Noise propagation with interlinked feed-forward pathways

Emergent Spatiotemporal Organization in Stochastic Intracellular Transport Dynamics

The interior of a living cell is an active, fluctuating, and crowded environment, yet it maintains a high level of coherent organization. This dichotomy is readily apparent in the intracellular transport system of the cell. Membrane-bound compartments called endosomes play a key role in carrying cargo, in conjunction with myriad components including cargo adaptor proteins, membrane sculptors, motor proteins, and the cytoskeleton. These components coordinate to effectively navigate the crowded cell interior and transport cargo to specific intracellular locations, even though the underlying protein interactions and enzymatic reactions exhibit stochastic behavior. A major challenge is to measure, analyze, and understand how, despite the inherent stochasticity of the constituent processes, the collective outcomes show an emergent spatiotemporal order that is precise and robust. This review focuses on this intriguing dichotomy, providing insights into the known mechanisms of noise suppression and noise utilization in intracellular transport processes, and also identifies opportunities for future inquiry.

Density physics-informed neural networks reveal sources of cell heterogeneity in signal transduction

The transduction time between signal initiation and final response provides valuable information on the underlying signaling pathway, including its speed and precision. Furthermore, multi-modality in a transduction-time distribution indicates that the response is regulated by multiple pathways with different transduction speeds. Here, we developed a method called density physics-informed neural networks (Density-PINNs) to infer the transduction-time distribution from measurable final stress response time traces. We applied Density-PINNs to single-cell gene expression data from sixteen promoters regulated by unknown pathways in response to antibiotic stresses. We found that promoters with slower signaling initiation and transduction exhibit larger cell-to-cell heterogeneity in response intensity. However, this heterogeneity was greatly reduced when the response was regulated by slow and fast pathways together. This suggests a strategy for identifying effective signaling pathways for consistent cellular responses to disease treatments. Density-PINNs can also be applied to understand other time delay systems, including infectious diseases.

Lhx3/4 initiates a cardiopharyngeal-specific transcriptional program in response to widespread FGF signaling

Individual signaling pathways, such as fibroblast growth factors (FGFs), can regulate a plethora of inductive events. According to current paradigms, signal-dependent transcription factors (TFs), such as FGF/MapK-activated Ets family factors, partner with lineage-determining factors to achieve regulatory specificity. However, many aspects of this model have not been rigorously investigated. One key question relates to whether lineage-determining factors dictate lineage-specific responses to inductive signals or facilitate these responses in collaboration with other inputs. We utilize the chordate model Ciona robusta to investigate mechanisms generating lineage-specific induction. Previous studies in C. robusta have shown that cardiopharyngeal progenitor cells are specified through the combined activity of FGF-activated Ets1/2.b and an inferred ATTA-binding transcriptional cofactor. Here, we show that the homeobox TF Lhx3/4 serves as the lineage-determining TF that dictates cardiopharyngeal-specific transcription in response to pleiotropic FGF signaling. Targeted knockdown of Lhx3/4 leads to loss of cardiopharyngeal gene expression. Strikingly, ectopic expression of Lhx3/4 in a neuroectodermal lineage subject to FGF-dependent specification leads to ectopic cardiopharyngeal gene expression in this lineage. Furthermore, ectopic Lhx3/4 expression disrupts neural plate morphogenesis, generating aberrant cell behaviors associated with execution of incompatible morphogenetic programs. Based on these findings, we propose that combinatorial regulation by signal-dependent and lineage-determinant factors represents a generalizable, previously uncategorized regulatory subcircuit we term "cofactor-dependent induction." Integration of this subcircuit into theoretical models will facilitate accurate predictions regarding the impact of gene regulatory network rewiring on evolutionary diversification and disease ontogeny.

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.

Scaling of intrinsic noise in an autocratic reaction network

Biochemical reactions in living cells often produce stochastic trajectories due to the fluctuations of the finite number of the macromolecular species present inside the cell. A significant number of computational and theoretical studies have previously investigated stochasticity in small regulatory networks to understand its origin and regulation. At the systems level regulatory networks have been determined to be hierarchical resembling social networks. In order to determine the stochasticity in networks with hierarchical architecture, here we computationally investigated intrinsic noise in an autocratic reaction network in which only the upstream regulators regulate the downstream regulators. We studied the effects of the qualitative and quantitative nature of regulatory interactions on the stochasticity in the network. We established an unconventional scaling of noise with average abundance in which the noise passes through a minimum indicating that the network can be noisy both in the low and high abundance regimes. We determined that the bursty kinetics of the trajectories are responsible for such scaling. The scaling of noise remains intact for a mixed network that includes democratic subnetworks within the autocratic network.

Qualitative and quantitative nature of mutual interactions dictate chemical noise in a democratic reaction network

The functions of a living cell rely on a complex network of biochemical reactions that allow it to respond against various internal and external cues. The outcomes of these chemical reactions are often stochastic due to intrinsic and extrinsic noise leading to population heterogeneity. The majority of calculations of stochasticity in reaction networks have focused on small regulatory networks addressing the role of timescales, feedback regulations, and network topology in propagation of noise. Here we computationally investigated chemical noise in a network with democratic architecture where each node is regulated by all other nodes in the network. We studied the effects of the qualitative and quantitative nature of mutual interactions on the propagation of both intrinsic and extrinsic noise in the network. We show that an increased number of inhibitory signals lead to ultrasensitive switching of average and that leads to sharp transition of intrinsic noise. The intrinsic noise exhibits a biphasic power-law scaling with the average, and the scaling coefficients strongly correlate with the strength of inhibitory signal. The noise strength critically depends on the strength of the interactions, where negative interactions attenuate both intrinsic and extrinsic noise.

A Practicable Method of Tuning the Noise Intensity at Protein Level

The expression of genes is inevitably subject to intracellular noise. Noise, for some regulatory networks, is constructive but detrimental to many others. The intensity of the noise is a determinant factor and the method of tuning it is of great value. In this study, we illustrated that the transcriptional delay in an incoherent feedforward loop (FFL) grants the target protein modulation the intensity of noise. Remarkably, for a wide range, the coefficient of variation (COV) of the target protein appeared to be about linear to the time span of the transcriptional delay. Without a noise-buffering method, the COV of the target protein is 0.455. While applying incoherent FFL, the COV reduced to 0.236. Then, it changed from 0.236 to 0.630 as the transcriptional delay raised from 0 to 1000 seconds. If we further increased the delay out of the linear range, the COV finally reached 0.779. In addition, we incorporated the distribution of the transcriptional delay in the delay stochastic simulation algorithm. This distribution is based on the experimental observation in the literature. The outcome suggested that the distributed delay slightly improved the ability of tuning noise. In conclusion, we demonstrated a noise-tuning method that altered only the intensity of noise without changing the deterministic steady-state behaviors. It is ready to be applied to various systems in the field of synthetic biology.

Hierarchical and Dynamic Regulation of Defense-Responsive Specialized Metabolism by WRKY and MYB Transcription Factors

The plant kingdom produces hundreds of thousands of specialized bioactive metabolites, some with pharmaceutical and biotechnological importance. Their biosynthesis and function have been studied for decades, but comparatively less is known about how transcription factors with overlapping functions and contrasting regulatory activities coordinately control the dynamics and output of plant specialized metabolism. Here, we performed temporal studies on pathogen-infected intact host plants with perturbed transcription factors. We identified WRKY33 as the condition-dependent master regulator and MYB51 as the dual functional regulator in a hierarchical gene network likely responsible for the gene expression dynamics and metabolic fluxes in the camalexin and 4-hydroxy-indole-3-carbonylnitrile (4OH-ICN) pathways. This network may have also facilitated the regulatory capture of the newly evolved 4OH-ICN pathway in Arabidopsis thaliana by the more-conserved transcription factor MYB51. It has long been held that the plasticity of plant specialized metabolism and the canalization of development should be differently regulated; our findings imply a common hierarchical regulatory architecture orchestrated by transcription factors for specialized metabolism and development, making it an attractive target for metabolic engineering.

Investigation of chemical noise in multisite phosphorylation chain using linear noise approximation

Quantitative and qualitative nature of chemical noise propagation in biochemical reaction networks depend crucially on the topology of the networks. Multisite reversible phosphorylation-dephosphorylation of target proteins is one such recurrently found topology that regulates host of key functions in living cells. Here we analytically calculated the stochasticity in multistep reversible chemical reactions by determining variance of phosphorylated species at the steady state using linear noise approximation to investigate the effect of mass action and Michaelis-Menten kinetics on the noise of phosphorylated species. We probed the dependence of noise on the number of phosphorylation sites and the equilibrium constants of the reaction equilibria to investigate the chemical noise propagation in the multisite phosphorylation chain.

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.

The Reaction of Dimerization by Itself Reduces the Noise Intensity of the Protein Monomer

Because of the small particle number of intracellular species participating in genetic circuits, stochastic fluctuations are inevitable. This intracellular noise is detrimental to precise regulation. To maintain the proper function of a cell, some natural motifs attenuate the noise at the protein level. In many biological systems, the protein monomer is used as a regulator, but the protein dimer also exists. In the present study, we demonstrated that the dimerization reaction reduces the noise intensity of the protein monomer. Compared with two common noise-buffering motifs, the incoherent feedforward loop (FFL) and negative feedback control, the coefficient of variation (COV) in the case of dimerization was 25% less. Furthermore, we examined a system with direct interaction between proteins and other ligands. Both the incoherent FFL and negative feedback control failed to buffer the noise, but the dimerization was effective. Remarkably, the formation of only one protein dimer was sufficient to cause a 7.5% reduction in the COV.

Increased gene expression noise in human cancers is correlated with low p53 and immune activities as well as late stage cancer

Gene expression in metazoans is delicately organized. As genetic information transmits from DNA to RNA and protein, expression noise is inevitably generated. Recent studies begin to unveil the mechanisms of gene expression noise control, but the changes of gene expression precision in pathologic conditions like cancers are unknown. Here we analyzed the transcriptomic data of human breast, liver, lung and colon cancers, and found that the expression noise of more than 74.9% genes was increased in cancer tissues as compared to adjacent normal tissues. This suggested that gene expression precision controlling collapsed during cancer development. A set of 269 genes with noise increased more than 2-fold were identified across different cancer types. These genes were involved in cell adhesion, catalytic and metabolic functions, implying the vulnerability of deregulation of these processes in cancers. We also observed a tendency of increased expression noise in patients with low p53 and immune activity in breast, liver and lung caners but not in colon cancers, which indicated the contributions of p53 signaling and host immune surveillance to gene expression noise in cancers. Moreover, more than 53.7% genes had increased noise in patients with late stage than early stage cancers, suggesting that gene expression precision was associated with cancer outcome. Together, these results provided genomic scale explorations of gene expression noise control in human cancers.

Efficient and flexible implementation of Langevin simulation for gene burst production

Gene expression involves bursts of production of both mRNA and protein, and the fluctuations in their number are increased due to such bursts. The Langevin equation is an efficient and versatile means to simulate such number fluctuation. However, how to include these mRNA and protein bursts in the Langevin equation is not intuitively clear. In this work, we estimated the variance in burst production from a general gene expression model and introduced such variation in the Langevin equation. Our approach offers different Langevin expressions for either or both transcriptional and translational bursts considered and saves computer time by including many production events at once in a short burst time. The errors can be controlled to be rather precise (<2%) for the mean and <10% for the standard deviation of the steady-state distribution. Our scheme allows for high-quality stochastic simulations with the Langevin equation for gene expression, which is useful in analysis of biological networks.

Regulating distal tip cell migration in space and time

Gonad morphogenesis in the nematode C. elegans is guided by two leader cells, the distal tip cells (DTC). The DTCs migrate along a stereotyped path, executing two 90° turns before stopping at the midpoint of the animal. This migratory path determines the double-U shape of the adult gonad, therefore, the path taken by the DTCs can be inferred from the final shape of the organ. In this review, we focus on the mechanism by which the DTC executes the first 90° turn from the ventral to dorsal side of the animal, and how it finds its correct stopping place at the midpoint of the animal. We discuss the role of heterochronic genes in coordinating DTC migration with larval development, the role of feedback loops and miRNA regulation in phenotypic robustness, and the role of RNA binding proteins in the cessation of DTC migration.