A thermomechanical framework for reconciling the effects of ultraviolet radiation exposure time and wavelength on connective tissue elasticity

Augmentation of the mechanical properties of connective tissue using ultraviolet (UV) radiation—by targeting collagen cross-linking in the tissue at predetermined UV exposure time \((t)\) and wavelength \((\lambda )\) —has been proposed as a therapeutic method for supporting the treatment for structural-related injuries and pathologies. However, the effects of \(\lambda \) and \(t\) on the tissue elasticity, namely elastic modulus \((E)\) and modulus of resilience \((u_\mathrm{Y})\) , are not entirely clear. We present a thermomechanical framework to reconcile the \(t\) - and \(\lambda \) -related effects on \(E\) and \(u_\mathrm{Y}\) . The framework addresses (1) an energy transfer model to describe the dependence of the absorbed UV photon energy, \(\xi \) , per unit mass of the tissue on \(t\) and \(\lambda \) , (2) an intervening thermodynamic shear-related parameter, \(G\) , to quantify the extent of UV-induced cross-linking in the tissue, (3) a threshold model for the \(G\) versus \(\xi \) relationship, characterized by   \(t_\mathrm{C}\) —the critical \(t\) underpinning the association of \(\xi \) with \(G\) —and (4) the role of \(G\) in the tissue elasticity. We hypothesized that \(G\) regulates \(E\) (UV-stiffening hypothesis) and \(u_\mathrm{Y}\) (UV-resilience hypothesis). The framework was evaluated with the support from data derived from tensile testing on isolated ligament fascicles, treated with two levels of \(\lambda \) (365 and 254 nm) and three levels of \(t\) (15, 30 and 60 min). Predictions from the energy transfer model corroborated the findings from a two-factor analysis of variance of the effects of \(t\) and \(\lambda \) treatments. Student’s t test revealed positive change in \(E\) and \(u_\mathrm{Y}\) with increases in \(G\) —the findings lend support to the hypotheses, implicating the implicit dependence of UV-induced cross-links on \(t\) and \(\lambda \) for directing tissue stiffness and resilience. From a practical perspective, the study is a step in the direction to establish a UV irradiation treatment protocol for effective control of exogenous cross-linking in connective tissues.     

DFT study of nano zinc/copper voltaic cells

To facilitate the development of new materials for use in batteries, it is necessary to develop ab initio full-electron computational techniques for modeling potential new battery materials. Here, we tested density functional theory procedures that are accurate enough to obtain the energetics of a zinc/copper voltaic cell. We found the magnitude of the zero-point energy correction to be 0.01–0.2 kcal/mol per atom or molecule and the magnitude of the dispersion correction to be 0.1–0.6 kcal/mol per atom or molecule for Zn _n , (H₂O) _n , \( \mathrm{Zn}{\left({\mathrm{H}}_2\mathrm{O}\right)}_n^{2+} \), \( \mathrm{Cu}{\left({\mathrm{H}}_2\mathrm{O}\right)}_n^{2+} \), and Cu _n . Counterpoise correction significantly affected the values of ?\( {E}_n^{\mathrm{abs}} \), ?\( {E}_n^{\mathrm{coh}} \), and ?E^solv by 1.0–3.1 kcal/mol per atom or molecule at the B3PW91/6-31G(d) level of theory, but by only 0.04–0.4 kcal/mol per atom or molecule at the B3PW91/cc-pVTZ level of theory. The application of B3PW91/6-31G(d) yielded results that differed from macroscopic experimental values by 0.1–7.1 kcal/mol per atom or molecule, whereas applying B3PW91/cc-pVTZ produced results that differed from macroscopic experimental values by 0.1–4.8 kcal/mol per atom or molecule, with the smallest differences occurring for reactions with a small macroscopic experimental ?E and the largest differences occurring for reactions with a large macroscopic experimental ?E, implying size consistency.     

Theoretical study on the tautomerization of 1,5-diaminotetrazole (DAT)

The ground and excited states, charge injection/transport, and phosphorescence properties of five N?heterocyclic carbine-functionalized Pt^II complexes were investigated by using the DFT method. By analyzing the nonradiative (k _nr) rate constant and energies at \( {\mathrm{S}}_0^{\mathrm{opt}} \) and \( {\mathrm{T}}_1^{\mathrm{opt}} \) states, it is possible to forecast that BC5 with the pyrrole ligand has a higher phosphorescence quantum yield than any of the other four complexes. Thus, we consider that BC5 will be an efficient phosphorescent material that has balanced electron/hole-transport performance as well as high phosphorescence quantum yield. The calculated results indicate that, for the studied complexes, the nature of the ligand strongly affected the energy of the emissive state and was able to tune the emission color. We hope that our study will aid better understanding of the structure–property relationship of phosphorescent Pt (II) complexes and provide constructive information for designing novel and highly efficient OLED materials in the future.     

The effects of temperature and exercise training on swimming performance in juvenile qingbo (Spinibarbus sinensis)

To investigate the effects of temperature and exercise training on swimming performance in juvenile qingbo (Spinibarbus sinensis), we measured the following: (1) the resting oxygen consumption rate $ \left( {{\dot{\text{M}}\text{O}}_{{ 2 {\text{rest}}}} } \right) $ , critical swimming speed (U _crit) and active oxygen consumption rate $ \left( {{\dot{\text{M}}\text{O}}_{{ 2 {\text{active}}}} } \right) $ of fish at acclimation temperatures of 10, 15, 20, 25 and 30 °C and (2) the $ \dot{M}{\text{O}}_{{ 2 {\text{rest}}}} $ , U _crit and $ \dot{M}{\text{O}}_{{ 2 {\text{active}}}} $ of both exercise-trained (exhaustive chasing training for 14 days) and control fish at both low and high acclimation temperatures (15 and 25 °C). The relationship between U _crit and temperature (T) approximately followed a bell-shaped curve as temperature increased: U _crit = 8.21/{1 + [(T ? 27.2)/17.0]²} (R ² = 0.915, P < 0.001, N = 40). The optimal temperature for maximal U _crit (8.21 BL s^?1) in juvenile qingbo was 27.2 °C. Both the $ \dot{M}{\text{O}}_{{ 2 {\text{active}}}} $ and the metabolic scope (MS, $ \dot{M}{\text{O}}_{{ 2 {\text{active}}}} - \dot{M}{\text{O}}_{{ 2 {\text{rest}}}} $ ) of qingbo increased with temperature from 10 to 25 °C (P < 0.05), but there were no significant differences between fish acclimated to 25 and 30 °C. The relationships between $ \dot{M}{\text{O}}_{{ 2 {\text{active}}}} $ or MS and temperature were described as $ {\dot{\text{M}}\text{O}}_{{ 2 {\text{active}}}} = 1,214.29/\left\{ {1 + \left[ {\left( {T - 28.8} \right)/10.6} \right]^{2} } \right\}\;\left( {R^{2} = 0.911,\;P < 0.001,\;N = 40} \right) $ and MS = 972.67/{1 + [(T ? 28.0)/9.34]²} (R ² = 0.878, P < 0.001, N = 40). The optimal temperatures for $ \dot{M}{\text{O}}_{{ 2 {\text{active}}}} $ and MS in juvenile qingbo were 28.8 and 28.0 °C, respectively. Exercise training resulted in significant increases in both U _crit and $ \dot{M}{\text{O}}_{{ 2 {\text{active}}}} $ at a low temperature (P < 0.05), but training exhibited no significant effect on either U _crit or $ \dot{M}{\text{O}}_{{ 2 {\text{active}}}} $ at a high temperature. These results suggest that exercise training had different effects on swimming performance at different temperatures. These differences may be related to changes in aerobic metabolic capability, arterial oxygen delivery, available dissolved oxygen, imbalances in ion fluxes and stimuli to remodel tissues with changes in temperature.     

Continuous cultivation of Lactobacillus brevis NCL912 for production of gamma-aminobutyric acid

A continuous cultivation method for Lactobacillus brevis NCL912 to synthesize gamma-aminobutyric acid was developed in this work. Different dilution rates were evaluated for obtaining steady state in continuous cultivation. The results showed that steady state could be achieved at dilution rates from 0.08 to 0.12 h^?1. The highest gamma-aminobutyric acid productivity (5.11 g L^?1?h^?1) was obtained at dilution rate of 0.09 h^?1. The kinetic models were established for continuous gamma-aminobutyric acid production by using the Monod equation for microbial growth, and the Luedeking–Piret equation for product formation. The microbial growth and product formation can be described by equations $ \mu = {{{0.1234{C_S}}} \left/ {{\left( {0.9338+{C_S}} \right)}} \right.} $ and $ {Q_P}=6.86\,\mathrm{g}\,{{\mathrm{g}}^{-1 }}\mathrm{cell}\,{{\mathrm{h}}^{-1 }} $ , respectively. The production of gamma-aminobutyric acid by L. brevis NCL912 was non-growth-associated.     

Alzheimer’s disease: analysis of a mathematical model incorporating the role of prions

We introduce a mathematical model of the in vivo progression of Alzheimer’s disease with focus on the role of prions in memory impairment. Our model consists of differential equations that describe the dynamic formation of \(\upbeta \) -amyloid plaques based on the concentrations of A \(\upbeta \)  oligomers, PrP^C proteins, and the A \(\upbeta \) - \(\times \) -PrP^Ccomplex, which are hypothesized to be responsible for synaptic toxicity. We prove the well-posedness of the model and provided stability results for its unique equilibrium, when the polymerization rate of \(\upbeta \) -amyloid is constant and also when it is described by a power law.     

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.     

Modeling analysis of the lipid bilayer–cytoskeleton coupling in erythrocyte membrane

Studies of thermal fluctuations in discocytes, echinocytes, and spherocytes suggest that the coupling between lipid bilayer and cytoskeleton can affect viscoelastic behavior of single erythrocyte membranes. To test this hypothesis, we developed a 3D constitutive model describing viscoelastic behavior of erythrocyte membranes, at long relaxation times \(t \in [0.20\,\mathrm {s}, 1.05\,\mathrm {s}]\) and short relaxation times \(t \in [0.03\,\mathrm {s}, 0.20\,\mathrm {s}]\) . The model was constructed using combination of spring and spring pot rheological elements arranged in parallel. The rearrangement of cytoskeleton induced by changing the bending state of lipid bilayer was described by a modified Eyring model. The model predictions point to an anomalous nature of energy dissipation and an ordered harmonic nature of the coupling mechanism described by a series of fractional derivatives of the order n \(\alpha \) (where \( n \in [- 1, 2]\) ). As a result, the stress generated within the lipid bilayer is related to the rate of change of the irreversible stress within the cytoskeleton.     

Dynamic permeability of the lacunar–canalicular system in human cortical bone

A new method for the experimental determination of the permeability of a small sample of a fluid-saturated hierarchically structured porous material is described and applied to the determination of the lacunar–canalicular permeability \((K_\mathrm{LC})\) in bone. The interest in the permeability of the lacunar–canalicular pore system (LCS) is due to the fact that the LCS is considered to be the site of bone mechanotransduction due to the loading-driven fluid flow over cellular structures. The permeability of this space has been estimated to be anywhere from \(10^{-17}\;\) to \(10^{-25}\; \hbox {m}^{2}\) . However, the vascular pore system and LCS are intertwined, rendering the permeability of the much smaller-dimensioned LCS challenging to measure. In this study, we report a combined experimental and analytical approach that allowed the accurate determination of the \(K_\mathrm{LC}\) to be on the order of \(10^{-22}\; \hbox {m}^{2}\) for human osteonal bone. It was found that the \(K_\mathrm{LC}\) has a linear dependence on loading frequency, decreasing at a rate of \(2 \times 10^{-24}\; \hbox {m}^{2}\) /Hz from 1 to 100 Hz, and using the proposed model, the porosity alone was able to explain 86 % of the \(K_\mathrm{LC}\) variability.     

Principal trabecular structural orientation predicted by quantitative ultrasound is strongly correlated with \upmu FEA determined anisotropic apparent stiffness

The microarchitecture and alignment of trabecular bone adapts to the particular mechanical milieu applied to it. Due to this anisotropic mechanical property, measurement orientation has to be taken into consideration when assessing trabecular bone quality and fracture risk prediction. Quantitative ultrasound (QUS) has demonstrated the ability in predicting the principal structural orientation (PSO) of trabecular bone. Although the QUS prediction for PSO is very close to that of \(\upmu \) CT, certain angle differences still exist. It remains unknown whether this angle difference can induce significant differences in mechanical properties or not. The objective of this study was to evaluate the mechanical properties in different PSOs predicted using different methods, QUS and \(\upmu \) CT, thus to investigate the ability of QUS as a means to predict the PSO of trabecular bone noninvasively. By validating the ability of QUS to predict the PSO of trabecular bone, it is beneficial for future QUS applications because QUS measurements in the PSO can provide information more correlated with the mechanical properties than with other orientations. In this study, seven trabecular bone balls from distal bovine femurs were used to generate finite element models based on the 3-dimensional \(\upmu \) CT images. Uniaxial compressive loading was performed on the bone ball models in the finite element analysis (FEA) in six different orientations (three anatomical orientations, two PSOs predicted by QUS and the longest vector of mean intercept length (MIL) tensor calculated by \(\upmu \) CT). The stiffness was calculated based on the reaction force of the bone balls under loading, and the von Mises stress results showed that both the mechanical properties in the PSOs predicted by QUS are significantly higher than the anatomical orientations and comparatively close to the longest vector of MIL tensor. The stiffness in the PSOs predicted by QUS is also highly correlated with the stiffness in the MIL tensor orientation (ATTmax vs. MIL, \(R^{2}\)  = 0.98, \(p<001\) ; UVmax vs. MIL, \(R^{2}\)  = 0.92, \(p<001\) ). These results were validated by in vitro mechanical testing on the bone ball samples. This study demonstrates that the PSO of trabecular bone predicted by QUS has an equally strong apparent stiffness with the orientation predicted by \(\upmu \) CT.     

N-site Phosphorylation Systems with 2N-1 Steady States

Multisite protein phosphorylation plays a prominent role in intracellular processes like signal transduction, cell-cycle control and nuclear signal integration. Many proteins are phosphorylated in a sequential and distributive way at more than one phosphorylation site. Mathematical models of \(n\) -site sequential distributive phosphorylation are therefore studied frequently. In particular, in Wang and Sontag (J Math Biol 57:29–52, 2008), it is shown that models of \(n\) -site sequential distributive phosphorylation admit at most \(2n-1\) steady states. Wang and Sontag furthermore conjecture that for odd \(n\) , there are at most \(n\) and that, for even \(n\) , there are at most \(n+1\) steady states. This, however, is not true: building on earlier work in Holstein et al. (Bull Math Biol 75(11):2028–2058, 2013), we present a scalar determining equation for multistationarity which will lead to parameter values where a \(3\) -site system has \(5\) steady states and parameter values where a \(4\) -site system has \(7\) steady states. Our results therefore are counterexamples to the conjecture of Wang and Sontag. We furthermore study the inherent geometric properties of multistationarity in \(n\) -site sequential distributive phosphorylation: the complete vector of steady state ratios is determined by the steady state ratios of free enzymes and unphosphorylated protein and there exists a linear relationship between steady state ratios of phosphorylated protein.     

A locally convergent rotationally invariant particle swarm optimization algorithm

Several well-studied issues in the particle swarm optimization algorithm are outlined and some earlier methods that address these issues are investigated from the theoretical and experimental points of view. These issues are the: stagnation of particles in some points in the search space, inability to change the value of one or more decision variables, poor performance when the swarm size is small, lack of guarantee to converge even to a local optimum (local optimizer), poor performance when the number of dimensions grows, and sensitivity of the algorithm to the rotation of the search space. The significance of each of these issues is discussed and it is argued that none of the particle swarm optimizers we are aware of can address all of these issues at the same time. To address all of these issues at the same time, a new general form of velocity update rule for the particle swarm optimization algorithm that contains a user-definable function \(f\) is proposed. It is proven that the proposed velocity update rule guarantees to address all of these issues if the function \(f\) satisfies the following two conditions: (i) the function \(f\) is designed in such a way that for any input vector \(\vec {y}\) in the search space, there exists a region \(A\) which contains \(\vec {y}\) and \( f\!\left( {\vec {y}} \right) \) can be located anywhere in \(A\) , and (ii) \(f\) is invariant under any affine transformation. An example of function \(f\) is provided that satisfies these conditions and its performance is examined through some experiments. The experiments confirm that the proposed algorithm (with an appropriate function \(f)\) can effectively address all of these issues at the same time. Also, comparisons with earlier methods show that the overall ability of the proposed method for solving benchmark functions is significantly better.     

Individual-Based Model for Quorum Sensing with Background Flow

Quorum sensing is a wide-spread mode of cell–cell communication among bacteria in which cells release a signalling substance at a low rate. The concentration of this substance allows the bacteria to gain information about population size or spatial confinement. We consider a model for \(N\) cells which communicate with each other via a signalling substance in a diffusive medium with a background flow. The model consists of an initial boundary value problem for a parabolic PDE describing the exterior concentration \(u\) of the signalling substance, coupled with \(N\) ODEs for the masses \(a_i\) of the substance within each cell. The cells are balls of radius \(R\) in \(\mathbb {R} ^3\) , and under some scaling assumptions we formally derive an effective system of \(N\) ODEs describing the behaviour of the cells. The reduced system is then used to study the effect of flow on communication in general, and in particular for a number of geometric configurations.     

Effect of the cosolutes trehalose and methanol on the equilibrium and phase-transition properties of glycerol-monopalmitate lipid bilayers investigated using molecular dynamics simulations

The influence of the cosolutes trehalose and methanol on the structural, dynamic and thermodynamic properties of a glycerol-1-monopalmitate (GMP) bilayer and on its main transition temperature \(T_m\) is investigated using atomistic molecular dynamics simulations (600 ns) of a GMP bilayer patch (2 × 8 × 8 lipids) at different temperatures in the range of 302 to 338 K and considering three different cosolute concentrations. Depending on the environment and temperature, these simulations present no or a single GL \(\rightarrow \) LC, LC \(\rightarrow \) GL or LC \(\rightarrow \) ID transition, where LC, GL and ID are the liquid crystal, gel and interdigitated phases, respectively. The trehalose molecules form a coating layer at the bilayer surface, promote the hydrogen-bonded bridging of the lipid headgroups, preserve the interaction of the headgroups with trapped water and induce a slight lateral expansion of the bilayer in the LC phase, observations that may have implications for the phenomenon of anhydrobiosis. However, this cosolute does not affect \(T_m\) and its dependence on hydration in the concentration range considered. On the other hand, methanol molecules intercalate between the lipid headgroups, promote a lateral expansion of the bilayer in the LC phase and induce a concentration dependent decrease of \(T_m\) , observations that may have implications for the phenomenon of anesthesia. The occurrence of an ID phase in the presence of this cosolute may be viewed as an extreme consequence of lateral expansion. The analysis of the simulations also suggests the existence of two basic conservation principles: (1) the hydrogen-bond saturation principle rests on the observation that for all species present in the different systems, the total numbers of hydrogen-bonds per molecule is essentially constant, the only factor of variability being their distribution among different partners; (2) the densest packing principle rests on the observation that the effective volume per methylene group in the interior of the bilayer is only weakly sensitive to the environment, with values comparable to those for liquid (LC) and solid (ID) alkanes, or intermediate (GL).     

Approximation of sojourn-times via maximal couplings: motif frequency distributions

Sojourn-times provide a versatile framework to assess the statistical significance of motifs in genome-wide searches even under non-Markovian background models. However, the large state spaces encountered in genomic sequence analyses make the exact calculation of sojourn-time distributions computationally intractable in long sequences. Here, we use coupling and analytic combinatoric techniques to approximate these distributions in the general setting of Polish state spaces, which encompass discrete state spaces. Our approximations are accompanied with explicit, easy to compute, error bounds for total variation distance. Broadly speaking, if \({\mathsf{T}}_n\) is the random number of times a Markov chain visits a certain subset \({\mathsf{T}}\) of states in its first \(n\) transitions, then we can usually approximate the distribution of \({\mathsf{T}}_n\) for \(n\) of order \((1-\alpha )^{-m}\) , where \(m\) is the largest integer for which the exact distribution of \({\mathsf{T}}_m\) is accessible and \(0\le \alpha \le 1\) is an ergodicity coefficient associated with the probability transition kernel of the chain. This gives access to approximations of sojourn-times in the intermediate regime where \(n\) is perhaps too large for exact calculations, but too small to rely on Normal approximations or stationarity assumptions underlying Poisson and compound Poisson approximations. As proof of concept, we approximate the distribution of the number of matches with a motif in promoter regions of C. elegans. Mathematical properties of the proposed ergodicity coefficients and connections with additive functionals of homogeneous Markov chains as well as ergodicity of non-homogeneous Markov chains are also explored.     

Interaction of ascorbate with photosystem I

Ascorbate is one of the key participants of the antioxidant defense in plants. In this work, we have investigated the interaction of ascorbate with the chloroplast electron transport chain and isolated photosystem I (PSI), using the EPR method for monitoring the oxidized centers \( {\text{P}}_{700}^{ + } \) and ascorbate free radicals. Inhibitor analysis of the light-induced redox transients of P₇₀₀ in spinach thylakoids has demonstrated that ascorbate efficiently donates electrons to \( {\text{P}}_{ 7 0 0}^{ + } \) via plastocyanin. Inhibitors (DCMU and stigmatellin), which block electron transport between photosystem II and Pc, did not disturb the ascorbate capacity for electron donation to \( {\text{P}}_{700}^{ + } \) . Otherwise, inactivation of Pc with CN^? ions inhibited electron flow from ascorbate to \( {\text{P}}_{700}^{ + } \) . This proves that the main route of electron flow from ascorbate to \( {\text{P}}_{700}^{ + } \) runs through Pc, bypassing the plastoquinone (PQ) pool and the cytochrome b ₆ f complex. In contrast to Pc-mediated pathway, direct donation of electrons from ascorbate to \( {\text{P}}_{700}^{ + } \) is a rather slow process. Oxidized ascorbate species act as alternative oxidants for PSI, which intercept electrons directly from the terminal electron acceptors of PSI, thereby stimulating photooxidation of P₇₀₀. We investigated the interaction of ascorbate with PSI complexes isolated from the wild type cells and the MenB deletion strain of cyanobacterium Synechocystis sp. PCC 6803. In the MenB mutant, PSI contains PQ in the quinone-binding A₁-site, which can be substituted by high-potential electron carrier 2,3-dichloro-1,4-naphthoquinone (Cl₂NQ). In PSI from the MenB mutant with Cl₂NQ in the A₁-site, the outflow of electrons from PSI is impeded due to the uphill electron transfer from A₁ to the iron-sulfur cluster F_X and further to the terminal clusters F_A/F_B, which manifests itself as a decrease in a steady-state level of \( {\text{P}}_{700}^{ + } \) . The addition of ascorbate promoted photooxidation of P₇₀₀ due to stimulation of electron outflow from PSI to oxidized ascorbate species. Thus, accepting electrons from PSI and donating them to \( {\text{P}}_{700}^{ + } \) , ascorbate can mediate cyclic electron transport around PSI. The physiological significance of ascorbate-mediated electron transport is discussed.     

Counting glycans revisited

We present an algorithm for counting glycan topologies of order \(n\) that improves on previously described algorithms by a factor \(n\) in both time and space. More generally, we provide such an algorithm for counting rooted or unrooted \(d\) -ary trees with labels or masses assigned to the vertices, and we give a “recipe” to estimate the asymptotic growth of the resulting sequences. We provide constants for the asymptotic growth of \(d\) -ary trees and labeled quaternary trees (glycan topologies). Finally, we show how a classical result from enumeration theory can be used to count glycan structures where edges are labeled by bond types. Our method also improves time bounds for counting alkanes.     

Reconstructing a Phylogenetic Level-1 Network from Quartets

We describe a method that will reconstruct an unrooted binary phylogenetic level-1 network on \(n\) taxa from the set of all quartets containing a certain fixed taxon, in \(O(n^3)\) time. We also present a more general method which can handle more diverse quartet data, but which takes \(O(n^6)\) time. Both methods proceed by solving a certain system of linear equations over the two-element field \(\mathrm{GF}(2)\) . For a general dense quartet set, i.e. a set containing at least one quartet on every four taxa, our \(O(n^6)\) algorithm constructs a phylogenetic level-1 network consistent with the quartet set if such a network exists and returns an \(O(n^2)\) -sized certificate of inconsistency otherwise. This answers a question raised by Gambette, Berry and Paul regarding the complexity of reconstructing a level-1 network from a dense quartet set, and more particularly regarding the complexity of constructing a cyclic ordering of taxa consistent with a dense quartet set.     

Head impact accelerations for brain strain-related responses in contact sports: a model-based investigation

Both linear \((\mathbf{a}_{\mathrm{lin}})\) and rotational \((\mathbf{a}_{\mathrm{rot}} )\) accelerations contribute to head impacts on the field in contact sports; however, they are often isolated in injury studies. It is critical to evaluate the feasibility of estimating brain responses using isolated instead of full degrees-of-freedom (DOFs) accelerations. In this study, we investigated the sensitivities of regional brain strain-related responses to resultant \(\mathbf{a}_{\mathrm{lin}}\) and \(\mathbf{a}_{\mathrm{rot}}\) as well as the relative contributions of these acceleration components to the responses via random sampling and linear regression using parameterized, triangulated head impacts with kinematic variable values based on on-field measurements. Two independently established and validated finite element models of the human head were employed to evaluate model-consistency and dependency in results: the Dartmouth Head Injury Model and Simulated Injury Monitor. For the majority of the brain, volume-weighted regional peak strain, strain rate, and von Mises stress accumulated from the simulation significantly correlated with the product of the magnitude and duration of \(\mathbf{a}_{\mathrm{rot}}\) , or effectively, the rotational velocity, but not to \(\mathbf{a}_{\mathrm{lin}}\) . Responses from \(\mathbf{a}_{\mathrm{rot}}\) -only were comparable to the full-DOF counterparts especially when normalized by injury-causing thresholds (e.g., volume fractions of large differences virtually diminished (i.e., \(<\) 1 %) at typical difference percentage levels of 1–4 % on average). These model-consistent results support the inclusion of both rotational acceleration magnitude and duration into kinematics-based injury metrics and demonstrate the feasibility of estimating strain-related responses from isolated \(\mathbf{a}_{\mathrm{rot}}\) for analyses of strain-induced injury relevant to contact sports without significant loss of accuracy, especially for the cerebrum.