A novel model for one-dimensional morphoelasticity. Part I - Theoretical foundations

While classical continuum theories of elasticity and viscoelasticity have long been used to describe the mechanical behaviour of solid biological tissues, they are of limited use for the description of biological tissues that undergo continuous remodelling. The structural changes to a soft tissue associated with growth and remodelling require a mathematical theory of ‘morphoelasticity’ that is more akin to plasticity than elasticity. However, previously-derived mathematical models for plasticity are difficult to apply and interpret in the context of growth and remodelling: many important concepts from the theory of plasticity do not have simple analogues in biomechanics.\ud \ud In this work, we describe a novel mathematical model that combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. While our focus here is on one-dimensional problems, our model builds on earlier work based on the multiplicative decomposition of the deformation gradient and can be adapted to develop a three-dimensional theory. The foundation of this work is the concept of ‘effective strain’, a measure of the difference between the current state and a hypothetical state where the tissue is mechanically relaxed. We develop one-dimensional equations for the evolution of effective strain, and discuss a number of potential applications of this theory. One significant application is the description of a contracting fibroblast-populated collagen lattice, which we further investigate in Part II

A novel model for one-dimensional morphoelasticity. Part II - Application to the contraction of fibroblast-populated collagen lattices

Fibroblast-populated collagen lattices are commonly used in experiments to study the interplay between fibroblasts and their pliable environment. Depending on the method by which\ud they are set, these lattices can contract significantly, in some cases contracting to as little as 10% of their initial lateral (or vertical) extent. When the reorganisation of such lattices by fibroblasts is interrupted, it has been observed that the gels re-expand slightly but do not return to their original size. In order to describe these phenomena, we apply our theory of one-dimensional morphoelasticity derived in Part I to obtain a system of coupled ordinary differential equations, which we use to describe the behaviour of a fibroblast-populated collagen lattice that is tethered by a spring of known stiffness. We obtain approximate solutions that describe the behaviour of the system at short times as well as those that are valid for long times. We also obtain an exact description of the behaviour of the system in the case where the lattice reorganisation is interrupted. In addition, we perform a perturbation analysis in the limit of large spring stiffness to obtain inner and outer asymptotic expansions for the solution, and examine the relation between force and traction stress in this limit. Finally, we compare predicted numerical values for the initial stiffness and viscosity of the gel with corresponding values for previously obtained sets of experimental data and also compare the qualitative behaviour with that of our model in each case. We find that our model captures many features of the observed behaviour of fibroblast-populated collagen lattices

Developmental Changes in the ECG of a Hamster Model of Muscular Dystrophy and Heart Failure

Aberrant autonomic signaling is being increasingly recognized as an important symptom in neuromuscular disorders. The δ-sarcoglycan-deficient BIO TO-2 hamster is recognized as a good model for studying mechanistic pathways and sequelae in muscular dystrophy and heart failure, including autonomic nervous system (ANS) dysfunction. Recent studies using the TO-2 hamster model have provided promising preclinical results demonstrating the efficacy of gene therapy to treat skeletal muscle weakness and heart failure. Methods to accelerate preclinical testing of gene therapy and new drugs for neuromuscular diseases are urgently needed. The purpose of this investigation was to demonstrate a rapid non-invasive screen for characterizing the ANS imbalance in dystrophic TO-2 hamsters. Electrocardiograms were recorded non-invasively in conscious ∼9-month old TO-2 hamsters (n = 10) and non-myopathic F1B control hamsters (n = 10). Heart rate was higher in TO-2 hamsters than controls (453 ± 12 bpm vs. 311 ± 25 bpm, P < 0.01). Time domain heart rate variability, an index of parasympathetic tone, was lower in TO-2 hamsters (12.2 ± 3.7 bpm vs. 38.2 ± 6.8, P < 0.05), as was the coefficient of variance of the RR interval (2.8 ± 0.9% vs. 16.2 ± 3.4%, P < 0.05) compared to control hamsters. Power spectral analysis demonstrated reduced high frequency and low frequency contributions, indicating autonomic imbalance with increased sympathetic tone and decreased parasympathetic tone in dystrophic TO-2 hamsters. Similar observations in newborn hamsters indicate autonomic nervous dysfunction may occur quite early in life in neuromuscular diseases. Our findings of autonomic abnormalities in newborn hamsters with a mutation in the δ-sarcoglycan gene suggest approaches to correct modulation of the heart rate as prevention or therapy for muscular dystrophies

A critical role for the chromatin remodeller CHD7 in anterior mesoderm during cardiovascular development

CHARGE syndrome is caused by spontaneous loss-of-function mutations to the ATP-dependant chromatin remodeller chromodomain-helicase-DNA-binding protein 7 (CHD7). It is characterised by a distinct pattern of congenital anomalies, including cardiovascular malformations. Disruption to the neural crest lineage has previously been emphasised in the aetiology of this developmental disorder. We present evidence for an additional requirement for CHD7 activity in the Mesp1-expressing anterior mesoderm during heart development. Conditional ablation of Chd7 in this lineage results in major structural cardiovascular defects akin to those seen in CHARGE patients, as well as a striking loss of cardiac innervation and embryonic lethality. Genome-wide transcriptional analysis identified aberrant expression of key components of the Class 3 Semaphorin and Slit-Robo signalling pathways in Chd7(fl/fl);Mesp1-Cre mutant hearts. CHD7 localises at the Sema3c promoter in vivo, with alteration of the local chromatin structure seen following Chd7 ablation, suggestive of direct transcriptional regulation. Furthermore, we uncover a novel role for CHD7 activity upstream of critical calcium handling genes, and demonstrate an associated functional defect in the ability of cardiomyocytes to undergo excitation-contraction coupling. This work therefore reveals the importance of CHD7 in the cardiogenic mesoderm for multiple processes during cardiovascular development

Probabilistic Clustering of Sequences: Inferring new bacterial regulons by comparative genomics

Genome wide comparisons between enteric bacteria yield large sets of conserved putative regulatory sites on a gene by gene basis that need to be clustered into regulons. Using the assumption that regulatory sites can be represented as samples from weight matrices we derive a unique probability distribution for assignments of sites into clusters. Our algorithm, 'PROCSE' (probabilistic clustering of sequences), uses Monte-Carlo sampling of this distribution to partition and align thousands of short DNA sequences into clusters. The algorithm internally determines the number of clusters from the data, and assigns significance to the resulting clusters. We place theoretical limits on the ability of any algorithm to correctly cluster sequences drawn from weight matrices (WMs) when these WMs are unknown. Our analysis suggests that the set of all putative sites for a single genome (e.g. E. coli) is largely inadequate for clustering. When sites from different genomes are combined and all the homologous sites from the various species are used as a block, clustering becomes feasible. We predict 50-100 new regulons as well as many new members of existing regulons, potentially doubling the number of known regulatory sites in E. coli.Comment: 27 pages including 9 figures and 3 table

Reticular formation responses to magnetic brain stimulation of primary motor cortex

Transcranial magnetic stimulation (TMS) of cerebral cortex is a popular technique for the non-invasive investigation of motor function. TMS is often assumed to influence spinal circuits solely via the corticospinal tract. We were interested in possible trans-synaptic effects of cortical TMS on the ponto-medullary reticular formation in the brainstem, which is the source of the reticulospinal tract and could also generate spinal motor output. We recorded from 210 single units in the reticular formation of three anaesthetized macaque monkeys whilst TMS was performed over primary motor cortex. Short latency responses were observed consistent with activation of a cortico-reticular pathway. However, we also demonstrated surprisingly powerful responses at longer latency, which often appeared at lower threshold than the earlier effects. These late responses seemed to be generated partly as a consequence of the sound click made by coil discharge, and changed little with coil location. This novel finding has implications for the design of future studies using TMS, as well as suggesting a means of non-invasively probing an otherwise inaccessible important motor centre