:b413699059 . _:b6011163 _:b6011205 . _:b6011163 _:b6011206 . _:b6011163 _:b6011207 . _:b413699364 . _:b413699108 . _:b413699058 . _:b413699069 . _:b413699068 . _:b413699669 . _:b413699071 . _:b6011227 . _:b413699070 . . _:b413699324 . _:b413699065 . _:b413699608 . _:b413699064 . _:b413699067 . . . _:b413699066 . . . . . . . _:b413699625 . _:b6011201 "model, in which one real number characterizes the regulatory effect of one gene on another, is (2) fit to quantitative gene expression data by (3) parallel Lam simulated annealing [28,29] or some other nonlinear optimization method [>>30<<\u201332], and finally (4) biological conclusions are obtained. This method has been successfully used to analyze both the pair-rule and gap systems [27,33\u201336] and performed better than other models in a comparative study [31]." . . . _:b413699557 . _:b413699588 . _:b413699231 . . _:b6011268 "With one exception [>>15<<], these studies only considered the hb border, while the work reported here correctly predicts the variation of six borders, some of which are not under the control of bcd." . _:b413699615 . _:b413699550 . _:b413699266 . . _:b413699607 . . _:b6011244 "This analysis is consistent with earlier results [>>31<<,36]. We briefly summarize the results here; see the captions of these figures and previous studies [31,36] for details." . . . _:b413699547 . . _:b413699135 . _:b413699474 . . _:b6011289 "These factors alter the profile of the Bcd gradient but have little effect on the border position of downstream targets [>>9<<,62]. We believe that the fixed-tissue Bcd profiles used in the present study capture this extra level of variability characteristic of natural populations." . . _:b413699678 . _:b6011261 "The gap gene circuit was fit to integrated gap gene data [>>6<<] using Parallel Lam Simulated Annealing (PLSA) [28,29]." . . _:b413699263 . . _:b413699213 . _:b413699658 . . . _:b413699396 . _:b413699676 . . _:b413699131 . _:b413699508 . . . . . _:b413699493 . _:b413699339 . _:b413699049 . _:b413699370 . _:b413699277 . _:b413699357 . . _:b6011242 "Using the parameters A and \u03B3rel(L) of the median Bcd profile (Figure 2B) we varied between \u22120.1 and 0.1 to generate Bcd profiles representing egg length variation of 20%, which corresponds to the range of egg lengths observed in data [>>9<<]." . _:b413699094 . _:b413699515 . _:b413699202 . _:b413699695 . _:b413699592 . . . . _:b413699112 . _:b413699399 . _:b413699423 . . _:b6011259 "The numerical implementation of the gene circuit equations is as described [>>35<<,36] with the addition of time varying external inputs (see Section S1.2 in Protocol S1)." . . _:b413699536 . . . . . . . _:b6011244 . _:b413699691 . _:b6011246 . . _:b413699435 . _:b413699287 . _:b413699285 . . . . _:b6011173 "Nevertheless, the variation in the boundary positions of gap and pair-rule expression domains is much lower than the variation in the maternal gradient of Bicoid (Bcd) protein [6,>>9<<,10]. Under the simplest model of specification, expression borders would form at a fixed threshold of its concentration [11]. The variation of the Bcd gradient can be measured in terms of the range (\u03C1Bcd) or standard deviation (\u03C3Bcd) of" . _:b413699490 . _:b6011222 . . . . . . _:b413699407 . _:b6011216 "It is known through antibody studies [>>6<<,9,12,43] and a recent GFP-Bcd [44] study that the Bcd profile is an exponential function of A\u2013P position x, so that The arithmetic mean of exponential curves is not exponential." . _:b6011226 "The contribution of Hb autoactivation, shown in red, does not set the border but merely sharpens it [9,>>36<<]. The colored bar inset shows the relative contributions of Bcd activation, Kr repression, and Kni repression to hb, showing that the repressive contribution is significant compared to the activating one. (B) The Kr border is set by Bcd" . _:b413699623 . . _:b413699330 . . _:b6011201 . _:b413699610 . _:b413699589 "2"^^ . _:b413699411 . _:b413699588 "2"^^ . . _:b6011204 . _:b413699591 "2"^^ . _:b6011166 "Theoretical studies have demonstrated that this phenotypic buffering is an intrinsic consequence of the adjustments of developmental trajectories postulated by Waddington [>>4<<], but direct evidence of developmental canalization was still lacking." . . . . _:b413699590 "2"^^ . _:b413699326 . _:b413699563 . _:b6011228 "They are known to influence the anterior pattern of trunk gap genes [>>25<<], and respond to Bcd in a concentration-dependent manner [49]." . _:b413699656 . _:b413699585 "2"^^ . _:b413699704 . _:b413699584 "2"^^ . _:b6011204 "This method has been successfully used to analyze both the pair-rule and gap systems [27,33\u201336] and performed better than other models in a comparative study [>>31<<]." . _:b413699543 . _:b413699587 "2"^^ . _:b413699381 . _:b413699586 "2"^^ . _:b413699597 "2"^^ . _:b6011214 "The Bcd gradient is essentially stationary during cleavage cycles 13 and 14 [6,>>43<<,44], and hence, its concentration v Bcd is assumed to be constant in time." . _:b413699641 . _:b413699376 . _:b6011195 . _:b413699220 . . _:b413699366 . . _:b413699596 "2"^^ . _:b413699599 "2"^^ . . _:b413699598 "2"^^ . _:b413699565 . _:b413699593 "2"^^ . _:b413699540 . _:b413699592 "2"^^ . _:b6011258 . . _:b413699621 . _:b413699595 "2"^^ . _:b413699485 . _:b413699140 . _:b413699594 "2"^^ . _:b413699124 . _:b413699702 . _:b6011198 . _:b413699689 . _:b413699605 "2"^^ . _:b413699604 "2"^^ . . . _:b413699607 "2"^^ . . _:b413699522 . . _:b413699606 "2"^^ . _:b413699601 "2"^^ . _:b413699600 "2"^^ . _:b413699603 "2"^^ . _:b413699388 . _:b413699602 "2"^^ . _:b413699195 . _:b413699613 "2"^^ . _:b413699612 "2"^^ . . _:b413699615 "2"^^ . . . _:b413699162 . _:b413699614 "2"^^ . . . _:b413699553 . . _:b413699609 "2"^^ . _:b413699608 "2"^^ . _:b413699611 "2"^^ . . _:b413699241 . _:b413699610 "2"^^ . . _:b413699621 "2"^^ . _:b6011227 "In the anterior, the head gap genes orthodenticle, empty spiracles, and buttonhead [>>46<<\u201348] are excluded." . _:b6011186 "The assumption that hb is under the sole control of Bcd is incorrect, because its border position changes in embryos mutant for giant (gt) [9], Kr\u00FCppel (Kr) [20], Kr\u00FCppel;knirps (Kr;kni) [20], and in embryos lacking Nanos [>>9<<]. Apart from the average position, the variation of the position is also increased in embryos lacking chromosome arm 3L or Nanos to \u223C2% EL and \u223C1.6% EL respectively [9], close to the Bcd variation measured in live embryos." . _:b413699620 "2"^^ . . _:b413699623 "2"^^ . . _:b413699622 "2"^^ . _:b6011163 "introduction" . _:b413699617 "2"^^ . _:b413699480 . _:b413699616 "2"^^ . _:b413699394 . . . . _:b413699619 "2"^^ . _:b6011262 "Search spaces, penalty function, and other annealing parameters were as described [>>27<<,36]. The circuit analyzed in detail had an RMS score of 10.76, corresponding to a proportional error in expression residuals of about 4\u20135%. Protocol S1 (Section S1.3) contains further details." . _:b413699618 "2"^^ . _:b6011193 "At this position, the Bcd-GFP data have a variance of \u223C4% EL (see Figure 5C in [>>16<<]), which is much larger than that of the kni border." . _:b413699629 "2"^^ . . _:b413699628 "2"^^ . . _:b413699631 "2"^^ . . _:b413699630 "2"^^ . _:b413699375 . _:b6011188 "The Bcd-dependent response of a fragment of the hb promoter has variation close to Bcd variation (see Figure 4 in [>>21<<]) (\u03C1Bcd \u223C 9% EL; compare with Figure 1A) and higher than the variation of endogenous hb (Figure 1B)." . _:b413699625 "2"^^ . . _:b413699624 "2"^^ . _:b6011246 "We briefly summarize the results here; see the captions of these figures and previous studies [>>31<<,36] for details." . _:b6011193 . _:b6011228 . _:b413699627 "2"^^ . _:b413699597 . _:b6011199 "Gene circuits [>>26<<,27] are dynamical models that can accurately reproduce observed gene expression patterns by reconstituting the required set of genetic interactions in silico." . _:b413699626 "2"^^ . . _:b413699637 "2"^^ . . _:b6011170 "These boundaries shift when maternal gradients are perturbed, and hence are at least in part under the control of these gradients [>>7<<,8]. Nevertheless, the variation in the boundary positions of gap and pair-rule expression domains is much lower than the variation in the maternal gradient of Bicoid (Bcd) protein [6,9,10]. Under the simplest model of specification," . _:b413699636 "2"^^ . _:b6011189 . . _:b413699299 . _:b6011295 "Waddington hypothesized that canalization arises from gene interactions [1,>>65<<\u201368]. We have identified specific regulatory interactions among the gap genes responsible for canalization." . _:b413699639 "2"^^ . _:b413699117 . _:b413699638 "2"^^ . _:b413699633 "2"^^ . _:b413699632 "2"^^ . . . _:b413699110 . _:b413699635 "2"^^ . _:b413699073 . _:b413699686 . _:b6011205 "kni under maternal control and including mutual gap\u2013gap interactions is sufficient to explain the reduction in the variance of gap gene domain border positions, showing that it is not necessary to postulate an undiscovered gradient [12,>>14<<,15] or active transport [13] to explain this property. In the Results section \u201CVariance Reduction by Gap Gene Cross Regulation and Experimental Verification,\u201D we characterize the regulatory interactions underlying variance reduction." . _:b413699634 "2"^^ . _:b413699710 . . _:b413699529 . _:b413699645 "2"^^ . . _:b413699539 . _:b413699535 . _:b413699644 "2"^^ . _:b413699400 . _:b6011178 . _:b413699647 "2"^^ . _:b413699646 "2"^^ . _:b6011179 . _:b413699166 . _:b413699641 "2"^^ . _:b413699640 "2"^^ . _:b413699643 "2"^^ . . . _:b413699383 . _:b413699642 "2"^^ . . _:b413699323 . . _:b413699331 . . _:b413699653 "2"^^ . _:b413699652 "2"^^ . _:b413699580 . _:b413699301 . _:b413699378 . _:b413699655 "2"^^ . . _:b413699654 "2"^^ . . _:b413699182 . _:b413699192 . . _:b413699649 "2"^^ . . _:b413699648 "2"^^ . _:b413699461 . _:b413699651 "2"^^ . _:b413699650 "2"^^ . _:b413699075 . . _:b413699661 "2"^^ . _:b413699382 . _:b413699087 . _:b413699660 "2"^^ . . . _:b413699663 "2"^^ . . _:b413699662 "2"^^ . _:b413699657 "2"^^ . _:b413699304 . _:b413699656 "2"^^ . _:b413699659 "2"^^ . _:b413699469 . _:b6011180 . _:b413699146 . . _:b413699658 "2"^^ . . _:b413699408 . _:b413699669 "2"^^ . _:b413699095 . _:b413699668 "2"^^ . _:b413699671 "2"^^ . . _:b413699416 . _:b6011219 . _:b413699670 "2"^^ . _:b413699665 "2"^^ . _:b6011279 "Third, when chromosome arm 3L is completely removed [>>9<<], the standard deviation of x Hb doubles." . _:b413699664 "2"^^ . _:b413699667 "2"^^ . _:b413699401 . _:b6011215 . _:b413699238 . _:b6011201 . _:b413699666 "2"^^ . _:b413699193 . _:b413699677 "2"^^ . _:b413699524 . . . _:b413699676 "2"^^ . _:b413699404 . _:b413699679 "2"^^ . _:b413699106 . _:b413699338 . _:b413699221 . _:b413699678 "2"^^ . . _:b413699673 "2"^^ . _:b413699347 . _:b6011271 "Furthermore, threshold concentrations of Bcd propagate toward the posterior of the embryo during the establishment of the Bicoid gradient, but gap domains in the posterior, in fact, shift in an anterior direction [>>35<<]. A third contradiction with experiment is that the model used by the authors of [21] produces incorrect mutually exclusive gap domains in the presence of diffusion." . _:b413699672 "2"^^ . _:b413699675 "2"^^ . _:b6011168 "The segmentation system of Drosophila melanogaster [5,>>6<<] is highly suitable for studies of canalization because it is already known that the first of the above requirements, decrease in phenotypic variability over time, is satisfied." . . _:b413699674 "2"^^ . _:b413699542 . _:b413699685 "2"^^ . _:b413699523 . _:b413699637 . _:b413699684 "2"^^ . _:b413699687 "2"^^ . _:b413699686 "2"^^ . _:b6011247 "We briefly summarize the results here; see the captions of these figures and previous studies [31,>>36<<] for details." . . _:b413699681 "2"^^ . _:b413699680 "2"^^ . _:b413699683 "2"^^ . . _:b413699682 "2"^^ . _:b413699582 . _:b413699693 "2"^^ . _:b413699692 "2"^^ . _:b6011299 "Our analysis [>>61<<] suggests that switching between attractors occurs in the gap gene system and is the mechanism by which the posterior border of the anterior hb domain forms." . . _:b6011220 "We obtained data from 88 cycle 13 embryos immunostained for Bcd and removed the background signal from the Bcd profiles as described [>>45<<]. Taking the logarithm of Equation 1, we get The background-removed profiles were then fit by linear least-squares to Equation 2. This procedure yielded two parameters for each profile, \u03B3 (length scale), and A (concentration scale)." . _:b413699214 . . _:b413699695 "2"^^ . _:b6011210 "The model computes the time course of nuclear protein concentrations in a time interval beginning at the start of cleavage cycle 13 and ending at the onset of gastrulation [>>41<<] (Figure S2 in Protocol S1)." . . _:b413699694 "2"^^ . . . _:b413699689 "2"^^ . _:b413699688 "2"^^ . _:b413699691 "2"^^ . . _:b413699690 "2"^^ . _:b413699701 "2"^^ . _:b413699335 . . _:b413699700 "2"^^ . _:b6011253 . _:b413699703 "2"^^ . _:b6011250 . _:b413699702 "2"^^ . . _:b413699444 . _:b413699697 "2"^^ . _:b413699699 . . _:b413699696 "2"^^ . _:b413699699 "2"^^ . _:b413699244 . _:b413699698 "2"^^ . _:b413699714 . _:b413699706 . _:b413699175 . _:b413699709 "2"^^ . _:b413699708 "2"^^ . _:b413699711 "2"^^ . _:b413699132 . . _:b413699710 "2"^^ . . . . _:b413699705 "2"^^ . _:b413699494 . . _:b413699207 . _:b413699056 . _:b413699057 . _:b413699704 "2"^^ . . _:b413699058 . _:b413699059 . . _:b413699060 . _:b413699061 . _:b413699707 "2"^^ . _:b413699062 . _:b6011188 . _:b413699063 . _:b413699064 . _:b413699065 . _:b413699706 "2"^^ . _:b413699066 . _:b413699067 . _:b413699068 . _:b413699069 . _:b413699070 . _:b413699594 . _:b413699552 . _:b413699071 . _:b413699682 . _:b413699161 . . . _:b413699044 . _:b413699045 . _:b413699046 . _:b413699047 . _:b413699048 . _:b413699049 . _:b413699050 . _:b413699051 . _:b413699167 . _:b413699052 . . _:b413699713 "2"^^ . _:b413699053 . _:b413699322 . _:b413699054 . _:b6011248 . _:b413699055 . _:b413699562 . _:b413699712 "2"^^ . . _:b6011211 "The initial conditions were specified using cleavage cycle 12 gene expression data [>>6<<] (Section S1 in Protocol S1)." . . _:b413699267 . . . _:b413699224 . _:b413699714 "2"^^ . . . _:b6011292 . _:b413699350 . _:b6011291 . _:b413699685 . . _:b413699668 . . _:b413699589 . _:b6011287 . . . _:b413699588 . _:b413699273 . _:b6011284 . . _:b413699591 . _:b413699590 . _:b413699052 . _:b413699585 . _:b413699584 . _:b6011280 . _:b413699587 . _:b413699586 . _:b413699597 . _:b6011253 "This experimental result strongly supports the model and rules out a picture in which Bcd provides the sole input to hb [>>16<<]." . . _:b413699596 . _:b6011276 . _:b413699599 . . . _:b413699639 . _:b413699598 . _:b413699561 . . _:b413699593 . _:b413699121 . _:b413699592 . "PMC0" . _:b413699595 . _:b6011273 . _:b413699594 . _:b6011270 . . _:b413699605 . _:b413699571 . _:b413699604 . _:b413699577 . _:b413699484 . _:b413699607 . _:b413699531 . _:b413699606 . _:b6011240 . _:b413699601 . _:b413699341 . _:b413699600 . _:b413699429 . _:b413699603 . _:b413699602 . . _:b413699613 . _:b413699612 . _:b413699615 . _:b413699181 . _:b6011298 "In an accompanying manuscript [>>61<<], we show that the trajectories of the gap gene system in individual nuclei do tend to converge and are stable against perturbations." . _:b413699614 . . . _:b413699609 . _:b413699105 . _:b413699608 . _:b413699333 . _:b413699611 . . _:b413699097 . _:b6011237 . _:b413699610 . _:b413699621 . _:b413699618 . _:b413699620 . _:b413699154 . _:b413699623 . _:b413699622 . . _:b413699617 . _:b413699616 . _:b413699650 . _:b413699460 . _:b413699256 . _:b413699229 . _:b413699619 . . . _:b413699618 . _:b413699409 . _:b413699629 . _:b413699628 . _:b413699631 . . _:b6011281 . _:b413699630 . . _:b413699294 . _:b413699625 . . . _:b413699624 . _:b413699317 . _:b413699627 . _:b6011238 "The stationary exponential profile of the Bcd gradient is consistent with the diffusion of the protein from the anterior tip and its degradation by a first-order process, and the gradient has been modeled as such [21,55,>>56<<]. Recently, an alternative model, in which degradation is replaced with the reversible trapping of the Bcd protein by the nuclei in the blastoderm, was proposed [57]. Both the trapping model and the diffusion-degradation model do not show" . _:b413699626 . _:b413699637 . _:b413699252 . _:b413699636 . . _:b6011192 "This border is located \u223C10% EL posterior to the hb border and has a positional variance of \u223C1% EL [>>6<<]. At this position, the Bcd-GFP data have a variance of \u223C4% EL (see Figure 5C in [16]), which is much larger than that of the kni border. This example clearly contradicts a picture of positional specification in which Bcd specifies all of" . _:b413699639 . _:b413699442 . . _:b413699638 . . . _:b413699633 . . _:b413699180 . _:b413699632 . . _:b413699367 . _:b413699635 . _:b413699634 . _:b413699645 . _:b413699056 . _:b413699644 . _:b413699620 . . _:b413699198 . _:b413699647 . . _:b413699646 . . . _:b413699641 . _:b6011285 "If the standard deviation of 2.2% EL seen here in Kr;kni double mutants is the unmodified response to Bcd at 47% EL, then the expected standard deviation at 29% EL is 1.3%, which is close to the 1.6% observed (see Figure 5C in [>>59<<]). Finally, the fact that the standard deviation of the posterior border of the anterior gt domain increases by less than that of hb in Kr;kni mutant embryos can be understood by noting that it is located at about 40% EL. At this" . . _:b413699640 . _:b413699541 . _:b413699643 . _:b413699642 . _:b413699626 . _:b413699653 . . _:b413699652 . _:b413699655 . . _:b413699654 . _:b413699217 . _:b6011295 . . _:b413699233 . _:b413699649 . _:b413699194 . _:b413699648 . _:b413699673 . _:b413699544 . _:b413699651 . _:b6011218 "It is known through antibody studies [6,9,12,>>43<<] and a recent GFP-Bcd [44] study that the Bcd profile is an exponential function of A\u2013P position x, so that The arithmetic mean of exponential curves is not exponential." . _:b413699153 . _:b413699527 . _:b413699650 . _:b413699661 . _:b413699660 . _:b413699663 . . _:b413699240 . _:b413699662 . _:b413699276 . . _:b413699657 . _:b413699656 . . . _:b413699659 . . . _:b413699658 . . . . _:b413699669 . _:b413699363 . _:b413699668 . _:b6011194 "Like hb, kni is not regulated by Bcd alone, but also by Caudal (Cad) [>>22<<,23], Hb [20,24], and Gt [25]. The examples of the hb and kni borders show that it is not possible to explain the variance of a single expression border position in isolation." . _:b413699671 . . _:b413699670 . _:b413699439 . _:b413699665 . _:b413699150 . . _:b413699664 . _:b413699667 . . _:b413699666 . _:b413699246 . . _:b413699677 . . _:b413699676 . _:b413699091 . _:b413699165 . _:b413699679 . . _:b413699422 . _:b413699678 . . _:b413699673 . _:b413699672 . _:b413699387 . _:b413699675 . _:b413699316 . _:b413699393 . _:b413699674 . . . _:b413699685 . . . _:b413699684 . _:b413699687 . _:b413699686 . _:b413699260 . . _:b413699681 . . _:b413699680 . _:b413699603 . _:b6011181 "The amount of variance reduction implied by this value of \u03C3Bcd is significantly smaller than the estimates from fixed-tissue experiments [>>6<<,9], presumably because the GFP measurements do not have scaling error introduced in the setting of microscope gain in separate fixed-tissue experiments." . _:b413699683 . _:b413699682 . . . _:b413699693 . . _:b6011250 "The low positional variation of the posterior border of the anterior hb domain has been studied extensively [9,12,>>14<<\u201316,59]. Our analysis shows that this border forms by Bcd activation and repression from Kr and Kni (Figure 4A)." . _:b413699692 . _:b413699695 . . _:b413699694 . _:b413699689 . _:b413699709 . . . _:b413699688 . _:b413699591 . . _:b413699691 . _:b413699690 . _:b413699701 . _:b413699700 . _:b413699537 . _:b413699703 . _:b6011164 . _:b413699057 . _:b413699702 . . _:b6011165 . _:b413699372 . _:b6011272 . . _:b413699697 . _:b6011166 . . _:b413699696 . _:b413699569 . _:b6011167 . _:b6011278 . _:b413699699 . . . _:b413699683 . _:b413699698 . . _:b413699709 . _:b413699551 . _:b6011245 "This analysis is consistent with earlier results [31,>>36<<]. We briefly summarize the results here; see the captions of these figures and previous studies [31,36] for details." . _:b413699420 . _:b413699708 . _:b6011230 . _:b6011163 . _:b413699711 . _:b6011172 . _:b413699710 . _:b6011173 . _:b413699047 "25"^^ . _:b413699705 . . _:b6011174 . _:b413699704 . _:b6011175 . _:b413699707 . . _:b6011168 . _:b413699050 "23"^^ . . _:b6011269 . _:b413699706 . . _:b413699307 . _:b6011241 "Equation 3 may also be arrived at by explicitly rescaling the diffusion-degradation model [21,55,>>56<<]." . _:b6011169 . _:b413699051 "18"^^ . _:b413699048 "23"^^ . _:b6011170 . _:b413699049 "23"^^ . _:b6011171 . _:b6011180 . . _:b413699052 "17"^^ . _:b6011181 . _:b413699053 "17"^^ . _:b413699713 . _:b6011182 . _:b413699272 . _:b413699054 "17"^^ . _:b413699712 . . _:b6011183 . _:b413699055 "16"^^ . . _:b6011176 . _:b413699056 "16"^^ . _:b413699714 . . _:b6011177 . _:b413699072 . _:b413699057 "16"^^ . _:b6011178 . _:b413699058 "16"^^ . _:b413699059 "15"^^ . _:b6011179 . _:b413699083 . _:b413699060 "15"^^ . _:b6011188 . _:b413699369 . _:b413699487 . _:b413699061 "14"^^ . _:b6011189 . . _:b413699062 "14"^^ . _:b6011190 . _:b413699318 . _:b413699183 . _:b413699063 "14"^^ . _:b6011191 . . . _:b413699071 "11"^^ . _:b6011184 . _:b413699045 "36"^^ . _:b413699119 . _:b6011185 . _:b6011178 . _:b413699070 "11"^^ . . _:b413699046 "31"^^ . _:b6011186 . . _:b413699044 "39"^^ . _:b413699069 "12"^^ . . _:b6011187 . _:b413699068 "13"^^ . _:b413699218 . _:b6011265 . _:b6011196 . . _:b413699314 . _:b413699067 "13"^^ . _:b413699511 . _:b413699249 . _:b6011197 . _:b413699066 "13"^^ . _:b6011198 . _:b413699065 "13"^^ . _:b6011199 . _:b413699434 . . _:b413699064 "13"^^ . . _:b6011192 . . _:b6011193 . _:b413699647 . . _:b413699613 . _:b413699077 . _:b6011194 . _:b6011291 "The gap gene borders are specified at a low enough molecular number of Bcd [>>16<<] that intrinsic fluctuations are a significant source of variation [16,60]." . _:b6011195 . _:b6011185 "The assumption that hb is under the sole control of Bcd is incorrect, because its border position changes in embryos mutant for giant (gt) [9], Kr\u00FCppel (Kr) [20], Kr\u00FCppel;knirps (Kr;kni) [>>20<<], and in embryos lacking Nanos [9]." . _:b6011204 . . _:b6011254 "methods" . . _:b6011205 . _:b6011218 . _:b6011206 . _:b413699466 . _:b6011207 . _:b6011219 "It is known through antibody studies [6,9,12,43] and a recent GFP-Bcd [>>44<<] study that the Bcd profile is an exponential function of A\u2013P position x, so that The arithmetic mean of exponential curves is not exponential." . . _:b6011200 . _:b413699617 . _:b413699545 . _:b6011201 . _:b413699630 . _:b6011202 . _:b6011203 . _:b6011212 . . _:b6011213 . _:b6011214 . . _:b413699315 . _:b6011215 . _:b413699279 . _:b6011208 . _:b413699257 . _:b6011209 . _:b413699574 . . _:b6011210 . _:b6011211 . _:b413699371 . _:b6011220 . . _:b6011221 . _:b413699122 . _:b6011222 . _:b6011223 . . . . _:b6011216 . _:b413699346 . _:b6011217 . _:b6011214 . _:b6011218 . _:b6011219 . _:b413699627 . . _:b6011228 . _:b6011229 . _:b6011230 . _:b413699431 . _:b413699559 . . _:b6011231 . _:b413699185 . _:b6011224 . _:b6011225 . _:b6011198 "Like hb, kni is not regulated by Bcd alone, but also by Caudal (Cad) [22,23], Hb [20,24], and Gt [>>25<<]. The examples of the hb and kni borders show that it is not possible to explain the variance of a single expression border position in isolation." . _:b6011226 . _:b413699501 . _:b413699443 . _:b413699118 . _:b6011227 . _:b6011236 . _:b413699445 . _:b6011237 . _:b413699133 . _:b6011238 . _:b413699336 . _:b413699377 . _:b6011239 . . _:b6011232 . . . _:b6011233 . _:b413699270 . _:b413699698 . _:b413699368 . _:b6011234 . _:b413699232 . _:b413699158 . _:b6011235 . _:b6011244 . _:b6011245 . _:b413699566 . . _:b6011246 . _:b413699226 . _:b6011247 . _:b413699296 . _:b6011240 . _:b6011241 . _:b413699219 . . _:b6011242 . _:b6011243 . _:b6011252 . _:b6011236 . . . _:b6011253 . _:b6011254 . _:b6011255 . . . _:b6011248 . _:b413699646 . _:b6011220 . _:b413699237 . _:b6011249 . _:b6011207 . _:b6011250 . _:b6011267 "The first two classes of models invoke either active transport [13] or a second gradient at the posterior pole of the embryo [12,14,>>15<<] as a mechanism for the reduction in variation of the hb border." . . _:b6011251 . . _:b6011260 . . _:b413699088 . _:b413699093 . _:b6011261 . _:b6011189 "(A) Fifteen Bcd-GFP concentration profiles replotted from the data of Gregor and colleagues (Figure 5A in [>>16<<])." . _:b6011262 . _:b413699113 . _:b413699139 . _:b413699079 . _:b6011263 . _:b413699344 . _:b6011256 . _:b6011257 . _:b6011258 . _:b6011287 "question concerns the reason for the correct prediction of gap gene domain border variation presented here, as it is clear that the fixed tissue Bcd data used for the theoretical study exaggerate the standard deviation of x Bcd [>>16<<]. We believe that the high degree of canalization observed (Figure 3A) makes the theoretical model quite insensitive to initial variation, as is true of the biological system itself." . _:b413699578 . _:b6011259 . _:b6011167 "The segmentation system of Drosophila melanogaster [>>5<<,6] is highly suitable for studies of canalization because it is already known that the first of the above requirements, decrease in phenotypic variability over time, is satisfied." . . _:b6011268 . _:b6011179 "Gregor and colleagues [>>16<<] measured the absolute concentration of Bcd in the nuclei at the hb border using a Bcd-GFP fusion rescue construct." . _:b413699406 . . _:b6011269 . . _:b413699489 . _:b6011270 . _:b6011227 . _:b6011221 "To compare with quantitative gene expression data [>>6<<], we calculate the solution of the model at multiple time points. The data are classified into time classes to give nine time points for comparison (see Table 1 and Figure S2 in Protocol S1)." . _:b6011271 . _:b413699189 . _:b413699068 . . _:b6011264 . _:b6011265 . _:b413699253 . _:b6011266 . . _:b6011267 . . . _:b6011276 . . . . . . . _:b413699636 . _:b6011277 . . _:b6011278 . _:b6011279 . . . _:b6011272 . . _:b6011273 . . _:b413699204 . _:b6011274 . _:b6011275 . _:b6011284 . _:b6011285 . "10.1371%2Fjournal.pbio.1000049" . _:b6011286 . _:b413699090 . _:b6011287 . _:b413699517 . . _:b6011280 . _:b413699701 . _:b6011281 . _:b413699201 . _:b6011282 . _:b6011283 . . . _:b413699533 . . _:b6011292 . . _:b6011272 "A third contradiction with experiment is that the model used by the authors of [>>21<<] produces incorrect mutually exclusive gap domains in the presence of diffusion." . _:b6011293 . _:b6011294 . . _:b6011209 "The protein products of these genes are transcription factors [>>37<<\u201340] and localize to nuclei." . _:b6011295 . . . _:b413699427 . _:b6011288 . . _:b6011289 . _:b6011290 . _:b6011291 . . _:b6011206 "under maternal control and including mutual gap\u2013gap interactions is sufficient to explain the reduction in the variance of gap gene domain border positions, showing that it is not necessary to postulate an undiscovered gradient [12,14,>>15<<] or active transport [13] to explain this property. In the Results section \u201CVariance Reduction by Gap Gene Cross Regulation and Experimental Verification,\u201D we characterize the regulatory interactions underlying variance reduction." . . . . _:b6011178 . . _:b6011296 . _:b6011297 . _:b413699478 . _:b413699333 . _:b6011298 . _:b413699332 . . . _:b6011299 . _:b413699335 . _:b413699664 . _:b413699334 . _:b413699329 . _:b413699234 . _:b413699328 . . _:b413699331 . _:b413699455 . _:b413699549 . _:b413699330 . _:b6011208 "results" . _:b413699325 . _:b413699208 . _:b413699341 . . _:b413699583 . . _:b413699340 . _:b413699343 . _:b413699342 . . _:b413699223 . _:b413699462 . _:b413699337 . _:b6011170 . _:b413699418 . _:b413699336 . . _:b413699177 . _:b413699339 . _:b413699338 . _:b413699349 . _:b6011264 . . _:b413699475 . _:b413699348 . _:b413699351 . _:b413699350 . _:b413699345 . _:b413699344 . . _:b413699347 . . _:b413699346 . . _:b413699357 . _:b413699356 . _:b413699058 . _:b413699359 . . _:b6011273 "puzzling experimental results concerning the variance of expression borders driven by Bcd can be understood in a simple and unified manner by considering our results together with two recent studies of the Bcd gradient, one in vivo [>>16<<] and the other in fixed tissue [18]. Our comparison of Bcd-GFP data with fixed tissue hb data (Figure 1) shows that the range of x Bcd in vivo is 10% EL, but that of x Hb in fixed tissue data is 5% EL." . _:b413699358 . _:b413699353 . _:b6011165 . _:b413699352 . _:b413699464 . _:b413699188 . _:b413699355 . _:b6011241 . _:b6011235 "These proposals specifically considered the scaling of the hb border, but one theoretical study suggests that the second gradient could scale multiple borders [>>15<<]. The hypothetical gradient would be set up from the posterior pole of the embryo and would directly regulate the gap genes or Bcd. The proposed posterior gradient would provide the target with a measure of distance from the posterior" . _:b413699354 . _:b413699365 . . _:b413699417 . _:b413699364 . . _:b413699386 . _:b413699367 . _:b413699366 . _:b6011229 . _:b413699044 . _:b413699705 . _:b413699361 . _:b413699360 . . . . _:b413699363 . _:b413699362 . _:b413699516 . _:b413699373 . . . _:b413699305 . _:b413699372 . _:b413699245 . _:b413699375 . _:b413699374 . _:b413699449 . _:b413699369 . . _:b413699368 . _:b6011199 . _:b6011238 . _:b413699403 . . _:b413699371 . _:b413699258 . . _:b413699370 . _:b413699381 . _:b413699486 . _:b413699380 . _:b413699611 . . _:b413699383 . . _:b413699382 . _:b6011232 "Although the location of eve stripes [>>53<<] and the posterior border of the anterior hb domain scale with egg length, the Bcd gradient and hence its threshold positions do not [9]." . . . _:b413699377 . _:b413699504 . _:b413699376 . . . . _:b413699379 . _:b413699629 . _:b6011163 . _:b413699470 . _:b413699378 . . _:b413699389 . _:b413699388 . . _:b6011223 "The circuit's gap gene patterns (Figure S4A and S4B in Protocol S1) are consistent with data except for two minor defects (Section S1.3 in Protocol S1) and the circuit has the same network topology that was obtained previously [31,>>35<<,36]." . _:b413699391 . . . _:b6011293 "The gap gene borders are specified at a low enough molecular number of Bcd [16] that intrinsic fluctuations are a significant source of variation [16,>>60<<]. The buffering of phenotypic variation against intrinsic fluctuations in molecular number, while not considered by Waddington, is likely to be an important aspect of canalization in biological systems. It is noteworthy that we were able" . _:b413699390 . . . _:b413699385 . . _:b413699384 . _:b413699387 . . _:b413699136 . _:b413699386 . _:b413699397 . . . _:b413699396 . _:b413699447 . _:b6011258 "The local maximum in a domain was determined using a quadratic spline approximation [>>74<<]." . _:b413699070 . _:b413699399 . _:b6011208 . _:b413699384 . _:b413699398 . . _:b413699393 . . . _:b413699392 . _:b413699395 . _:b413699394 . . _:b413699405 . _:b413699518 . _:b413699404 . _:b413699546 . _:b413699407 . _:b413699406 . _:b413699401 . _:b413699400 . _:b413699674 . _:b6011254 . _:b413699403 . . _:b413699268 . _:b413699402 . _:b413699413 . . _:b413699126 . _:b413699082 . . _:b413699412 . _:b413699633 . _:b413699415 . _:b413699414 . . _:b413699409 . . _:b413699408 . . _:b6011257 . _:b413699411 . _:b413699410 . _:b413699428 . _:b413699421 . . . _:b413699420 . _:b413699355 . _:b413699423 . . _:b413699422 . _:b413699417 . _:b413699416 . . _:b413699419 . _:b413699418 . _:b413699429 . _:b413699320 . . _:b413699428 . _:b413699431 . . _:b413699430 . _:b413699425 . . . _:b413699653 . _:b413699424 . _:b413699459 . _:b413699427 . _:b413699159 . _:b413699426 . _:b413699321 . _:b413699437 . . _:b413699197 . . _:b413699609 . _:b413699436 . . _:b413699439 . . _:b6011263 "Search spaces, penalty function, and other annealing parameters were as described [27,>>36<<]. The circuit analyzed in detail had an RMS score of 10.76, corresponding to a proportional error in expression residuals of about 4\u20135%. Protocol S1 (Section S1.3) contains further details." . . _:b413699438 . _:b413699433 . _:b413699640 . _:b413699170 . _:b413699289 . _:b413699432 . _:b413699435 . _:b413699313 . . _:b6011175 "In our data \u03C3Bcd = 4.6% egg length (EL), whereas gap gene domain border positions have \u03C3 \u223C 1% EL [>>6<<]. Pair-rule stripe border positions also have similar low variation [6] compared to the Bcd threshold position." . _:b413699434 . . . _:b413699445 . _:b413699444 . _:b6011203 . _:b413699079 "10"^^ . _:b413699447 . _:b413699078 "10"^^ . _:b413699446 . _:b413699077 "10"^^ . _:b413699288 . _:b413699441 . _:b413699679 . . . _:b413699076 "11"^^ . . _:b413699440 . _:b413699065 . . _:b413699075 "11"^^ . _:b413699443 . _:b413699216 . . _:b413699269 . _:b413699074 "11"^^ . . _:b413699442 . _:b413699696 . _:b413699073 "11"^^ . _:b413699453 . _:b413699303 . . _:b413699072 "11"^^ . _:b413699196 . _:b413699452 . _:b413699455 . _:b413699103 . _:b413699086 "9"^^ . . _:b413699454 . . _:b413699087 "9"^^ . _:b413699191 . . _:b413699449 . _:b413699190 . _:b413699084 "9"^^ . . _:b413699448 . _:b413699085 "9"^^ . _:b413699451 . _:b413699199 . _:b413699082 "9"^^ . _:b413699450 . _:b413699083 "9"^^ . _:b413699081 "10"^^ . _:b413699461 . _:b6011255 "The methods used to obtain and characterize the quantitative data are as described in earlier work [>>6<<]. All gene expression levels are on a scale of 0\u2013255, chosen to maximize dynamic range without saturation." . _:b413699080 "10"^^ . _:b413699657 . _:b413699460 . . . _:b413699413 . _:b413699155 . _:b413699463 . _:b413699094 "8"^^ . _:b413699458 . _:b413699462 . _:b413699688 . _:b413699095 "8"^^ . . . . . _:b413699457 . _:b413699092 "9"^^ . . _:b413699093 "8"^^ . _:b413699456 . _:b413699642 . . _:b413699459 . _:b413699090 "9"^^ . _:b413699373 . _:b413699458 . _:b413699091 "9"^^ . _:b413699348 . _:b413699060 . . _:b413699469 . _:b413699088 "9"^^ . _:b413699468 . _:b413699089 "9"^^ . _:b413699471 . _:b413699102 "8"^^ . . . _:b413699470 . _:b413699103 "8"^^ . . _:b413699100 "8"^^ . . _:b413699465 . _:b413699280 . . _:b413699101 "8"^^ . _:b413699464 . _:b6011290 . _:b413699467 . _:b413699098 "8"^^ . _:b413699651 . _:b413699466 . _:b413699099 "8"^^ . _:b413699477 . _:b413699096 "8"^^ . _:b413699476 . _:b413699097 "8"^^ . _:b413699104 . _:b413699110 "7"^^ . _:b413699479 . _:b413699222 . _:b413699111 "7"^^ . _:b413699478 . _:b413699425 . _:b413699473 . _:b413699108 "8"^^ . _:b413699109 "7"^^ . _:b413699472 . _:b413699465 . _:b413699475 . _:b413699106 "8"^^ . _:b413699474 . _:b6011174 "Under the simplest model of specification, expression borders would form at a fixed threshold of its concentration [>>11<<]. The variation of the Bcd gradient can be measured in terms of the range (\u03C1Bcd) or standard deviation (\u03C3Bcd) of the position (x Bcd) where it crosses the threshold concentration. In our data \u03C3Bcd = 4.6% egg length (EL), whereas gap gene" . _:b413699107 "8"^^ . _:b413699424 . _:b413699485 . _:b413699104 "8"^^ . _:b413699293 . _:b413699484 . _:b6011243 . _:b413699105 "8"^^ . _:b413699457 . _:b413699118 "7"^^ . _:b413699487 . . _:b6011207 "and including mutual gap\u2013gap interactions is sufficient to explain the reduction in the variance of gap gene domain border positions, showing that it is not necessary to postulate an undiscovered gradient [12,14,15] or active transport [>>13<<] to explain this property. In the Results section \u201CVariance Reduction by Gap Gene Cross Regulation and Experimental Verification,\u201D we characterize the regulatory interactions underlying variance reduction." . _:b413699119 "7"^^ . _:b413699486 . _:b413699114 . _:b413699116 "7"^^ . _:b413699481 . _:b413699117 "7"^^ . _:b413699480 . _:b6011183 "The assumption that hb is under the sole control of Bcd is incorrect, because its border position changes in embryos mutant for giant (gt) [>>9<<], Kr\u00FCppel (Kr) [20], Kr\u00FCppel;knirps (Kr;kni) [20], and in embryos lacking Nanos [9]." . _:b413699114 "7"^^ . _:b413699483 . . _:b413699440 . _:b413699115 "7"^^ . _:b413699586 . _:b413699482 . _:b413699666 . _:b413699112 "7"^^ . _:b413699493 . _:b6011172 "Nevertheless, the variation in the boundary positions of gap and pair-rule expression domains is much lower than the variation in the maternal gradient of Bicoid (Bcd) protein [>>6<<,9,10]. Under the simplest model of specification, expression borders would form at a fixed threshold of its concentration [11]. The variation of the Bcd gradient can be measured in terms of the range (\u03C1Bcd) or standard deviation (\u03C3Bcd) of" . . _:b413699164 . _:b413699113 "7"^^ . _:b413699492 . _:b413699126 "6"^^ . _:b6011282 . _:b413699495 . . . _:b413699127 "6"^^ . _:b413699494 . . _:b413699124 "7"^^ . . _:b413699489 . _:b413699125 "6"^^ . _:b413699385 . _:b413699488 . . _:b413699122 "7"^^ . _:b413699491 . . _:b413699123 "7"^^ . . _:b413699490 . _:b413699120 "7"^^ . _:b413699501 . . _:b6011197 . _:b413699121 "7"^^ . _:b413699500 . _:b413699134 "6"^^ . _:b413699432 . . _:b413699503 . _:b413699602 . _:b413699135 "6"^^ . _:b6011277 "This is a key point, because the larger standard deviation of x Bcd observed in data from fixed tissue here and elsewhere [>>9<<] appeared to imply that variance reduction still took place in double mutants, albeit at a reduced level." . _:b413699502 . _:b413699132 "6"^^ . . _:b413699497 . . _:b6011293 . _:b413699133 "6"^^ . _:b413699397 . _:b413699496 . _:b413699130 "6"^^ . . _:b413699499 . _:b413699131 "6"^^ . _:b413699498 . _:b413699128 "6"^^ . _:b413699509 . . _:b413699129 "6"^^ . _:b413699508 . _:b413699142 "6"^^ . _:b413699511 . _:b413699143 "6"^^ . . _:b413699510 . _:b413699392 . _:b413699140 "6"^^ . _:b413699505 . _:b413699495 . _:b413699141 "6"^^ . . . _:b413699504 . _:b413699138 "6"^^ . _:b6011288 "In a companion work [>>61<<], we show that robust insensitivity to initial conditions is an inherent mathematical property of the gene circuit equations for this system." . _:b413699151 . _:b413699507 . _:b413699139 "6"^^ . _:b413699144 . _:b413699163 . _:b413699506 . _:b413699074 . _:b413699136 "6"^^ . _:b413699517 . . . _:b413699137 "6"^^ . . _:b413699516 . _:b413699150 "6"^^ . _:b413699519 . _:b413699151 "6"^^ . _:b413699518 . . _:b413699148 "6"^^ . . _:b413699513 . _:b6011266 "The first two classes of models invoke either active transport [13] or a second gradient at the posterior pole of the embryo [12,>>14<<,15] as a mechanism for the reduction in variation of the hb border." . _:b413699149 "6"^^ . . _:b413699512 . _:b413699146 "6"^^ . _:b413699507 . _:b413699693 . _:b413699515 . _:b413699147 "6"^^ . _:b413699129 . _:b413699514 . . . _:b413699144 "6"^^ . . _:b413699525 . . _:b413699145 "6"^^ . _:b413699505 . _:b413699524 . _:b413699527 . _:b413699157 "5"^^ . _:b6011210 . _:b413699526 . _:b413699156 "5"^^ . _:b413699141 . . _:b413699521 . _:b413699159 "5"^^ . _:b413699290 . _:b413699520 . . _:b413699158 "5"^^ . . _:b413699523 . _:b413699153 "5"^^ . . _:b6011196 "Like hb, kni is not regulated by Bcd alone, but also by Caudal (Cad) [22,23], Hb [>>20<<,24], and Gt [25]. The examples of the hb and kni borders show that it is not possible to explain the variance of a single expression border position in isolation." . _:b413699522 . _:b413699080 . _:b413699152 "6"^^ . . _:b413699533 . _:b413699155 "5"^^ . _:b413699532 . _:b413699154 "5"^^ . _:b413699535 . _:b413699165 "5"^^ . . . _:b413699661 . _:b413699534 . _:b413699164 "5"^^ . _:b413699529 . _:b413699167 "5"^^ . _:b413699438 . . _:b413699528 . . _:b413699166 "5"^^ . _:b413699531 . _:b413699161 "5"^^ . _:b413699328 . _:b413699451 . _:b413699530 . _:b413699160 "5"^^ . _:b413699541 . . _:b413699163 "5"^^ . . _:b6011289 . _:b413699540 . _:b413699162 "5"^^ . _:b413699543 . _:b413699173 "5"^^ . _:b413699542 . _:b413699069 . _:b413699172 "5"^^ . . _:b413699537 . _:b413699175 "5"^^ . _:b6011237 "The stationary exponential profile of the Bcd gradient is consistent with the diffusion of the protein from the anterior tip and its degradation by a first-order process, and the gradient has been modeled as such [>>21<<,55,56]. Recently, an alternative model, in which degradation is replaced with the reversible trapping of the Bcd protein by the nuclei in the blastoderm, was proposed [57]. Both the trapping model and the diffusion-degradation model do" . . _:b413699243 . _:b413699536 . _:b413699174 "5"^^ . . . _:b413699539 . _:b413699169 "5"^^ . . _:b413699538 . _:b413699168 "5"^^ . _:b413699215 . . _:b413699549 . _:b413699171 "5"^^ . _:b413699402 . _:b413699548 . _:b413699170 "5"^^ . . _:b413699134 . _:b413699551 . _:b413699181 "5"^^ . _:b413699448 . _:b413699550 . _:b413699180 "5"^^ . . . _:b6011294 . _:b413699545 . . _:b413699183 "5"^^ . . _:b413699544 . _:b413699361 . _:b413699182 "5"^^ . . _:b413699547 . _:b413699177 "5"^^ . _:b6011256 . _:b413699546 . _:b413699176 "5"^^ . _:b413699638 . _:b413699557 . _:b413699179 "5"^^ . _:b413699556 . _:b6011230 "In the posterior terminal region huckebein (hkb) [>>50<<\u201352] has been omitted from the model." . _:b413699178 "5"^^ . _:b413699559 . _:b413699189 "5"^^ . _:b6011279 . _:b413699558 . _:b413699188 "5"^^ . _:b413699553 . _:b413699662 . _:b413699191 "5"^^ . _:b413699598 . _:b6011277 . _:b413699552 . _:b413699190 "5"^^ . . . _:b413699555 . _:b413699185 "5"^^ . _:b413699568 . _:b413699554 . _:b413699184 "5"^^ . _:b413699128 . . _:b413699565 . _:b413699096 . _:b413699187 "5"^^ . _:b413699564 . _:b413699186 "5"^^ . _:b413699567 . . _:b413699197 "5"^^ . _:b413699510 . _:b6011239 . _:b413699566 . _:b6011177 "Of the large number of gene expression borders that have lesser variation than Bcd, the posterior border of the anterior hunchback (hb) domain has received intense scrutiny [>>9<<,12\u201318]. Gregor and colleagues [16] measured the absolute concentration of Bcd in the nuclei at the hb border using a Bcd-GFP fusion rescue construct." . _:b413699196 "5"^^ . . _:b413699561 . _:b413699199 "5"^^ . _:b413699560 . _:b413699198 "5"^^ . _:b413699563 . _:b413699193 "5"^^ . _:b413699186 . _:b413699562 . _:b413699192 "5"^^ . _:b6011290 "These factors alter the profile of the Bcd gradient but have little effect on the border position of downstream targets [9,>>62<<]. We believe that the fixed-tissue Bcd profiles used in the present study capture this extra level of variability characteristic of natural populations." . _:b413699573 . _:b413699195 "5"^^ . _:b413699572 . _:b413699194 "5"^^ . _:b6011176 "Pair-rule stripe border positions also have similar low variation [>>6<<] compared to the Bcd threshold position." . . _:b413699575 . _:b413699205 "4"^^ . _:b413699684 . . _:b413699574 . _:b413699204 "4"^^ . . _:b413699297 . . _:b413699207 "4"^^ . _:b413699569 . _:b413699206 "4"^^ . _:b413699568 . . . _:b413699201 "4"^^ . _:b413699571 . . . _:b413699200 "4"^^ . _:b413699570 . _:b413699334 . _:b413699528 . . _:b413699581 . _:b413699203 "4"^^ . _:b6011178 "Of the large number of gene expression borders that have lesser variation than Bcd, the posterior border of the anterior hunchback (hb) domain has received intense scrutiny [9,>>12<<\u201318]. Gregor and colleagues [16] measured the absolute concentration of Bcd in the nuclei at the hb border using a Bcd-GFP fusion rescue construct." . _:b6011249 . _:b413699202 "4"^^ . _:b413699580 . _:b413699089 . _:b413699352 . . _:b413699583 . _:b413699213 "4"^^ . . _:b413699212 "4"^^ . _:b413699582 . _:b6011252 . _:b413699116 . _:b413699577 . _:b413699436 . _:b413699215 "4"^^ . . _:b413699214 "4"^^ . _:b413699576 . _:b6011242 . _:b413699209 "4"^^ . _:b413699579 . _:b413699208 "4"^^ . _:b413699578 . . _:b413699211 "4"^^ . _:b413699077 . . _:b413699076 . _:b413699210 "4"^^ . . _:b413699079 . _:b413699221 "4"^^ . _:b413699187 . . _:b413699078 . _:b413699220 "4"^^ . . _:b413699073 . _:b413699223 "4"^^ . _:b413699072 . _:b413699222 "4"^^ . _:b413699178 . _:b413699075 . _:b413699217 "4"^^ . . _:b413699148 . . _:b413699624 . _:b413699216 "4"^^ . _:b413699074 . _:b413699671 . _:b413699085 . _:b413699219 "4"^^ . _:b413699488 . _:b413699327 . _:b413699102 . _:b6011233 . _:b413699084 . _:b413699218 "4"^^ . . . _:b413699229 "4"^^ . _:b413699087 . . _:b413699086 . _:b413699228 "4"^^ . . . _:b413699081 . _:b413699231 "4"^^ . . . . _:b413699230 "4"^^ . _:b413699080 . _:b413699083 . _:b413699225 "4"^^ . . _:b413699082 . _:b6011203 . _:b413699224 "4"^^ . _:b413699405 . _:b413699093 . _:b413699227 "4"^^ . _:b6011262 . _:b6011225 . _:b6011270 "This model has been invalidated by the experimental demonstration that intranuclear Bcd concentrations are in fact constant during this period of time [>>44<<]. Furthermore, threshold concentrations of Bcd propagate toward the posterior of the embryo during the establishment of the Bicoid gradient, but gap domains in the posterior, in fact, shift in an anterior direction [35]. A third" . _:b413699092 . _:b413699226 "4"^^ . . _:b413699095 . _:b413699237 "4"^^ .