Linear and nonlinear stiffness and friction in biological rhythmic movements

Biological rhythmic movements can be viewed as instances of self-sustained oscillators. Auto-oscillatory phenomena must involve a nonlinear friction function, and usually involve a nonlinear elastic function. With respect to rhythmic movements, the question is: What kinds of nonlinear friction and elastic functions are involved? The nonlinear friction functions of the kind identified by Rayleigh (involving terms such as $\dot \theta ^3 $ ) and van der Pol (involving terms such as $\theta ^2 \dot \theta $ ), and the nonlinear elastic functions identified by Duffing (involving terms such as $\theta ^3 $ ), constitute elementary nonlinear components for the assembling of self-sustained oscillators. Recently, additional elementary nonlinear friction and stiffness functions expressed, respectively, through terms such as $\theta ^2 \dot \theta ^3 $ and $\theta \dot \theta ^2 $ , and a methodology for evaluating the contribution of the elementary components to any given cyclic activity have been identified. The methodology uses a quantification of the continuous deviation of oscillatory motion from ideal (harmonic) motion. Multiple regression of this quantity on the elementary linear and nonlinear terms reveals the individual contribution of each term to the oscillator's non-harmonic behavior. In the present article the methodology was applied to the data from three experiments in which human subjects produced pendular rhythmic movements under manipulations of rotational inertia (experiment 1), rotational inertia and frequency (experiment 2), and rotational inertia and amplitude (experiment 3). The analysis revealed that the pendular oscillators assembled in the three experiments were compositionally rich, braiding linear and nonlinear friction and elastic functions in a manner that depended on the nature of the task.     

Instantaneous kinematic phase reflects neuromechanical response to lateral perturbations of running cockroaches

Instantaneous kinematic phase calculation allows the development of reduced-order oscillator models useful in generating hypotheses of neuromechanical control. When perturbed, changes in instantaneous kinematic phase and frequency of rhythmic movements can provide details of movement and evidence for neural feedback to a system-level neural oscillator with a time resolution not possible with traditional approaches. We elicited an escape response in cockroaches (Blaberus discoidalis) that ran onto a movable cart accelerated laterally with respect to the animals’ motion causing a perturbation. The specific impulse imposed on animals (0.50 $\pm $ 0.04 m s $^{-1}$ ; mean, SD) was nearly twice their forward speed (0.25 $\pm $ 0.06 m s $^{-1})$ . Instantaneous residual phase computed from kinematic phase remained constant for 110 ms after the onset of perturbation, but then decreased representing a decrease in stride frequency. Results from direct muscle action potential recordings supported kinematic phase results in showing that recovery begins with self-stabilizing mechanical feedback followed by neural feedback to an abstracted neural oscillator or central pattern generator. Trials fell into two classes of forward velocity changes, while exhibiting statistically indistinguishable frequency changes. Animals pulled away from the side with front and hind legs of the tripod in stance recovered heading within 300 ms, whereas animals that only had a middle leg of the tripod resisting the pull did not recover within this period. Animals with eight or more legs might be more robust to lateral perturbations than hexapods.     

D-Amino acid oxidase of Streptomyces coelicolor and the effect of D-amino acids on the bacterium

The homologous gene of D-amino acid oxidase (DAO) in prokaryotic organisms is predominantly found in a group of bacteria called the Actinobacteria. We have analyzed the DAO of the model actinomycete Streptomyces coelicolor and the effect of D-amino acids on this bacterium. When expressed in Escherichia coli, the translated product of the putative dao gene of this bacterium exhibited oxidase activity against neutral and basic D-amino acids, with a higher activity toward D-valine and D-isoleucine, but not to their corresponding L-amino acids. This substrate specificity was largely different from that of the DAO of the actinobacterium Arthrobacter protophormiae. The gene message and DAO activity were constitutively detected in S. coelicolor cells, and unlike eukaryotic DAOs, the presence of a D-amino acid did not significantly induce expression. The D-amino acids that were a good substrate for S. coelicolor DAO inhibited cell growth, delayed morphological development and affected cell morphology, but they did not inhibit biofilm formation. Disruption of the dao gene had no effect on the morphology and morphological development of S. coelicolor cells, the assimilation of D-valine or the sensitivity to growth inhibition by D-valine under the experimental conditions, showing that in this bacterium DAO does not play a significant role in either morphological development or the assimilation and detoxification of D-amino acids.     

When does pathogen evolution maximize the basic reproductive number in well-mixed host–pathogen systems?

Pathogen evolution towards the largest basic reproductive number, $\mathcal R _0$ , has been observed in many theoretical models, but this conclusion does not hold universally. Previous studies of host–pathogen systems have defined general conditions under which $\mathcal R _0$ maximization occurs in terms of $\mathcal R _0$ itself. However, it is unclear what constraints these conditions impose on the functional forms of pathogen related processes (e.g. transmission, recover, or mortality) and how those constraints relate to the characteristics of natural systems. Here we focus on well-mixed SIR-type host–pathogen systems and, via a synthesis of results from the literature, we present a set of sufficient mathematical conditions under which evolution maximizes $\mathcal R _0$ . Our conditions are in terms of the functional responses of the system and yield three general biological constraints on when $\mathcal R _0$ maximization will occur. First, there are no genotype-by-environment interactions. Second, the pathogen utilizes a single transmission pathway (i.e. either horizontal, vertical, or vector transmission). Third, when mortality is density dependent: (i) there is a single infectious class that individuals cannot recover from, (ii) mortality in the infectious class is entirely density dependent, and (iii) the rates of recovery, infection progression, and mortality in the exposed classes are independent of the pathogen trait. We discuss how this approach identifies the biological mechanisms that increase the dimension of the environmental feedback and prevent $\mathcal R _0$ maximization.     

Exploring the allosteric mechanism of dihydrodipicolinate synthase by reverse engineering of the allosteric inhibitor binding sites and its application for lysine production

Dihydrodipicolinate synthase (DHDPS, EC 4.2.1.52) catalyzes the first committed reaction of l-lysine biosynthesis in bacteria and plants and is allosterically regulated by l-lysine. In previous studies, DHDPSs from different species were proved to have different sensitivity to l-lysine inhibition. In this study, we investigated the key determinants of feedback regulation between two industrially important DHDPSs, the l-lysine-sensitive DHDPS from Escherichia coli and l-lysine-insensitive DHDPS from Corynebacterium glutamicum, by sequence and structure comparisons and site-directed mutation. Feedback inhibition of E. coli DHDPS was successfully alleviated after substitution of the residues around the inhibitor’s binding sites with those of C. glutamicum DHDPS. Interestingly, mutagenesis of the lysine binding sites of C. glutamicum DHDPS according to E. coli DHDPS did not recover the expected feedback inhibition but an activation of DHDPS by l-lysine, probably due to differences in the allosteic signal transduction in the DHDPS of these two organisms. Overexpression of l-lysine-insensitive E. coli DHDPS mutants in E. coli MG1655 resulted in an improvement of l-lysine production yield by 46 %.     

The Basic Reproduction Number for Cellular SIR Networks

The basic reproduction number \(R_0\) is the average number of new infections produced by a typical infective individual in the early stage of an infectious disease, following the introduction of few infective individuals in a completely susceptible population. If \(R_0<1\) , then the disease dies, whereas for \(R_0>1\) the infection can invade the host population and persist. This threshold quantity is well studied for SIR compartmental or mean field models based on ordinary differential equations, and a general method for its computation has been proposed by van den Driessche and Watmough. We concentrate here on SIR epidemiological models that take into account the contact network N underlying the transmission of the disease. In this context, it is generally admitted that \(R_{0}\) can be approximated by the average number \(R_{2,3}\) of infective individuals of generation three produced by an infective of generation two. We give here a simple analytic formula of \(R_{2,3}\) for SIR cellular networks. Simulations on two-dimensional cellular networks with von Neumann and Moore neighborhoods show that \(R_{2,3}\) can be used to capture a threshold phenomenon related the dynamics of SIR cellular network and confirm the good quality of the simple approach proposed recently by Aparicio and Pascual for the particular case of Moore neighborhood.     

A model for a non-chemical form of life: Crystalline physiology

A definition of fundamental living units is given according to which they are constituted by the material support of some ‘memory’ the latter is required

- to be stable,

- to contain rich information,

- to diffuse it into the surrounding medium.

It is then shown that the complex dislocation networks encountered in crystals can in some cases follow these criteria and lead to a crystalline physiology. The places of possible occurrence in nature of this kind of physiology, terrestrial and extraterrestrial rocks, interplanetary dust, white dwarfs and neutron stars are then discussed.     

Seasonal dynamics in an SIR epidemic system

We consider a seasonally forced SIR epidemic model where periodicity occurs in the contact rate. This periodical forcing represents successions of school terms and holidays. The epidemic dynamics are described by a switched system. Numerical studies in such a model have shown the existence of periodic solutions. First, we analytically prove the existence of an invariant domain $D$ containing all periodic (harmonic and subharmonic) orbits. Then, using different scales in time and variables, we rewrite the SIR model as a slow-fast dynamical system and we establish the existence of a macroscopic attractor domain $K$ , included in $D$ , for the switched dynamics. The existence of a unique harmonic solution is also proved for any value of the magnitude of the seasonal forcing term which can be interpreted as an annual infection. Subharmonic solutions can be seen as epidemic outbreaks. Our theoretical results allow us to exhibit quantitative characteristics about epidemics, such as the maximal period between major outbreaks and maximal prevalence.     

Excitonic connectivity between photosystem II units: what is it, and how to measure it?

In photosynthetic organisms, light energy is absorbed by a complex network of chromophores embedded in light-harvesting antenna complexes. In photosystem II (PSII), the excitation energy from the antenna is transferred very efficiently to an active reaction center (RC) (i.e., with oxidized primary quinone acceptor Q _A), where the photochemistry begins, leading to O₂ evolution, and reduction of plastoquinones. A very small part of the excitation energy is dissipated as fluorescence and heat. Measurements on chlorophyll (Chl) fluorescence and oxygen have shown that a nonlinear (hyperbolic) relationship exists between the fluorescence yield (Φ _F ) (or the oxygen emission yield, $ \Phi _{{{\text{O}}_{2} }} $ ) and the fraction of closed PSII RCs (i.e., with reduced Q _A). This nonlinearity is assumed to be related to the transfer of the excitation energy from a closed PSII RC to an open (active) PSII RC, a process called PSII excitonic connectivity by Joliot and Joliot (CR Acad Sci Paris 258: 4622–4625, 1964). Different theoretical approaches of the PSII excitonic connectivity, and experimental methods used to measure it, are discussed in this review. In addition, we present alternative explanations of the observed sigmoidicity of the fluorescence induction and oxygen evolution curves.     

Detection of d-amino acids in purified proteins synthesized in Escherichia coli

It has long been believed that amino acids comprising proteins of all living organisms are only of the l-configuration, except for Gly. However, peptidyl d-amino acids were observed in hydrolysates of soluble high molecular weight fractions extracted from cells or tissues of various organisms. This strongly suggests that significant amounts of d-amino acids are naturally present in usual proteins. Thus we analyzed the d-amino acid contents of His-tag-purified β-galactosidase and human urocortin, which were synthesized by Escherichia coli grown in controlled synthetic media. After acidic hydrolysis for various times at 110°C, samples were derivatized with 4-fluoro-7-nitro-2, 1, 3-benzoxadiazole (NBD-F) and separated on a reverse-phase column followed by a chiral column into d- and l-enantiomers. The contents of d-enantiomers of Ala, Leu, Phe, Val, Asp, and Glu were determined by plotting index d/(d + l) against the incubation time for hydrolysis and extrapolating the linear regression line to 0 h to eliminate the effect of racemization of amino acids during the incubation. Significant contents of d-amino acids were reproducibly detected, the d-amino acid profile being specific to an individual protein. This finding indicated the likelihood that d-amino acids are in fact present in the purified proteins. On the other hand, the d-amino acid contents of proteins were hardly influenced by the addition of d- or l-amino acids to the cultivation medium, whereas intracellular free d-amino acids sensitively varied according to the extracellular conditions. The origin of these d-amino acids detected in proteins was discussed.     

Analysis of endogenous d-amino acid-containing peptides in Metazoa

Peptides are chiral molecules with their structure determined by the composition and configuration of their amino acid building blocks. The naturally occurring amino acids, except glycine, possess two chiral forms. This allows the formation of multiple peptide diastereomers that have the same sequence. Although living organisms use l-amino acids to make proteins, a group of d-amino acid-containing peptides (DAACPs) has been discovered in animals that have at least one of their residues isomerized to the d-form via an enzyme-catalyzed process. In many cases, the biological functions of these peptides are enhanced due to this structural conversion. These DAACPs are different from those known to occur in bacterial cell wall and antibiotic peptides, the latter of which are synthesized in a ribosome-independent manner. DAACPs have now also been identified in a number of distinct groups throughout the Metazoa. Their serendipitous discovery has often resulted from discrepancies observed in bioassays or in chromatographic behavior between natural peptide fractions and peptides synthesized according to a presumed all-l sequence. Because this l to d post-translational modification is subtle and not detectable by most sequence determination approaches, it is reasonable to suspect that many studies have overlooked this change; accordingly, DAACPs may be more prevalent than currently thought. Although diastereomer separation techniques developed with synthetic peptides in recent years have greatly aided in the discovery of natural DAACPs, there is a need for new, more robust methods for naturally complex samples. In this review, a brief history of DAACPs in animals is presented, followed by discussion of a variety of analytical methods that have been used for diastereomeric separation and detection of peptides.     

l-Amino acid oxidases from microbial sources: types,properties, functions,and applications

l-Amino acid oxidases (LAAOs), which catalyze the stereospecific oxidative deamination of l-amino acids to α-keto acids and ammonia, are flavin adenine dinucleotide-containing homodimeric proteins. l-Amino acid oxidases are widely distributed in diverse organisms and have a range of properties. Because expressing LAAOs as recombinant proteins in heterologous hosts is difficult, their biotechnological applications have not been thoroughly advanced. LAAOs are thought to contribute to amino acid catabolism, enhance iron acquisition, display antimicrobial activity, and catalyze keto acid production, among other roles. Here, we review the types, properties, structures, biological functions, heterologous expression, and applications of LAAOs obtained from microbial sources. We expect this review to increase interest in LAAO studies.     

Synchronicity of movement paths of barren-ground caribou and tundra wolves

Movement patterns of highly mobile animals can reveal life history strategies and ecological relationships. We hypothesized that wolves (Canis lupus) would display similar movement patterns as their prey, barren-ground caribou (Rangifer tarandus groenlandicus), and that movements of the two species would co-vary with season. We tested for interspecific movement dynamics using animal locations from wolves and caribou monitored concurrently from mid-October to June, across the Northwest Territories and Nunavut, Canada. We used a correlated random walk as a null model to test for pattern in movements and the bearing procedure to detect whether movements were consistently directional. There was a statistical difference between the movements of caribou and wolves (F _1,9 = 13.232, P = 0.005), when compared to a correlated random walk, and a significant interaction effect between season and species (F _1,9 = 6.815, P = 0.028). During winter, the movements of caribou were strongly correlated with the 80°–90° ( $\overline{X}$ X ¯ r = 0.859, SE = 0.065) and 270°–280° ( $\overline{X}$ X ¯ r = 0.875, SE = 0.059) bearing classes suggesting an east–west movement gradient. Wolf movements during winter showed large variation in direction, but were generally east to west. Peak mean correlation for caribou movements during spring was distinct at 40°–50° ( $\overline{X}$ X ¯ r = 0.978, SE = 0.006) revealing movement to the north-east calving grounds. During spring, wolf movements correlated with the 80°–90° ( $\overline{X}$ X ¯ r = 0.861, SE = 0.043) and 270°–280° ( $\overline{X}$ X ¯ r = 0.850, SE = 0.064) bearing class. Directionality of movement suggested that during winter, caribou and wolves had a similar distribution at the large spatial scales we tested. During spring migration, however, caribou and wolves employed asynchronous movement strategies. Our findings demonstrate the utility of the correlated random walk and bearing procedure for quantifying the movement patterns of co-occurring species.     

Modeling Endocrine Control of the Pituitary–Ovarian Axis: Androgenic Influence and Chaotic Dynamics

Mathematical models of the hypothalamus-pituitary-ovarian axis in women were first developed by Schlosser and Selgrade in 1999, with subsequent models of Harris-Clark et al. (Bull. Math. Biol. 65(1):157–173, 2003) and Pasteur and Selgrade (Understanding the dynamics of biological systems: lessons learned from integrative systems biology, Springer, London, pp. 38–58, 2011). These models produce periodic in-silico representation of luteinizing hormone (LH), follicle stimulating hormone (FSH), estradiol (E2), progesterone (P4), inhibin A (InhA), and inhibin B (InhB). Polycystic ovarian syndrome (PCOS), a leading cause of cycle irregularities, is seen as primarily a hyper-androgenic disorder. Therefore, including androgens into the model is necessary to produce simulations relevant to women with PCOS. Because testosterone (T) is the dominant female androgen, we focus our efforts on modeling pituitary feedback and inter-ovarian follicular growth properties as functions of circulating total T levels. Optimized parameters simultaneously simulate LH, FSH, E2, P4, InhA, and InhB levels of Welt et al. (J. Clin. Endocrinol. Metab. 84(1):105–111, 1999) and total T levels of Sinha-Hikim et al. (J. Clin. Endocrinol. Metab. 83(4):1312–1318, 1998). The resulting model is a system of 16 ordinary differential equations, with at least one stable periodic solution. Maciel et al. (J. Clin. Endocrinol. Metab. 89(11):5321–5327, 2004) hypothesized that retarded early follicle growth resulting in “stockpiling” of preantral follicles contributes to PCOS etiology. We present our investigations of this hypothesis and show that varying a follicular growth parameter produces preantral stockpiling and a period-doubling cascade resulting in apparent chaotic menstrual cycle behavior. The new model may allow investigators to study possible interventions returning acyclic patients to regular cycles and guide developments of individualized treatments for PCOS patients.     

Studies on the progenies of hybrids from theArabis hirsuta complex

Progenies of triploid and diploid hybrids of tetraploidArabis hirsuta (L.)Scop. s. str. and diploidA. sagittata (Bertol.) DC. andA. planisiliqua (Pers.) Reichenb. were studied. The observations concerned morphology, cytology, sterility degree of plants and embryological backgrounds. The evolutionary consequences of breakage of the sterility barriers within the complex connected with well pronouced morphological and karyological variability of hybrids are discussed.     

Morphological features of F1 generation inRosa hybrids 1. Hybrids of some species of the sect.Caninae withRosa rugosa

In the present paper morphological features of hybrids from crossing of four species ofRosa sect.Caninae (R. canina L.,R. zalana Wiesb.,R. rubiginosa L. andR. sherardii Davies) withR. rugosa Thumbg. (sect.Cinnamomeae) and their heredity are described. F₁ generation appears more or less uniform, certain morphological features are patroclinal, other ones are matroclinal and intermediary. The general appearance of these hybrids is intermediary; there seems to be no reason to consider them matroclinal.     

Biaxial mechanical properties of the human thoracic and abdominal aorta,common carotid,subclavian, renal and common iliac arteries

The biomechanics of large- and medium-sized arteries influence the pathophysiology of arterial disease and the response to therapeutic interventions. However, a comprehensive comparative analysis of human arterial biaxial mechanical properties has not yet been reported. Planar biaxial extension was used to establish the passive mechanical properties of human thoracic (TA, \(n=8\) ) and abdominal (AA, \(n=7\) ) aorta, common carotid (CCA, \(n=21\) ), subclavian (SA, \(n=12\) ), renal (RA, \(n=13\) ) and common iliac (CIA, \(n=16\) ) arteries from 11 deceased subjects ( \(54\pm 21\)  years old). Histological evaluation determined the structure of each specimen. Experimental data were used to determine constitutive parameters for a structurally motivated nonlinear anisotropic constitutive model. All arteries demonstrated appreciable anisotropy and large nonlinear deformations. Most CCA, SA, TA, AA and CIA specimens were stiffer longitudinally, while most RAs were stiffer circumferentially. A switch in anisotropy was occasionally demonstrated for all arteries. The CCA was the most compliant, least anisotropic and least frequently diseased of all arteries, while the CIA and AA were the stiffest and the most diseased. The severity of atherosclerosis correlated with age, but was not affected by laterality. Elastin fibers in the aorta, SA and CCA were uniformly and mostly circumferentially distributed throughout the media, while in the RA and CIA, elastin was primarily axially aligned and concentrated in the external elastic lamina. Constitutive modeling provided good fits to the experimental data for most arteries. Biomechanical and architectural features of major arteries differ depending on location and functional environment. A better understanding of localized arterial mechanical properties may support the development of site-specific treatment modalities for arterial disease.     

l-Carnitine is essential to β-oxidation of quarried fatty acid from mitochondrial membrane by PLA2

Mitochondrial β-oxidation is an important system involved in the energy production of various cells. In this system, the function of l-carnitine is essential for the uptake of fatty acids to mitochondria. However, it is unclear whether or not endogenous respiration, ADP-induced O₂ consumption without substrates, is caused by l-carnitine treatment. In this study, we investigated whether l-carnitine is essential to the β-oxidation of quarried fatty acids from the mitochondrial membrane by phospholipase A₂ (PLA₂) using isolated mitochondria from the liver of rats. Intact mitochondria were incubated in a medium containing Pi, CoA and l-carnitine. The effect of l-carnitine treatment on ADP-induced mitochondrial respiration was observed without exogenous respiratory substrate. Increase in mitochondrial respiration was induced by treatment with l-carnitine in a concentration-dependent manner. Treatment with rotenone, a complex I blocker, completely inhibited ADP-induced oxygen consumption even in the presence of l-carnitine. Moreover, the l-carnitine dependent ADP-induced mitochondrial oxygen consumption did not increase when PLA₂ inhibitors were treated before ADP treatment. The l-carnitine-dependent ADP-induced oxygen consumption did contribute to ATP productions but not heat generation via an uncoupling system. These results suggest that l-carnitine might be essential to the β-oxidation of quarried fatty acids from the mitochondrial membrane by PLA₂.     

Random generation of RNA secondary structures according to native distributions

Background

Random biological sequences are a topic of great interest in genome analysis since, according to a powerful paradigm, they represent the background noise from which the actual biological information must differentiate. Accordingly, the generation of random sequences has been investigated for a long time. Similarly, random object of a more complicated structure like RNA molecules or proteins are of interest.

Results

In this article, we present a new general framework for deriving algorithms for the non-uniform random generation of combinatorial objects according to the encoding and probability distribution implied by a stochastic context-free grammar. Briefly, the framework extends on the well-known recursive method for (uniform) random generation and uses the popular framework of admissible specifications of combinatorial classes, introducing weighted combinatorial classes to allow for the non-uniform generation by means of unranking. This framework is used to derive an algorithm for the generation of RNA secondary structures of a given fixed size. We address the random generation of these structures according to a realistic distribution obtained from real-life data by using a very detailed context-free grammar (that models the class of RNA secondary structures by distinguishing between all known motifs in RNA structure). Compared to well-known sampling approaches used in several structure prediction tools (such as SFold) ours has two major advantages: Firstly, after a preprocessing step in time for the computation of all weighted class sizes needed, with our approach a set of m random secondary structures of a given structure size n can be computed in worst-case time complexity while other algorithms typically have a runtime in . Secondly, our approach works with integer arithmetic only which is faster and saves us from all the discomforting details of using floating point arithmetic with logarithmized probabilities.

Conclusion

A number of experimental results shows that our random generation method produces realistic output, at least with respect to the appearance of the different structural motifs. The algorithm is available as a webservice at http://wwwagak.cs.uni-kl.de/NonUniRandGen and can be used for generating random secondary structures of any specified RNA type. A link to download an implementation of our method (in Wolfram Mathematica) can be found there, too.