Proximal termination generates a transcriptional state that determines the rate of establishment of Polycomb silencing.

The mechanisms and timescales controlling de novo establishment of chromatin-mediated transcriptional silencing by Polycomb repressive complex 2 (PRC2) are unclear. Here, we investigate PRC2 silencing at Arabidopsis FLOWERING LOCUS C (FLC), known to involve co-transcriptional RNA processing, histone demethylation activity, and PRC2 function, but so far not mechanistically connected. We develop and test a computational model describing proximal polyadenylation/termination mediated by the RNA-binding protein FCA that induces H3K4me1 removal by the histone demethylase FLD. H3K4me1 removal feeds back to reduce RNA polymerase II (RNA Pol II) processivity and thus enhance early termination, thereby repressing productive transcription. The model predicts that this transcription-coupled repression controls the level of transcriptional antagonism to PRC2 action. Thus, the effectiveness of this repression dictates the timescale for establishment of PRC2/H3K27me3 silencing. We experimentally validate these mechanistic model predictions, revealing that co-transcriptional processing sets the level of productive transcription at the locus, which then determines the rate of the ON-to-OFF switch to PRC2 silencing.

Dissecting Mechanisms of Epigenetic Memory Through Computational Modeling.

Understanding the mechanistic basis of epigenetic memory has proven to be a difficult task due to the underlying complexity of the systems involved in its establishment and maintenance. Here, we review the role of computational modeling in helping to unlock this complexity, allowing the dissection of intricate feedback dynamics. We focus on three forms of epigenetic memory encoded in gene regulatory networks, DNA methylation, and histone modifications and discuss the important advantages offered by plant systems in their dissection. We summarize the main modeling approaches involved and highlight the principal conceptual advances that the modeling has enabled through iterative cycles of predictive modeling and experiments. Lastly, we discuss remaining gaps in our understanding and how intertwined theory and experimental approaches might help in their resolution. Expected final online publication date for the Annual Review of Plant Biology, Volume 75 is May 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

COOLAIR and PRC2 function in parallel to silence FLC during vernalization.

Noncoding transcription induces chromatin changes that can mediate environmental responsiveness, but the causes and consequences of these mechanisms are still unclear. Here, we investigate how antisense transcription (termed COOLAIR) interfaces with Polycomb Repressive Complex 2 (PRC2) silencing during winter-induced epigenetic regulation of Arabidopsis FLOWERING LOCUS C (FLC). We use genetic and chromatin analyses on lines ineffective or hyperactive for the antisense pathway in combination with computational modeling to define the mechanisms underlying FLC repression. Our results show that FLC is silenced through pathways that function with different dynamics: a COOLAIR transcription-mediated pathway capable of fast response and in parallel a slow PRC2 switching mechanism that maintains each allele in an epigenetically silenced state. Components of both the COOLAIR and PRC2 pathways are regulated by a common transcriptional regulator (NTL8), which accumulates by reduced dilution due to slow growth at low temperature. The parallel activities of the regulatory steps, and their control by temperature-dependent growth dynamics, create a flexible system for registering widely fluctuating natural temperature conditions that change year on year, and yet ensure robust epigenetic silencing of FLC.

Integrating analog and digital modes of gene expression at Arabidopsis FLC.

Quantitative gene regulation at the cell population level can be achieved by two fundamentally different modes of regulation at individual gene copies. A 'digital' mode involves binary ON/OFF expression states, with population-level variation arising from the proportion of gene copies in each state, while an 'analog' mode involves graded expression levels at each gene copy. At the Arabidopsis floral repressor FLOWERING LOCUS C (FLC), 'digital' Polycomb silencing is known to facilitate quantitative epigenetic memory in response to cold. However, whether FLC regulation before cold involves analog or digital modes is unknown. Using quantitative fluorescent imaging of FLC mRNA and protein, together with mathematical modeling, we find that FLC expression before cold is regulated by both analog and digital modes. We observe a temporal separation between the two modes, with analog preceding digital. The analog mode can maintain intermediate expression levels at individual FLC gene copies, before subsequent digital silencing, consistent with the copies switching OFF stochastically and heritably without cold. This switch leads to a slow reduction in FLC expression at the cell population level. These data present a new paradigm for gradual repression, elucidating how analog transcriptional and digital epigenetic memory pathways can be integrated.

Working at the interface of physics and biology: An early career researcher perspective.

We are a network of Early Career Researchers (ECRs) and a Project Manager who are working on UKRI's "Physics of Life" grants which aim to merge ideas and techniques predominantly used in physics and apply them to biological questions. We have been collaborating since early 2021 to share research, experiences, and provide peer to peer support. Interdisciplinary projects are known for presenting challenges, bringing together disparate subjects and people with not only different knowledge bases, methods, and equipment but also varying ways of working and common languages. This has been the subject of commentary by researchers and funders from a management perspective, and we wanted to add to this discourse, using our experience to share the lessons and challenges we have encountered, from an ECR perspective.

Investigating Histone Modification Dynamics by Mechanistic Computational Modeling.

The maintenance of transcriptional states regulated by histone modifications and controlled switching between these states are fundamental concepts in our understanding of nucleosome-mediated epigenetic memory. Any approach relying on genome-wide bioinformatic analyses alone offers limited scope for dissecting the molecular mechanisms involved in maintenance and switching. Mechanistic mathematical models-describing the dynamics of histone modifications at individual genomic loci-offer an alternative way to investigate these mechanisms. These models, in conjunction with quantitative experimental data-ChIP data, quantification of mRNA levels, and single-cell fluorescence tracking in clonal lineages-can generate predictions that drive more targeted experiments, allowing us to understand mechanisms that would be challenging to unravel by a purely experimental approach. In this chapter, we describe a generic stochastic modeling framework that can be used to capture histone modification dynamics and associated molecular processes-including transcription and read-write feedback by chromatin modifying complexes-at individual genomic loci. Using a specific example-transcriptional silencing by Polycomb-mediated H3K27 methylation-we demonstrate how to construct and simulate a stochastic histone modification model. We provide a step-by-step guide to programming simulations for such a model and discuss how to analyze the simulation output.

Spatial localisation meets biomolecular networks.

Spatial organisation through localisation/compartmentalisation of species is a ubiquitous but poorly understood feature of cellular biomolecular networks. Current technologies in systems and synthetic biology (spatial proteomics, imaging, synthetic compartmentalisation) necessitate a systematic approach to elucidating the interplay of networks and spatial organisation. We develop a systems framework towards this end and focus on the effect of spatial localisation of network components revealing its multiple facets: (i) As a key distinct regulator of network behaviour, and an enabler of new network capabilities (ii) As a potent new regulator of pattern formation and self-organisation (iii) As an often hidden factor impacting inference of temporal networks from data (iv) As an engineering tool for rewiring networks and network/circuit design. These insights, transparently arising from the most basic considerations of networks and spatial organisation, have broad relevance in natural and engineered biology and in related areas such as cell-free systems, systems chemistry and bionanotechnology.

The second law: information theory and self-assembly.

An interplay between algorithmic and mechanistic viewpoints is necessary to quantify the rates of transition between different states in developmental pathways. An ab initio method that uses only information theory and geometry to model the conformational entropy of linkages is discussed. This approach also reveals some ties between biological questions and the foundations of mathematics.

Digital paradigm for Polycomb epigenetic switching and memory.

How epigenetic memory states are established and maintained is a central question in gene regulation. A major epigenetic process important for developmental biology involves Polycomb-mediated chromatin silencing. Significant progress has recently been made on elucidating Polycomb silencing in plant systems through analysis of Arabidopsis FLOWERING LOCUS C (FLC). Quantitative silencing of FLC by prolonged cold exposure was shown to represent an ON to OFF switch in an increasing proportion of cells. Here, we review the underlying all-or-nothing, digital paradigm for Polycomb epigenetic silencing. We then examine other Arabidopsis Polycomb-regulated targets where digital regulation may also be relevant.

Applications of hepatic round ligament/falciform ligament flap and graft in abdominal surgery-a review of their utility and efficacy.

BACKGROUND AND PURPOSE: Despite their ubiquitous presence, easy availability and diverse possibilities, falciform ligament and hepatic round ligament have been used less frequently than their potential dictates. This article aims to comprehensively review the applications of hepatic round ligament/falciform ligament flap and graft in abdominal surgery and assess their utility and efficacy. METHODS: Medical literature/indexing databases were searched, using internet search engines, for pertinent articles and analysed. RESULTS: The studied flap and graft have found utility predominantly in the management of diaphragmatic hernias, gastro-oesophageal reflux disease, peptic perforations, biliary reconstruction, venous reconstruction, post-operative pancreatic fistula, post-pancreatectomy haemorrhage, hepatic cyst cavity obliteration, liver bleed, sternal dehiscence, splenectomy, reinforcement of aortic stump, feeding access, diagnostic/therapeutic access into portal system, composite tissue allo-transplant and ventriculo-peritoneal shunting where they have exhibited the desired efficacy. CONCLUSIONS: Hepatic round ligament/falciform ligament flap and graft are versatile and have multifarious applications in abdominal surgery with some novel and unique uses in hepatopancreaticobiliary surgery including liver transplantation. Their evident efficacy needs wider adoption to realise their true potential.

Design Principles for Compartmentalization and Spatial Organization of Synthetic Genetic Circuits.

Compartmentalization is a hallmark of cellular systems and an ingredient actively exploited in evolution. It is also being engineered and exploited in synthetic biology, in multiple ways. While these have demonstrated important experimental capabilities, understanding design principles underpinning compartmentalization of genetic circuits has been elusive. We develop a systems framework to elucidate the interplay between the nature of the genetic circuit, the spatial organization of compartments, and their operational state (well-mixed or otherwise). In so doing, we reveal a number of unexpected features associated with compartmentalizing synthetic and template-based circuits. These include (i) the consequences of distributing circuits including trade-offs and how they may be circumvented, (ii) hidden constraints in realizing a distributed circuit, and (iii) appealing new features of compartmentalized circuits. We build on this to examine exemplar applications, which consolidate and extend the design principles we have obtained. Our insights, which emerge from the most basic and general considerations of compartmentalizing genetic circuits, are relevant in a broad range of settings.

Erich arch bar versus hanger plate technique for intermaxillary fixation in fracture mandible: A prospective comparative study.

INTRODUCTION: Various methods have been described for intermaxillary fixation (IMF) for treatment of faciomaxillary injuries. Many studies have been described to evaluate the efficacy of different methods. Hanger plate method has not been commonly used. The aim of the present study was to compare the advantages and disadvantages of this method over Erich arch bar in mandibular fracture. MATERIALS AND METHODS: Sixty patients of only mandibular fracture presenting to trauma center requiring open reduction and internal fixation under general anesthesia were randomly allocated to Group A and Group B comprising thirty patients in each. Group A included patients who received IMF with Erich arch bar. Group B included patients who received IMF with hanger plate method. The two groups were compared for time duration of intermaxillary procedure, total duration of surgery, oral hygiene score, postoperative occlusion, and complications. RESULTS: The average time of intermaxillary procedure, total duration of surgery, and wire prick injuries were more in Group A. Oral hygiene score was significantly better in Group B. Postoperative occlusion was comparable between the two groups. There was screw loosening in four patients in Group B, but none had tooth root injury. The cost of material for IMF was more in Group B. CONCLUSION: IMF with hanger plate method is more safe and efficacious compared to Erich arch bar in the treatment of mandibular fractures.

Modelling compartmentalization towards elucidation and engineering of spatial organization in biochemical pathways.

Compartmentalization is a fundamental ingredient, central to the functioning of biological systems at multiple levels. At the cellular level, compartmentalization is a key aspect of the functioning of biochemical pathways and an important element used in evolution. It is also being exploited in multiple contexts in synthetic biology. Accurate understanding of the role of compartments and designing compartmentalized systems needs reliable modelling/systems frameworks. We examine a series of building blocks of signalling and metabolic pathways with compartmental organization. We systematically analyze when compartmental ODE models can be used in these contexts, by comparing these models with detailed reaction-transport models, and establishing a correspondence between the two. We build on this to examine additional complexities associated with these pathways, and also examine sample problems in the engineering of these pathways. Our results indicate under which conditions compartmental models can and cannot be used, why this is the case, and what augmentations are needed to make them reliable and predictive. We also uncover other hidden consequences of employing compartmental models in these contexts. Or results contribute a number of insights relevant to the modelling, elucidation, and engineering of biochemical pathways with compartmentalization, at the core of systems and synthetic biology.

Bridging the gap between modules in isolation and as part of networks: A systems framework for elucidating interaction and regulation of signalling modules.

While signalling and biochemical modules have been the focus of numerous studies, they are typically studied in isolation, with no examination of the effects of the ambient network. In this paper we formulate and develop a systems framework, rooted in dynamical systems, to understand such effects, by studying the interaction of signalling modules. The modules we consider are (i) basic covalent modification, (ii) monostable switches, (iii) bistable switches, (iv) adaptive modules, and (v) oscillatory modules. We systematically examine the interaction of these modules by analyzing (a) sequential interaction without shared components, (b) sequential interaction with shared components, and (c) oblique interactions. Our studies reveal that the behaviour of a module in isolation may be substantially different from that in a network, and explicitly demonstrate how the behaviour of a given module, the characteristics of the ambient network, and the possibility of shared components can result in new effects. Our global approach illuminates different aspects of the structure and functioning of modules, revealing the importance of dynamical characteristics as well as biochemical features; this provides a methodological platform for investigating the complexity of natural modules shaped by evolution, elucidating the effects of ambient networks on a module in multiple cellular contexts, and highlighting the capabilities and constraints for engineering robust synthetic modules. Overall, such a systems framework provides a platform for bridging the gap between non-linear information processing modules, in isolation and as parts of networks, and a basis for understanding new aspects of natural and engineered cellular networks.

Self-assembly of mesoscale isomers: the role of pathways and degrees of freedom.

The spontaneous self-organization of conformational isomers from identical precursors is of fundamental importance in chemistry. Since the precursors are identical, it is the multi-unit interactions, characteristics of the intermediates, and assembly pathways that determine the final conformation. Here, we use geometric path sampling and a mesoscale experimental model to investigate the self-assembly of a model polyhedral system, an octahedron, that forms two isomers. We compute the set of all possible assembly pathways and analyze the degrees of freedom or rigidity of intermediates. Consequently, by manipulating the degrees of freedom of a precursor, we were able to experimentally enrich the formation of one isomer over the other. Our results suggest a new approach to direct pathways in both natural and synthetic self-assembly using simple geometric criteria. We also compare the process of folding and unfolding in this model with a geometric model for cyclohexane, a well-known molecule with chair and boat conformations.

Universality in numerical computations with random data.

The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance) is a random variable, called the halting time. Two-component universality is observed for the fluctuations of the halting time--i.e., the histogram for the halting times, centered by the sample average and scaled by the sample variance, collapses to a universal curve, independent of the input data distribution, as the dimension increases. Thus, up to two components--the sample average and the sample variance--the statistics for the halting time are universally prescribed. The case studies include six standard numerical algorithms as well as a model of neural computation and decision-making. A link to relevant software is provided for readers who would like to do computations of their own.

Building polyhedra by self-assembly: theory and experiment.

We investigate the utility of a mathematical framework based on discrete geometry to model biological and synthetic self-assembly. Our primary biological example is the self-assembly of icosahedral viruses; our synthetic example is surface-tension-driven self-folding polyhedra. In both instances, the process of self-assembly is modeled by decomposing the polyhedron into a set of partially formed intermediate states. The set of all intermediates is called the configuration space, pathways of assembly are modeled as paths in the configuration space, and the kinetics and yield of assembly are modeled by rate equations, Markov chains, or cost functions on the configuration space. We review an interesting interplay between biological function and mathematical structure in viruses in light of this framework. We discuss in particular: (i) tiling theory as a coarse-grained description of all-atom models; (ii) the building game-a growth model for the formation of polyhedra; and (iii) the application of these models to the self-assembly of the bacteriophage MS2. We then use a similar framework to model self-folding polyhedra. We use a discrete folding algorithm to compute a configuration space that idealizes surface-tension-driven self-folding and analyze pathways of assembly and dominant intermediates. These computations are then compared with experimental observations of a self-folding dodecahedron with side 300 µm. In both models, despite a combinatorial explosion in the size of the configuration space, a few pathways and intermediates dominate self-assembly. For self-folding polyhedra, the dominant intermediates have fewer degrees of freedom than comparable intermediates, and are thus more rigid. The concentration of assembly pathways on a few intermediates with distinguished geometric properties is biologically and physically important, and suggests deeper mathematical structure.