The role of clearance mechanisms in the kinetics of pathological protein aggregation involved in neurodegenerative diseases.

The deposition of pathological protein aggregates in the brain plays a central role in cognitive decline and structural damage associated with neurodegenerative diseases. In Alzheimer's disease, the formation of amyloid-ß plaques and neurofibrillary tangles of the tau protein is associated with the appearance of symptoms and pathology. Detailed models for the specific mechanisms of aggregate formation, such as nucleation and elongation, exist for aggregation in vitro where the total protein mass is conserved. However, in vivo, an additional class of mechanisms that clear pathological species is present and is believed to play an essential role in limiting the formation of aggregates and preventing or delaying the emergence of disease. A key unanswered question in the field of neuro-degeneration is how these clearance mechanisms can be modeled and how alterations in the processes of clearance or aggregation affect the stability of the system toward aggregation. Here, we generalize classical models of protein aggregation to take into account both production of monomers and the clearance of protein aggregates. We show that, depending on the specifics of the clearance process, a critical clearance value emerges above which accumulation of aggregates does not take place. Our results show that a sudden switch from a healthy to a disease state can be caused by small variations in the efficiency of the clearance process and provide a mathematical framework to explore the detailed effects of different mechanisms of clearance on the accumulation of aggregates.

The morpho-mechanical basis of ammonite form.

Ammonites are a group of extinct cephalopods that garner tremendous interest over a range of scientific fields and have been a paradigm for biochronology, palaeobiology, and evolutionary theories. Their defining feature is the spiral geometry and ribbing pattern through which palaeontologists infer phylogenetic relationships and evolutionary trends. Here, we develop a morpho-mechanical model for ammonite morphogenesis. While a wealth of observations have been compiled on ammonite form, and several functional interpretations may be found, this study presents the first quantitative model to explain rib formation. Our approach, based on fundamental principles of growth and mechanics, gives a natural explanation for the morphogenesis and diversity of ribs, uncovers intrinsic laws linking ribbing and shell geometry, and provides new opportunities to interpret ammonites' and other mollusks' evolution.

Synaptic bistability due to nucleation and evaporation of receptor clusters.

We introduce a bistability mechanism for long-term synaptic plasticity based on switching between two metastable states that contain significantly different numbers of synaptic receptors. One state is characterized by a two-dimensional gas of mobile interacting receptors and is stabilized against clustering by a high nucleation barrier. The other state contains a receptor gas in equilibrium with a large cluster of immobile receptors, which is stabilized by the turnover rate of receptors into and out of the synapse. Transitions between the two states can be initiated by either an increase (potentiation) or a decrease (depotentiation) of the net receptor flux into the synapse. This changes the saturation level of the receptor gas and triggers nucleation or evaporation of receptor clusters.

Mechanical growth and morphogenesis of seashells.

Seashells grow through the local deposition of mass along the aperture. Many mathematical descriptions of the shapes of shells have been provided over the years, and the basic logarithmic coiling seen in mollusks can be simulated with few parameters. However, the developmental mechanisms underlying shell coiling are largely not understood and the ubiquitous presence of ornamentation such as ribs, tubercles, or spines presents yet another level of difficulty. Here we develop a general model for shell growth based entirely on the local geometry and mechanics of the aperture and mantle. This local description enables us to efficiently describe both arbitrary growth velocities and the evolution of the shell aperture itself. We demonstrate how most shells can be simulated within this framework. We then turn to the mechanics underlying the shell morphogenesis, and develop models for the evolution of the aperture. We demonstrate that the elastic response of the mantle during shell deposition provides a natural mechanism for the formation of three-dimensional ornamentation in shells.

Perspectives on biological growth and remodeling.

The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years. Many aspects of these problems are now well-understood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation. In this perspective paper we review the state of the field and highlight open questions, challenges, and avenues for further development.

Bulging brains.

Brain swelling is a serious condition associated with an accumulation of fluid inside the brain that can be caused by trauma, stroke, infection, or tumors. It increases the pressure inside the skull and reduces blood and oxygen supply. To relieve the intracranial pressure, neurosurgeons remove part of the skull and allow the swollen brain to bulge outward, a procedure known as decompressive craniectomy. Decompressive craniectomy has been preformed for more than a century; yet, its effects on the swollen brain remain poorly understood. Here we characterize the deformation, strain, and stretch in bulging brains using the nonlinear field theories of mechanics. Our study shows that even small swelling volumes of 28 to 56 ml induce maximum principal strains in excess of 30%. For radially outward-pointing axons, we observe maximal normal stretches of 1.3 deep inside the bulge and maximal tangential stretches of 1.3 around the craniectomy edge. While the stretch magnitude varies with opening site and swelling region, our study suggests that the locations of maximum stretch are universally shared amongst all bulging brains. Our model has the potential to inform neurosurgeons and rationalize the shape and position of the skull opening, with the ultimate goal to reduce brain damage and improve the structural and functional outcomes of decompressive craniectomy in trauma patients.

Advanced paternal age effects in neurodevelopmental disorders-review of potential underlying mechanisms.

Multiple epidemiological studies suggest a relationship between advanced paternal age (APA) at conception and adverse neurodevelopmental outcomes in offspring, particularly with regard to increased risk for autism and schizophrenia. Conclusive evidence about how age-related changes in paternal gametes, or age-independent behavioral traits affect neural development is still lacking. Recent evidence suggests that the origins of APA effects are likely to be multidimensional, involving both inherited predisposition and de novo events. Here we provide a review of the epidemiological and molecular findings to date. Focusing on the latter, we present the evidence for genetic and epigenetic mechanisms underpinning the association between late fatherhood and disorder in offspring. We also discuss the limitations of the APA literature. We propose that different hypotheses relating to the origins of the APA effects are not mutually exclusive. Instead, multiple mechanisms likely contribute, reflecting the etiological complexity of neurodevelopmental disorders.

Munster, a novel paired-class homeobox gene specifically expressed in the Drosophila larval eye.

Munster (Mu) is a homeobox-containing gene of the Paired-class which is specifically expressed in the developing Bolwig organs, the Drosophila larval eyes. This expression is first detected during early germ band retraction stage (stage 12 from 7 h 20 at 25 degrees C) and persists until the end of embryogenesis. Mu homeodomain is most similar to that of Aristaless and D-Goosecoid. Strikingly, the Munster gene maps within 6 kb of D-goosecoid, in the same genomic region as aristaless, suggesting that these genes are part of a homeobox gene cluster.

c-Irx2 expression reveals an early subdivision of the neural plate in the chick embryo.

We have cloned c-Irx2, a chick homologue of the Xiro2 and mIrx2 genes and a new member of the Iroquois family of homeodomain-containing transcription factors. Strikingly, c-Irx2 expression reveals an early subdivision of the neural plate at late primitive streak stages which later transiently resolves to a single stripe within the developing hindbrain corresponding to rhombomere 1.

Cellular evidence for selfish spermatogonial selection in aged human testes.

Owing to a recent trend for delayed paternity, the genomic integrity of spermatozoa of older men has become a focus of increased interest. Older fathers are at higher risk for their children to be born with several monogenic conditions collectively termed paternal age effect (PAE) disorders, which include achondroplasia, Apert syndrome and Costello syndrome. These disorders are caused by specific mutations originating almost exclusively from the male germline, in genes encoding components of the tyrosine kinase receptor/RAS/MAPK signalling pathway. These particular mutations, occurring randomly during mitotic divisions of spermatogonial stem cells (SSCs), are predicted to confer a selective/growth advantage on the mutant SSC. This selective advantage leads to a clonal expansion of the mutant cells over time, which generates mutant spermatozoa at levels significantly above the background mutation rate. This phenomenon, termed selfish spermatogonial selection, is likely to occur in all men. In rare cases, probably because of additional mutational events, selfish spermatogonial selection may lead to spermatocytic seminoma. The studies that initially predicted the clonal nature of selfish spermatogonial selection were based on DNA analysis, rather than the visualization of mutant clones in intact testes. In a recent study that aimed to identify these clones directly, we stained serial sections of fixed testes for expression of melanoma antigen family A4 (MAGEA4), a marker of spermatogonia. A subset of seminiferous tubules with an appearance and distribution compatible with the predicted mutant clones were identified. In these tubules, termed 'immunopositive tubules', there is an increased density of spermatogonia positive for markers related to selfish selection (FGFR3) and SSC self-renewal (phosphorylated AKT). Here we detail the properties of the immunopositive tubules and how they relate to the predicted mutant clones, as well as discussing the utility of identifying the potential cellular source of PAE mutations.

Possible role of differential growth in airway wall remodeling in asthma.

Airway remodeling in patients with chronic asthma is characterized by a thickening of the airway walls. It has been demonstrated in previous theoretical models that this change in thickness can have an important mechanical effect on the properties of the wall, in particular on the phenomenon of mucosal folding induced by smooth muscle contraction. In this paper, we present a model for mucosal folding of the airway in the context of growth. The airway is modeled as a bilayered cylindrical tube, with both geometric and material nonlinearities accounted for via the theory of finite elasticity. Growth is incorporated into the model through the theory of morphoelasticity. We explore a range of growth possibilities, allowing for anisotropic growth as well as different growth rates in each layer. Such nonuniform growth, referred to as differential growth, can change the properties of the material beyond geometrical changes through the generation of residual stresses. We demonstrate that differential growth can have a dramatic impact on mucosal folding, in particular on the critical pressure needed to induce folding, the buckling pattern, as well as airway narrowing. We conclude that growth may be an important component in airway remodeling.

Continuous representations of proteins: construction of coordinate models from curvature profiles.

A representation of proteins based on the geometry of space curves is described. This representation enables the application of continuum methods to the analysis of macromolecular structure and form that cannot be applied to the more familiar discrete atomic coordinate models. It is shown that the continuous modeling method defines the geometry of the protein fold very efficiently. An analytical solution for curve construction is employed from which both continuous and coordinate models can be obtained. The method is applied to five representative test proteins which are used to assess the accuracy and efficiency of the modeling procedure.

The determination of sense organs in Drosophila: effect of the neurogenic mutations in the embryo.

We have examined the early pattern of sensory mother cells in embryos mutant for six different neurogenic loci. Our results show that the neurogenic loci are required to restrict the number of competent cells that will become sensory mother cells, but are not involved in controlling the localization or the position-dependent specification of competent cells. We conclude that these loci are involved in setting up a system of mutual inhibition, which transforms graded differences within the proneural clusters into an all-or-none difference between one cell, which becomes the sense organ progenitor cell, and the other cells, which remain epidermal.

Dynamics of helical strips

The dynamics of inertial elastic helical thin rods with noncircular cross sections and arbitrary intrinsic curvature, torsion, and twist is studied. The classical Kirchhoff equations are used together with a perturbation scheme at the level of the director basis, and the dispersion relation for helical strips is derived and analyzed. It is shown that all naturally straight helical strips are unstable whereas free-standing helices are always stable. There exists a one-parameter family of stationary helical solutions depending on the ratio of curvature to torsion. A bifurcation analysis with respect to this parameter is performed, and bifurcation curves in the space of elastic parameters are identified. The different modes of instabilities are analyzed.

A functional homologue of goosecoid in Drosophila.

We have cloned a Drosophila homologue (D-gsc) of the vertebrate homeobox gene goosecoid (gsc). In the Gsc proteins, the pressure for conservation has been imposed on the homeodomain, the functional domain of the protein: sequence homology is limited to the homeodomain (78% identity) and to a short stretch of 7 aminoacids also found in other homeoproteins such as Engrailed. Despite this weak homology, D-gsc is able to mimic gsc function in a Xenopus assay, as shown by its ability to rescue the axis development of a UV-irradiated embryo. Moreover, our data suggest that the position of insect and vertebrate gsc homologues within a regulatory network has also been conserved: D-gsc expression is controlled by decapentaplegic, orthodenticle, sloppy-paired and tailless whose homologues control gsc expression (for BMP4 and Otx-2), or are expressed at the right time and the right place (for XFKH1/Pintallavis and Tlx) to be interacting with gsc during vertebrate development. However, the pattern of D-gsc expression in ectodermal cells of the nervous system and foregut cannot easily be reconciled with that of vertebrate gsc mesodermal expression, suggesting that its precise developmental function might have diverged. Still, this comparison of domains of expression and functions among Gsc proteins could shed light on a common origin of gut formation and/or on basic cellular processes. The identification of gsc target genes and/or other genes involved in similar developmental processes will allow the definition of the precise phylogenetic relationship among Gsc proteins.

Lune/eye gone, a Pax-like protein, uses a partial paired domain and a homeodomain for DNA recognition.

Pax proteins, characterized by the presence of a paired domain, play key regulatory roles during development. The paired domain is a bipartite DNA-binding domain that contains two helix-turn-helix domains joined by a linker region. Each of the subdomains, the PAI and RED domains, has been shown to be a distinct DNA-binding domain. The PAI domain is the most critical, but in specific circumstances, the RED domain is involved in DNA recognition. We describe a Pax protein, originally called Lune, that is the product of the Drosophila eye gone gene (eyg). It is unique among Pax proteins, because it contains only the RED domain. eyg seems to play a role both in the organogenesis of the salivary gland during embryogenesis and in the development of the eye. A high-affinity binding site for the Eyg RED domain was identified by using systematic evolution of ligands by exponential enrichment techniques. This binding site is related to a binding site previously identified for the RED domain of the Pax-6 5a isoform. Eyg also contains another DNA-binding domain, a Prd-class homeodomain (HD), whose palindromic binding site is similar to other Prd-class HDs. The ability of Pax proteins to use the PAI, RED, and HD, or combinations thereof, may be one mechanism that allows them to be used at different stages of development to regulate various developmental processes through the activation of specific target genes.

Bistable helices.

We extend elasticity theory of filaments to encompass systems, such as bacterial flagella, that display competition between two helical structures of opposite chirality. A general, fully intrinsic formulation of the dynamics of bend and twist degrees of freedom is developed using the natural frame of space curves, spanning from the inviscid limit to the viscously overdamped regime applicable to cellular biology. Aspects of front propagation found in flagella are discussed.