Noise Decomposition Principle in a Coherent Feed-Forward Transcriptional Regulatory Loop

Feedforward regulatory logic controls the specification-to-differentiation transition and terminal cell fate during Caenorhabditis elegans endoderm development

The architecture of gene regulatory networks determines the specificity and fidelity of developmental outcomes. We report that the core regulatory circuitry for endoderm development in Caenorhabditis elegans operates through a transcriptional cascade consisting of six sequentially expressed GATA-type factors that act in a recursive series of interlocked feedforward modules. This structure results in sequential redundancy, in which removal of a single factor or multiple alternate factors in the cascade leads to a mild or no effect on gut development, whereas elimination of any two sequential factors invariably causes a strong phenotype. The phenotypic strength is successfully predicted with a computational model based on the timing and levels of transcriptional states. We found that one factor in the middle of the cascade, END-1, which straddles the distinct events of specification and differentiation, functions in both processes. Finally, we reveal roles for key GATA factors in establishing spatial regulatory state domains by repressing other fates, thereby defining boundaries in the digestive tract. Our findings provide a paradigm that could account for the genetic redundancy observed in many developmental regulatory systems.

Systematic analysis of noise reduction properties of coupled and isolated feed-forward loops

Cells can maintain their homeostasis in a noisy environment since their signaling pathways can filter out noise somehow. Several network motifs have been proposed for biological noise filtering and, among these, feed-forward loops have received special attention. Specific feed-forward loops show noise reducing capabilities, but we notice that this feature comes together with a reduced signal transducing performance. In posttranslational signaling pathways feed-forward loops do not function in isolation, rather they are coupled with other motifs to serve a more complex function. Feed-forward loops are often coupled to other feed-forward loops, which could affect their noise-reducing capabilities. Here we systematically study all feed-forward loop motifs and all their pairwise coupled systems with activation-inactivation kinetics to identify which networks are capable of good noise reduction, while keeping their signal transducing performance. Our analysis shows that coupled feed-forward loops can provide better noise reduction and, at the same time, can increase the signal transduction of the system. The coupling of two coherent 1 or one coherent 1 and one incoherent 4 feed-forward loops can give the best performance in both of these measures.

Cellular behavior can be affected by noise in molecular interactions. Signaling pathways should process noisy input signals and support cellular decision making by properly transducing the signals, while removing noise from them. Three component networks of feed-forward loops (FFLs) have been proposed to serve as ideal noise reducers, while linear pathways were shown to be good signal transducers. These signaling units do not work in isolation, so there is a possibility that a combination of various feed-forward loops can provide good noise reduction, while maintaining good signal transduction. To test this hypothesis, we have systematically tested the noise reducing and signal transducing capabilities of all possible combinations of feed-forward loops and compared them with the performance of individual FFLs. We built mathematical models of all these systems and compared their capabilities at reducing noise in the input signal while maintaining responses to meaningful changes in the incoming signal. We found that a combination of two copies of a special type of fully positive signaling FFLs is the best noise reducer, while a combination of two incoherent (one positive, one negative signal) FFLs can provide the best signal transduction. The combination of these two FFLs could provide good signal processing where both noise reduction and signal transduction are achieved.

Role of integrated noise in pathway-specific signal propagation in feed-forward loops

Cells impose optimal noise control mechanism in diverse situations to cope with distinct environmental cues. Sometimes, it is desirable for the cell to utilize fluctuations for noise-driven processes. In other cases, noise can be harmful to the cell to show optimal fitness. It is, therefore, important to unravel the noise propagation mechanism inside the cell. Such noise controlling mechanism is accomplished by using gene transcription regulatory networks. One such gene regulatory network is feed-forward loop, having three regulatory nodes S, X and Y. Here, we consider the most abundant type 1 of coherent and incoherent feed-forward loops with both OR and AND logic functions, forming four different architectures. In OR logic function, the functions representing S and X act additively for the regulation of Y, while in AND logic function, the same functions (S and X) act multiplicatively for the regulation of Y. Measurement of susceptibility of the signal at output Y is done using elasticity of each regulation in FFLs. Using susceptibility, we demonstrate the nature of pathway integration by which one-step and two-step pathways get overlapped. The integration type is competitive for motifs having OR gate, while it is noncompetitive for the same with AND gate. The pathway integration property explains the output noise behavior of the motifs properly but cannot infer about the mechanism by which the upstream noise propagates to output. To account this, the total output noise is decomposed, which results in integrated noise as an additional noise source along with pathway-specific noise components. The integrated noise is found to appear as a consequence of integration between the pathways and has different functional characteristics explaining noise amplification and noise attenuation property of coherent and incoherent feed-forward loops, respectively. The noise decomposition also quantifies the contribution of different noise sources toward total noise. Finally, the noise propagation is being tuned as a function of input signal noise and its time scale of fluctuations, which shows considerable intrinsic noise strength and relatively slow relaxation time scale causes a higher degree of noise propagation in FFLs.

Noisy signal propagation and amplification in phenotypic transition cascade of colonic cells

Like genes and proteins, cells can use biochemical networks to sense and process information. The differentiation of the cell state in colonic crypts forms a typical unidirectional phenotypic transitional cascade, in which stem cells differentiate into the transit-amplifying cells (TACs), and TACs continue to differentiate into fully differentiated cells. In order to quantitatively describe the relationship between the noise of each compartment and the amplification of signals, the gain factor is introduced, and the gain-fluctuation relation is obtained by using the linear noise approximation of the master equation. Through the simulation of these theoretical formulas, the characters of noise propagation and amplification are studied. It is found that the transmitted noise is an important part of the total noise in each downstream cell. Therefore, a small number of downstream cells can only cause its small inherent noise, but the total noise may be very large due to the transmitted noise. The influence of the transmitted noise may be the indirect cause of colon cancer. In addition, the total noise of the downstream cells always has a minimum value. As long as a reasonable value of the gain factor is selected, the number of cells in colonic crypts will be controlled within the normal range. This may be a good method to intervene the uncontrollable growth of tumor cells and effectively control the deterioration of colon cancer.

Stochastic Dynamics of Gene Switching and Energy Dissipation for Gene Expression

Stochastic dynamics of gene switching and energy dissipation for gene expression are largely unknown, mainly due to the complexity of non-equilibrium mechanisms. Here, based on an important double-deck loop model, the stochastic mechanisms of gene switching and energy dissipation are studied. First, the probability distributions of steady states are calculated theoretically. It is found that the signal can strengthen the choice of gene switching between the "off" and "on" states. Our analysis of energy consumption illustrates that, compared with the synthesis and degradation of proteins, the process of gene switching costs little energy. Our theoretical analysis reveals some interesting insights into the determination of cell state and energy dissipation for gene expression.

Identifying functions and prognostic biomarkers of network motifs marked by diverse chromatin states in human cell lines

Epigenetic modifications play critical roles in modulating gene expression, yet their roles in regulatory networks in human cell lines remain poorly characterized. We integrated multiomics data to construct directed regulatory networks with nodes and edges labeled with chromatin states in human cell lines. We observed extensive association of diverse chromatin states and network motifs. The gene expression analysis showed that diverse chromatin states of coherent type-1 feedforward loop (C1-FFL) and incoherent type-1 feedforward loops (I1-FFL) contributed to the dynamic expression patterns of targets. Notably, diverse chromatin state compositions could help C1- or I1-FFL to control a large number of distinct biological functions in human cell lines, such as four different types of chromatin state compositions cooperating with K562-associated C1-FFLs controlling “regulation of cytokinesis,” “G1/S transition of mitotic cell cycle,” “DNA recombination,” and “telomere maintenance,” respectively. Remarkably, we identified six chromatin state-marked C1-FFL instances (HCFC1-NFYA-ABL1, THAP1-USF1-BRCA2, ZNF263-USF1-UBA52, MYC-ATF1-UBA52, ELK1-EGR1-CCT4, and YY1-EGR1-INO80C) could act as prognostic biomarkers of acute myelogenous leukemia though influencing cancer-related biological functions, such as cell proliferation, telomere maintenance, and DNA recombination. Our results will provide novel insight for better understanding of chromatin state-mediated gene regulation and facilitate the identification of novel diagnostic and therapeutic biomarkers of human cancers.

Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise

This work is devoted to investigating the evolution of concentration in a genetic regulation system, when the synthesis reaction rate is under additive and multiplicative asymmetric stable Lévy fluctuations. By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that via examining the mean first exit time (MFET) and the first escape probability (FEP), the asymmetric fluctuations, interacting with nonlinearity in the system, lead to peculiar likelihood for transcription. This includes, in the additive noise case, realizing higher likelihood of transcription for larger positive skewness (i.e., asymmetry) index β, causing a stochastic bifurcation at the non-Gaussianity index value α = 1 (i.e., it is a separating point or line for the likelihood for transcription), and achieving a turning point at the threshold value β≈-0.5 (i.e., beyond which the likelihood for transcription suddenly reversed for α values). The stochastic bifurcation and turning point phenomena do not occur in the symmetric noise case (β = 0). While in the multiplicative noise case, non-Gaussianity index value α = 1 is a separating point or line for both the MFET and the FEP. We also investigate the noise enhanced stability phenomenon. Additionally, we are able to specify the regions in the whole parameter space for the asymmetric noise, in which we attain desired likelihood for transcription. We have conducted a series of numerical experiments in "regulating" the likelihood of gene transcription by tuning asymmetric stable Lévy noise indexes. This work offers insights for possible ways of achieving gene regulation in experimental research.