Chromatin stability generated by stochastic binding and unbinding of cross-linkers at looping sites revealed by Markov models

Mapping Intimacies ◽

10.1101/2020.05.22.111039 ◽

2020 ◽

Author(s):

Andrea Papale ◽

David Holcman

Keyword(s):

Markov Models ◽

Coarse Grain ◽

Chromatin Loops ◽

Markov Chain Approach ◽

Long Time ◽

A Cell ◽

Cross Linker ◽

Passage Times ◽

Chemical Rate ◽

Loop Stability

Chromatin loops inside the nucleus can be stable for a very long time, which remains poorly understood. Such a time is crucial for chromatin organization maintenance and stability. We explore here several physical scenarios, where loop maintenance is due to diffusing cross-linkers such as cohesin and CTCF that can bind and unbind at the base of chromatin loops. Using a Markov chain approach to coarse-grain the binding and unbinding, we consider that a stable loop disappears when the last cross-linker (CTCF or cohesin molecule) is unbound. We derive expressions for this last passage times that we use to quantify the loop stability for various value parameters, such as the chemical rate constant or the number of cross-linkers. The present analysis suggests that this binding and unbinding mechanism is sufficient to guarantee that there are always cross-linkers in place because they generate a positive feed-back mechanism that stabilizes the loop over long-time. To conclude, we propose that tens to hundreds cross-linkers per loop are sufficient to guarantee the loop stability in the genome over a cell cycle.

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A Nonstationary Hidden Markov Model with Approximately Infinitely-Long Time-Dependencies

International Journal of Artificial Intelligence Tools ◽

10.1142/s0218213016400017 ◽

2016 ◽

Vol 25 (05) ◽

pp. 1640001 ◽

Cited By ~ 3

Author(s):

Sotirios Chatzis ◽

Dimitrios Kosmopoulos ◽

George Papadourakis

Keyword(s):

Markov Models ◽

Hidden Markov ◽

Mean Field ◽

Sequential Data ◽

First Order ◽

Order Markov Chain ◽

Inference Algorithms ◽

Unrealistic Assumption ◽

Long Time ◽

Time Dependencies

Hidden Markov models (HMMs) are a popular approach for modeling sequential data, typically based on the assumption of a first-order Markov chain. In other words, only one-step back dependencies are modeled which is a rather unrealistic assumption in most applications. In this paper, we propose a method for postulating HMMs with approximately infinitely-long time-dependencies. Our approach considers the whole history of model states in the postulated dependencies, by making use of a recently proposed nonparametric Bayesian method for modeling label sequences with infinitely-long time dependencies, namely the sequence memoizer. We manage to derive training and inference algorithms for our model with computational costs identical to simple first-order HMMs, despite its entailed infinitely-long time-dependencies, by employing a mean-field-like approximation. The efficacy of our proposed model is experimentally demonstrated.

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Design and interpretation of cell trajectory assays

Journal of The Royal Society Interface ◽

10.1098/rsif.2013.0630 ◽

2013 ◽

Vol 10 (88) ◽

pp. 20130630 ◽

Cited By ~ 3

Author(s):

Lucie G. Bowden ◽

Matthew J. Simpson ◽

Ruth E. Baker

Keyword(s):

Cell Biology ◽

Time Interval ◽

Short Time Interval ◽

Trajectory Data ◽

Time Intervals ◽

Different Types ◽

Long Time ◽

A Cell ◽

Cell Trajectory ◽

Short Time

Cell trajectory data are often reported in the experimental cell biology literature to distinguish between different types of cell migration. Unfortunately, there is no accepted protocol for designing or interpreting such experiments and this makes it difficult to quantitatively compare different published datasets and to understand how changes in experimental design influence our ability to interpret different experiments. Here, we use an individual-based mathematical model to simulate the key features of a cell trajectory experiment. This shows that our ability to correctly interpret trajectory data is extremely sensitive to the geometry and timing of the experiment, the degree of motility bias and the number of experimental replicates. We show that cell trajectory experiments produce data that are most reliable when the experiment is performed in a quasi-one-dimensional geometry with a large number of identically prepared experiments conducted over a relatively short time-interval rather than a few trajectories recorded over particularly long time-intervals.

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An in vitro model of erythroid egress in bone marrow

Blood ◽

10.1182/blood.v68.1.250.250 ◽

1986 ◽

Vol 68 (1) ◽

pp. 250-257 ◽

Cited By ~ 7

Author(s):

RE Waugh ◽

M Sassi

Keyword(s):

Bone Marrow ◽

In Vitro Model ◽

Physical Parameters ◽

In Vitro System ◽

Wafer Thickness ◽

Pore Cells ◽

A Cell ◽

Vitro Model ◽

Passage Times

Abstract An in vitro system has been developed that mimics the passage of erythrocytes from the bone marrow to the circulation. Bone marrow egress and its proper regulation are vital physiologic processes. However, because of the inaccessibility of the marrow, it is difficult to evaluate the various factors important in controlling these processes or even to define the precise mechanism by which egress occurs. The in vitro system has been designed to evaluate the importance of different physical parameters in regulating egress. It consists of a thin silicon wafer (thickness approximately equal to 1.0 micron) cemented over the tip of a large (15.0 micron ID) micropipette. The wafer contains a single circular pore. Cells were observed under the microscope as they passed through the pore under controlled pressures. The rate and duration of passage were obtained from videorecordings of the experiment. The measured passage times agreed well with the predictions of a simple analytical model of a cell passing through a thin aperture. The experimental results confirm the conclusion reached from the analysis that the pressures needed to drive a cell through the pore are well within the physiologic range, and the time needed to complete egress is typically less than 1.0 seconds. These results support the hypothesis that erythrocyte egress may be driven by a hydrostatic pressure difference across the pore.

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Calculating Mean First Passage Times from Markov Models of Proteins

10.1063/1.2793397 ◽

2007 ◽

Author(s):

Christian H. Jensen ◽

Dmitry Nerukh ◽

Robert C. Glen ◽

Arno P. J. M. Siebes ◽

Michael R. Berthold ◽

...

Keyword(s):

Markov Models ◽

First Passage Times ◽

First Passage ◽

Mean First Passage Times ◽

Passage Times

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Quantitative Estimates for the Long-Time Behavior of an Ergodic Variant of the Telegraph Process

Advances in Applied Probability ◽

10.1239/aap/1354716586 ◽

2012 ◽

Vol 44 (4) ◽

pp. 977-994 ◽

Cited By ~ 7

Author(s):

Joaquin Fontbona ◽

Hélène Guérin ◽

Florent Malrieu

Keyword(s):

Markov Models ◽

Bacterial Chemotaxis ◽

Explicit Construction ◽

Time Behavior ◽

Long Time Behavior ◽

Telegraph Process ◽

Exponential Ergodicity ◽

Quantitative Estimates ◽

Long Time ◽

Variation Distance

Motivated by stability questions on piecewise-deterministic Markov models of bacterial chemotaxis, we study the long-time behavior of a variant of the classic telegraph process having a nonconstant jump rate that induces a drift towards the origin. We compute its invariant law and show exponential ergodicity, obtaining a quantitative control of the total variation distance to equilibrium at each instant of time. These results rely on an exact description of the excursions of the process away from the origin and on the explicit construction of an original coalescent coupling for both the velocity and position. Sharpness of the obtained convergence rate is discussed.

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Quantitative Estimates for the Long-Time Behavior of an Ergodic Variant of the Telegraph Process

Advances in Applied Probability ◽

10.1017/s0001867800006017 ◽

2012 ◽

Vol 44 (04) ◽

pp. 977-994

Author(s):

Joaquin Fontbona ◽

Hélène Guérin ◽

Florent Malrieu

Keyword(s):

Markov Models ◽

Bacterial Chemotaxis ◽

Explicit Construction ◽

Time Behavior ◽

Long Time Behavior ◽

Telegraph Process ◽

Exponential Ergodicity ◽

Quantitative Estimates ◽

Long Time ◽

Variation Distance

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Markov Chain Approach to a Process with Long-Time Memory

Journal of Physical Oceanography ◽

10.1175/1520-0485(2003)033<0293:mcatap>2.0.co;2 ◽

2003 ◽

Vol 33 (1) ◽

pp. 293-298 ◽

Cited By ~ 2

Author(s):

Guglielmo Lacorata ◽

Rubén A. Pasmanter ◽

Angelo Vulpiani

Keyword(s):

Markov Chain ◽

Markov Chain Approach ◽

Long Time

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A Cell type-specific Class of Chromatin Loops Anchored at Large DNA Methylation Nadirs

10.1101/212928 ◽

2017 ◽

Cited By ~ 7

Author(s):

Mira Jeong ◽

Xingfan Huang ◽

Xiaotian Zhang ◽

Jianzhong Su ◽

Muhammad S. Shamim ◽

...

Keyword(s):

Dna Methylation ◽

Cell Function ◽

Cell Types ◽

Specific Class ◽

Hematopoietic Stem ◽

Cell State ◽

Chromatin Loops ◽

Stem And Progenitor Cells ◽

A Cell ◽

Cell Type Specific

AbstractHigher order chromatin structure and DNA methylation are implicated in multiple developmental processes, but their relationship to cell state is unknown. Here, we found that large (~10kb) DNA methylation nadirs can form long loops connecting anchor loci that may be dozens of megabases apart, as well as interchromosomal links. The interacting loci comprise ~3.5Mb of the human genome. The data are more consistent with the formation of these loops by phase separation of the interacting loci to form a genomic subcompartment, rather than with CTCF-mediated extrusion. Interestingly, unlike previously characterized genomic subcompartments, this subcompartment is only present in particular cell types, such as stem and progenitor cells. Further, we identify one particular loop anchor that is functionally associated with maintenance of the hematopoietic stem cell state. Our work reveals that H3K27me3-marked large DNA methylation nadirs represent a novel set of very long-range loops and links associated with cellular identity.SummaryHi-C and DNA methylation analyses reveal novel chromatin loops between distant sites implicated in stem and progenitor cell function.

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Oxygen Starvation Effects on PEMFC Durability

ASME 2010 8th International Fuel Cell Science, Engineering and Technology Conference: Volume 1 ◽

10.1115/fuelcell2010-33173 ◽

2010 ◽

Author(s):

Mathias Gerard ◽

Jean-Philippe Poirot-Crouvezier ◽

Daniel Hissel ◽

Marie-Cecile Pe´ra

Keyword(s):

Peak Power ◽

Cathode Side ◽

Local Conditions ◽

Local Current ◽

Oxygen Starvation ◽

Long Time ◽

A Cell ◽

Starvation Effects ◽

Semi Empirical ◽

Stack Model

The problem of oxygen starvation on PEMFC is often observed (partially or totally in a cell). It is caused by water management problems (water droplet in the channels) or air management faults (delay during peak power). In our previous work, the current distribution has been measured along the cell during air starvation and calculated by modeling; the effects of the local temperature and the hygrometry in the MEA have been identified. However the mechanisms of degradation are still not completely understood. Several points have to be investigated like the short and long dated changes in performances and the degradation mechanisms in such a condition. In this paper, the study is completed by two sets of experiments. The first one is carried out with a bi-cell stack developed with specific design to compute the local current density by measuring the local induced magnetic field. Secondly, a long time ageing test is run with a 6 cells stack (220 cm2) during oxygen starvation cycling conditions. Both tests (with characterizations) coupled with the 2D serpentine meshing stack model (taking into account transport phenomena, heat transfer and semi-empirical electrochemical reactions) provide information on the MEA local conditions effects during oxygen starvation. Especially the different reaction mechanisms at the cathode side are explained likewise the consequences on ageing.

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