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The Polycomb system epigenetically represses selected developmental genes to enforce gene expression programs of differentiated cells. The system requires the coordinated action of dozens of structurally unrelated proteins assembled in two evolutionarily conserved polycomb repressive complexes, PRC1 and PRC2. Genes repressed by the Polycomb system are enriched in histone H3 trimethylated at lysine 27 (H3K27me3), an epigenetic mark that propagates the repressed state after DNA replication. Despite the impressive progress in dissecting molecular functions of the Polycomb group proteins, the fundamental questions of how the Polycomb system represses transcription or how the H3K27me3 mark is translated to benefit the repression are still open. Multiple observations indicate that the binding of PRC1, PRC2, and elevated H3K27me3 correlate with changes in the chromatin structure of target genes, which may be integral for the associated epigenetic repression. In this Review, we summarize our current understanding of these observations. We discuss the chromatin folding inside the loci repressed by the Polycomb system, consider molecular processes causing it and reflect upon its possible impact on transcription and epigenetic memory of the repressed state.

Bacteria live in diverse communities, forming complex networks of interacting species. A central question in bacterial ecology is whether species engage in cooperative or competitive interactions. But this question often neglects the role of the environment. Here, we use genome-scale metabolic networks from two different open-access collections (AGORA and CarveMe) to assess pairwise interactions of different microbes in varying environmental conditions (provision of different environmental compounds). By computationally simulating thousands of environments for 10,000 pairs of bacteria from each collection, we found that most pairs were able to both compete and cooperate depending on the availability of environmental resources. This modeling approach allowed us to determine commonalities between environments that could facilitate the potential for cooperation or competition between a pair of species. Namely, cooperative interactions, especially obligate, were most common in less diverse environments. Further, as compounds were removed from the environment, we found interactions tended to degrade towards obligacy. However, we also found that on average at least one compound could be removed from an environment to switch the interaction from competition to facultative cooperation or vice versa. Together our approach indicates a high degree of plasticity in microbial interactions in response to the availability of environmental resources.

Deep-burrowing earthworms (anecic and endogeic species) can dry soils by reworking mineral soil layers. Although this ‘drying effect’ has been reported across many ecosystems, including the Fennoscandian tundra, little is known about the driving processes. In this study, we measure plant transpiration in combination with controlled experiments of water holding capacity and evaporation to assess drivers of soil–water losses in tundra soil as the result of endogeic and anecic earthworms. Our experimental system was a common garden experiment with shrub-dominated (heath) and forb-dominated (meadow) vegetation (N = 48), where long-term monitoring revealed drier soils due to the addition of earthworms. Although we found that tundra plant transpiration was highest during the peak growing season and that meadow soil had a higher field capacity, our earthworm treatment did not strongly affect these two parameters. Evaporation, on the other hand, was on average 14 % higher in the meadow with earthworms although no such effect was observed in the heath soil. Using a network model of macropore vapor transfer that measures evaporation effects, we found an increase in macropore conductance between the subsoil and the atmosphere and that the vaporization rate in relation to the diffusion rate controls the strength of the evaporation effect. Our findings underscore the need to account for evaporation due to the reworking of pore architectures by soil biota when predicting changes in soil–water availability.

Chromosome capture techniques like Hi-C have expanded our understanding of mammalian genome 3D architecture and how it influences gene activity. To analyze Hi-C data sets, researchers increasingly treat them as DNA-contact networks and use standard community detection techniques to identify mesoscale 3D communities. However, there are considerable challenges in finding significant communities because the Hi-C networks have cross-scale interactions and are almost fully connected. This paper presents a pipeline to distill 3D communities that remain intact under experimental noise. To this end, we bootstrap an ensemble of Hi-C datasets representing noisy data and extract 3D communities that we compare with the unperturbed dataset. Notably, we extract the communities by maximizing local modularity (using the Generalized Louvain method), which considers the multifractal spectrum recently discovered in Hi-C maps. Our pipeline finds that stable communities (under noise) typically have above-average internal contac,t frequencies and tend to be enriched in active chromatin marks. We also find they fold into more nested cross-scale hierarchies than less stable ones. Apart from presenting how to systematically extract robust communities in Hi-C data, our paper offers new ways to generate null models that take advantage of the network’s multifractal properties. We anticipate this has a broad applicability to several network applications.

We present a novel framework for understanding node target search in systems organized as hierarchical networks-within-networks. Our work generalizes traditional search models on complex networks, where the mean-first passage time is typically inversely proportional to the node degree. However, real-world search processes often span multiple network layers, such as moving from an external environment into a local network, and then navigating several internal states. This multilayered complexity appears in scenarios such as international travel networks, tracking email spammers, and the dynamics of protein-DNA interactions in cells. Our theory addresses these complex systems by modeling them as a three-layer multiplex network: an external source layer, an intermediate spatial layer, and an internal state layer. We derive general closed-form solutions for the steady-state flux through a target node, which serves as a proxy for inverse mean-first passage time. Our results reveal a universal relationship between search efficiency and network-specific parameters. This work extends the current understanding of multiplex networks by focusing on systems with hierarchically connected layers. Our findings have broad implications for fields ranging from epidemiology to cellular biology and provide a more comprehensive understanding of search dynamics in complex, multilayered environments.

Cells regulate fates and complex body plans using spatiotemporal signaling cascades that alter gene expression. Short DNA sequences, known as enhancers (50–1500 base pairs), help coordinate these cascades by attracting regulatory proteins that enhance the transcription by binding to distal gene promoters. In humans, there are hundreds of thousands of enhancers dispersed across the genome, which poses a challenging coordination task to prevent unintended gene activation. To mitigate this problem, the genome contains insulator elements that block enhancer-promoter interactions. However, there is an open problem with how the insulation works, especially as enhancer-insulator pairs may be separated by millions of base pairs. Based on recent empirical data from Hi-C experiments, this paper proposes a new mechanism that challenges the common paradigm that rests on specific insulator-insulator interactions. Instead, this paper introduces a stochastic looping model where insulators bind weakly to chromatin rather than other insulators. After calibrating the model to experimental data, we use simulations to study the broad distribution of hitting times between an enhancer and a promoter when insulators are present. We find parameter regimes with large differences between average and most probable hitting times. This makes it difficult to assign a typical timescale and hints at highly defocused regulation times. We also map our computational model onto a resetting problem that allows us to derive several analytical results. Besides offering new insights into enhancer-insulator interactions, our paper advances the understanding of gene regulatory networks and causal connections between genome folding and gene activation.

The most common gene regulation mechanism is when a protein binds to a regulatory sequence to change RNA transcription. However, these sequences are short relative to the genome length, so finding them poses a challenging search problem. This chapter presents two mathematical frameworks capturing different aspects of this problem. First, we study the interplay between diffusional flux through a target where the searching proteins get sequestered on DNA far from the target because of non-specific interactions. From this model, we derive a simple formula for the optimal protein-DNA unbinding rate, maximizing the particle flux. Second, we study how the flux flows through a target on a single antenna with variable length. Here, we identify a non-trivial logarithmic correction to the linear behavior relative to the target size proposed by Smoluchowski’s flux formula.

Lysine-specific histone demethylase 1 (LSD1), which demethylates mono- or di- methylated histone H3 on lysine 4 (H3K4me1/2), is essential for early embryogenesis and development. Here we show that LSD1 is dispensable for mouse embryonic stem cell (ESC) self-renewal but is required for mouse ESC growth and differentiation. Reintroduction of a catalytically-impaired LSD1 (LSD1MUT) recovers the proliferation capability of mouse ESCs, yet the enzymatic activity of LSD1 is essential to ensure proper differentiation. Indeed, increased H3K4me1 in Lsd1 knockout (KO) mouse ESCs does not lead to major changes in global gene expression programs related to stemness. However, ablation of LSD1 but not LSD1MUT results in decreased DNMT1 and UHRF1 proteins coupled to global hypomethylation. We show that both LSD1 and LSD1MUT control protein stability of UHRF1 and DNMT1 through interaction with HDAC1 and the ubiquitin-specific peptidase 7 (USP7), consequently, facilitating the deacetylation and deubiquitination of DNMT1 and UHRF1. Our studies elucidate a mechanism by which LSD1 controls DNA methylation in mouse ESCs, independently of its lysine demethylase activity.

Even when split into several chromosomes, DNA molecules that make up our genome are too long to fit into the cell nuclei unless massively folded. Such folding must accommodate the need for timely access to selected parts of the genome by transcription factors, RNA polymerases, and DNA replication machinery. Here, we review our current understanding of the genome folding inside the interphase nuclei. We consider the resulting genome architecture at three scales with a particular focus on the intermediate (meso) scale and summarize the insights gained from recent experimental observations and diverse computational models.

Researchers developed chromosome capture methods such as Hi-C to better understand DNA's 3D folding in nuclei. The Hi-C method captures contact frequencies between DNA segment pairs across the genome. When analyzing Hi-C data sets, it is common to group these pairs using standard bioinformatics methods (e.g., PCA). Other approaches handle Hi-C data as weighted networks, where connected node represent DNA segments in 3D proximity. In this representation, one can leverage community detection techniques developed in complex network theory to group nodes into mesoscale communities containing similar connection patterns. While there are several successful attempts to analyze Hi-C data in this way, it is common to report and study the most typical community structure. But in reality, there are often several valid candidates. Therefore, depending on algorithm design, different community detection methods focusing on slightly different connectivity features may have differing views on the ideal node groupings. In fact, even the same community detection method may yield different results if using a stochastic algorithm. This ambiguity is fundamental to community detection and shared by most complex networks whenever interactions span all scales in the network. This is known as community inconsistency. This paper explores this inconsistency of 3D communities in Hi-C data for all human chromosomes. We base our analysis on two inconsistency metrics, one local and one global, and quantify the network scales where the community separation is most variable. For example, we find that TADs are less reliable than A/B compartments and that nodes with highly variable node-community memberships are associated with open chromatin. Overall, our study provides a helpful framework for data-driven researchers and increases awareness of some inherent challenges when clustering Hi-C data into 3D communities.