Critical test of bead–spring model to resolve the scaling laws of polymer melts: a molecular dynamics study

Abstract

To examine the intrinsic nature of the bead–spring Kremer–Grest (KG) model, long-time molecular dynamics simulations are performed. Certain scaling laws for representative polymer properties are compared with theoretical predictions. The results for static properties satisfy the expected static Gaussian nature, irrespective of the chain length. In contrast, the results for the dynamic properties of short chains show a clear discrepancy from theoretical predictions that assume ideal chain motion. This is clear evidence that the Gaussian nature of the dynamics of short chains is not necessarily established for the actual KG model, despite it being designed to have Gaussian characteristics by virtue of its stochastic equations of motion. This intrinsic nature of the KG model should be considered carefully when using this model for applications that involve relatively short chains.     

Mechanical explanation of nature and its limits in Kant’s Critique of judgment

In this paper I discuss two questions. What does Kant understand by mechanical explanation in the Critique of judgment? And why does he think that mechanical explanation is the only type of the explanation of nature available to us? According to the interpretation proposed, mechanical explanations in the Critique of judgment refer to a particular species of empirical causal laws. Mechanical laws aim to explain nature by reference to the causal interaction between the forces of the parts of matter and the way in which they form into complex material wholes. Just like any other empirical causal law, however, mechanical laws can never be known with full certainty. The conception according to which we can explain all of nature by means of mechanical laws, it turns out, is based on what Kant calls ‘regulative’ or ‘reflective’ considerations about nature. Nothing in Kant’s Critique of judgment suggests that these considerations can ever be justified by reference to how the natural world really is. I suggest that what, upon first consideration, appears to be a thoroughly mechanistic conception of nature in Kant is much more limited than one might have expected.     

Mechanical explanation of nature and its limits in Kant's Critique of judgment

In this paper I discuss two questions. What does Kant understand by mechanical explanation in the Critique of judgment? And why does he think that mechanical explanation is the only type of the explanation of nature available to us? According to the interpretation proposed, mechanical explanations in the Critique of judgment refer to a particular species of empirical causal laws. Mechanical laws aim to explain nature by reference to the causal interaction between the forces of the parts of matter and the way in which they form into complex material wholes. Just like any other empirical causal law, however, mechanical laws can never be known with full certainty. The conception according to which we can explain all of nature by means of mechanical laws, it turns out, is based on what Kant calls 'regulative' or 'reflective' considerations about nature. Nothing in Kant's Critique of judgment suggests that these considerations can ever be justified by reference to how the natural world really is. I suggest that what, upon first consideration, appears to be a thoroughly mechanistic conception of nature in Kant is much more limited than one might have expected.     

Robust scaling in ecosystems and the meltdown of patch size distributions before extinction

Robust critical systems are characterized by power laws which occur over a broad range of conditions. Their robust behaviour has been explained by local interactions. While such systems could be widespread in nature, their properties are not well understood. Here, we study three robust critical ecosystem models and a null model that lacks spatial interactions. In all these models, individuals aggregate in patches whose size distributions follow power laws which melt down under increasing external stress. We propose that this power-law decay associated with the connectivity of the system can be used to evaluate the level of stress exerted on the ecosystem. We identify several indicators along the transition to extinction. These indicators give us a relative measure of the distance to extinction, and have therefore potential application to conservation biology, especially for ecosystems with self-organization and critical transitions.     

The GABAA receptor as a target for photochromic molecules

Photochromic ligands, molecules that can be induced to change their physical properties through applied light, are currently the topic of much chemical biology research. This specialized class of small organic structures are, surprisingly to many, fairly common in nature. At the core of a number of natural biological processes lies a small molecule that changes shape or some other measurable property in response to light absorption. For instance, conformational changes invoked by reversible photoisomerization of a retinoid small molecule found in the photoreceptors of the human eye leads to vision. In plants, photoisomerization of a cinnamate moiety leads to altered gene expression. The photosensitive molecule can be viewed simply as a nanosensor of light, much like a photosensitive electrical component might be added to a circuit to sense day versus night to turn an electrical circuit on or off. Synthetic organic chemists and chemical biologists have been, for at least the last 15 years, trying to either mimic or exploit the native photochromism found in nature. Here, we describe the design process to develop a photochromic molecule to be used in neurobiology.     

Ecological laws: what would they be and why would they matter?

There remains considerable debate over the existence of ecological laws. However, this debate has not made use of an adequate account of what a relationship would have to be like in order for it to qualify as an ecological law. As a result, confusions have persisted not only over how to show that ecological laws do (or do not) exist, but also regarding why their existence would matter – other than to whether ecology looks like physics. I argue that ecological laws would have to possess collectively a distinctive kind of invariance under counterfactual perturbations. I call this invariance "stability." A law of physics, such as the law that all bodies travel no faster than the speed of light, is not only true, but also necessary in a physically significant sense. (A body must travel no faster than light; it couldn't do otherwise, even if it were subjected to a greater force.) Likewise, the stability of ecological laws would render them necessary in an ecologically relevant sense. Furthermore, ecological laws would differ from fundamental laws of physics in the range of counterfactual perturbations under which they are invariant. Therefore, I argue, the existence of ecological laws would make ecological explanations irreducible to even the most complete possible physical explanations of the same phenomena. Ecological laws would make ecology genuinely autonomous from physics.     

Mathematical models, explanation, laws, and evolutionary biology

It is commonly agreed in the literature on laws of nature that there are at least two necessary conditions for lawhood--that a law must have empirical content and that it must be universal. The main reason offered for the requirement that laws be empirical is as follows: a priori statements are consistent with any imaginable set of observations, so they cannot be informative about the world and therefore they cannot provide explanations. However, we care about laws because we think that laws provide explanations and allow us to make predictions. Thus, if one of the functions of laws is to provide explanations and a priori propositions cannot fulfill this function, they cannot properly be viewed as laws. In this paper, I will aim to show that this argument for the claim that laws must be empirical does not work.     

Visible light-induced nitric oxide release from a novel nitrobenzene derivative cross-conjugated with a coumarin fluorophore

Nitric oxide (NO) is a well-known free-radical molecule which is endogenously biosynthesised and shows various functions in mammals. To investigate NO functions, photocontrollable NO donors, compounds which release NO in response to light, are expected to be potentially useful. However, most of the conventional NO donors require harmful ultra-violet light for NO release. In this study, two dimethylnitrobenzene derivatives conjugated with coumarins were designed, synthesized and evaluated as photocontrollable NO donors. The optical properties and efficiency of photo-induced NO release were dependent upon the nature of the conjugation system. One of these compounds, Bhc-DNB (1), showed spatiotemporally well-controlled NO release in cultured cells upon exposure to light in the less-cytotoxic visible wavelength range (400–430 nm).     

Lighting, backlighting and watercolor illusions and the laws of figurality

We report some novel 'lighting' and 'backlighting' effects in plane figures similar to those which induce the 'watercolor illusion', that is, figures made with outlines composed of juxtaposed parallel lines varying in brightness and chromatic color. These new effects show 'illumination' as an emergent percept, and show how arrangements of 'dark and light' along the boundaries of various plane figures model the volume and strengthen the illusion of depth. To account for these various effects we propose several phenomenological 'laws of figurality' to add to the Gestalt laws of organization and figure-ground segregation. We offer a set of meta-laws which are speculative but which serve to integrate and organize the phenomenological laws. These laws indicate how luminance gradient profiles across boundary contours define both the 3D appearance of figures and the properties of the light reflected from their volumetric shapes.     

Theory and Measurement of the buffer value of bicarbonate in saliva

All known sensory systems have at least two components, which will tend to counteract and compensate for each other. For light, the sensitivity of the eye is some function of the area of the pupil (aperture of the iris diaphragm) and the relative amount of unbleached pigment (visual purple or rhodopsin). An intermittent light will result in a constriction of the pupil and a bleaching of the pigment. The interaction between these two processes results in a total response with components of both a logarithmic and an arithmetic function of the light intensity and duration. The sensitivity of the eye is a linear function of the logarithm of the intensity of incident light (Weber's and Fechner's laws, Fig. 6), yet a rapidly oscillating light causes approximately the same sensitivity as a steady light of the same intensity as the arithmetic average of the fluctuating light (Talbot's and Bloch's laws, Fig. 9c).     

Some dynamic properties of linear, hyperbolic and sigmoidal multi-enzyme systems with feedback control

Numerical solutions of equations (3) (see scheme I) have been obtained for a wide range of parameters. For cases wherein limit cycles arise, the relationships between the amplitude, the period, the nature of the rate laws for the enzyme-catalyzed reactions (e.g. linear, hyperbolic, or sigmoidal), the number of kinetically important steps, the metabolic flux into the system, and the stoichiometry of the feedback were determined. Periods and amplitudes for systems with hyperbolic rate laws usually exceed periods and amplitudes for systems with corresponding linear rate laws, and periods and amplitudes for systems with sigmoidal rate laws are usually less than the periods and amplitudes for corresponding linear or hyperbolic systems. Furthermore, limit cycles can arise in hyperbolic systems which, if linear, would possess global asymptotic stability; limit cycles can arise in linear systems which, if sigmoidal, would possess global asymptotic stability. These results have been observed for systems wherein all the rate laws have been changed in the indicated manner, and in systems where some of the rate laws have been changed. The effect is usually (but not always) a monotonic function of the number of altered rate laws. The rate law for the last step is usually the most important, and the rate law for the first step can be much more important than the rate law for the steps between the first and the last. The rate laws for all these intermediate steps are usually of approximately equal importance.A striking feature of these results is that there are exceptions to all the “rules”. The waveforms of the oscillations can be “smooth” or “squared”, depending upon the parameters (including the nature of the rate laws) used. The period and the amplitude usually increase or decrease together, but in certain cases the amplitude increases as a function of a parametric variation that causes the period to decrease. Even the individual relationships between the amplitude or the period and certain parameters is not always the same. For example, the amplitude is usually an asymptotic function of the flux into the system, but in some systems there is an optimum amplitude at an intermediate flux. The period can be nearly independent of the flux, or it can depend nearly linearly on the flux. One important aspect of this result is that the period can be in the range of a day or two, or in the range of seconds, but the period is most likely to be insensitive to the flux when the flux is high and the period long.At the end of this paper I have included some speculative remarks about how these results might relate to biological timing mechanisms or to cellular differentiation.     

A quantum-chemical study of the binding ability of βXaaHisGlyHis towards copper(II) ion

The present study analyzed binding of Cu²⁺ to tetrapeptides in water solution at several levels of theoretical approximation. The methods used to study the energetic and structural properties of the complexes in question include semiempirical hamiltonians, density functional theory as well as ab initio approaches including electron correlation effects. In order to shed light on the character of interactions between Cu²⁺ and peptides, which are expected to be mainly electrostatic in nature, decomposition of interaction energy into physically meaningful components was applied.     

Spicules of hexactinellid sponges (Hexactinellida: Porifera) as natural composite materials

This paper reviews studies on the hexactinellid glass sponges (Hexactinellida: Porifera) that have organic silica spicules. According to its physical properties (microdensity, Young’s modulus, and light transmission), the material of the spicules is similar to amorphous silica; however, sponge spicules are birefringent, which suggests that they have a highly ordered crystal-like nature. Mineralized remnants of siliceous spicules composed of chemically inert materials are preserved in sedimentary rocks and provide evidence of the ecological state of the ancient biosphere. Sponges occur in waters with low temperatures; therefore, they grow very slowly and live for hundreds of years. The organic silica spicules exhibit the capacity for triboluminescence. The generated light emission may be used by symbiotic bacteria on the spicule surface.     

Single molecule thermodynamics in biological motors

Biological molecular machines use thermal activation energy to carry out various functions. The process of thermal activation has the stochastic nature of output events that can be described according to the laws of thermodynamics. Recently developed single molecule detection techniques have allowed each distinct enzymatic event of single biological machines to be characterized providing clues to the underlying thermodynamics. In this study, the thermodynamic properties in the stepping movement of a biological molecular motor have been examined. A single molecule detection technique was used to measure the stepping movements at various loads and temperatures and a range of thermodynamic parameters associated with the production of each forward and backward step including free energy, enthalpy, entropy and characteristic distance were obtained. The results show that an asymmetry in entropy is a primary factor that controls the direction in which the motor will step. The investigation on single molecule thermodynamics has the potential to reveal dynamic properties underlying the mechanisms of how biological molecular machines work.     

Laws of nature and laws of ecology

We address the question of whether there are laws in ecology. Although there has been a great deal of recent interest in this topic, much of the relevant debate has been conducted under some common misconceptions about what laws of nature are. Once these misconceptions are cleared up, the case for ecology having laws is much stronger. Indeed, we suggest that the case for laws in ecology is no better or worse than the case for laws in physics.     

Plant physiology in theory and practice: An analysis of the WBE model for vascular plants

The theoretical model of West, Brown and Enquist (hereafter WBE) proposed the fractal geometry of the transport system as the origin of the allometric scaling laws observed in nature. The WBE model has either been criticized for some restrictive and biologically unrealistic constraints or its reliability debated on the evidence of empirical tests. In this work, we revised the structure of the WBE model for vascular plants, highlighting some critical assumptions and simplifications and discuss them with regard to empirical evidence from plant anatomy and physiology. We conclude that the WBE model had the distinct merit of shedding light on some important features such as conduit tapering. Nonetheless, it is over-simplistic and a revised model would be desirable with an ontogenetic perspective that takes some important phenomena into account, such as the transformation of the inner sapwood into heartwood and the effect of hydraulic constraints in limiting the growth in height.     

Observations on the Occurrence of Prickles on the Leaves of Ilex aquifolium

The number of prickles upon the edge of a leaf is related bycomplex laws to the size of the leaf, the number of prickleson the other edge, the number of prickles on other leaves ofthe shoot, the phyllotaxy of the shoot, and the intrinsic asymmetryof the leaf. The available evidence indicates that pricklesarise by the interaction of not less than five recognizablephysiological systems. The physical nature of these systemsis unknown but their mathematical properties have been partlyelucidated. Some of them are found to involve the transmissionof morphogenetic impulses while others may be purely local intheir action. As one of the consequences of this physiologicalsituation it is found that shoots having opposite directionsof phyllotaxy differ quantitatively as well as qualitatively.     

Internal transport properties of macroporous sugar polyacrylate hydrogels: microsphere diffusion described by phenomenological laws

We have determined the internal transport properties of heterogeneous, macroporous hydrogels based on the regioregular sugar polyacrylate poly(6-acryloyl-beta-O-methyl-galactopyranoside). This was accomplished by measuring the diffusive flux of variously sized polystyrene microspheres and combining these results with solutions of phenomenological transport laws (the Navier-Stokes equations and Fick's Law with an assumption of first-order irreversible sphere capture by the gel polymer). This enabled calculation of gel properties such as average pore diameters (ca. 11.76 microm) and the diffusivities of the polystyrene spheres in the gel. These values range from 76% to 83% of that in free solution and correlate closely with the equilibrium solution content of the gel (82.3%). This approach has also enabled calculation of the sphere capture rates (2.4 x 10(-3) to 9.6 x 10(-5) s(-1)). These low capture rates indicate that the gel is extremely non-adhesive towards the spheres, and a linear correlation with sphere form drag area (r(2) = 1) was found. The pore sizes of the hydrated gel were observed via DIC light microscopy and the visible effective diameters corresponded very closely to the calculated values (11.66 vs. 11.76 microm). The diffusion/capture of inert spheres in the hydrogel can thus be described in a non-destructive manner by straightforward application of phenomenological transport laws. This result is significant in that these laws were intended to describe macroscopic ensembles of very large numbers of particles in continuous media, not small numbers (i.e., hundreds) in discontinuous media.     

My Sentence Is Over But Will My Punishment Ever End

While America has increasingly become known for having a higher rate of persons in prison or under correctional supervision than any other country in the world; over the last two decades, new laws have begun emerging in America, placing restrictions on former offenders long after their correctional supervision has ended. These laws directly impact the lives of millions of ex-offenders who are no longer under correctional supervision, placing restrictions on where they may live, work and travel. The following essay, by a former offender who discharged parole in December 2000, highlights the punitive and destructive nature of these laws.     

Network analysis of the protein chain tertiary structures of heterocomplexes

In this paper, the tertiary structures of protein chains of heterocomplexes were mapped to 2D networks; based on the mapping approach, statistical properties of these networks were systematically studied. Firstly, our experimental results confirmed that the networks derived from protein structures possess small-world properties. Secondly, an interesting relationship between network average degree and the network size was discovered, which was quantified as an empirical function enabling us to estimate the number of residue contacts of the protein chains accurately. Thirdly, by analyzing the average clustering coefficient for nodes having the same degree in the network, it was found that the architectures of the networks and protein structures analyzed are hierarchically organized. Finally, network motifs were detected in the networks which are believed to determine the family or superfamily the networks belong to. The study of protein structures with the new perspective might shed some light on understanding the underlying laws of evolution, function and structures of proteins, and therefore would be complementary to other currently existing methods.