Modelling of auxetic networked polymers built from calix[4]arene building blocks

Auxetic materials (i.e. materials with a negative Poisson's ratio) expand laterally when stretched and become thinner when compressed. This unusual yet very useful property arises from the way by which the nano or microstructure of the material deforms when subjected to uniaxial mechanical loads. This paper discusses a novel class of molecular-level auxetic (networked polymers) built from calix[4]arene building blocks. These calix[4]arene subunits are connected in such a way that they mimic the shape of a “folded macrostructure” which is known to exhibit auxetic behaviour. We confirm through force-field based simulations that these newly proposed networked polymers exhibit negative Poisson's ratios, the magnitudes of which can be changed by introducing slight variations in the molecular structure of these polymers. We also develop simple geometry-based models which explain the values of the Poisson's ratios obtained through the force-field based simulations, and which give an insight into the features of the molecular structure that are responsible for the auxetic effect.     

Empirical modelling using dummy atoms (EMUDA): an alternative approach for studying “auxetic” structures

Auxetics (materials or structures) are systems with a negative Poisson's ratio, a property that arises from the way various geometric features in the structure (or internal structure in the case of materials) deform when subjected to uniaxial loads. Such systems are normally studied by examining the behaviour of idealised representations of structures, which deform in a controlled fashion (e.g. deforming solely through hinging or stretching). Methods used for the analysis typically involve construction of real physical macro-models and/or derivation of analytical expressions for the mechanical properties. This paper proposes an alternative method for analysing such structures whereby idealised “hinging” or “stretching” structures are constructed within a molecular modelling environment using dummy atoms and examined using standard molecular mechanics techniques. We will show that this methodology of “empirical modelling using dummy atoms” (EMUDA) successfully reproduces the known properties of 2D conventional and auxetic hexagonal honeycombs hence confirming the suitability of this technique for studying auxetic structures.     

Constitutive properties of contacting materials with a finite-sized microstructure

Materials consisting of macro-molecules that are set in a structure and interact via contact interactions are investigated. The analysis is analytical, based on the methodology developed for granular materials by Jenkins J.T. and Koenders M.A. “The incremental response of random aggregates of round particles” European Physics Journal E., 13, 2004 113–123. The stiffness tensor is obtained and the results are screened for auxetic properties. Two-dimensional materials are investigated. For regular packings isotropic and anisotropic structures are examined. It is demonstrated that isotropic materials in this category are never auxetic. Heterogeneous materials are also analysed. It is shown that auxetic behaviour is enhanced when structural variation is present. By contrast, auxetic behaviour is suppressed when constitutive heterogeneity is present. The results of the analysis may be employed to scrutinize numerical simulations.     

Mechanical equilibrium,a prerequisite to unveil auxetic properties in molecular compounds

The unique physical properties of auxetic compounds make them very attractive materials. Nevertheless, no synthesised materials known to exhibit negative Poisson’s ratio at the molecular level have been made. One way to explore such compounds is to predict potential candidates prior to their synthesis. To achieve it, multi-atom simulation is a powerful predicting tool. However, the lack of existing systems means that the crucial step of validation cannot be carried out. This paper aims to provide a procedure to predict the auxeticity of proposed molecular systems. The strategy is based on first revealing the determinant step in reaching the mechanical equilibrium of existing isotropic compounds such as polymers, or organic glasses, to compute efficiently mechanical properties. The Poisson’s ratio is found in good agreement with experimental data. The procedure is thus modified to be applied to anisotropic compounds, liquid crystals. The agreement with experimental behaviour allowed us to extrapolate the procedure to potentially auxetic compounds, thus offering great opportunities to reveal auxetic properties prior to the synthesis of the molecules.     

The Effect of Loops on the Structural Organization of α-Helical Membrane Proteins

Loops connecting the transmembrane (TM) α-helices in membrane proteins are expected to affect the structural organization of the thereby connected helices and the helical bundles as a whole. This effect, which has been largely ignored previously, is studied here by analyzing the x-ray structures of 41 α-helical membrane proteins. First we define the loop flexibility ratio, R, and find that 53% of the loops are stretched, where a stretched loop constrains the distance between the two connected helices. The significance of this constraining effect is supported by experiments carried out with bacteriorhodopsin and rhodopsin, in which cutting or eliminating their (predominately stretched) loops has led to a decrease in protein stability, and for rhodopsin, in most cases, also to the destruction of the structure. We show that for nonstretched loops in the extramembranous regions, the fraction of hydrophobic residues is comparable to that for soluble proteins; furthermore (as is also the case for soluble proteins), the hydrophobic residues in these regions are preferentially buried. This is expected to lead to the compact structural organization of the loops, which is transferred to the TM helices, causing them to assemble. We argue that a soluble protein complexed with a membrane protein similarly promotes compactness; other properties of such complexes are also studied. We calculate complementary attractive interactions between helices, including hydrogen bonds and van der Waals interactions of sequential motifs, such as GXXXG. The relative and combined effects of all these factors on the association of the TM helices are discussed and protein structures with only a few of these factors are analyzed. Our study emphasizes the need for classifying membrane proteins into groups according to structural organization. This classification should be considered when procedures for structural analysis or prediction are developed and applied. Detailed analysis of each structure is provided at http://flan.blm.cs.cmu.edu/memloop/     

Analysis of Chlorophyll Fluorescence Decays of Isolated Thylakoids in Various Stages of Greening

The decay of chlorophyll (Chl) fluorescence of etiochloroplasts isolated in various stage of greening of cucumber cotyledons was analysed in order to get structural information on a photosynthetic apparatus. Two model decays, multiexponential and stretched exponential, were applied in the analysis. The quality of fit in these two models was different in various stages of chloroplast greening. The two-exponent model did not provide a good fit at early greening stages. To improve the fit it was necessary to introduce an additional third component which became very low at later stages. However, chloroplasts in the early stage of greening could also be described by a stretched exponential with parameters indicating rather planar (two-dimensional) arrangement of donor and acceptor molecules. The chloroplasts treated by DCMU and/or photooxidized by strong irradiance exhibit a similar character of fractal decay as untreated samples but in the multiexponential model the exact values of lifetimes and amplitudes of components vary. This suggests that the structure of investigated system does not dramatically change as a result of these two types of treatment.     

Parkinsonian tremor and simplification in network dynamics

We explore the behavior of richly connected inhibitory neural networks under parameter changes that correspond to weakening of synaptic efficacies between network units, and show that transitions from irregular to periodic dynamics are common in such systems. The weakening of these connections leads to a reduction in the number of units that effectively drive the dynamics and thus to simpler behavior. We hypothesize that the multiple interconnecting loops of the brain’s motor circuitry, which involve many inhibitory connections, exhibit such transitions. Normal physiological tremor is irregular while other forms of tremor show more regular oscillations. Tremor in Parkinson’s disease, for example, stems from weakened synaptic efficacies of dopaminergic neurons in the nigro-striatal pathway, as in our general model. The multiplicity of structures involved in the production of symptoms in Parkinson’s disease and the reversibility of symptoms by pharmacological and surgical manipulation of connection parameters suggest that such a neural network model is appropriate. Furthermore, fixed points that can occur in the network models are suggestive of akinesia in Parkinson’s disease. This model is consistent with the view that normal physiological systems can be regulated by robust and richly connected feedback networks with complex dynamics, and that loss of complexity in the feedback structure due to disease leads to more orderly behavior.     

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Recently, disordered photonic materials have been suggested as an alternative to periodic crystals for the formation of a complete photonic bandgap (PBG). In this article we will describe the methods for constructing and characterizing macroscopic disordered photonic structures using microwaves. The microwave regime offers the most convenient experimental sample size to build and test PBG media. Easily manipulated dielectric lattice components extend flexibility in building various 2D structures on top of pre-printed plastic templates. Once built, the structures could be quickly modified with point and line defects to make freeform waveguides and filters. Testing is done using a widely available Vector Network Analyzer and pairs of microwave horn antennas. Due to the scale invariance property of electromagnetic fields, the results we obtained in the microwave region can be directly applied to infrared and optical regions. Our approach is simple but delivers exciting new insight into the nature of light and disordered matter interaction.Our representative results include the first experimental demonstration of the existence of a complete and isotropic PBG in a two-dimensional (2D) hyperuniform disordered dielectric structure. Additionally we demonstrate experimentally the ability of this novel photonic structure to guide electromagnetic waves (EM) through freeform waveguides of arbitrary shape.     

Protein secondary structure assignment revisited: a detailed analysis of different assignment methods

Background  

A number of methods are now available to perform automatic assignment of periodic secondary structures from atomic coordinates, based on different characteristics of the secondary structures. In general these methods exhibit a broad consensus as to the location of most helix and strand core segments in protein structures. However the termini of the segments are often ill-defined and it is difficult to decide unambiguously which residues at the edge of the segments have to be included. In addition, there is a "twilight zone" where secondary structure segments depart significantly from the idealized models of Pauling and Corey. For these segments, one has to decide whether the observed structural variations are merely distorsions or whether they constitute a break in the secondary structure.     

Mechanisms Responsible for Extraordinary Optical Transmission Through One-Dimensional Periodic Arrays of Infinite Sub-wavelength Slits: the Origin of Previous EOT Position Prediction Misinterpretations

We have studied theoretically and numerically the effect of extraordinary optical transmission of light propagating through the one-dimensional periodic arrays of infinite slits with sub-wavelength dimensions. In our study, we have concentrated on mechanisms which are responsible for this effect. Within our analysis, we have attempted to draw the attention towards the origin and reasons of earlier misinterpretations concerning the spectral position of EOT prediction and the related role of surface plasmon polaritons in manifestation of the effect. Using the sequence of suitable parameter two-dimensional spaces (in terms of structure period-filling factor; thickness-wavelength; wavelength-angle), we were able to look into subtle physical mechanisms operating in the background of this extraordinary optical transmission effect. To study these effects associated with the extraordinary optical transmission, we have applied our efficient two-dimensional numerical technique based on the rigorous coupled-wave analysis. Within the thickness-wavelength parameter space, we have been able to identify and describe three distinct interaction regions, with specific behaviour. Finally, we have proposed and discussed the supporting mechanism explaining the interaction, based on the interference of resonant and non-resonant contributions at the slit openings.     

Modelling of the mechanical and mass transport properties of auxetic molecular sieves: an idealised inorganic (zeolitic) host–guest system

Force field based simulations have been employed to model the structure, and mechanical and mass transport properties of the all-silica zeolite MFI (ZSM5—Si₉₆O₁₉₂). Undeformed and deformed MFI subject to uniaxial loading in each of the three principal directions were investigated. The mechanical properties are predicted to include negative on-axis Poisson's ratios (auxetic behaviour) in the x ₁–x ₃ plane of the undeformed structure, and are strain-dependent. Transformation from positive-to-negative Poisson's ratio behaviour, and vice versa, is predicted for most on-axis Poisson's ratios at critical loading strains. Simulations of the simultaneous sorption of neopentane and benzene guest molecules onto the undeformed host MFI framework indicate a low neopentane-to-benzene loading ratio, consistent with experimental observation. The sorption of these two molecular species onto deformed MFI is Poisson's ratio- and strain-dependent. Uniaxial tensile loading along a direction containing a negative on-axis Poisson's ratio leads to an increase in the loading of the larger neopentane molecules with respect to benzene, strongly correlated with the increase in volume associated with auxetic behaviour.     

Simulating localised cellular inflammation and substrate properties in a strain energy density based bone remodelling algorithm for use in modelling trauma

Bone responds to mechanical stimulus and a range of pre-existing finite element models have been suggested to reproduce the internal physiological structure of bone. Inflammation effects are not included in these models, yet inflammation is a key component of bone repair in trauma. Therefore, a model is proposed and tested here that extends these methods to include parameters that could be considered to represent the behaviour of bone remodelling when influenced by inflammation. The proposed model regulates remodelling based on findings from recent studies into the nature of heterotopic ossification, the formation of heterotopic bone, which have revealed information about the nature of bone after high levels of trauma. These parameters include consideration of the distance from the zone of trauma, the density of mesenchymal stem cells, and substrate stiffness as a trigger for cells becoming osteogenic. The method is tested on a two-dimensional plate model and shows that the new extended algorithm can produce a range of structures depending on inputs that could be used in the future to replicate physiological scenarios.     

Structural Hierarchy Governs Fibrin Gel Mechanics

Fibrin gels are responsible for the mechanical strength of blood clots, which are among the most resilient protein materials in nature. Here we investigate the physical origin of this mechanical behavior by performing rheology measurements on reconstituted fibrin gels. We find that increasing levels of shear strain induce a succession of distinct elastic responses that reflect stretching processes on different length scales. We present a theoretical model that explains these observations in terms of the unique hierarchical architecture of the fibers. The fibers are bundles of semiflexible protofibrils that are loosely connected by flexible linker chains. This architecture makes the fibers 100-fold more flexible to bending than anticipated based on their large diameter. Moreover, in contrast with other biopolymers, fibrin fibers intrinsically stiffen when stretched. The resulting hierarchy of elastic regimes explains the incredible resilience of fibrin clots against large deformations.     

Quasi-equilibrium reduction in a general class of stoichiometric producer–consumer models

This article compares a general closed nutrient, stoichiometric producer–consumer model to a two-dimensional ‘quasi-equilibrium’ approximation. We demonstrate that the quasi-equilibrium system can be rigorously analysed, resulting in nullcline-based criteria for the local stability of system equilibria and for the non-existence of periodic orbits. These results are applied to a study of the dependence of the reduced system on nutrient and energy enrichment. When energy and nutrient enrichment are considered together, the associated bifurcation structures of the two models are seen to share the same essential qualitative characteristics. However, numerical simulations of the three-dimensional parent model show highly complex domains of the persistence and extinction that by Poincare–Bendixson theory are not possible for the two-dimensional reduction. This complexity demonstrates a major difference between the two models, and suggests potential challenges in the use of either model for predicting the long-term behaviour of real-world systems at specific nutrient and energy levels.     

Quasi-equilibrium reduction in a general class of stoichiometric producer-consumer models

This article compares a general closed nutrient, stoichiometric producer-consumer model to a two-dimensional 'quasi-equilibrium' approximation. We demonstrate that the quasi-equilibrium system can be rigorously analysed, resulting in nullcline-based criteria for the local stability of system equilibria and for the non-existence of periodic orbits. These results are applied to a study of the dependence of the reduced system on nutrient and energy enrichment. When energy and nutrient enrichment are considered together, the associated bifurcation structures of the two models are seen to share the same essential qualitative characteristics. However, numerical simulations of the three-dimensional parent model show highly complex domains of the persistence and extinction that by Poincare-Bendixson theory are not possible for the two-dimensional reduction. This complexity demonstrates a major difference between the two models, and suggests potential challenges in the use of either model for predicting the long-term behaviour of real-world systems at specific nutrient and energy levels.     

Using a multiscale image processing method to characterize the periodic growth patterns on scallop shells

The fine periodic growth patterns on shell surfaces have been widely used for studies in the ecology and evolution of scallops. Modern X‐ray CT scanners and digital cameras can provide high‐resolution image data that contain abundant information such as the shell formation rate, ontogenetic age, and life span of shellfish organisms. We introduced a novel multiscale image processing method based on matched filters with Gaussian kernels and partial differential equation (PDE) multiscale hierarchical decomposition to segment the small tubular and periodic structures in scallop shell images. The periodic patterns of structures (consisting of bifurcation points, crossover points of the rings and ribs, and the connected lines) could be found by our Space‐based Depth‐First Search (SDFS) algorithm. We created a MATLAB package to implement our method of periodic pattern extraction and pattern matching on the CT and digital scallop images available in this study. The results confirmed the hypothesis that the shell cyclic structure patterns encompass genetically specific information that can be used as an effective invariable biomarker for biological individual recognition. The package is available with a quick‐start guide and includes three examples: http://mgb.ouc.edu.cn/novegene/html/code.php .     

Macromolecular design, nucleic acid junctions, and crystal formation

The simplest form of macromolecular design involves the ligation of nucleic acids. Recent results on the concatenation of nucleic acid junctions show that these molecules can act as fairly rigid macromolecular valence clusters on the nanometer scale. These clusters can be joined to form closed stick figures in which each edge is double helical DNA or RNA and each vertex is a nucleic acid junction. The geometrical criteria for forming discrete-closed and periodic structures from these components are established. The helicity of each edge limits the possible structures that can be formed. The formation of a periodic array from nucleic acid junction building blocks is compared with the crystallization of molecular systems. This comparison leads to a new interpretation of the nature of order in the solid state for molecular crystals. The suggestion is made that the structure of a solid molecular system described by the fewest unique orthogonal (Fourier) components is the one which will be entropically favored, since it contains the least information. This is the crystalline state, with a small number of molecules per asymmetric unit. The free energy from the proposed entropic driving force responsible for this behavior is available, in principle, to correct small deviations from ideality in forming covalent crystals from nucleic acid junction components, as well as in non-bonded molecular systems. Nucleic acid junction periodic arrays provide an appropriate vehicle with which to test this interpretation.     

Bifurcation of orbits and synchrony in inferior olive neurons

Inferior olive neurons (IONs) have rich dynamics and can exhibit stable, unstable, periodic, and even chaotic trajectories. This paper presents an analysis of bifurcation of periodic orbits of an ION when its two key parameters (a, μ) are varied in a two-dimensional plane. The parameter a describes the shape of the parabolic nonlinearity in the model and μ is the extracellular stimulus. The four-dimensional ION model considered here is a cascade connection of two subsystems (S(a) and S(b)). The parameter plane (a - μ) is delineated into several subregions. The ION has distinct orbit structure and stability property in each subregion. It is shown that the subsystem S(a) or S(b) undergoes supercritical Poincare-Andronov-Hopf (PAH) bifurcation at a critical value μ(c)(a) of the extracellular stimulus and periodic orbits of the neuron are born. Based on the center manifold theory, the existence of periodic orbits in the asymptotically stable S(a), when the subsystem S(b) undergoes PAH bifurcation, is established. In such a case, both subsystems exhibit periodic orbits. Interestingly when S(b) is under PAH bifurcation and S(a) is unstable, the trajectory of S(a) exhibits periodic bursting, interrupted by periods of quiescence. The bifurcation analysis is followed by the design of (i) a linear first-order filter and (ii) a nonlinear control system for the synchronization of IONs. The first controller uses a single output of each ION, but the nonlinear control system uses two state variables for feedback. The open-loop and closed-loop responses are presented which show bifurcation of orbits and synchronization of oscillating neurons.