Toward convergence of experimental studies and theoretical modeling of the chromatin fiber

Understanding the structural organization of eukaryotic chromatin and its control of gene expression represents one of the most fundamental and open challenges in modern biology. Recent experimental advances have revealed important characteristics of chromatin in response to changes in external conditions and histone composition, such as the conformational complexity of linker DNA and histone tail domains upon compact folding of the fiber. In addition, modeling studies based on high-resolution nucleosome models have helped explain the conformational features of chromatin structural elements and their interactions in terms of chromatin fiber models. This minireview discusses recent progress and evidence supporting structural heterogeneity in chromatin fibers, reconciling apparently contradictory fiber models.     

Nucleosomes and the chromatin fiber

During the past year and a half, significant progress has been made in understanding the structure and dynamics of nucleosomes and the chromatin fiber, the mechanism of action of the core histone amino termini, the structure and function of histone variants, and the function of linker histones in the chromatin fiber.     

Computational modeling of dendrites

Computational methods have been part of neuroscience for many years. For example, models developed with these methods have provided a theory that helps explain the action potential. More recently, as experimental patch-electrode techniques have revealed new biophysics related to dendritic function and synaptic integration, computational models of dendrites have been developed to explain and further illuminate these results, and to predict possible additional behavior. Here, a collection of computational models of dendrites is reviewed. The goal is to help explain how such computational techniques work, some of their limitations, and what one can hope to learn about dendrites by modeling them.     

Nucleosome and chromatin fiber dynamics

Chromosomal DNA is packaged into condensed nucleoprotein suprastructures, yet the DNA can be accessed as needed within this structural context. Recently, progress has been made concerning how the nucleosomal subunits of chromatin fibers are disassembled and reassembled in vitro and in vivo. At the level of the chromatin fiber, the conformational organization of condensed 30 nm secondary structures has been elucidated. A great deal of progress also has been made toward understanding how chromatin architectural proteins, such as MeCP2, MENT, polycomb and HP1alpha, assemble different specific types of secondary and tertiary chromatin structures. The emerging picture is that the inherent dynamics of nucleosomal assemblages at all structural levels are a key link between the condensed domains found in eukaryotic genomes and the functions that take place within them.     

Computer simulation of the 30-nanometer chromatin fiber

A new Monte Carlo model for the structure of chromatin is presented here. Based on our previous work on superhelical DNA and polynucleosomes, it reintegrates aspects of the "solenoid" and the "zig-zag" models. The DNA is modeled as a flexible elastic polymer chain, consisting of segments connected by elastic bending, torsional, and stretching springs. The electrostatic interaction between the DNA segments is described by the Debye-Hückel approximation. Nucleosome core particles are represented by oblate ellipsoids; their interaction potential has been parameterized by a comparison with data from liquid crystals of nucleosome solutions. DNA and chromatosomes are linked either at the surface of the chromatosome or through a rigid nucleosome stem. Equilibrium ensembles of 100-nucleosome chains at physiological ionic strength were generated by a Metropolis-Monte Carlo algorithm. For a DNA linked at the nucleosome stem and a nucleosome repeat of 200 bp, the simulated fiber diameter of 32 nm and the mass density of 6.1 nucleosomes per 11 nm fiber length are in excellent agreement with experimental values from the literature. The experimental value of the inclination of DNA and nucleosomes to the fiber axis could also be reproduced. Whereas the linker DNA connects chromatosomes on opposite sides of the fiber, the overall packing of the nucleosomes leads to a helical aspect of the structure. The persistence length of the simulated fibers is 265 nm. For more random fibers where the tilt angles between two nucleosomes are chosen according to a Gaussian distribution along the fiber, the persistence length decreases to 30 nm with increasing width of the distribution, whereas the other observable parameters such as the mass density remain unchanged. Polynucleosomes with repeat lengths of 212 bp also form fibers with the expected experimental properties. Systems with larger repeat length form fibers, but the mass density is significantly lower than the measured value. The theoretical characteristics of a fiber with a repeat length of 192 bp where DNA and nucleosomes are connected at the core particle are in agreement with the experimental values. Systems without a stem and a repeat length of 217 bp do not form fibers.     

Computational modeling of membrane proteins

The determination of membrane protein (MP) structures has always trailed that of soluble proteins due to difficulties in their overexpression, reconstitution into membrane mimetics, and subsequent structure determination. The percentage of MP structures in the protein databank (PDB) has been at a constant 1–2% for the last decade. In contrast, over half of all drugs target MPs, only highlighting how little we understand about drug‐specific effects in the human body. To reduce this gap, researchers have attempted to predict structural features of MPs even before the first structure was experimentally elucidated. In this review, we present current computational methods to predict MP structure, starting with secondary structure prediction, prediction of trans‐membrane spans, and topology. Even though these methods generate reliable predictions, challenges such as predicting kinks or precise beginnings and ends of secondary structure elements are still waiting to be addressed. We describe recent developments in the prediction of 3D structures of both α‐helical MPs as well as β‐barrels using comparative modeling techniques, de novo methods, and molecular dynamics (MD) simulations. The increase of MP structures has (1) facilitated comparative modeling due to availability of more and better templates, and (2) improved the statistics for knowledge‐based scoring functions. Moreover, de novo methods have benefited from the use of correlated mutations as restraints. Finally, we outline current advances that will likely shape the field in the forthcoming decade. Proteins 2015; 83:1–24. © 2014 Wiley Periodicals, Inc.     

Electrostatic background of chromatin fiber stretching

We have carried out an investigation of the electrostatic forces involved in gradual removal of the DNA from the histone proteins in chromatin. Two simple models of DNA-histone core dissociation were considered. Calculations of the electrostatic free energy within the Poisson-Boltzmann theory gave similar results for the both models, which turned out to be in a qualitative agreement with recent optical tweezers stretching experiments measuring the force necessary to unwrap DNA from the histone core. Our analysis shows that the electrostatic interactions between the highly negatively charged polymeric DNA and the positively charged histones play a determining role in stabilizing the nucleosomes at physiological conditions.     

Computational modeling of extracellular mechanotransduction

Mechanotransduction may occur through numerous mechanisms, including potentially through autocrine signaling in a dynamically changing extracellular space. We developed a computational model to analyze how alterations in the geometry of an epithelial lateral intercellular space (LIS) affect the concentrations of constitutively shed ligands inside and below the LIS. The model employs the finite element method to solve for the concentration of ligands based on the governing ligand diffusion-convection equations inside and outside of the LIS, and assumes idealized parallel plate geometry and an impermeable tight junction at the apical surface. Using the model, we examined the temporal relationship between geometric changes and ligand concentration, and the dependence of this relationship on system characteristics such as ligand diffusivity, shedding rate, and rate of deformation. Our results reveal how the kinetics of mechanical deformation can be translated into varying rates of ligand accumulation, a potentially important mechanism for cellular discrimination of varying rate-mechanical processes. Furthermore, our results demonstrate that rapid changes in LIS geometry can transiently increase ligand concentrations in underlying media or tissues, suggesting a mechanism for communication of mechanical state between epithelial and subepithelial cells. These results underscore both the plausibility and complexity of the proposed extracellular mechanotransduction mechanism.     

To the 30-nm chromatin fiber and beyond

Chromatin fibers are intrinsically dynamic macromolecular complexes whose biological functions are intimately linked with their structure and interactions with chromatin-associated proteins (CAPs). Three-dimensional architectural transitions between or within the two co-existing chromatin types referred to as euchromatin and heterochromatin have been associated with activation or repression of nuclear functions. The presence of specific subsets of chromosomal proteins co-existing with the different chromatin conformations suggests a functional significance for their co-localization. The major points of emphasis of this review will assess the structure, function and recently documented exchanges amongst various members of the CAP family.     

Computational modeling of acute myocardial infarction

Myocardial infarction, commonly known as heart attack, is caused by reduced blood supply and damages the heart muscle because of a lack of oxygen. Myocardial infarction initiates a cascade of biochemical and mechanical events. In the early stages, cardiomyocytes death, wall thinning, collagen degradation, and ventricular dilation are the immediate consequences of myocardial infarction. In the later stages, collagenous scar formation in the infarcted zone and hypertrophy of the non-infarcted zone are auto-regulatory mechanisms to partly correct for these events. Here we propose a computational model for the short-term adaptation after myocardial infarction using the continuum theory of multiplicative growth. Our model captures the effects of cell death initiating wall thinning, and collagen degradation initiating ventricular dilation. Our simulations agree well with clinical observations in early myocardial infarction. They represent a first step toward simulating the progression of myocardial infarction with the ultimate goal to predict the propensity toward heart failure as a function of infarct intensity, location, and size.     

Computational challenges of tumor spheroid modeling

The speed and the versatility of today's computers open up new opportunities to simulate complex biological systems. Here we review a computational approach recently proposed by us to model large tumor cell populations and spheroids, and we put forward general considerations that apply to any fine-grained numerical model of tumors. We discuss ways to bypass computational limitations and discuss our incremental approach, where each step is validated by experimental observations on a quantitative basis. We present a few results on the growth of tumor cells in closed and open environments and of tumor spheroids. This study suggests new ways to explore the initial growth phase of solid tumors and to optimize antitumor treatments.