Host-feeding strategies of parasitoid wasps

Summary Three models of the evolution of host-feeding behaviour in parasitoid wasps are developed. The first assumes that the wasp host feeds purely to obtain resources to mature eggs (limited resource model) while the second assumes that host feeding provides energy for maintenance (pro-ovigenic model). The third model assumes that host feeding provides resources for both maintenance and egg maturation (resource pool model). Two variants of the third model are examined: the first assumes that the risk of mortality is constant and state-independent, the second that resource-depleted individuals suffer a higher risk of mortality. The models are analysed using a combination of stochastic dynamic programming and analytical techniques. The models make different predictions about the relationships between the probability of host feeding and egg load and host density. The available experimental evidence best supports the resource pool model.     

Mechanics of cranial sutures during simulated cyclic loading

Previous computational and experimental analyses revealed that cranial sutures, fibrous joints between the bones, can reduce the strain experienced by the surrounding skull bones during mastication. This damping effect reflects the importance of including sutures in finite element (FE) analyses of the skull. Using the FE method, the behaviour of three suture morphologies of increasing complexity (butt-ended, moderate interdigitated, and complex interdigitated) during static loading was recently investigated, and the sutures were assumed to have linear elastic properties. In the current study, viscoelastic properties, derived from published experimental results of the nasofrontal suture of young pigs (Sus scrofa), are applied to the three idealised bone-suture models. The effects of suture viscoelasticity on the stress, strain, and strain energy in the models were computed for three different frequencies (corresponding to periods of 1, 10, and 100s) and compared to the results of a static, linear elastic analysis. The range of applied frequencies broadly represents different physiological activities, with the highest frequency simulating mastication and the lowest frequency simulating growth and pressure of the surrounding tissues. Comparing across all three suture morphologies, strain energy and strain in the suture decreased with the increase in suture complexity. For each suture model, the magnitude of strain decreased with an increase in frequency, and the magnitudes were similar for both the elastic and 1s frequency analyses. In addition, a viscous response is less apparent in the higher frequency analyses, indicating that viscous properties are less important to the behaviour of the suture during those analyses. The FE results suggest that implementation of viscoelastic properties may not be necessary for computational studies of skull behaviour during masticatory loading but instead might be more relevant for studies examining lower frequency physiological activities.     

Power Dissipation in the Cochlea Can Enhance Frequency Selectivity

The cochlear cavity is filled with viscous fluids, and it is partitioned by a viscoelastic structure called the organ of Corti complex. Acoustic energy propagates toward the apex of the cochlea through vibrations of the organ of Corti complex. The dimensions of the vibrating structures range from a few hundred (e.g., the basilar membrane) to a few micrometers (e.g., the stereocilia bundle). Vibrations of microstructures in viscous fluid are subjected to energy dissipation. Because the viscous dissipation is considered to be detrimental to the function of hearing—sound amplification and frequency tuning—the cochlea uses cellular actuators to overcome the dissipation. Compared to extensive investigations on the cellular actuators, the dissipating mechanisms have not been given appropriate attention, and there is little consensus on damping models. For example, many theoretical studies use an inviscid fluid approximation and lump the viscous effect to viscous damping components. Others neglect viscous dissipation in the organ of Corti but consider fluid viscosity. We have developed a computational model of the cochlea that incorporates viscous fluid dynamics, organ of Corti microstructural mechanics, and electrophysiology of the outer hair cells. The model is validated by comparing with existing measurements, such as the viscoelastic response of the tectorial membrane, and the cochlear input impedance. Using the model, we investigated how dissipation components in the cochlea affect its function. We found that the majority of acoustic energy dissipation of the cochlea occurs within the organ of Corti complex, not in the scalar fluids. Our model suggests that an appropriate dissipation can enhance the tuning quality by reducing the spread of energy provided by the outer hair cells’ somatic motility.     

Acoustical response of hair receptors in insects

Summary A detailed mechanical model is developed to account for the behaviour of hair-like acoustical sensory receptors in insects. For the small hair diameters commonly found, it is concluded that the force acting on the moving hair is caused almost entirely by the viscosity of the air, as analyzed long ago by Stokes. The result of this viscous force is to provide a bending moment about the base of the hair that is proportional to the acoustic particle velocity but that lags behind it by about 135°. In addition the viscous force increases the moment of inertia of the hair by a large and frequency dependent addition, and provides a viscous damping term of sufficient magnitude to reduce the Q value to near unity.The measurements of Tautz (1977) on the thoracic hairs of the caterpillarBarathra brassicae are discussed in detail in terms of the model. Many of these observations are well accounted for, though a few discrepancies remain.This work is part of a programme in biological acoustics supported by the Australian Research Grants Committee.     

Linear propagation of pulsatile waves in viscoelastic tubes

An experimental and theoretical analysis is made of pulsatile wave propagation in deformable latex tubes as a model of the propagation of pressure pulses in arteries. A quasi one-dimensional linear model is used in which, in particular, attention is paid to the viscous phenomena in fluid and tube wall. The agreement between experimental and theoretical results is satisfactory. It appeared that the viscoelastic behaviour of the tube wall dominates the damping of the pressure pulse. Several linear models are used to describe the wall behaviour. No significant differences between the results of these models were found.     

An orthotropic viscoelastic material model for passive myocardium: theory and algorithmic treatment

This contribution presents a novel constitutive model in order to simulate an orthotropic rate-dependent behaviour of the passive myocardium at finite strains. The motivation for the consideration of orthotropic viscous effects in a constitutive level lies in the disagreement between theoretical predictions and experimentally observed results. In view of experimental observations, the material is deemed as nearly incompressible, hyperelastic, orthotropic and viscous. The viscoelastic response is formulated by means of a rheological model consisting of a spring coupled with a Maxwell element in parallel. In this context, the isochoric free energy function is decomposed into elastic equilibrium and viscous non-equilibrium parts. The baseline elastic response is modelled by the orthotropic model of Holzapfel and Ogden [Holzapfel GA, Ogden RW. 2009. Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos Trans Roy Soc A Math Phys Eng Sci. 367:3445–3475]. The essential aspect of the proposed model is the account of distinct relaxation mechanisms for each orientation direction. To this end, the non-equilibrium response of the free energy function is constructed in the logarithmic strain space and additively decomposed into three anisotropic parts, denoting fibre, sheet and normal directions each accompanied by a distinct dissipation potential governing the evolution of viscous strains associated with each orientation direction. The evolution equations governing the viscous flow have an energy-activated nonlinear form. The energy storage in the Maxwell branches has a quadratic form leading to a linear stress–strain response in the logarithmic strain space. On the numerical side, the algorithmic aspects suitable for the implicit finite element method are discussed in a Lagrangian setting. The model shows excellent agreement compared to experimental data obtained from the literature. Furthermore, the finite element simulations of a heart cycle carried out with the proposed model show significant deviations in the strain field relative to the elastic solution.     

A viscoelastic model of mechanically induced and spontaneous contractions of vascular smooth muscle

A new viscoelastic model was developed for the mathematical characterisation of mechanically induced and intrinsic contractional responses of the vascular smooth muscle. To this end, the elastic and viscous analogue elements were supplemented with a new active element generating stress proportional to its momentary elongation. The four-element model consisting of an active element, a parallel viscous element and both series and parallel elastic elements predicted biphasic or damped oscillatory stress relaxation and creep responses which were similar to that found experimentally earlier. Above a certain exciting frequency the model exhibited dissipative and below energy producing behaviour, as indicated by the sign change of the hysteresis loop area. In the case of sinusoidal modulation of the stress generation parameter the model showed parametric resonance, which was regarded as a simulation of intrinsic oscillation of the smooth muscle.     

Optimal posture control of a musculo-skeletal arm model

 In this paper maximal performance posture control of the human arm is investigated by means of model simulations. Recent experiments (F.C.T. van der Helm, submitted, 2000) have shown that the reflexive feedback during postural control varies with the bandwidth of the applied force disturbances. This paper focusses on the influence of the frequency content of force disturbances on the reflexive feedback gains by means of optimization. The arm is modelled by a non-linear musculo-skeletal model with two degrees of freedom and six muscles. To facilitate the optimization of the model parameters, the arm model is linearized. A performance criterion is minimized for stochastic force disturbances in a two-step procedure: (1) optimization of static muscle activations using an additional energy criterion to obtain a unique and energy-efficient solution; and (2) optimization of reflex gains using an additional control effort criterion to obtain a unique solution. The optimization reveals that for the given task and posture, the shoulder muscles have the largest contribution, whereas the bi-articular muscles have a relatively small contribution to the behaviour. The dynamics at the endpoint level are estimated so that a comparison can be made with the experiments. Compared to the experiments, the intrinsic damping of the model is relatively large (about 150%), whereas the intrinsic stiffness is relatively small (about 60%). These differences can be attributed to unmodelled mechanical effects of cross-bridges in Hill-type muscle models. The optimized reflex gains show remarkable similarities with the values found in the experiments, implying that humans can adjust their reflexive feedback gains in an optimal way, weighting the performance and energy. The approach in this paper could be useful in the study of various posture tasks, for example in the prediction of the relation between the control parameters of various musculo-skeletal models and different experimental variables. Received: 24 January 2000 / Accepted in revised form: 7 July 2000     

Viscous Damping of Vibrations in Microtubules

Pokorný et al. have recently suggested that metabolic processes drivemicrotubules in a cell to vibrate at Megahertz frequencies, but the theorydoes not explicitly consider dissipative effects which will tend to damp outthe vibrations. To examine the effects of viscous damping on the structure,we determine viscous forces and rate of energy loss in a cylinderundergoing longitudinal oscillations in water. A nondimensional expressionis obtained for the viscous drag on the cylinder. When applied to amicrotubule, the results indicate that viscous damping is several orders ofmagnitude too large to allow resonant vibrations.     

A mechanistic model of photosynthesis in microalgae

A dynamic model of photosynthesis is developed, accounting for factors such as photoadaptation, photoinhibition, and the "flashing light effect." The model is shown to explain the reported photosynthesis-irradiance responses observed under various conditions (constant low light, constant intense irradiance, flashing light, diurnal variation in irradiance). As significant distinguishing features, the model assumes: (1) The stored photochemical energy is consumed in an enzyme-mediated process that obeys Michaelis-Menten kinetics; and (2) photoinhibition has a square-root dependence on irradiance. Earlier dynamic models of photosynthesis assumed a first-order dependence of photoinhibition on irradiance and different kinetics of consumption of the stored energy than used in this work. These earlier models could not explain the photosynthesis-irradiance behavior under the full range of irradiance scenarios-a shortcoming that is overcome in the model developed in this work.     

Vibration of DNA polymer in viscous solvent

The problem of viscous damping of vibrating DNA polymer in solution is solved in the low-amplitude limit for all acoustic branches of the spectrum. The acoustic spectrum covers the microwave region of frequencies. Analytic solutions are obtained for a model describing the DNA polymer as a smooth circular cylinder. Numerical solutions are presented for a model describing the DNA polymer as a twisted cylinder of elliptical cross section. The amount of mass loading is determined for both models and the damped spectrum for the mass-loaded oscillator is calculated. The viscous damping is found to be a strong function of frequency, singular at very low frequencies for all modes except the torsional mode of the circular cylinder. All acoustic modes are overdamped, implying that the observation of well-defined resonances in DNA requires either highly structured water on the molecular level or very dry material.     

Conventional and complex modal analyses of a finite element model of human head and neck

This study employs both the traditional and the complex modal analyses of a detailed finite element model of human head–neck system to determine modal responses in terms of resonant frequencies and mode shapes. It compares both modal responses without ignoring mode shapes, and these results are reasonably in agreement with the literature. Increasing displacement contour loops within the brain in higher frequency modes probably exhibits the shearing and twisting modes of the brain. Additional and rarely reported modal responses such as ‘mastication’ mode of the mandible and flipping mode of nasal lateral cartilages are identified. This suggests a need for detailed modelling to identify all the additional frequencies of each individual part. Moreover, it is found that a damping factor of above 0.2 has amplifying effect in reducing higher frequency modes, while a diminishing effect in lowering peak biomechanical responses, indicating the importance of identifying the appropriate optimised damping factor.     

Sex ratios and the evolution of eusociality in the hymenoptera

The potential role of sex ratio biassing in the evolution of worker behaviour in male-haploid hymenopteran insects is examined using a deterministic genetic model. The model is based on a bivoltine life cycle with annual colonies and it assumes five gene loci, each of them controlling a specific feature of the life cycle (particularly brood sex ratios). The hypothetical gene controlling worker behaviour is assumed to be expressed either in the mothers (parental manipulation models) or in the female offspring (offspring altruism models). The threshold of the worker efficiency required for the worker behaviour to evolve is 0.5 under parental manipulation and 1.0 under offspring altruism when the sex ratios are not skewed. Worker evolution by offspring altruism can evolve more easily if the first workers initially raise mainly female brood. With such a sex ratio bias, the threshold of worker efficiency allowing eusociality to evolve drops below 1.0, even close to 0.8. Worker evolution is also favoured by the elimination of males from the first of the two annually occurring offspring generations. It is concluded that the male-haploid sex determination can, through the control of sex ratios, play a significant role in the evolution of eusociality in hymenopteran insects.     

Additive mixed effect model for clustered failure time data

We propose an additive mixed effect model to analyze clustered failure time data. The proposed model assumes an additive structure and includes a random effect as an additional component. Our model imitates the commonly used mixed effect models in repeated measurement analysis but under the context of hazards regression; our model can also be considered as a parallel development of the gamma-frailty model in additive model structures. We develop estimating equations for parameter estimation and propose a way of assessing the distribution of the latent random effect in the presence of large clusters. We establish the asymptotic properties of the proposed estimator. The small sample performance of our method is demonstrated via a large number of simulation studies. Finally, we apply the proposed model to analyze data from a diabetic study and a treatment trial for congestive heart failure.     

Human ankle joint stiffness over the full range of muscle activation levels

System identification techniques have been used to track changes in dynamic stiffness of the human ankle joint over a wide range of muscle contraction levels. Subjects lay supine on an experimental table with their left foot encased in a rigid, low-inertia cast which was fixed to an electro-hydraulic actuator operating as a position servo. Subjects generated tonic plantarflexor or dorsiflexor torques of different magnitudes ranging from rest to maximum voluntary contractions (MVC) during repeated presentations of a stochastic ankle angular position perturbation. Compliance impulse response functions (IRF) were determined from every 2.5 s perturbation sequence. The gain (G), natural frequency (omega n), and damping (zeta) parameters of the second-order model providing the best fit to each IRF were determined and used to compute the corresponding inertial (I), viscous (B) and elastic (K) stiffness parameters. The behaviour of these parameters with mean torque was found to follow two simple rules. First, the elastic parameter (K) increased in proportion to mean ankle torque as it was varied from rest to MVC; these changes were considerable involving increases of more than an order of magnitude. Second, the damping parameter (zeta) remained almost invariant over the entire range of contractions despite the dramatic changes in K.     

Resonant ac-dc magnetic fields: calculated response

An elementary model consisting of one charged particle in a viscous medium exposed to weak ac-dc low-frequency magnetic fields is analyzed to identify and explain the fundamental characteristics of the physical mechanisms that result in a resonance response, which is similar to the familiar cyclotron resonance. The model predicts both frequency and amplitude windows, which are explained in terms of synchronization of the particle with electric fields. Although extrapolation of model results to biological systems is limited by the elementary nature of the model, the model results indicate that observed resonant responses by others of biological systems to ac-dc magnetic fields are probably not due to resonant response of ions in solution, since the model predicts that no resonant response is possible unless the viscous damping is very low, many orders of magnitude lower than the viscous damping of ions in solution.     

Likelihood models for detecting positively selected amino acid sites and applications to the HIV-1 envelope gene.

Several codon-based models for the evolution of protein-coding DNA sequences are developed that account for varying selection intensity among amino acid sites. The "neutral model" assumes two categories of sites at which amino acid replacements are either neutral or deleterious. The "positive-selection model" assumes an additional category of positively selected sites at which nonsynonymous substitutions occur at a higher rate than synonymous ones. This model is also used to identify target sites for positive selection. The models are applied to a data set of the V3 region of the HIV-1 envelope gene, sequenced at different years after the infection of one patient. The results provide strong support for variable selection intensity among amino acid sites The neutral model is rejected in favor of the positive-selection model, indicating the operation of positive selection in the region. Positively selected sites are found in both the V3 region and the flanking regions.     

Models of skeletal muscle to explain the increase in passive stiffness in desmin knockout muscle

Absence of desmin in skeletal muscle was found to induce an increase in passive stiffness. The present study aimed at developing rheological models of passive muscle to explain this stiffening. Models were elaborated by using experimental data depicting muscle viscoelastic behaviour. The experimental protocol included stepwise extension tests applied on control and desmin knockout soleus muscles from mice. Linear and non-linear models were composed of elastic and viscous elements. They were constructed with the aim at taking the presence or absence of desmin into account by simulating desmin as an elastic element. Furthermore, associated adaptation of connective tissues in absence of desmin was modelled as an additional elastic element. Differences in passive behaviour induced by absence of desmin were predicted by using a linear model and a non-linear one. The non-linear model was selected because: (1) it is able to predict experimental viscoelastic kinetics accounting for the increase in passive stiffness in muscles lacking desmin, (2) its design is consistent with morphological data, and (3) stiffness characteristics of its elements are in accordance with the literature. Finally, this modelling approach demonstrates that both absence of desmin and adaptation of connective tissue are required to explain the increase in passive stiffness in desmin knockout muscles.