Biomedical subjects

Alain Goriely

Publications and source records attributed to Alain Goriely.

13 recordsLinked to original sources

PubMed2007

Component retention in principal component analysis with application to cDNA microarray data.

Shannon entropy is used to provide an estimate of the number of interpretable components in a principal component analysis. In addition, several ad hoc stopping rules for dimension determination are reviewed and a modification of the broken stick model is presented. The modification incorporates a test for the presence of an "effective degeneracy" among the subspaces spanned by the eigenvectors of the correlation matrix of the data set then allocates the total variance among subspaces. A summary of the performance of the methods applied to both published microarray data sets and to simulated data is given.

Journal Article↗

PubMed2006

On the definition and modeling of incremental, cumulative, and continuous growth laws in morphoelasticity.

In the theory of elastic growth, a growth process is modeled by a sequence of growth itself followed by an elastic relaxation ensuring integrity and compatibility of the body. The description of this process is local in time and only corresponds to an incremental step in the total growth process. As time evolves, these incremental growth steps are compounded and a natural question is the description of the overall cumulative growth and whether a continuous description of this process is possible. These ideas are discussed and further studied in the case of incompressible shells.

Algorithms↗

PubMed2006

Mechanics of climbing and attachment in twining plants.

Twining plants achieve vertical growth by revolving around supports of different sizes on which they exert a pressure. This observation raises many intriguing questions that are addressed within the framework of elastic filamentary structures by modeling the stem close to the apex as a growing elastic rod. The analysis shows that vertical growth is achieved thanks to discrete contact points and regions with continuous contact, that the contact pressure creates tension in the stem as observed experimentally, and that there is a maximal radius of the pole around which a twiner can climb.

Journal Article↗

PubMed2006

Dynamic buckling of morphoelastic filaments.

The equilibrium shapes of biological structures as diverse as plant tendrils and bacterial filaments can be altered by externally imposed stresses of sufficient duration. We study the simplest model for this morphoelasticity--a filament whose intrinsic curvatures relax to the local curvatures--and illustrate its properties in the context of dynamic Euler buckling and writhing. When a thrust or twist is ramped in time the effective elastic properties of the filament depend on the load rate. Slow ramps interrupted by removal of the external forces can leave in equilibrium any of a whole continuum of buckled shapes. Morphoelastic relaxation can also allow a filament to bypass a bifurcation.

Animals↗

PubMed2006

Helices.

Helices are among the simplest shapes that are observed in the filamentary and molecular structures of nature. The local mechanical properties of such structures are often modeled by a uniform elastic potential energy dependent on bending and twist, which is what we term a rod model. Our first result is to complete the semi-inverse classification, initiated by Kirchhoff, of all infinite, helical equilibria of inextensible, unshearable uniform rods with elastic energies that are a general quadratic function of the flexures and twist. Specifically, we demonstrate that all uniform helical equilibria can be found by means of an explicit planar construction in terms of the intersections of certain circles and hyperbolas. Second, we demonstrate that the same helical centerlines persist as equilibria in the presence of realistic distributed forces modeling nonlocal interactions as those that arise, for example, for charged linear molecules and for filaments of finite thickness exhibiting self-contact. Third, in the absence of any external loading, we demonstrate how to construct explicitly two helical equilibria, precisely one of each handedness, that are the only local energy minimizers subject to a nonconvex constraint of self-avoidance.

Biophysical Phenomena↗

PubMed2006

Repeat protein architectures predicted by a continuum representation of fold space.

It is an open question whether nature has utilized all possible protein folds. For a simple protein architecture, the helical repeats, we report a method to address this question based on a mapping between the set of repetitive curves and a space of parameters specifying the curve. The exploration of the parameter space for a particular architecture enables a systematic exploration of the fold space for that protein architecture. In a planar subspace of the parameter space of helical repeats we have identified points corresponding to both naturally occurring folds and potential folds not observed so far.

Algorithms↗

PubMed2006

Estimates of biomechanical forces in Magnaporthe grisea.

The mechanical actions of the fungus Magnaporthe grisea raise many intriguing questions concerning the forces involved. These include: (1) the material properties of the appressorial wall; (2) the strength of the adhesive that keeps the appressorium anchored to the rice leaf surface; and (3) the forces involved in the penetration process whereby a peg is driven through the host cell wall. In this paper we give order of magnitude estimates for all three of these quantities. A simple Young-Laplace law type argument is used to show that the appressorial wall elastic modulus is of order 10-100 MPa; and an adaptation of standard adhesion theory indicates a lower bound on the strength of the appressorial adhesive to be of the order 500 J/m(2). Drawing on ideas from plasticity theory and ballistics, estimates of the penetration force raise interesting questions about experiments performed on the penetration of inert substrates by the fungus.

Biomechanical Phenomena↗

PubMed2005

Biomechanical model for appressorial design in Magnaporthe grisea.

The fungus Magnaporthe grisea, commonly referred to as the rice blast fungus, is responsible for destroying from 10% to 30% of the world's rice crop each year. The fungus attaches to the rice leaf and forms a dome-shaped structure, the appressorium, in which enormous pressures are generated that are used to blast a penetration peg through the rice cell walls and infect the plant. We develop a model of the appressorial design in terms of a bioelastic shell that can explain the shape of the appressorium, and its ability to maintain that shape under the enormous increases in turgor pressure that can occur during the penetration phase.

Biomechanical Phenomena↗

PubMed2005

Differential growth and instability in elastic shells.

Differential growth in elastic materials can produce stress either through incompatibility of growth or by interaction with the surrounding medium. In many situations, this stress can be sufficient to induce shape instability in the growing medium. To gain better insight in growth-induced instabilities, the growth of an elastic shell loaded with hydrostatic pressure or embedded in an elastic medium is studied. The residual stress arising from the incompatibility of growth and the contact stress arising from the interaction with the surrounding medium are computed with respect to growth and geometric parameters and critical values for instability are obtained. Depending on these parameters, different modes of instability can be obtained.

Biomechanical Phenomena↗

PubMed2005

Growth induced curve dynamics for filamentary micro-organisms.

The growth of filamentary micro-organisms is described in terms of the geometry of evolving planar curves in which the dynamics is determined by an underlying growth process. Steadily propagating tip shapes in two and three dimensions are found that are consistent with experimentally observed growth sequences.

Actinobacteria↗

PubMed2003

Biomechanical models of hyphal growth in actinomycetes.

The tip growth of filamentary actinomycetes is investigated within the framework of large deformation membrane theory in which the cell wall is represented as a growing elastic membrane with geometry-dependent elastic properties. The model exhibits realistic hyphal shapes and indicates a self-similar tip growth mechanism consistent with that observed in experiments. It also demonstrates a simple mechanism for hyphal swelling and beading that is observed in the presence of a lysing agent.

Actinobacteria↗

PubMed2003

Self-similar tip growth in filamentary organisms.

The growth of a family of filamentary microorganisms is described in terms of self-similar growth at the tip which is driven by pressure and sustained by a wall-building growth process. The cell wall is modeled biomechanically as a stretchable elastic membrane using large-deformation elasticity theory. Incorporation of geometry dependent elastic moduli and a self-similar ansatz shows how these equations can generate realistic tip shapes corresponding to a self-similar expansion process.

Actinobacteria↗

PubMed2002

Shape of a cracking whip.

The crack of a whip is produced by a shock wave created by the supersonic motion of the tip of the whip in the air. A simple dynamical model for the propagation and acceleration of waves in the motion of whips is presented. The respective contributions of tension, tapering, and boundary conditions in the acceleration of an initial impulse are studied theoretically and numerically.

Journal Article↗