An enriched network motif family regulates multistep cell fate transitions with restricted reversibility
Cell fate transition , including differentiation , de-differentiation and trans-differentiation , is a fundamental biological process in which the function of a cell gets specialized , reprogrammed or altered ., The process often involves significant changes of multiple cellular properties , including the morphology , the self-renewal capacity and the potentials to commit to alternative lineages 1 , 2 ., These changes are controlled by the dynamics of interacting transcription factors ( TFs ) and the modulation of chromatin structures , which in term are governed by complex regulatory networks in the cells 3–5 ., Interestingly , the fate transitions in many systems are achieved by sequential commitments to a series of cellular states with stepwise changes in their transcriptional profile towards the final stage of the program ( Fig 1 ) 6–11 ., The intermediate states between the initial state ( e . g . the undifferentiated state in the case of cell differentiation ) and the final state may be important for multiple purposes , such as facilitating ‘checkpoints’ that ensure appropriate development of cellular behaviors , or allowing the cells to make correct decisions at the lineage branching points 11–15 ., One example of these stepwise cell lineage transitions is the development of T lymphocytes in the thymus ., The differentiation from multipotent pre-thymic progenitor cells to committed T cells involves multiple cellular states with stepwise changes of their cellular properties and the transcriptional profiles ( Table 1 ) 16–19 ., Several lines of evidence suggest that the transition states at an early phase of the differentiation can serve as stable checkpoints for sequential lineage commitments ., The progress through these intermediate states is accompanied by stepwise loss of their potentials to differentiate into other cell types: pre-thymic progenitor cells can be converted to a few types of cells , including B cells , natural killer ( NK ) cells , dendritic cells ( DCs ) etc . , whereas the multipotency of the intermediate cell types is more limited but not completely lost 20–26 ., In addition , the stability of these intermediate states is substantial because the loss of differentiation signals does not result in de-differentiation of some intermediate states 20 , suggesting restricted reversibility ( or complete irreversibility ) of the multiple transitions ., In addition , the lymphoid progenitor cells need to divide for a certain number of times at an intermediate state before committing to the T cell lineage , and the stable activities of the lineage defining transcriptional program at the intermediate stages may be important for the proliferations 27 ., Finally , the loss of certain transcription factors ( e . g . BCL11B ) can lead to the termination of the differentiation at some intermediate states , which is often associated with diseases such as leukemia 18 , 20 , 28 ., This further suggests that the intermediate states are cellular ‘attractors’ between the initial and the final stages of the differentiation ( Fig 1 , bottom panel ) ., Similar stable intermediate states during cell lineage transitions are observed in other systems , such as the epithelial-mesenchymal transition , and the skin development ( Table 1 ) , and those states also serve as regulatory stages for altering cellular properties including self-renewal and migration 10 , 29–37 ., Therefore , the multiple intermediate states are involved in diverse normal development and pathological conditions ., Understanding the regulatory programs for the sequential cell lineage commitments is a key step towards the elucidation of mechanisms underlying various biological processes involving multistep lineage transitions ., Despite the accumulating data and observations on these stepwise lineage commitments , general mechanisms governing these differentiation processes with multiple intermediate cellular states remain unclear ., In this study , we explored the strategies in terms of the transcriptional network design that gives rise to stepwise transitions during cell differentiation ., We first used a generic form of networks containing three interacting TFs to find network motifs that can produce four attractors ( the minimum number of attractors in the examples of T cell development , epithelial-mesenchymal transition and skin development ) with stepwise changes of transcriptional factor levels ., We found two types of network motifs , both involving interconnections of positive feedback loops , which can generate the four-attractor systems ., These motifs constitute a large family of gene regulatory networks ., We found that there is an enrichment of these motifs in a network controlling the early T cell development ., We built a specific model using known interactions among key transcription factors in developing T cells , and the model shows that the transcriptional network governs multistep and irreversible transitions in the development process ., To investigate the stochastic dynamics for early T cell development , we mapped out the quasi-energy landscape for the early T cell development ., This landscape characterizes the four attractors representing four stages of early T cell development quantitatively ., In addition , by calculating the minimum action paths ( MAPs ) between different attractors , we quantified the dynamics of the key factors in response to Notch signal with fluctuations , which are in good agreement with experimental observations ., Finally , we identified the critical factors influencing T cell development by global sensitivity analysis based on the landscape topography ., Overall , our model for early T cell development elucidates the mechanisms underlying the stepwise loss of multipotency and multiple stable checkpoints at various stages of differentiation ., The network topologies for multiple attractors found in this study and our motif discovery strategy combined with the landscape methodology can be useful for analyzing a wide range of cell differentiation systems with multiple intermediate states ., To find transcriptional network topologies that can generate multiple intermediate states during cell fate transition , we first performed random parameter sampling with a network family containing up to 3 nodes ( Fig 2A ) ., In this framework of network topology , each node represents a transcription factor ( TF ) that can potentially influence the transcription levels of other two TFs and itself ., Topology searching with a 3-node network was used for motif discovery for various performance objectives in previous studies 38 , 39 ., We performed exhaustive search for topologies with up to 6 regulations from a total of 9 regulations of the network family , and constructed a mathematical model for each topology ( see Methods for details ) ., For each model , we performed random sampling in the parameter space from uniformly distributed values ( S1 Table ) ., We selected topologies containing at least one parameter set that is able to generate four attractors with stepwise changes of transcriptional levels ., We define the system with four attractors with the stepwise changes of transcriptional levels as the scenario in which there are four stable steady states and they can be consistently ordered by the concentrations of any pairs of TFs ., In other words , one TF always monotonically increases or decreases with another TF in these four states , and we term these states ‘ordered’ attractors in this paper ., Among the 2114 network topologies that we searched , we found 216 topologies that can produce such behavior ., In addition , we found 417 topologies that can only produce four unordered steady states ( TF concentrations are non-monotonically correlated among the states ) ( S11 Fig , S12 Fig ) ., To visualize the relationships among these topologies , we constructed a complexity atlas ( Fig 2B ) , in which the nodes represent the network structures that gave rise to four attractors , and the edges connect pairs of topologies that differ by a single regulation ( addition or removal of a transcriptional interaction ) 40 ., We define the minimum topologies as those of which the reduction of complexity , or the removal of any regulation from the network , will abolish its capability to generate four attractors ( solid nodes in Fig 2B and examples in Fig 2C ) ., We found 29 such minimum topologies which represent the non-redundant structures for producing the four-attractor system ., Interestingly , all of the 216 topologies obtained from our search contain three distinct positive feedback loops ( including double-negative feedback loops ) , and they can be categorized into two types of motifs ( Fig 2B , bottom panel ) ., The Type I motif contains three positive feedback loops that are closed at a single TF ( red nodes and edges in Fig 2B ) ., The Type II motif contains three connected positive feedback loops , two of which do not share any TF but are connected via the third loop ( blue nodes and edges in Fig 2B ) ., There is a remarkable diversity of each of the motif types because the interconnected positive feedback loops can share multiple TFs ( S1 and S2 Figs ) ., Based on the complexity atlas ( Fig 2B ) , we found that Type II motifs contain 4–6 regulations , and Type I motifs contain 5–6 regulations ., Some of the networks with 6 regulations contain subnetworks of both Type I and Type II motifs ( Hybrid type , green nodes ) ., The four attractors in the space of two TFs exhibit a variety of patterns of nonlinear monotonic correlations ( Fig 2C , S3 Fig ) , which are governed by intersections of highly nonlinear nullclines in the state space containing the two TFs ( Fig 2D , S1 and S2 Figs ) ., The definitions of various types of motifs are listed in Table 2 , and the statistics of the topologies discovered are summarized in Table 3 ( also see S11 Fig for an illustration ) ., Overall , this motif family represents a large number of networks that can produce a common type of behaviors: multiple stable intermediate states in terms the transcriptional activity ., We next asked whether there is a difference between Type I and Type II motifs in terms of their ability to generate systems with four ordered attractors ., We found that with the same number of sampled parameter sets , Type II motifs have greater fractions of parameter sets that give rise to four ordered attractors than Type I motifs do ( Fig 3A and 3B , p-value < 0 . 0001 , Mann-Whitney U test ) ., This suggests that Type II motifs may be more robust for governing the four ordered attractors ., However , among the 15 Type I and 14 Type II minimum motifs , all Type II motifs are able to generate four unordered attractors ( Some TFs are not monotonically correlated . See S12 Fig ) , whereas there is no Type I motif that has any parameter set that gives rise to four unordered attractors ( Fig 3C ) ., This suggests that as compared to Type II motifs , Type I motifs has higher specificity in generating four ordered attractors , which is more relevant to the stepwise cell fate transitions than the unordered ones ., Moreover , we observed that the inter-attractor distances between neighboring attractors in the gene expression space were generally more variable with Type I motifs than those with Type II motifs ( Fig 3D , magenta boxes ) ., In particular , among the three inter-attractor distances for each model , Type I motifs generated smaller minimum distance than Type II motifs did ( Fig 3D , orange boxes . p-value < 0 . 0001 , Mann-Whitney U test ) ., We did not observe any significant difference between Type I and Type II motifs in terms of the stabilities of the attractors and the kinetic paths that they generate ( S13 Fig See Methods for calculation of quasi-energy landscape and kinetic path ) ., In addition to the effects of motif types , we also asked whether the fractions of positive or negative regulations in the network can influence the function of generating four-attractor systems ., We found that the fraction of positive regulations has a weak but significant correlation with the fraction of successful parameter sets generating four-attractor systems ( S14A and S14B Fig ) ., Although negative regulations are slightly less favorable , they might be important to ensure that the levels of some TFs are inversely correlated during multistep cell fate transitions , which is necessary for having at least one highly expressed TFs in each of the initial and the final cell states ( S14C Fig ) ., In summary , we found two types of network motifs that generate four attractors with stepwise changes of the transcriptional profile ., Two of these attractors represent the multiple intermediate states observed in various biological systems ., This exploratory analysis elicits several interesting questions: what are the biological examples of such network motifs ?, Can the conclusions with respect to the two types of motifs be generalized to networks with more than three TFs ?, Is there any advantage of combining both types of motifs ?, How are the transitions among these states triggered deterministically and stochastically ?, To provide insights into these questions in a more biologically meaningful context , we will use a specific biological system to describe more detailed analysis of these motifs and their underlying gene regulatory networks in the following sections ., We asked whether the motifs that we discovered can be found in any known transcriptional network that potentially control multistep cell differentiation ., We used the early T cell differentiation in the thymus as an example to address this question ., The differentiation from multipotent lymphoid progenitor cells to unipotent early T cells involves multiple stages at which the cells have differential potentials to commit to non-T lineages and other cellular properties such as proliferation rates ., At the early phase of this process , four stages of development T cells ( ETP/DN1 , DN2a , DN2b , DN3 ) were identified experimentally , and the progression through these stages is controlled by a myriad of transcription factors including four core factors , TCF-1 , PU . 1 , GATA3 and BCL11B ., These TFs form a complex network among themselves ( see Fig 4A and supporting experimental observations in S3 Table ) , and the stepwise changes in the levels of these TFs were observed in the four developmental stages of T cells 20 , 28 ., The interactions involving these core TFs were shown to be critical for the irreversible commitment to the T cell lineage by forming a bistable switch 41 ., Among these factors , PU . 1 level decreases as the cells commit to later stages , whereas the levels of other three factors increase in this process ., It is unclear , however , whether this transcriptional network can serve as a regulatory unit that governs the multistep nature of the T cell differentiation ., We noticed that this T cell transcriptional network contains the motifs that we found in our analysis using the generic form of networks , we therefore hypothesized that the models based on this network can have four attractors with sequential changes of the four TFs ., Indeed , using random sampling we were able to find parameter sets that give rise to four-attractor systems similar to what we obtained with the generic 3-node framework ., To find the functional components that generate this behavior , we analyzed the subnetworks of the complex T cell regulatory network 42 ., We removed the regulations from the network systematically , and we found that out of the non-redundant 1553 topologies ( 2047 subnetworks ) , there are 568 topologies ( 701 subnetworks ) that can generate four attractors with stepwise changes of the TFs ( Fig 4B ) ., We used a complexity atlas to visualize the relationships among these subnetworks ( Fig 4C ) ., We found that the network can be reduced to one of the 66 minimum topologies ( 97 minimum subnetworks ) which retains the four-attractor property ( solid nodes in Fig 4C ) ., Notably , these networks can be classified into the two types of motifs described earlier ( Fig 2B ) ., Similar to the networks that we obtained through the generic framework , the two types of minimum motif have 4–6 regulations ., Subnetworks with both types of motifs ( green nodes and edges ) start to appear when the number of regulations reaches six ., The numbers of motifs and subnetworks obtained for the generic framework and the T cell model are summarized in Table 3 ., We next quantified the enrichment of the two motif families in the early T cell transcription network ., We first generated random networks by perturbing the existing regulations in the network model and computed the empirical p-values for observing the numbers of different types of network motifs ., The T cell network contains a large number of positive feedback loops and the two types of motifs that we described earlier ( Fig 5 , top panel ) ., As expected , the network is significantly enriched with positive feedback loops in general ( Fig 5 , middle panel , red bars ) ., However , the enrichments of Type I motifs and the combinations of Type I and Type II motifs are even more significant than that of the single positive feedback loops ( Fig 5 , middle panel , red bars ) ., To exclude the possibility that this differential significance was observed due to the way we generate random networks which gives low p-values ( <10−4 ) in general , we used another method to generate random networks with an augmented number of regulations ( Fig 5 , middle panel , blue bars ) ., Each pair of TFs were assigned with a pair of random regulations ( positive , negative or none ) ., Consistent with the previous method , the T cell transcriptional network is enriched with positive feedback loops overall , but the enrichment is more significant for Type I motifs or for the combination of Type I and Type II motifs ., Interestingly , motifs that are similar to Type I motif but have higher complexity ( more positive feedback loops ) do not show more significant enrichment than Type I motif does ( S15 Fig ) ., In addition , we found that networks controlling switch-like behaviors , but not multistep cell fate transitions , are not enriched with Type I or Type II motif 43–46 ., These results suggest the possibility that the network has been evolved to reach more complex performance objectives than those enabled by simple positive feedback loops alone ., Since the minimum motifs alone can generate the four-attractor system , we asked whether the combination of these motifs enhances the ability of the network to produce the system ., We therefore compared a subnetwork containing only one minimum Type I motif with another one containing multiple such motifs in terms of the performance to generate a particular four-attractor system ( Fig 6A See Methods and S1 Text for details ) ., We found that the subnetwork with multiple Type I motifs ( Network, 1 ) outperforms the one with only one motif ( Network, 2 ) in that Network 1 can give a better fit to a hypothetical four-attractor system ( Fig 6A–6C ) ., In this hypothetical ‘target’ system , the four attractors are assumed to be determined by dynamics of PU . 1 with multiple feedback loops ., The assumed degradation ( Fig 6B , gray curve ) and production rate functions of PU . 1 ( Fig 6B , green curve ) are specified ., The curves of these two functions have 7 intersections , four of which represent attractors ., The optimized production function obtained from Network 1 ( Fig 6B , purple curve ) has more robust intersections with the degradation curve than one obtained from Network 2 ( Fig 6B , red curve ) ., This difference was observed for production functions of these two categories from multiple runs of optimization ( Fig 6C ) ., This suggests the advantage of combining multiple motifs with similar functions to enhance its overall performance ., We next compared the 66 minimum motifs ( Fig 4C bottom solid nodes ) and the full topology ( Fig 4C top node ) in terms of the parameter values that gave rise to the four-attractor systems ., We found that the full model contains more parameter sets that have low nonlinearity of the regulations than the minimum motifs do ( S16A Fig ) , and the parameter values are distributed in larger regions with the full model than those with the minimum motifs ( S16B Fig ) ., We next asked whether the topologies that contain both Type I and Type II motifs have greater probabilities to generate the four-attractor system than the topologies with one type of motifs do ., When we explored the parameter space randomly for each topology with a fixed number of samples , a larger number of parameter sets that can generate the four-attractor system were found with the topologies containing both motifs than with those containing either Type I or Type II motifs only ( S5 Fig and Fig 6D ) ., This suggests that the combination of both motifs might be a robust strategy to generate the four-attractor system ., This pattern was observed for all the topologies in the complexity atlas ( S6 Fig ) as well as those with the same degree of complexity ( Fig 6D , networks with 7 regulations were chosen because they have comparable fractions of the three types of motifs ) ., In summary , we found that the core transcriptional network controlling early T cell differentiation are enriched with Type I and Type II network motifs ., The network composed of these two types of motifs governs a dynamical system containing four attractors , corresponding to four known stages in the early T cell development ., The networks with both types of motifs and greater number of such motifs have more robust capability of generating the four-attractor systems than those networks with fewer types of numbers of motifs do ., We next characterized the dynamical features of the four-attractor system of the T cell development model in response to differentiation signals ., For this and subsequent analysis , we focused on a model describing the network topology shown in Fig 4A ( the full model ) ., We first performed bifurcation analysis of the system to the changes of Notch signaling ( Fig 7A ) ., With the increasing Notch signal , the system undergoes three saddle-node bifurcations , at which the stability of the proceeding cellular states is lost ( Fig 7A , black arrows ) ., These bifurcation points therefore represent the cell state transitions from one stage to the next ., The structure of the bifurcation diagram shows a remarkable robust multistep commitment program governed by the T cell transcription network: the commitment to each stage of the program has restricted reversibility in that the attenuation or withdrawal of the Notch signaling does not result in de-differentiation of the developing T cells ( i . e . the return of the transcription profile to earlier stages that may have greater multipotency ) ., It was previously shown that the commitment from DN2a to DN2b is an irreversible process with respect to Notch signaling , and this transition eliminates developing T cells’ potential to be diverted to any other lineages when Notch signaling is abolished 20 , 41 ., However , simple toggle-switch models do not explain the observation that the multipotency of the early T cells is lost in a stepwise manner ., For example , cells at ETP can be differentiated into B cells , macrophages , dendritic cells ( DCs ) , granulocytes , natural killer ( NK ) cells and Innate lymphoid cellsubset2 ( ILC2 ) , whereas the potentials to commit to many of the lineages are blocked even in the absence of Notch signaling at the DN2a stage , at which the cells can only be differentiated into NK cells and ILC2 20 ., Therefore , the stepwise , irreversible transcriptional transitions revealed by our model is consistent with the experimental observations with respect to the loss of multipotency in the stepwise manner ., Although the absence of Notch signal does not allow the reversal of lineage progression , it was previously shown that the absence of BLC11B in lymphoid progenitor cells blocks its ability to progress to DN2b stage , whereas the Cre-controlled knockout of Bcl11b in committed T cells ( e . g . DN3 cells ) reverts its transcriptional profile to DN2a-like cells 28 ., Upon blocking the production of BCL11B in our model , we observed the loss of attractors of DN2b and DN3 , and the DN2a state is the only stable stage even in the presence of the strong Notch signaling ( Fig 7B ) ., As a result , increasing Notch signaling only triggers one saddle-node bifurcation , representing the transition from ETP to DN2a cell ( Fig 7B black arrow ) , whereas the decrease of the BCL11B production triggers the transition back to DN2a instead of ETP ( Fig 7C ) ., These results are in agreement with the previous experimental findings 28 , and they further support the importance of the multistep differentiation system revealed by our model ., The bifurcation analysis shows how the lineage progression is influenced by stably increasing or decreasing Notch signal strengths ., We next asked how the duration of Notch signal may control the multistep lineage transition ., By inducing the differentiation with varying durations of the Notch signaling , we found that cells experiencing transient Notch signals may only commit to intermediate stages of differentiation ( Fig 8A ) ., In addition , the system is able to integrate the information of the signal intensity and duration to make decision on the lineage progression ., These results suggest that the multistep lineage transition can be triggered by the increasing strength of the signal , the increasing duration of the signal , or the combination of both types of signal dynamics ., Earlier experimental studies have shown that transient Notch signaling can irreversibly drive the cells to an intermediate , but committed stage with a definitive T cell identity ( DN2b ) 28 , 41 , 47 ., This is in agreement with our results , and our model further suggests that the commitment to other intermediate states is also irreversible with respect to the lineage progression ( note that this irreversibility does not refer to the establishment of T cell identity ) ., One possible advantage of the multi-stable system is its robustness of response in facing fluctuating signals ., We therefore performed numerical simulations of the dynamical system under increasing Notch signaling with significant fluctuations ., Under this condition , transient reduction of Notch signaling halted the progress of the lineage commitment but did not trigger the de-differentiation ( Fig 8B ) ., Our model suggests that the design of transcriptional network allows the system to stop at intermediate stages before proceeding to the next ones ., This strategy has several potential physiological benefits:, 1 ) it protects the cell lineage progression against sporadic fluctuations of Notch signaling;, 2 ) it facilitates the ‘checkpoints’ before lineage commitment in the middle of the developmental process and, 3 ) it allows the stable storage of differentiation intermediates which can be differentiated into mature T cells rapidly when there is an urgent need of new T cells with a diverse T cell receptor repertoire ., With the deterministic modeling and bifurcation approaches , we described the local stability for multi-stable T cell model ., However , the global stability is less clear from the bifurcation analysis alone ., In addition , it is important to consider the stochastic dynamics for T cell development model because the intracellular noise may play crucial roles in cellular behaviors 48 , 49 ., The Waddington landscape has been proposed as a metaphor to explain the development and differentiation of cells 50 ., Recently , the Waddington epigenetic landscape for the biological networks has been quantified and employed to investigate the stochastic dynamics of stem cell development and cancer 51–57 ., Following a self-consistent approximation approach ( see Methods ) , we calculated the steady state probability distribution and then obtained the energy landscape for the model of the early T cell development ( full model in Fig 4A ) ., For visualization , we selected two TFs ( PU . 1 and TCF-1 ) as the coordinates and projected the 4-dimensional landscape into a two-dimensional space by integrating the other 2 TF variables ( Fig 9A ) ., Here TCF-1 is a representative T cell lineage TF , and PU . 1 is a TF for alternative cell fates ., We also displayed the landscape in a four-dimensional figure , where the three axes represent three TFs ( TCF-1 , BCL11B and PU . 1 ) , and the color represents the energy U ( Fig 9B ) ., Note that our major conclusions do not depend on the specific choice of the coordinate ( see S7 and S8 Figs for landscapes with PU . 1/BCL11B and PU . 1/GATA3 as the coordinates ) ., In the case without Notch signal ( N = 0 ) , four stable cell states emerge on the landscape for the T cell developmental system ( Fig 9 ) ., On the landscape surface , the blue region represents lower potential or higher probability , and the yellow region represents higher potential or lower probability ., The four basins of attraction on the landscape represent four different cell states characterized by different TF expression patterns in the 4-dimensional state space ( Fig 9A and 9B provide two types of projections of the whole 4-dimensional landscape ) ., These states separately correspond to ETP/DN1 ( high PU . 1/low TCF-1/low BCL11B/low GATA3 expression ) , DN3 state ( low PU . 1/high TCF-1/high BCL11B/high GATA3 expression ) , and two intermediate states ( DN2a and DN2b , intermediate expression for the four TFs ) ., The existence of four stable attractors is consistent with experiments 16–19 ., As the Notch signal ( N ) increases , the landscape changes from a quadristable ( four stable states coexist ) , to a tristable ( DN2a , DN2b and DN3 ) , to a bistable ( DN2b and DN3 ) and finally to a monostable DN3 state ( S9 Fig ) ., These results provide a straightforward explanation for the irreversibility observed in experiments for the stepwise T cell lineage commitment ., To check whether our modelling results match experimental data quantitatively , we acquired two sets of gene expression data of the four core TFs for T cell development from previous publications 17 , 47 , and mapped the normalized values ( see Methods ) to the landscape ( Fig 9A and 9B , S7 and S8 Figs ) ., Here , the golden balls represent the four steady states ( characterizing four stages of T cell development ) from the models , the red balls represent the gene expression data points ( Data1 ) from Zhang et al . 47 , and the green balls represent the gene expression data points ( Data2 ) from Mingueneau et al . 17 ., We found that these gene expression data agree well with our landscape models in the sense that each data point is almost positioned in the corresponding basin ( Fig 9A and 9B , S7 and S8 Figs ) ., We found that the landscapes give a better fit to Data2 ( green points ) , since each green data point can be well positioned in one of the four basins , corresponding to four stages of T cell development ., In fact , the two sets of data points are not very close to each other or to the steady states ( golden points ) from the models ., This is reasonable because these two sets of experimental data are measured separately , probably in different conditions , and these data usually delineate the average of multiple measurements from different samples ., Also , the gene expression fluctuations are common in biological systems ., Therefore , our landscape pictures provide a natural way to reconcile the two different experimental data , i . e . the gene expression data do not have to be at the positions of steady states ., Instead , the gene expression data for each individual stage could be somewhere around that basin because of the fluctuations ., This reflects the original spirit of the classic Waddington developmental landscape ., To examine the transitions among individual cell types , we calculated kinetic transition paths by minimizing the transition actions between attractors 
Multistep cell fate transitions with stepwise changes of transcriptional profiles are common to many developmental , regenerative and pathological processes ., The multiple intermediate cell lineage states can serve as differentiation checkpoints or branching points for channeling cells to more than one lineages ., However , mechanisms underlying these transitions remain elusive ., Here , we explored gene regulatory circuits that can generate multiple intermediate cellular states with stepwise modulations of transcription factors ., With unbiased searching in the network topology space , we found a motif family containing a large set of networks can give rise to four attractors with the stepwise regulations of transcription factors , which limit the reversibility of three consecutive steps of the lineage transition ., We found that there is an enrichment of these motifs in a transcriptional network controlling the early T cell development , and a mathematical model based on this network recapitulates multistep transitions in the early T cell lineage commitment ., By calculating the energy landscape and minimum action paths for the T cell model , we quantified the stochastic dynamics of the critical factors in response to the differentiation signal with fluctuations ., These results are in good agreement with experimental observations and they suggest the stable characteristics of the intermediate states in the T cell differentiation ., These dynamical features may help to direct the cells to correct lineages during development ., Our findings provide general design principles for multistep cell linage transitions and new insights into the early T cell development ., The network motifs containing a large family of topologies can be useful for analyzing diverse biological systems with multistep transitions .
The functions of cells are dynamically controlled in many biological processes including development , regeneration and disease progression ., Cell fate transition , or the switch of cellular functions , often involves multiple steps ., The intermediate stages of the transition provide the biological systems with the opportunities to regulate the transitions in a precise manner ., These transitions are controlled by key regulatory genes of which the expression shows stepwise patterns , but how the interactions of these genes can determine the multistep processes was unclear ., Here , we present a comprehensive analysis on the design principles of gene circuits that govern multistep cell fate transition ., We found a large network family with common structural features that can generate systems with the ability to control three consecutive steps of the transition ., We found that this type of networks is enriched in a gene circuit controlling the development of T lymphocyte , a crucial type of immune cells ., We performed mathematical modeling using this gene circuit and we recapitulated the stepwise and irreversible loss of stem cell properties of the developing T lymphocytes ., Our findings can be useful to analyze a wide range of gene regulatory networks controlling multistep cell fate transitions .
blood cells, medicine and health sciences, immune cells, gene regulation, immunology, notch signaling, cell differentiation, developmental biology, mathematics, network analysis, computer and information sciences, white blood cells, transcriptional control, network motifs, animal cells, gene expression, t cells, signal transduction, cell biology, genetics, biology and life sciences, cellular types, physical sciences, topology, cell signaling