The segmentation gene network in early Drosophila embryo provides a powerful model system to study the role of genes in pattern formation ., This network solves the fundamental problem of embryonic patterning: how to establish a periodic pattern of gene expression , which determines both the positions and the identities of body segments 1 , 2 ., The developmental process which performs this task is called segment determination ., The fruit fly segments are arranged sequentially along the anterior-posterior axis of the embryo ., All segments are determined simultaneously during the blastoderm stage , just before the onset of gastrulation 3 ., The segmentation genes have been subdivided into 4 classes based on their mutant phenotype 1 , 2 ., The maternal coordinate genes are expressed from the mother and form broad protein gradients in the anterior , posterior or terminal regions of the embryo 4–7 ., Other genes , which belong to gap , pair-rule and segment-polarity classes , are zygotic , i . e expressed in the embryo ., Most of segmentation genes encode transcription factors , which in turn regulate the expression of many other genes , including segmentation genes themselves ., It was demonstrated by genetic analysis that segmentation genes form a hierarchical regulatory cascade , in which genes in higher layers ( e . g . maternal coordinate genes ) regulate genes in lower layers ( e . g . gap genes ) , but not vice versa ., In addition genes in the same hierarchical level interact with each other ., The gap gene system establishes discrete territories of gene expression based on regulatory input from a long-range protein maternal gradients , Bicoid ( Bcd ) and Hunchback ( Hb ) in the anterior and Caudal ( Cad ) in the posterior of the embryo 8 , 9 ., Gap genes Kr , kni , hb , gt and tll are expressed in from one to three domains , each about 10–20 nuclei wide 10 ., Early gap gene expression of the trunk gap genes Kr , hb , gt and kni is established through feed-forward regulation by maternal gradients , after initial establishment gap domain borders sharpen , moreover both sharpening and maintenance of gap domain boundaries requires gap-gap cross-regulatory interactions 11 ., This process is accompanied by the anterior shift of Kr , kni and gt expression domains in the posterior region of the embryo 10 , 12 , 13 ., Kr plays a central role in segmental pattern formation as indicated by strong alteration of expression patterns of almost all zygotic segmentation genes in mutants 14–16 ., Kr null mutants show deletion of thoracic and anterior abdominal segments as well as frequent mirror duplications in the abdomen 15 , 17 ., At the level of gene expression this mutation manifests in the large shift of posterior Gt domain , resulting in overlap of positions of posterior Gt and Kni domains 15 , 18 ., During sharpening and maintenance stage of gap gene expression Kr acts a repressor of gt and hb 15 , 19 , 20 ., The repression of gt , which expression domains are strictly complementary to those of Kr , is strong , while the effect of Kr on hb is more subtle 21–24 ., It was observed in assays with cell lines carrying reporter constructs that the regulatory effect of Kr is concentration-dependent: Kr monomer is transcriptional activator , while at high concentrations Kr forms a homodimer and becomes a repressor that function through the same target sequence as the activator ., However it is difficult to establish whether such an effect occurs at physiologically relevant regulators concentrations 25 ., The segmentation gene network is one of the few examples of developmental networks studied using data-driven mathematical modeling 13 , 26–28 ., These models fall into two categories ., The phenomenological models do not require any a priory information about regulatory mechanism 29 , 30 and try to reconstruct it by solving the inverse problem of mathematical modelling ., A major shortcoming of these models is that their parameters have no explicit connection to the genomic DNA sequence ., The second modelling approach seeks to extract information about gene regulation from the sequences of cis-regulatory regions and the measured or inferred binding of sequence-specific transcription factors to these elements 26–28 , however it still neglects major features of the transcription process , such as chromatin structure and modifications , binding site orientation and proximity to transcription start site , etc ., Current simplifications and unknown features limit the predictive power of these models , but more powerful and complex models may be generated in future using better datasets such as in vivo transcription factors occupancy , relative accessibility of different DNA regions , in vivo data on interplay between different transcription factors , nucleosome and chromatin remodelling enzymes ., In this paper we apply a phenomenological model known as gene circuits to reconstruct the gap gene network in Kr null mutants ., This model considers a row of nuclei along the A-P axis of the embryo ., Between nuclear divisions the model describes three basic processes , namely protein synthesis , protein decay and diffusion of proteins between neighboring nuclei of syncitial blastoderm ., A few basic assumptions about eukaryotic transcriptional regulation were incorporated into the model ., First a sigmoid regulation-expression function was used to introduce regulatory inputs into the model ., Secondly , each regulatory interaction can be represented by a single parameter which sign indicates the type of regulatory interaction: activation ( if it is positive ) , repression ( if negative ) , no interaction ( if it is close to zero ) ., Third it was assumed that regulatory inputs are additive and independent of each other ., The gene circuit models were successfully applied to correctly reproduce the quantitative features of gap gene expression in wild type 12 , 13 ., This study revealed five regulatory mechanisms responsible for sharpening and maintenance of gap gene expression domains: broad activation by maternal gradients of Bcd and Cad; gap gene auto-activation; strong mutual repression between gap genes which show complementary expression patterns ( hb and kni; Kr and gt ) ; weaker asymmetric repression between overlapping gap genes ( Hb on gt , Gt on kni , Kni on Kr , Kr on hb and Hb on Kr ) and repression by terminal gene tll at the embryo termini ., The asymmetric repression between overlapping gap genes is responsible for shifts of gap gene domains in the posterior region of the embryo ., It is important to note that the wild type gap gene circuit model has the predictive power when molecular fluctuations of the input factors are taken into account 31 , 32 ., It is evident that to understand the gap gene network we need not only to describe the mechanism underlying its functioning in intact state , but also to comprehend what happens when certain stimuli or disruptions occur ., Recently Papatsenko and Levine ( 2011 ) constructed a dynamic model based on a modular design for the gap gene network , which involves two relatively independent network domains with elements of fractional site occupancy ., This model requires only 5–7 parameters to fit quantitative spatial expression data for gap gradients in wild type and explained many expression patterns in segmentation gene mutants obtained in studies published mainly in the late 1980s and early 1990s ., However these patterns were characterized qualitatively by visual inspection , that may not capture the fine details of gene expression ., For example , previous studies based on qualitative visual analysis of gene expression patterns showed that a Kr null mutation results in large shift of posterior Gt domain , overlap of positions of posterior Gt and Kni domains and decrease in the level of gt expression in the second half of cycle 14A 15 ., Here we obtained a large dataset on gap gene expression in Kr null mutants and extracted quantitative gene expression data using a data pipeline established previously 33 ., The analysis of this data allowed us to characterize the expression of other gap genes at unprecedented level of detail ., In particular we showed that the significant decrease in the level of gene expression in the second half of cycle 14A is common to all gap gene expression domains ., This novel biological result seems counterintuitive , because genetics studies show that Kr acts as a repressor , and therefore should come under close scrutiny ., The most serious limitation of the gap gene circuit models is their inability to correctly reproduce the expression patterns in trunk gap gene null mutants at quantitative level , although a theoretical study had shown previously that such prediction is possible if gene circuits models were fit to simulated , noise-free data 29 and simulating null mutants of the terminal gap genes tll and hkb was successful 12 , 13 , 34 ., A variety of reasons could be responsible for the failure , of which , from our point of view , the most important is the oversimplified representation of transcriptional regulation in the model ., Indeed , as was already mentioned above , the action of regulator on its target gene is represented by a single parameter , whereas it is well known that the cis-regulatory elements ( CRE ) of segmentation genes often reproduce only one of expression domains of an endogenous gene when placed upstream of a reporter gene 35–37 ., Moreover different CREs of one gene can have different transcription binding site composition , i . e . different regulatory inputs ., For example , computational prediction of transcription factor binding sites showed that regulatory sequences which drive expression of gt in the anterior and posterior domains have different transcription binding site composition: the anterior gt domain has regulatory inputs from Bcd and Kni , while the posterior domain contains inputs from Hb and Cad , which are absent in the sequences responsible for anterior expression 37 ., Similar to gt , two CREs essential for hb expression in anterior domain and in central stripe and posterior domain differ in transcription binding site composition 38–40 ., It is evident that current gene circuits models do not consider the mechanism of gene regulation at such a level of detail ., This defect does not interfere with the ability of these models to fit gap gene expression patterns in wild type , however in mutant background with deficient set of regulators the failure of the model to take into account such features may suddenly become essential ., To avoid such problems we use a revised model which builds on separate treatment of domains with different regulatory inputs ., This is possible by narrowing down the spatial domain of the model and considering only the posterior half of the blastoderm ( region from 47 to 92% embryo length ( EL ) ) , in which each of the trunk gap genes is expressed in one domain ., As opposed to previous gap gene circuit models , which have a constant Bcd gradient and did not consider Cad data from late time points just before the onset of gastrulation 12 , 32 , and similar to approach used in 30 , we implement Bcd as a time-variable input and use data on late Cad expression to represent the rapidly changing expression dynamics of these two genes ., After cleavage cycle 12 Bcd nuclear gradient starts to decay 41 ., Analysis of data from fixed embryos showed that Bcd protein reached its maximal level near the beginning of cycle 14A and thereafter starts to decrease slowly that culminates in an almost twofold decline by gastrulation 10 ., From the second quarter of cleavage cycle 14A onward the cad expression in abdominal region start to gradually decrease and by gastrulation cad expression in the posterior region sharpens to a stripe which spans from 75 to 90% EL 10 ., The gene circuit models do not require any assumption about regulatory interactions within a gene network ., Instead the regulatory topology of the network is obtained by solving the inverse problem of mathematical modeling , i . e . by fitting the model to the data 29 ., To obtain the estimates for regulatory parameters that predict a specific network topology in mutants we fitted the model to gap gene expression patterns in wild type and in embryos with homozygous null mutation in Kr gene simultaneously ., The logical justification of such an approach is to use the parameters of the wild type gap gene network as specific constraints on regulatory weights in mutants in order to obtain the consistent parameter estimates for both genotypes on one hand and on the other hand to preserve the characteristic features of gene regulation in mutant ., The parameter estimates obtained in such a way were further studied by applying identifiability analysis , that confirmed that fitting to two genotypes simultaneously substantially increases the statistical significance of parameter values ., We use the modeling framework outlined above to explain the characteristic features of gap gene expression in Kr null mutants and in the posterior half of the blastoderm ., In what follows we describe the expression patterns of gap genes in Kr null mutants and analyze quantitative gene expression data extracted from these patterns ., We then use these data as input to a new gap gene circuit model ., We show that in contrast to earlier models , this model correctly reproduces the characteristic features of gap gene expression in Kr mutants ., In particular , it reproduces correctly the greater shift of posterior Gt domain than in wild type and significant decrease in the level of gap gene expression in the second half of cycle 14A ., We next obtain the parameter estimates for the model ( and hence the predicted gap gene network topology in wild type and mutant ) and perform identifiability analysis to understand how reliable are these estimates ., We study the dynamical behavior of our model and analyze the role of individual regulatory loops in gap gene expression in wild type and mutants ., We show that a remarkable transformation of gap gene expression patterns in Kr mutants can be explained by dynamic decrease of activating effect of Cad on a target gene and exclusion of Kr gene from the complex network of gap gene interactions , that makes it possible for other interactions , in particular , between hb and gt , to come into effect ., Our model also predicts the derepression of the anterior border of Hb posterior domain in Kr;kni double mutants , that is established in the absence of key repressors ., We validate this prediction and show the correctness of network topology inferred in this work ., In wild type Drosophila embryos gap genes are expressed as large intersecting domains along the A-P axis ( Figure 1A ) ., In general , all these domains exhibit similar temporal dynamics: after formation they start to grow , reach maximum expression levels around mid-cycle 14A and decline by gastrulation ., In the course of cycle 14A gap gene domains change their positions and shift to the anterior 10 ., We have shown that the asymmetric gap-gap cross-repression with the posterior dominance is responsible for these shifts 12 ., In Kr null mutants gap gene expression is significantly altered ( Figure 1B ) ., It has been previously reported that in these mutants the posterior domain of gt is expanded towards the center of the embryo 42 , 43 ., We detect that in the course of cycle 14A the posterior domain of gt shifts dynamically on 15% embryo length ( EL ) in the anterior direction and overlaps with Kni domain ., Thus , by gastrulation , the difference in position of gt domain in mutants and wild type embryos constitutes approximately 10% EL ., The anterior shift of the Kni domain maxima in Kr mutants constitutes only 1 . 8% EL ., Hb posterior domain in mutants is formed at the beginning of cycle 14A and shifts on about 3% EL in the anterior direction during this cycle ., Thus , the positional dynamics of this domain in mutants and wild type is similar ., The level of hb posterior expression in mutants is nearly the same as in wild type until time class 3 , but declines afterwards ., By gastrulation it constitutes only a half of the wild type expression level ( Figure 1C , F ) ., Gt posterior domain is initially lower than in wild type , it grows up to time class 4 and significantly declines thereafter ( Figure 1D , G ) ., The level of kni expression remains constantly low throughout cycle 14A ( Figure 1E , H ) with a slight decrease at the very end of this cycle ( not shown ) ., The features of the gap gene expression in Kr mutants described above raise many questions ., Namely , the regulatory mechanisms underlying a decrease in gene expression levels , as well as a much larger shift of Gt posterior domain should be explained ., In the following sections , we describe our modification of the gene circuit model 12 , 13 , 29 , 44 that correctly reproduces the gap gene expression in Kr mutants and hence can serve as a tool to answer these questions ., The gene circuit model used in this work differs from previous implementations in several aspects ., First we narrowed down the spatial domain of the model by considering only the posterior half of the blastoderm ( region from 47 to 92% embryo length ( EL ) ) , in which each of the trunk gap genes is expressed in one domain ., This allows us to avoid the inherent limitation of the model , in which the action of regulator on its target gene is represented by a single parameter ., Secondly , as opposed to previous gap gene circuit models which have a constant Bcd gradient and did not consider Cad data from late time points just before the onset of gastrulation 12 , 32 , we implement Bcd as a time-variable input and use data on late Cad expression to represent the rapidly changing expression dynamics of these two genes at that stage ., We used bcd and cad profiles from FlyEx database for cycle 13 and eight temporal classes of cycle 14A as external inputs to our model equations ., We used the modeling framework outlined above to explain the characteristic features of gap gene expression in Kr null mutants and in the posterior half of the blastoderm ., To obtain the estimates for regulatory parameters that predict a specific network topology in mutants the model was fitted to gap gene expression patterns in wild type and in embryos with homozygous null mutation in Kr gene simultaneously ., DEEP method was applied to minimize the sum of squared differences between experimental observations and model patterns 45 , 46 and find all parameters of model equations , i . e . regulatory weights , synthesis rates , decay and diffusion constants , that allow to reproduce the characteristic features of gap gene expression in Kr null mutants as closely as possible ., We performed over 200 runs with different initial parameter approximations and control variables ., The search space was sampled uniformly for each parameter in the interval defined by biologically relevant limits ., Two step procedure was applied to construct the ensemble of parameter sets ., On the first stage , the residual mean square ( RMS ) was checked and the sets with RMS less than 5% of the maximal gene expression value ( equals 255 in our data ) were accepted for further analysis ., Secondly , we inspected the model expression patterns visually ., Consequently , the ensemble of 11 parameter sets was obtained that correctly reproduces the dynamics of gene expression in wild type and mutant embryos , in particular the decrease of gap gene expression levels and the anterior shift of gt domain ., To infer the topology of regulatory network we classified the estimates of regulatory weights ( the elements of T and E matrices ) into the following three categories: ‘activation’ ( parameter values greater than 0 . 005 ) , ‘repression’ ( parameter values less than −0 . 005 ) and ‘no interaction’ ( between −0 . 005 and 0 . 005 ) ., This leads to a predicted regulatory topology of the network based on which category a majority of parameter estimates falls into ( summarized in Figure 2 ) ., There are several networks in the ensemble called consensus networks , in which the signs of regulatory parameters coincide with the predicted network topology inferred from the fits ., Figure 2A shows simulation results together with experimental data and Table S1 presents parameters for one of such networks ., It is evident that in spite of some patterning defects especially at early stages the model correctly reproduces the dynamics of gene expression in wild type and mutant embryos ., Some basic features of the gap gene network topology in wild type and mutant become immediately obvious from inspection of Figure 2B and Table S1 ., First , Cad activates zygotic gap gene expression ., Second , hb , Kr , kni , and gt show autoactivation ., Third , Bcd activates Kr , gt , kni in all parameter sets , however in case of hb it shows activation in approximately the same number of circuits as it shows repression ., Fourth , all reciprocal interactions among trunk gap genes are either zero or repressive ., An important exception is activation of hb by Gt ., Finally tll represses kni and Kr and weakly activates gt ., The identifiability analysis was conducted with respect to parameters of the model estimated by fitting to experimental data ., The model considers the time evolution of protein concentrations of four gap genes hb , Kr , gt , and kni in two genotypes: wild type and in embryos with homozygous null mutation in Kr gene ., The total parameter set that minimizes the cost functional 0 consists of 40 parameters and is denoted as ., The set includes four subsets , , , and of 10 parameters each , that describe regulatory action on each target gene ., In mutants the model is only fitted to quantitative gene expression data for 3 genes , gt , hb and kni , and hence the parameters from are estimated using data points from wild type embryos only ( half of all data points ) ., All the other parameter subsets are estimated from the whole dataset ., Due to lack of space we denote the elements of inter-connectivity matrices T and E by single-letter notations of genes , namely , H , K , G , N , B , C , and T stand for gt , Kr , gt , kni , bcd , cad , and tll , respectively ., For example , characterizes the regulatory action of Hb on kni ., The sensitivity of the model solution to parameter changes is characterized by the size of confidence intervals ., The confidence intervals ( 2 ) ( see Methods ) are constructed under the assumption of normally distributed error in data , that is not satisfied for gene expression data ., The error in data almost linearly increases with the mean concentration that is typical rather for the Poisson than for normal distribution ., To make the error independent of the mean we applied the variance-stabilizing transform to both data and model solution ., The transformed objective functional was minimized using the parameter estimates obtained for non-transformed functional as initial values for the optimization procedure ., The new solutions were found in a very close vicinity of initial parameter sets ., The 11 parameter sets , which minimize the transformed model functional , are given in Table S2 and will be referred to as circuit parameter sets ., The newly estimated regulatory weights were classified into regulatory categories as described in subsection Gene Network Topology ., This classification results in predicted regulatory topology of the network ( Figure 2C ) , which is largely the same as in Figure 2B , however not all the entries in two tables coincide ., The estimates of some parameters not-uniquely determine the type of gene regulation in different circuits , i . e . in some circuits the parameter estimates exceed the threshold 0 . 005 in absolute value , while in the others are below the threshold ., It is also true for new parameter sets , however , the number of such circuits is different than those given in Figure 2B ., The confidence intervals for individual parameters are constructed in the vicinity of the model solution ., The results for one representative circuit are presented in Figure 3 ., Most of the values of regulatory parameters are very close to zero , and it is important to make sure whether the value ( more precisely , the sign ) of a regulatory parameter is significant ., The hypothesis that the parameter estimate is non-zero is tested as follows: if a confidence interval includes both positive and negative values , the hypothesis is rejected , otherwise , accepted ., Our classification method to infer the topology of regulatory network used in this work , was based on comparison of the values of regulatory parameters with the threshold ., However , as it has already been mentioned , estimates of some parameters take values , which only exceed the threshold in part of circuits ., By exploration of confidence intervals for these parameters we came to the conclusion , that almost all the estimates , that are close in absolute value to the threshold , are insignificant ., This result explains the discrepancies between the network topologies presented in Figures 2B and 2C: the conclusions about the type of gene interaction that are based on insignificant parameter estimates are unreliable ., The analysis of confidence intervals conducted for all the circuits ( Figures S2 and S3 ) allowed us to refine the predicted regulatory network topology ( Figure 2C ) ., We classify parameters as insignificant activation/repression if the parameter estimates are positive/negative in almost all the circuits but their confidence intervals contain zero , and hence the parameter sign cannot be identified ., As a result the non-identifiable regulatory parameters are , , , , , , and and therefore we cannot draw any conclusion about these interactions ., Interestingly most of these interactions involve Kr as a target gene or Bcd as a regulator of gap gene domains located in the posterior of the embryo ., Other regulatory parameters are well identifiable and , hence , the identifiability analysis corroborates the gene network topology drawn from classifying parameter values only ., It should be stressed that the confidence intervals provide the full information about the parameter estimates only in case of parameter independency , otherwise the intervals are overestimated ., Moreover , strong correlation between parameters may lead to their non-identifiability , because a change in one parameter value can be compensated by the appropriate changes of another parameters and , hence , does not significantly influence the solution ., In view of this we investigate the dependencies between parameters using the collinearity analysis of the sensitivity matrix ., This method allows to reveal correlated and hence non-identifiable subsets of parameters ., The sensitivity matrix defined in Methods was analyzed in the vicinity of 11 points in the parameter space that define the optimal model solutions ., The collinearity index ( equation ( 3 ) in Methods ) was computed for all the subsets of dimension k of the parameter set ., The threshold value for was chosen equal to 7 ., This value in case of corresponded to approximately 99% pairwise Pearson correlation between columns of the sensitivity matrix ., The method allowed to detect subsets of dimension 2 and 3 with the collinearity index exceeding the threshold value , i . e . subsets of poorly or non-identifiable parameters ., Most of parameter combinations in these subsets were the same for all 11 circuits ( see Table 1 ) ., Almost all the pairs of parameters in subsets of dimension 2 belonged to , i . e . were related to Kr target gene ., To explain this result we additionally compute the collinearity indices between columns of the upper half of the sensitivity matrix , that only include the partial derivatives computed at 1532 wildtype observations ., The method detected much more parameter subsets with collinearity indices greater than the threshold , that included the parameters characterizing the input of all four genes ., The parameters of the full model fitted to two genotypes thus are better identifiable than those of the model that solely describes the wild type data ., However , the parameters from cannot be identified from the full model as are just estimated from the wild type observations ., The subsets of dimension 3 with the highest collinearity indices ( ) are also common for the most of the circuits ., Most of these combinations are related to gt and Kr , i . e . , include parameters from and ., The two approaches applied to characterize parameter identifiability are closely connected and complement each other ., By exploration of confidence intervals we can see to what extent the model solution is sensitive to parameter changes and test the significance of parameter sign , but this method does not give any explanations to the sources of non-identifiabilities ., One of such explanations can be provided by collinearity analysis ., The correlation between parameters revealed by this approach can clarify insignificance or unreliability of parameter estimates with large confidence intervals ., For example , we derive non-identifiability of from the large size of its confidence interval and at the same time the analysis of the sensitivity matrix allows us to detect the subset of parameters and with high mean collinearity index equal to 7 . 76 ( see Table 1 ) ., Thus , poor identifiability of can be explained by correlation between two regulatory parameters , that is reflected in their high collinearity index ., The gene network topology inferred from both classifying the parameter values and parameter identifiability analysis is presented in Figure 2C ., As Figure S4 shows it is largely in agreement with topologies predicted by earlier models 13 , 31 , 34 , 47 ., Strong constraints for mutual repression are present for kni and hb , which show complementary expression patterns ., Besides , strong repressive action exert both Kr on hb and Hb on gt ., Some previous models had predicted the repressive action of Kr on hb 31 , while most showed no interaction 13 , 34 , 47 ., Many repressive interactions between gap genes show weaker constraints toward repression , and interestingly we have found very weak or no dynamical constraints for repression of Gt on Kr , the interaction with strong constraint for repression in all wild type gene circuit models 13 , 31 , 34 , 47 , 48 ., In addition our model predicts weak repressive interactions between Kni and gt and Kr and kni ., In earlier gap gene circuit models the first interaction was predicted as no interaction 13 , activation 34 or activation in about half the circuits , and repression in the other half 31 ., The repressive action of Kr on kni is only observed in our model , all other models predicted no interaction between the two genes ., In addition in current model Bcd shows activation of hb in approximately the same number of circuits as it shows repression , while in all previous models this interaction was predicted as activation ., Weak activation of gt by Tll is now present in 10 parameter sets , while previous results predicted this interaction as repression ., Finally our model predicts no interaction between Tll and hb ., Some previous models had classified this interaction as activation 31 , 34 , while other predicted it as repression or no interaction 13 , 48 , 49 ., Null mutation in Kr gene results in strong alteration of expression patterns of almost all zygotic segmentation genes ., In gap gene network this mutation manifests in significant reduction of gap gene expression levels in cycle 14A , as well as in large shift of posterior Gt domain and overlap of positions of posterior Gt and Kni domains ., Previous gap gene circuit models fail to correctly model the gap gene expression patterns in the embryos homozygous for null mutation in a trunk gap gene ., A new model introduced here correctly reproduces 
The segmentation gene network in Drosophila embryo solves the fundamental problem of embryonic patterning: how to establish a periodic pattern of gene expression , which determines both the positions and the identities of body segments ., The gap gene network constitutes the first zygotic regulatory tier in this process ., Here we have applied the systems-level approach to investigate the regulatory effect of gap gene Kruppel ( Kr ) on segmentation gene expression ., We acquired a large dataset on the expression of gap genes in Kr null mutants and demonstrated that the expression levels of these genes are significantly reduced in the second half of cycle 14A ., To explain this novel biological result we applied the gene circuit method which extracts regulatory information from spatial gene expression data ., Previous attempts to use this formalism to correctly and quantitatively reproduce gap gene expression in mutants for a trunk gap gene failed , therefore here we constructed a revised model and showed that it correctly reproduces the expression patterns of gap genes in Kr null mutants ., We found that the remarkable alteration of gap gene expression patterns in Kr mutants can be explained by the dynamic decrease of activating effect of Cad on a target gene and exclusion of Kr gene from the complex network of gap gene interactions , that makes it possible for other interactions , in particular , between hb and gt , to come into effect ., The successful modeling of the quantitative aspects of gap gene expression in mutant for the trunk gap gene Kr is a significant achievement of this work ., This result also clearly indicates that the oversimplified representation of transcriptional regulation in the previous models is one of the reasons for unsuccessful attempts of mutant simulations .
Systems biology is aimed to develop an understanding of biological function or process as a system of interacting components ., Here we apply the systems-level approach to understand how the blueprints for segments in the fruit fly Drosophila embryo arise ., We obtain gene expression data and use the gene circuits method which allow us to reconstruct the segment determination process in the computer ., To understand the system we need not only to describe it in detail , but also to comprehend what happens when certain stimuli or disruptions occur ., Previous attempts to model segmentation gene expression patterns in a mutant for a trunk gap gene were unsuccessful ., Here we describe the extension of the model that allows us to solve this problem in the context of Kruppel ( Kr ) gene ., We show that remarkable alteration of gap gene expression patterns in Kr mutants can be explained by dynamic decrease of the activating effect of Cad on a target gene and exclusion of Kr from the complex network of gap gene interactions , that makes it possible for other interactions , in particular between hb and gt , to come into effect .
systems biology, developmental biology, gene regulation, gene expression, regulatory networks, molecular genetics, biology, computational biology, genetics, gene networks, pattern formation, genetics and genomics