Effect of Interaction between Chromatin Loops on Cell-to-Cell Variability in Gene Expression

The Blueprint of Logical Decisions in a NF-κB Signaling System

Nearly identical cells can exhibit substantially different responses to the same stimulus that causes phenotype diversity. Such interplay between phenotype diversity and the architecture of regulatory circuits is crucial since it determines the state of a biological cell. Here, we theoretically analyze how the circuit blueprints of NF-κB in cellular environments are formed and their role in determining the cells' metabolic state. The NF-κB is a collective name for a developmental conserved family of five different transcription factors that can form homodimers or heterodimers and often promote DNA looping to reprogram the inflammatory gene response. The NF-κB controls many biological functions, including cellular differentiation, proliferation, migration, and survival. Our model shows that nuclear localization of NF-κB differentially promotes logic operations such as AND, NAND, NOR, and OR in its regulatory network. Through the quantitative thermodynamic model of transcriptional regulation and systematic variation of promoter-enhancer interaction modes, we can account for the origin of various logic gates as formed in the NF-κB system. We further show that the interconversion or switching of logic gates yielded under systematic variations of the stimuli activity and DNA looping parameters. Such computation occurs in regulatory and signaling pathways in individual cells at a molecular scale, which one can exploit to design a biomolecular computer.

Genome-wide inference reveals that feedback regulations constrain promoter-dependent transcriptional burst kinetics

Gene expression in mammalian cells is highly variable and episodic, resulting in a series of discontinuous bursts of mRNAs. A challenge is to understand how static promoter architecture and dynamic feedback regulations dictate bursting on a genome-wide scale. Although single-cell RNA sequencing (scRNA-seq) provides an opportunity to address this challenge, effective analytical methods are scarce. We developed an interpretable and scalable inference framework, which combined experimental data with a mechanistic model to infer transcriptional burst kinetics (sizes and frequencies) and feedback regulations. Applying this framework to scRNA-seq data generated from embryonic mouse fibroblast cells, we found Simpson's paradoxes, i.e. genome-wide burst kinetics exhibit different characteristics in two cases without and with distinguishing feedback regulations. We also showed that feedbacks differently modulate burst frequencies and sizes and conceal the effects of transcription start site distributions on burst kinetics. Notably, only in the presence of positive feedback, TATA genes are expressed with high burst frequencies and enhancer-promoter interactions mainly modulate burst frequencies. The developed inference method provided a flexible and efficient way to investigate transcriptional burst kinetics and the obtained results would be helpful for understanding cell development and fate decision.

Exploring the role of eRNA in regulating gene expression

eRNAs as the products of enhancers can regulate gene expression via various possible ways, but which regulation way is more reasonable is debatable in biology, and in particular, how eRNAs impact gene expression remains unclear. Here we introduce a mechanistic model of gene expression to address these issues. This model considers three possible regulation ways of eRNA: Type-I by which eRNA regulates transcriptional activity by facilitating the formation of enhancer-promoter (E-P) loop, Type-II by which eRNA directly promotes the mRNA production rate, and mixed regulation (i.e., the combination of Type-I and Type-II). We show that with the increase of the E-P loop length, mRNA distribution can transition from unimodality to bimodality or vice versa in all the three regulation cases. However, in contrast to the other two regulations, Type-II regulation can lead to the highest mean mRNA level and the lowest mRNA noise, independent of the E-P loop length. These results would not only reveal the essential mechanism of how eRNA regulates gene expression, but also imply a new mechanism for phenotypic switching, namely the E-P loop can induce phenotypic switching.

Anticipating response function in gene regulatory networks

The origin of an ordered genetic response of a complex and noisy biological cell is intimately related to the detailed mechanism of protein-DNA interactions present in a wide variety of gene regulatory (GR) systems. However, the quantitative prediction of genetic response and the correlation between the mechanism and the response curve is poorly understood. Here, we report in silico binding studies of GR systems to show that the transcription factor (TF) binds to multiple DNA sites with high cooperativity spreads from specific binding sites into adjacent non-specific DNA and bends the DNA. Our analysis is not limited only to the isolated model system but also can be applied to a system containing multiple interacting genes. The controlling role of TF oligomerization, TF-ligand interactions, and DNA looping for gene expression has been also characterized. The predictions are validated against detailed grand canonical Monte Carlo simulations and published data for the lac operon system. Overall, our study reveals that the expression of target genes can be quantitatively controlled by modulating TF-ligand interactions and the bending energy of DNA.

Correlation between external regulators governs the mean-noise relationship in stochastic gene expression

Gene transcription in single cells is inherently a probabilistic process. The relationship between variance ($ \sigma^{2} $) and mean expression ($ \mu $) is of paramount importance for investigations into the evolutionary origins and consequences of noise in gene expression. It is often formulated as $ \log \left({{{\sigma}^{2}}}/{{{\mu}^{2}}}\; \right) = \beta\log\mu+\log\alpha $, where $ \beta $ is a key parameter since its sign determines the qualitative dependence of noise on mean. We reveal that the sign of $ \beta $ is controlled completely by external regulation, but independent of promoter structure. Specifically, it is negative if regulators as stochastic variables are independent but positive if they are correlated. The essential mechanism revealed here can well interpret diverse experimental phenomena underlying expression noise. Our results imply that external regulation rather than promoter sequence governs the mean-noise relationship.

Exploring dissipative sources of non-Markovian biochemical reaction systems

Many biological processes including important intracellular processes are governed by biochemical reaction networks. Usually, these reaction systems operate far from thermodynamic equilibrium, implying free-energy dissipation. On the other hand, single reaction events happen often in a memory manner, leading to non-Markovian kinetics. A question then arises: how do we calculate free-energy dissipation (defined as the entropy production rate) in this physically real case? We derive an analytical formula for calculating the energy consumption of a general reaction system with molecular memory characterized by nonexponential waiting-time distributions. It shows that this dissipation is composed of two parts: one from broken detailed balance of an equivalent Markovian system with the same topology and substrates, and the other from the direction-time dependence of waiting-time distributions. But, if the system is in a detailed balance and the waiting-time distribution is direction-time independent, there is no energy dissipation even in the non-Markovian case. These general results provide insights into the physical mechanisms underlying nonequilibrium processes. A continuous-time random-walk model and a generalized model of stochastic gene expression are chosen to clearly show dissipative sources and the relationship between energy dissipation and molecular memory.

Urn models for stochastic gene expression yield intuitive insights into the probability distributions of single-cell mRNA and protein counts

Fitting the probability mass functions from analytical solutions of stochastic models of gene expression to the single-cell count distributions of mRNA and protein molecules can yield valuable insights into mechanisms underlying gene expression. Solutions of chemical master equations are available for various kinetic schemes but, even for the basic ON-OFF genetic switch, they take complex forms with generating functions given as hypergeometric functions. Interpretation of gene expression dynamics in terms of bursts is not consistent with the complete range of parameters for these functions. Physical insights into the probability mass functions are essential to ensure proper interpretations but are lacking for models considering genetic switches. To fill this gap, we develop urn models for stochastic gene expression. We sample RNA polymerases or ribosomes from a master urn, which represents the cytosol, and assign them to recipient urns of two or more colors, which represent time intervals in which no switching occurs. Colors of the recipient urns represent sub-systems of the promoter states, and the assignments to urns of a specific color represent gene expression. We use elementary principles of discrete probability theory to solve a range of kinetic models without feedback, including the Peccoud-Ycart model, the Shahrezaei-Swain model, and models with an arbitrary number of promoter states. In the last case, we obtain a novel result for the protein distribution. For activated genes, we show that transcriptional lapses, which are events of gene inactivation for short time intervals separated by long active intervals, quantify the transcriptional dynamics better than bursts. We show that the intuition gained from our urn models may also be useful in understanding existing solutions for models with feedback. We contrast our models with urn models for related distributions, discuss a generalization of the Delaporte distribution for single-cell data analysis, and highlight the limitations of our models.

Stochastic fluctuations in apoptotic threshold of tumour cells can enhance apoptosis and combat fractional killing

Fractional killing, which is a significant impediment to successful chemotherapy, is observed even in a population of genetically identical cancer cells exposed to apoptosis-inducing agents. This phenomenon arises not from genetic mutation but from cell-to-cell variation in the activation timing and level of the proteins that regulates apoptosis. To understand the mechanism behind the phenomenon, we formulate complex fractional killing processes as a first-passage time (FPT) problem with a stochastically fluctuating boundary. Analytical calculations are performed for the FPT distribution in a toy model of stochastic p53 gene expression, where the cancer cell is killed only when the p53 expression level crosses an active apoptotic threshold. Counterintuitively, we find that threshold fluctuations can effectively enhance cellular killing by significantly decreasing the mean time that the p53 protein reaches the threshold level for the first time. Moreover, faster fluctuations lead to the killing of more cells. These qualitative results imply that fluctuations in threshold are a non-negligible stochastic source, and can be taken as a strategy for combating fractional killing of cancer cells.

Control strategies for the timing of intracellular events

While the timing of intracellular events is essential for many cellular processes, gene expression inside a single cell can exhibit substantial cell-to-cell variability, raising the question of how cells ensure precision in event timing despite such stochasticity. We address this question by analyzing a biologically reasonable model of gene expression in the context of first passage time (FPT), focusing on two experimentally measurable statistics: mean FPT (MFPT) and timing variability (TV). We show that (1) transcriptional burst size (BS) and burst frequency (BF) can minimize the TV; (2) translational BS monotonically reduces the MFPT to a nonzero low bound; (3) the timescale of promoter kinetics can minimize both the MFPT and the TV, depending on the ratio of the on-switching rate over the off-switching rate; and (4) positive feedback regulation of any form can all minimize the TV, whereas negative feedback regulation of transcriptional BF or BS always enhances the TV. These control strategies can have broad implications for diverse cellular processes relying on precise temporal triggering of events.

Intrinsic Dynamics of a Human Gene Reveal the Basis of Expression Heterogeneity

Transcriptional regulation in metazoans occurs through long-range genomic contacts between enhancers and promoters, and most genes are transcribed in episodic "bursts" of RNA synthesis. To understand the relationship between these two phenomena and the dynamic regulation of genes in response to upstream signals, we describe the use of live-cell RNA imaging coupled with Hi-C measurements and dissect the endogenous regulation of the estrogen-responsive TFF1 gene. Although TFF1 is highly induced, we observe short active periods and variable inactive periods ranging from minutes to days. The heterogeneity in inactive times gives rise to the widely observed "noise" in human gene expression and explains the distribution of protein levels in human tissue. We derive a mathematical model of regulation that relates transcription, chromosome structure, and the cell's ability to sense changes in estrogen and predicts that hypervariability is largely dynamic and does not reflect a stable biological state.

The free-energy cost of interaction between DNA loops

From the viewpoint of thermodynamics, the formation of DNA loops and the interaction between them, which are all non-equilibrium processes, result in the change of free energy, affecting gene expression and further cell-to-cell variability as observed experimentally. However, how these processes dissipate free energy remains largely unclear. Here, by analyzing a mechanic model that maps three fundamental topologies of two interacting DNA loops into a 4-state model of gene transcription, we first show that a longer DNA loop needs more mean free energy consumption. Then, independent of the type of interacting two DNA loops (nested, side-by-side or alternating), the promotion between them always consumes less mean free energy whereas the suppression dissipates more mean free energy. More interestingly, we find that in contrast to the mechanism of direct looping between promoter and enhancer, the facilitated-tracking mechanism dissipates less mean free energy but enhances the mean mRNA expression, justifying the facilitated-tracking hypothesis, a long-standing debate in biology. Based on minimal energy principle, we thus speculate that organisms would utilize the mechanisms of loop-loop promotion and facilitated tracking to survive in complex environments. Our studies provide insights into the understanding of gene expression regulation mechanism from the view of energy consumption.

Perspectives: using polymer modeling to understand the formation and function of nuclear compartments

Compartmentalization is a ubiquitous feature of cellular function. In the nucleus, early observations revealed a non-random spatial organization of the genome with a large-scale segregation between transcriptionally active—euchromatin—and silenced—heterochromatin—parts of the genome. Recent advances in genome-wide mapping and imaging techniques have strikingly improved the resolution at which nuclear genome folding can be analyzed and have revealed a multiscale spatial compartmentalization with increasing evidences that such compartment may indeed result from and participate to genome function. Understanding the underlying mechanisms of genome folding and in particular the link to gene regulation requires a cross-disciplinary approach that combines the new high-resolution techniques with computational modeling of chromatin and chromosomes. In this perspective article, we first present how the copolymer theoretical framework can account for the genome compartmentalization. We then suggest, in a second part, that compartments may act as a “nanoreactor,” increasing the robustness of either activation or repression by enhancing the local concentration of regulators. We conclude with the need to develop a new framework, namely the “living chromatin” model that will allow to explicitly investigate the coupling between spatial compartmentalization and gene regulation.