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.     

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.     

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.     

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.     

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 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.     

Computational modeling of the immune response to tumor antigens

Vaccination protocols designed to elicit anti-cancer immune responses have, many times, failed in producing tumor eradication and in prolonging patient survival. Usually in cancer vaccination, epitopes from one organism are included in the genome or linked with some protein of another in the hope that the immunogenic properties of the latter will boost an immune response to the former. However, recent results have demonstrated that injections of two different vectors encoding the same recombinant antigen generate high levels of specific immunity. Systematic comparison of the efficacy of different vaccination protocols has been hampered by technical limitations, and clear evidence that the use of multiple vectors has advantages over single carrier injections is lacking. We used a computational model to investigate the dynamics of the immune response to different anti-cancer vaccines based on randomly generated antigen/carrier compounds. The computer model was adapted for simulations to this new area in immunology research and carefully validated to the purpose. As a matter of fact, it reproduces a relevant number of experimental observations. The model shows that when priming and boosting with the same construct, competition rather than cooperation develops amongst T cell clones of different specificities. Moreover, from the simulations, it appears that the sequential use of multiple carriers may generate more robust anti-tumor immune responses and may lead to effective tumor eradication in a higher percentage of cases. Our results provide a rational background for the design of novel strategies for the achievement of immune control of cancer.     

Computational modeling of the catalytic reaction in triosephosphate isomerase

We present a comprehensive analysis of the catalytic cycle of the enzyme triosephosphate isomerase (TIM), including both the reactive chemistry and the catalytic loop and side-chain motions. Combining accurate mixed quantum mechanics/molecular mechanics (QM/MM) and protein structure prediction methods, we have modeled both the structural and chemical aspects of the reversible isomerization of dihydroxyacetone phosphate (DHAP) to d-glyceraldehyde 3-phosphate (GAP), for which there is a wealth of experimental data. The conjunction of this novel computational approach with the use of the recent near-atomic resolution TIM-DHAP Michaelis complex PDB structure, 1NEY.pdb, has enabled us to obtain robust qualitative and, where available, quantitative agreement with a wide range of experimental data. Among the principal conclusions that we are able to draw are the importance of the monoanionic (as opposed to dianioic) form of the substrate phosphate group in the catalytic cycle, detailed positioning and energetics of the key catalytic residues in the active-site, the flexible nature of Glu165, which favors its direct involvement in the formation of the enediol intermediate, energetics of the open and closed form of the catalytic loop region in the presence and absence of substrate, and quantitative reproduction of various experimentally measured reaction rates, typically to within approximately 1 kcal/mol. Our results are consistent with the available experimental data, and provide an initial picture as to why loop opening when GAP is the product has a higher barrier than when DHAP is the product.     

Computational modeling of evolutionary learning processes in the brain

The evolutionary selection circuits model of learning has been specified algorithmically. The basic structural components of the selection circuits model are enzymatic neurons, that is, neurons whose firing behavior is controlled by membrane-bound macromolecules called excitases. Learning involves changes in the excitase contents of neurons through a process of variation and selection. In this paper we report on the behavior of a basic version of the learning algorithm which has been developed through extensive interactive experiments with the model. This algorithm is effective in that it enables single neurons or networks of neurons to learn simple pattern classification tasks in a number of time steps which appears experimentally to be a linear function of problem size, as measured by the number of patterns of presynaptic input. The experimental behavior of the algorithm establishes that evolutionary mechanisms of learning are competent to serve as major mechanisms of neuronal adaptation. As an example, we show how the evolutionary learning algorithm can contribute to adaptive motor control processes in which the learning system develops the ability to reach a target in the presence of randomly imposed disturbances.     

Computational modeling and design of renin inhibitors

The recently introduced field-based QSAR was employed to develop robust quantitative 3D QSAR models to comprehend the activity of several structurally diverse classes of small molecule renin inhibitors reported in literature. A reasonable predictive model with an r² (pred) of ～0.67 and rmse of 0.79 was achieved for an external validation set of ～150 compounds centered on the model developed using ～450 training set compounds. Based on the developed 3D QSAR models and additional insights gained from reported X-ray structures, opportunity for activity improvements in the [aza]indole scaffold was explored using a carefully designed virtual library of ～2300 compounds. The potential for success of such combined structure-guided and ligand-based approach was justified when the resulting prediction was compared against a representative with supporting experimental results.     

A triple helix model for the structure of chromatin fiber

A model of chromatin fiber structure is presented in which a repeating unit of a trinucleosome forms a 3-dimensional zigzag. Twisting and compression of the zigzag result in a triple helix structure. The model is built mainly on the flow linear dichroism data showing that nucleosomal disc faces are tilted relative to the fiber axis, the orientation of nucleosomes does not change upon folding and unfolding of chromatin, and the orientation of nucleosomes is maintained by the globular domain of histone H1.     

Higher-order structures of chromatin: the elusive 30 nm fiber

Despite progress in understanding chromatin function, the structure of the 30 nm chromatin fiber has remained elusive. However, with the recent crystal structure of a short tetranucleosomal array, the 30 nm fiber is beginning to come into view.