Patrick D. Shipman

Modeling the contribution of individual proteins to mixed skeletal muscle protein synthetic rates over increasing periods of label incorporation

Advances in stable isotope approaches, primarily the use of deuterium oxide ((2)H2O), allow for long-term measurements of protein synthesis, as well as the contribution of individual proteins to tissue measured protein synthesis rates. Here, we determined the influence of individual protein synthetic rates, individual protein content, and time of isotopic labeling on the measured synthesis rate of skeletal muscle proteins. To this end, we developed a mathematical model, applied the model to an established data set collected in vivo, and, to experimentally test the impact of different isotopic labeling periods, used (2)H2O to measure protein synthesis in cultured myotubes over periods of 2, 4, and 7 days. We first demonstrated the influence of both relative protein content and individual protein synthesis rates on measured synthesis rates over time. When expanded to include 286 individual proteins, the model closely approximated protein synthetic rates measured in vivo. The model revealed a 29% difference in measured synthesis rates from the slowest period of measurement (20 min) to the longest period of measurement (6 wk). In support of these findings, culturing of C2C12 myotubes with isotopic labeling periods of 2, 4, or 7 days revealed up to a doubling of the measured synthesis rate in the shorter labeling period compared with the longer period of labeling. From our model, we conclude that a 4-wk period of labeling is ideal for considering all proteins in a mixed-tissue fraction, while minimizing the slowing effect of fully turned-over proteins. In addition, we advocate that careful consideration must be paid to the period of isotopic labeling when comparing mixed protein synthetic rates between studies.

Anomalous patterns and nearly defect-free ripples produced by bombarding silicon and germanium with a beam of gold ions

We demonstrate that surface ripples with an exceptionally high degree of order can develop when germanium is bombarded with a broad beam of gold ions. In contrast, if silicon is sputtered with an Au− beam, patches of ripples with two distinct wave vectors can emerge. These types of order can be understood if the coupling between the surface morphology and composition is taken into account.

Highly ordered nanoscale surface ripples produced by ion bombardment of binary compounds

Nanoscale surface ripples generated by oblique-incidence ion bombardment of a solid are generally full of defects, and this has prevented the widespread adoption of ion bombardment as a nanofabrication tool. We advance a theory that predicts that remarkably defect-free ripples can be produced by ion bombardment of a binary material if the ion species, energy and angle of incidence are appropriately chosen. This high degree of order results from the coupling between the surface height and composition, and cannot be achieved by bombarding an elemental material.

Producing nanodot arrays with improved hexagonal order by patterning surfaces before ion sputtering.

When the surface of a nominally flat binary material is bombarded with a broad, normally incident ion beam, disordered hexagonal arrays of nanodots can form. Shipman and Bradley have derived equations of motion that govern the coupled dynamics of the height and composition of such a surface [Shipman and Bradley, Phys. Rev. B 84, 085420 (2011)]. We investigate the influence of initial conditions on the hexagonal order yielded by integration of those equations of motion. The initial conditions studied are hexagonal and sinusoidal templates, straight scratches, and nominally flat surfaces. Our simulations indicate that both kinds of templates lead to marked improvements in the hexagonal order if the initial wavelength is approximately equal to or double the linearly selected wavelength. Scratches enhance the hexagonal order in their vicinity if their width is close to or less than the linearly selected wavelength. Our results suggest that prepatterning a binary material can dramatically increase the hexagonal order achieved at large ion fluences.

A NEW INVARIANT IN PLANT PHYLLOTAXIS

It has been known for centuries that the configurations of phylla (flowers, bracts) on plants have special properties. The difference in angular positions of successive phylla is locally constant (called the divergence angle) and is close to the golden angle; the radial positions are related by the locally constant plastichrone ratio. The phylla themselves lie on clockwise and counterclockwise families of spirals and the numbers in each family follow, for many plants, the regular Fibonacci sequence. We introduce a new invariant related to the self-similar nature of the phyllotactic pattern which essentially tells one about the shapes of the deformations from which the pattern is formed.

Optimally Topologically Transitive Orbits in Discrete Dynamical Systems

Abstract Every orbit of a rigid rotation of a circle by a fixed irrational angle is dense. However, the apparent uniformity of the distribution of iterates after a finite number of iterations appears strikingly different for various choices of a rotation angle. Motivated by this observation, we introduce a scalar function on the orbits of a discrete dynamical system defined on a bounded metric space, called the linear limit density, which we interpret as a measure of an orbits approach to density. Utilizing the three-distance theorem, we compute the exact value of the linear limit density of orbits of rigid rotations by irrational rotation angles with period-1 continued fraction expansions. We further show that any discrete dynamical system defined by an orientation-preserving diffeomorphism of the circle has an orbit with a larger linear limit density than any orbit of the rigid rotation by the golden number. Bernoulli shift maps acting on sequences over a finite alphabet provide another illustrative class of dynamical systems with dense orbits. Our study of the efficiency of an orbits approach to density leads us to demonstrate the existence of a class of infinite sequences with finite linear limit density constructed by recursively extending finite de Bruijn sequences.

Simple yet Hidden Counterexamples in Undergraduate Real Analysis

Abstract We study situations in introductory analysis in which students affirmed false statements as true, despite simple counterexamples that they easily recognized afterwards. The study draws attention to how simple counterexamples can become hidden in plain sight, even in an active learning atmosphere where students proposed simple (as well as more complex) counterexamples daily in class. We provide perspective on these observations in the context of an informative body of related work in undergraduate mathematics studies.

Enhanced skeletal muscle regrowth and remodelling in massaged and contralateral non‐massaged hind limb

Muscle fibre cross sectional area is enhanced with massage in the form of cyclic compressive loading during regrowth after atrophy. Massage enhances protein synthesis of the myofibrillar and cytosolic, but not the mitochondrial fraction, in muscle during regrowth. Focal adhesion kinase activation and satellite cell number are elevated in muscles undergoing massage during regrowth. Muscle fibre cross sectional area and protein synthesis of the myofibrillar fraction, but not DNA synthesis, are elevated in muscle of the contralateral non‐massaged limb. Massage in the form of cyclic compressive loading is a potential anabolic intervention during muscle regrowth after atrophy.

The role of water and fire in driving tree dynamics in Australian savannas

Summary Ecologists rely on models to explore tree compositional changes especially when occurring over decades or centuries. In this article, we construct a theoretical, mathematical model to investigate the long-term relationships between savanna stand structure, water resource availability and fire disturbance. We show how dry season length, rather than mean annual precipitation, leads to savanna stability, and how the soil properties and variation in annual rainfall distribution determines a climatic equilibrium for woody total basal area, with fire disturbance acting as a perturbation away from this state. This leads to our premise that rainfall and tree population dynamics drives the savanna state leading to grasses and fire, rather than grasses promoting fire to drive the savannas. The model predicts that savanna tree stands undergo cyclic variation in tree populations as a result of long-term population cycles and germination events. This outcome is true regardless of the presence of fire, however, fire does introduce a more heterogeneous stand size structure. Synthesis. Using a mathematically transparent model for water resource availability and stand structure in savannas, we demonstrate how seasonal rainfall distribution, specifically seasonal drought, acts as the primary determinant for stand structure through stand water dynamics, with frequent fire disturbance able to reduce the populations from the climatically induced state.

Modeling the presence probability of invasive plant species with nonlocal dispersal.

Mathematical models for the spread of invading plant organisms typically utilize population growth and dispersal dynamics to predict the time-evolution of a population distribution. In this paper, we revisit a particular class of deterministic contact models obtained from a stochastic birth process for invasive organisms. These models were introduced by Mollison (J R Stat Soc 39(3):283, 1977). We derive the deterministic integro-differential equation of a more general contact model and show that the quantity of interest may be interpreted not as population size, but rather as the probability of species occurrence. We proceed to show how landscape heterogeneity can be included in the model by utilizing the concept of statistical habitat suitability models which condense diverse ecological data into a single statistic. As ecologists often deal with species presence data rather than population size, we argue that a model for probability of occurrence allows for a realistic determination of initial conditions from data. Finally, we present numerical results of our deterministic model and compare them to simulations of the underlying stochastic process.