The modelling of fibre reorientation in soft tissue

In this paper, a hyperelastic and thermodynamically consistent model for soft tissue is developed that is able to describe the change of the initial orientation of the collagen fibres. Full numerical implementation is considered as well. The collagen architecture is assumed to reorient driven by a specific thermodynamical force. The anisotropy is described by a strain energy function, which is decomposed into a part related to the matrix and a part related to the fibres. The initial fibre orientation is defined by a structural tensor, while the current orientation is described by a time-dependent structural tensor, which results from the initial one by a rotational transformation. The rotation tensor is obtained via an integration process of a rate tensor, which depends on an adequately defined thermodynamical force. The integration is achieved via an exponential map algorithm, where it is shown that the rotation is necessarily a two-parametric one. Efficiency of the proposed formulation is demonstrated using some numerical examples.     

Effect of binding on melting transitions in polymer–diluent systems

An expression is derived for the melting point of a polymer when in equilibrium with a solution in which binding of low molecular weight compounds to the polymer takes place. Allowance is made for the possibility that the crystalline polymer itself is a complex. The argument is a purely thermodynamic one and is based on a consideration of the change in free energy as a result of a change in binding. Allowance is made also for non-specific polymer–solvent interactions, in which the mixture of low molecular weight solvents is treated as a single solvent. Special attention is paid to “inverted” melting transitions, i.e., cases in which the melting point increases with increasing dilution of the polymer. It is shown that as a rule this is accompanied by a corresponding, inverted effect of the solvent composition on the melting point. It is further shown that-in the absence of binding, “normal” behavior at the critical point (i.e., phase separation is induced by lowering the temperature) is always accompanied by “normal” melting behavior (i.e., a decrease in melting point when the polymer is diluted). Also, “inverted” melting always implies that phase separation at the critical point is induced by heating, but the reverse is not necessarily true.     

A graph theoretic approach to the development of minimal phylogenetic trees

Summary The problem of determining the minimal phylogenetic tree is discussed in relation to graph theory. It is shown that this problem is an example of the Steiner problem in graphs which is to connect a set of points by a minimal length network where new points can be added. There is no reported method of solving realistically-sized Steiner problems in reasonable computing time. A heuristic method of approaching the phylogenetic problem is presented, together with a worked example with 7 mammalian cytochrome c sequences. It is shown in this case that the method develops a phylogenetic tree that has the smallest possible number of amino acid replacements. The potential and limitations of the method are discussed. It is stressed that objective methods must be used for comparing different trees. In particular it should be determined how close a given tree is to a mathematically determined lower bound. A theorem is proved which is used to establish a lower bound on the length of any tree and if a tree is found with a length equal to the lower bound, then no shorter tree can exist.     

Length control of extended protein structures in bacteria and bacteriophages

The length of the tail of bacteriophages is controlled by a protein which acts as a molecular ruler. The needle of the injectisome, which is assembled by the polymerization of subunits that are exported through the nascent injectisome, is functionally related to the tail of bacteriophages. Interestingly, its length is controlled by a protein, which is itself exported and acts as a molecular ruler that is coupled to a substrate specificity switch. The bacterial flagellum is evolutionarily related to the injectisome. The length of the hook is also controlled by a secreted protein. This protein acts as a substrate specificity switch and, possibly, also as a ruler.     

Formation of segregated regions of feature detecting cells in self-organizing nerve field

This paper investigates the formation of a segregated region for a specific set of input signals in a nerve field. The segregated region is formed by a feature detecting cell group which fires only for a specific set of input signals. This firing region is called the region of feature detecting cells for the corresponding input set. First, a basic self-organizing model is given. The model is composed of the first input layer, the second nerve cell layer with lateral inhibitory interactions (it is called a lateral-inhibition type nerve field) and an inhibitory nerve cell. An input signal is an-dimensional vector whose components assume continuous values. Next, the condition which gurantees the formation of a segregated region for a specific set of input signals is derived, and the properties of the model are discussed based on the derived condition. In addition, the behavior of the model is examined through computer-simulated experiments. The following observations are made: When a certain condition is satisfied, a segregated region is formed in the nerve field according to a specific set of input signals. By varying the parameters of learning, the region is formed depending on the similarity between input signals. The regions for similar input signals are formed near each other in the nerve field. The region is created depending on the occurence probability of the input signal and its norm.     

A physical characterization of biological information and communication system model of ecosystems

What is information for living organisms? An answer to this question is given on a physical basis and a contrast between genetic information and sensory information is stressed with a relation to information theory. A simple model of an environment of living organisms is investigated on the basis of communication systems model proposed by the author and a cost of information transmission is taken into consideration through capacity cost theory. It is shown that channel capacity of information theory can be interpreted as an environment, and furthermore that a large diversity of genetic messages needs a large capacity of the environment. In addition, a definition of life in terms of information is proposed and a unified view on life processes is suggested.     

The elastic behavior of the urinary bladder for large deformations

The purpose of this paper is to investigate the theoretical basis for the pressure-distension behavior of the urinary bladder. A finite strain theory is developed for hollow spherical structures and it is shown that the Treloar model is a good prototype only for rubber balloons. The pressure-extension ratio relationship is inverted to lead a general form of strain energy function, and fitted by an empirical relation involving one exponential. The following form of strain energy function is derived: W(lambda, lambda, lambda -2) = C1 (P(1), a) + P(1)C2 (a, lambda)ea(lambda -1). Where C1(P(1), a) is a constant (N m-2), P(1) is the initial pressure, a is the rate of pressure increase and C2 (a, lambda) a third degree polynomial relation. P(1) and a are experimentally determined through volumetric pressure-distension data. It is verified that this type of energy function is also valid for uniaxial loading experiments by testing strips coming from the same bladder for which P(1) and a were computed. There is a good agreement between the experimental points and the theoretical stress-strain relation. Finally, the strain energy function is plotted as a function of the first strain invariant and appears to be of an exponential nature.     

On religious ritual as deference and communicative excess

I shall argue that most religious ritual is a performance that not only invokes but also performs communication. The ethnographic material from which I derive this argument is from China, in particular the temple rituals of local festivals. My argument is that a deep obeisance of welcome and departure that is both like and not like the normal ritual of greeting marks a religious from a non-religious ritual occasion and place. It is a ritual doubling that makes the honoured guest also a host. Religious ritual is a medium, and as a medium it is double in another sense. It is deference and deferral, a repeated transmission of obeisance to authority that has the authority of repetition. As well as doubling, religious ritual is excessively communicative. The medium is a performance not only of invitation and departure but also of communicative response, and it repeats this communication as a test of communicative response over and over again. Religious ritual performs both the opening and closing of communication, both the seeking and the responsive reciprocation of gift offerings with bounteousness. It is shadowed by the possibility of no response, of giving offence, of being abandoned. This possibility is acknowledged by being prevented, while the possibility that the performers are their own responders is disavowed.     

Forming sparse representations by local anti-Hebbian learning

How does the brain form a useful representation of its environment? It is shown here that a layer of simple Hebbian units connected by modifiable anti-Hebbian feed-back connections can learn to code a set of patterns in such a way that statistical dependency between the elements of the representation is reduced, while information is preserved. The resulting code is sparse, which is favourable if it is to be used as input to a subsequent supervised associative layer. The operation of the network is demonstrated on two simple problems.     

Universal common ancestry,LUCA, and the Tree of Life: three distinct hypotheses about the evolution of life

Common ancestry is a central feature of the theory of evolution, yet it is not clear what “common ancestry” actually means; nor is it clear how it is related to other terms such as “the Tree of Life” and “the last universal common ancestor”. I argue these terms describe three distinct hypotheses ordered in a logical way: that there is a Tree of Life is a claim about the pattern of evolutionary history, that there is a last universal common ancestor is an ontological claim about the existence of an entity of a specific kind, and that there is universal common ancestry is a claim about a causal pattern in the history of life. With these generalizations in mind, I argue that the existence of a Tree of Life entails a last universal common ancestor, which would entail universal common ancestry, but neither of the converse entailments hold. This allows us to make sense of the debates surrounding the Tree, as well as our lack of knowledge about the last universal common ancestor, while still maintaining the uncontroversial truth of universal common ancestry.     

The Influence of Temperature on the Effect of Bacteriostatic Concentrations of Phenol Against Escherichia coli

S ummary . During early exponential growth of Escherichia coli in the absence of phenol there is a natural death rate at 20, 30, and 44° but at the optimum temperature around 37° there is little if any significant death. The influence of a rise in temperature from 20 to 44° is to decrease the generation time and at 44° the lower generation time compensates for a reduced generation index. The main effect of sub-bacteriostatic concentrations of phenol is to increase the generation time but at 30, 37 and 44° there is a significant reduction in the generation index at the higher concentrations resulting in a dynamic bacteriostasis. At 20° bacteriostasis is due mainly to a large generation time but there is a little growth and so bacteriostasis is essentially dynamic. There is also evidence to suggest that the effect of a particular concentration of phenol on the generation index is not merely influenced by the temperature but by the generation time under the particular set of conditions. If phenol is added to rapidly growing cultures of E. coli the effect of a rise in temperature is to reduce the concentration required for bacteriostasis but if it is added during the lag phase there is a maximum in the bacteriostatic concentration between 20 and 37°.     

A self-organized chemical model and reaction cascade

Some reaction cascades in biological systems are analyzed by a self-organized chemical model, an autocatalytic reaction. This model is described by the coupling of a primary system which stabilizes the initial stage of the reaction rapidly and a partial system which controls the primary system slowly. By the internal force caused by a trigger above the threshold, the coupled system in near-equilibrium is broken and changed into a new state. From the rate equation for the coupled system, a dimensionless nonlinear state equation, n = -n3 - un - v, is derived, where n is the concentration of intermediate, and u, v are dynamic variables of the system. This equation is similar to a nonequilibrium tri-molecular reaction. By using this chemical network theory, fibrin polymerization. F + F----fm----fp + X, where F is a fibrinogen molecule, fm is a fibrin monomer, fp is fibrin polymer, and X is small peptides released from fibrinogen, is discussed as an excellent example of the enzyme reaction cascade.     

The transfer of J blood-group activity from J-containing bovine serum to J-negative erythrocytes.

The J blood-group activity of bovine serum is contained both in a lipid and in a nonlipid fraction. This is also true for calf serum. It demonstrated that the J determinant is transferred from a serum protein onto the erythrocyte membrane by incubation in vitro. Even though the donor of J activity is a lipid-free serum protein (probably a glycoprotein), the transferred J activity is detectable only in the lipid fraction of erythrocytes. Thus, the J determinant (probably a carbohydrate unit) must have been detached from a serum glycoprotein and transferred to a lipidic receptor (probably a glycosphingolipid) at the erythrocyte membrane. It is suggested than an enzyme system located in or at the erythrocyte membrane is responsible for the transfer of J substance. The transfer of J substance is inhibited by a polar lipid present in bovine serum.     

Artificial life and speciation, a case study: heterochromatin and speciation in the Microtus savii Group (Rodentia-Arvicolinae).

Artificial life is a tool which is used for simulation of peculiar cases of evolutionary events. The main characteristic of artificial life is that with this technique it is possible to simulate for a high number of generations the evolution of a population of individuals. Each individual is characterised by a small number of parameters, but each individual has its own evolutive story. So far it is possible to simulate the evolution of a population of some thousands specimens, for a high number of generations. The realistic aspect of the simulation is that each specimen is taken individually. In our opinion this instrument is very useful to simulate the evolution of the hybrids barrier during speciation. For this reason it is applied to a peculiar case of speciation, that of the Savi pine vole (Microtus savii) whose experimental data were recently investigated.     

Ewens' sampling formula and related formulae: combinatorial proofs, extensions to variable population size and applications to ages of alleles

Ewens' sampling formula, the probability distribution of a configuration of alleles in a sample of genes under the infinitely-many-alleles model of mutation, is proved by a direct combinatorial argument. The distribution is extended to a model where the population size may vary back in time. The distribution of age-ordered frequencies in the population is also derived in the model, extending the GEM distribution of age-ordered frequencies in a model with a constant-sized population. The genealogy of a rare allele is studied using a combinatorial approach. A connection is explored between the distribution of age-ordered frequencies and ladder indices and heights in a sequence of random variables. In a sample of n genes the connection is with ladder heights and indices in a sequence of draws from an urn containing balls labelled 1,2,...,n; and in the population the connection is with ladder heights and indices in a sequence of independent uniform random variables.     

Design‐based inference on Bernstein type estimators for continuous populations

The estimation of the values of a variable at any point of a study area is performed using Bernstein polynomials when the sampling scheme is implemented by selecting a point in each polygon of a regular grid overimposed onto the area. The evaluation of the precision of the resulting estimates is investigated under a completely design‐based framework. Moreover, as the main contribution to the mean squared error of the Bernstein‐type estimator is due to the bias, also a pseudo‐jackknife estimator is proposed. The performance of both estimators is investigated theoretically and by means of a simulation study. An application to a soil survey performed in Berkshire Downs in Oxfordshire (UK) is considered.     

A contribution to the mathematical biology of the rates of historical development

The paper is a second step toward a biomathematical theory of the rates of spread of new nonconformist ideas or behaviors in a society. It is intended as a preliminary and purely theoretical study of a very oversimplified case. An equation which determines the distribution function of the tendencies toward conformist and nonconformist behaviors is set up under a number of oversimplified assumptions, and a solution by successive approximations is indicated. The expression for the first approximation is given, and an estimate of the order of magnitude of the rates of changes is made. In conclusion an outline is given for further improvement of the theory.     

Fluorescence polarization immunoassay: detection of antibody to Brucella abortus

Fluorescence polarization immunoassay (FPA) is a homogeneous immunoassay useful for rapid and accurate detection of antibody or antigen. The principle of the assay is that a fluorescent dye (attached to an antigen or an antibody fragment) can be excited by plane-polarized light at the appropriate wavelength. As a rule, a small molecule rotates faster when in solution than a larger molecule. The rotation rate may be assessed by measuring light intensity in the vertical and horizontal planes. Generally, the time it takes a molecule to rotate through a given angle is an indication of its size. When a small molecule that rotates rapidly is bound to a larger molecule, the rotation rate is decreased and this decrease is measured. Because it is a primary antigen-antibody interaction, the rate of reaction is very rapid and usually a result may be obtained in minutes. This technology was applied to the detection of antibody to Brucella abortus in serum and milk, providing for the first time a rapid primary binding assay that is cost effective for use in the field.     

Toward an optimal design principle in relational biology

A vulnerability criterion is posed for a biological system within the context of representing the system as a relational set, i.e., a collection of components whose interdependency is described by means of a set of binary relations. The criterion provides a numerical value for each representation and therefore a means for comparing one representation against another. Choice of the criterion is such that the larger a numerical value a representation has then the less vulnerable to destruction is the system represented. Other things being equal, it is argued that the representation which endows the system with the least vulnerability is more likely to be a valid representation. A selection criterion is thereby achieved for narrowing down the choice ofa priori representations.