Stoicheiometric analysis in studies of metabolism

Stoicheiometric analysis of metabolic pathways provides a systematic way of determining which metabolite concentrations are subject to constraints, information that may otherwise be very difficult to recognize in a large branched pathway. The procedure involves representing the pathway structure in the form of a matrix and then carrying out row operations to convert the matrix into "row echelon form": this is a form in which as many as possible of the elements on the main diagonal are non-zero, and all of the elements below the main diagonal are zero. If exactly the same operations are carried out on a unit matrix of order equal to the number of intermediate metabolites in the pathway, the resulting matrix allows the stoicheiometric constraints to be read off directly.     

Membrane sorting via the extracellular matrix

We consider the coupling between a membrane and the extracellular matrix. Computer simulations demonstrate that the latter coupling is able to sort lipids. It is assumed that membranes are elastic manifolds, and that this manifold is disrupted by the extracellular matrix. For a solid-supported membrane with an actin network on top, regions of positive curvature are induced below the actin fibers. A similar mechanism is conceivable by assuming that the proteins which connect the cytoskeleton to the membrane induce local membrane curvature. The regions of non-zero curvature exist irrespective of any phase transition the lipids themselves may undergo. For lipids that prefer certain curvature, the extracellular matrix thus provides a spatial template for the resulting lateral domain structure of the membrane.     

Analysis of creep strain during tensile fatigue of cortical bone

During fatigue tests of cortical bone specimens, at the unload portion of the cycle (zero stress) non-zero strains occur and progressively accumulate as the test progresses. This non-zero strain is hypothesised to be mostly, if not entirely, describable as creep. This work examines the rate of accumulation of this strain and quantifies its stress dependency. A published relationship determined from creep tests of cortical bone (Journal of Biomechanics 21 (1988) 623) is combined with knowledge of the stress history during fatigue testing to derive an expression for the amount of creep strain in fatigue tests. Fatigue tests on 31 bone samples from four individuals showed strong correlations between creep strain rate and both stress and "normalised stress" (sigma/E) during tensile fatigue testing (0-T). Combined results were good (r(2)=0.78) and differences between the various individuals, in particular, vanished when effects were examined against normalised stress values. Constants of the regression showed equivalence to constants derived in creep tests. The universality of the results, with respect to four different individuals of both sexes, shows great promise for use in computational models of fatigue in bone structures.     

Nonuniform swelling-induced residual strains in articular cartilage

Swelling effects in cartilage originate from an interstitial osmotic pressure generated by the presence of negatively charged proteoglycans in the tissue. This swelling pressure gives rise to a non-zero residual strain in the cartilage solid matrix in the absence of externally applied loads. Previous studies have quantified swelling effects in cartilage as volumetric or dimensional change of excised samples in varying osmotically active solutions. This study presents a new optical technique for measuring two-dimensional swelling-induced residual strain fields in planar samples of articular cartilage attached to the bone (i.e., in situ). Osmotic loading was applied to canine cartilage bone samples by equilibration in external baths of varying NaCl concentration. Non-zero swelling-induced strains were measured in physiological saline, giving evidence of the existence of residual strains in articular cartilage. Only one component of planar strain (i.e., in thickness direction) was found to be non-zero. This strain was found to be highly non-uniform in the thickness direction, with evidence of compressive strain in the deep zone of cartilage and tensile strain in the middle and surface zones. The obtained results can be used to characterize the material properties of the articular cartilage solid matrix, with estimated values of 26 M Pa for the tensile modulus for middle zone cartilage. The method provides the basis to obtain material properties of the cartilage solid matrix from a simple, free-swelling test and may be useful for quantifying changes in cartilage properties with injury, degeneration and repair.     

Pattern recognition in neural networks with competing dynamics: coexistence of fixed-point and cyclic attractors

We study the properties of the dynamical phase transition occurring in neural network models in which a competition between associative memory and sequential pattern recognition exists. This competition occurs through a weighted mixture of the symmetric and asymmetric parts of the synaptic matrix. Through a generating functional formalism, we determine the structure of the parameter space at non-zero temperature and near saturation (i.e., when the number of stored patterns scales with the size of the network), identifying the regions of high and weak pattern correlations, the spin-glass solutions, and the order-disorder transition between these regions. This analysis reveals that, when associative memory is dominant, smooth transitions appear between high correlated regions and spurious states. In contrast when sequential pattern recognition is stronger than associative memory, the transitions are always discontinuous. Additionally, when the symmetric and asymmetric parts of the synaptic matrix are defined in terms of the same set of patterns, there is a discontinuous transition between associative memory and sequential pattern recognition. In contrast, when the symmetric and asymmetric parts of the synaptic matrix are defined in terms of independent sets of patterns, the network is able to perform both associative memory and sequential pattern recognition for a wide range of parameter values.     

Bio-array images processing and genetic networks modelling

The new tools available for gene expression studies are essentially the bio-array methods using a large variety of physical detectors (isotopes, fluorescent markers, ultrasounds...). Here we present first rapidly an image-processing method independent of the detector type, dealing with the noise and with the peaks overlapping, the peaks revealing the detector activity (isotopic in the presented example), correlated with the gene expression. After this primary step of bio-array image processing, we can extract information about causal influence (activation or inhibition) a gene can exert on other genes, leading to clusters of genes co-expression in which we extract an interaction matrix M and an associated interaction graph G explaining the genetic regulatory dynamics correlated to the studied tissue function. We give two examples of such interaction matrices and graphs (the flowering genetic regulatory network of Arabidopsis thaliana and the lytic/lysogenic operon of the phage Mu) and after some theoretical rigorous results recently obtained concerning the asymptotic states generated by the genetic networks having a given interaction matrix and reciprocally concerning the minimal (in the sense of having a minimal number of non-zero coefficients) matrices having given stationary stable states.     

Patch-size and isolation effects in the Fisher–Kolmogorov equation

We examine the classical problem of the existence of a threshold size for a patch to allow for survival of a given population in the case where the patch is not completely isolated. The surrounding habitat matrix is characterized by a non-zero carrying capacity. We show that a critical patch size cannot be strictly defined in this case. We also obtain the saturation density in such a patch as a function of the size of the patch and the relative carrying capacity of the outer region. We argue that this relative carrying capacity is a measure of the isolation of the patch. Our results are then compared with conclusions drawn from observations of the population dynamics of understorey birds in fragments of the Amazonian forest and shown to qualitatively agree with them, offering an explanation for the importance of dispersal and isolation in these observations. Finally, we show that a generalized critical patch size can be introduced resorting to threshold densities for the observation of a given species.     

Simulating the role of microtubules in depolymerization-driven transport: a Monte Carlo approach.

In this paper we present a model that simulates the role of microtubules in depolymerization-driven transport. The model simulates a system that consists of a 13-protofilament microtubule with "five-start" helical structure and a motor protein-coated bead that moves along one of the protofilaments of the microtubule, as in in vitro experiments. The microtubule is simulated using the lateral cap model, with substantial generalizations. For the new terminal configurations in the presence of the bead, rate constants for association and dissociation events of tubulin molecules are calculated by exploring the geometric similarities between different patterns of terminal configurations and by decomposing complex patterns into simpler patterns whose corresponding rate constants are known. In comparison with a previous model, in which simplifications are made about the structure of the microtubule and in which the microtubule can only depolymerize, the detailed structure of the microtubule is taken into account in the present model. Furthermore, the microtubule can be either polymerizing or depolymerizing. Force-velocity curves are obtained for both zero and non-zero tubulin guanosine 5'-triphosphate (GTP) concentrations. By analyzing the trajectory of the bead under different parameters, the condition for "run and pause" is analyzed, and the time scale of "run" and "pause" is found to be different for different motor proteins. We also suggest experiments that can be used to examine the results predicted by the model.     

Length and pH-dependent energetics of (CCG)n and (CGG)n trinucleotide repeats

Trinucleotide repeats are involved in a number of debilitating diseases such as fragile-X syndrome and myotonic dystrophy. Eighteen to 75 base-long (CCG)(n) and (CGG)(n) oligodeoxynucleotides were analysed using a combination of biophysical (UV-absorbance, differential scanning calorimetry) and biochemical methods (non-denaturing gel electrophoresis, enzymatic footprinting). All oligomers formed stable intramolecular structures under near physiological conditions with a melting temperature which was only weakly dependent on oligomer length. Thermodynamic analysis of the denaturation process by UV-melting and calorimetric experiments revealed a length-dependent discrepancy between the enthalpy values deduced from model-dependent (UV-melting) and model-independent experiments (calorimetry), as recently shown for CTG and CAG trinucleotides (Nucleic Acids Res. 33 (2005) 4065). Evidence for non-zero molar heat capacity changes was also derived from the analysis of the Arrhenius plots. Such behaviour is analysed in the framework of an intramolecular "branched" or "broken" hairpin model, in which long oligomers do not fold into a simple long hairpin-stem intramolecular structure, but allow the formation of several independent folding units of unequal stability. These results suggest that this observation may be extended to various trinucleotide repeats-containing sequences.     

Persistence of species obeying difference equations

The question of persistence of interacting species is one of the most important in theoretical ecology; when the system is governed by difference equations this question is particularly difficult to resolve because of the complicated dynamics of the model. The problem has usually been tackled via the concepts of asymptotic stability and global asymptotic stability, however the first is not a strong enough restriction since only orbits starting near a rest point are guaranteed to converge to the rest point, while the second as well as usually being extremely difficult to establish is surely too strong a condition, since it rules out for example a stable limit cycle. It is proposed here that a more biologically realistic criterion, and incidentally one which turns out to be more tractable, is that of cooperativeness, where all orbits are required eventually to enter and remain in a region at a non-zero distance from the boundary (corresponding to a zero value of at least one population). A theorem is proved giving conditions for cooperativeness, and is applied to some examples of predator-prey interactions, simple conditions on the parameters being obtained even for some ranges of the parameters where the dynamics are chaotic.     

A nuclear-derived proteinaceous matrix embeds the microtubule spindle apparatus during mitosis

The concept of a spindle matrix has long been proposed. Whether such a structure exists, however, and what its molecular and structural composition are have remained controversial. In this study, using a live-imaging approach in Drosophila syncytial embryos, we demonstrate that nuclear proteins reorganize during mitosis to form a highly dynamic, viscous spindle matrix that embeds the microtubule spindle apparatus, stretching from pole to pole. We show that this "internal" matrix is a distinct structure from the microtubule spindle and from a lamin B-containing spindle envelope. By injection of 2000-kDa dextran, we show that the disassembling nuclear envelope does not present a diffusion barrier. Furthermore, when microtubules are depolymerized with colchicine just before metaphase the spindle matrix contracts and coalesces around the chromosomes, suggesting that microtubules act as "struts" stretching the spindle matrix. In addition, we demonstrate that the spindle matrix protein Megator requires its coiled-coil amino-terminal domain for spindle matrix localization, suggesting that specific interactions between spindle matrix molecules are necessary for them to form a complex confined to the spindle region. The demonstration of an embedding spindle matrix lays the groundwork for a more complete understanding of microtubule dynamics and of the viscoelastic properties of the spindle during cell division.     

The nuclear matrix from cells of different origin. Evidence for a common set of matrix proteins

We compared the protein composition of the nuclear matrix isolated from several murine embryonal carcinoma cells and mature tissues by two-dimensional gel electrophoresis. Two nuclear matrix fractions were investigated: the "peripheral" nuclear matrix (matrix proteins that remain insoluble after reduction), and the "internal" nuclear matrix (matrix proteins released by reduction). The two subfractions have completely different protein compositions. Although numerous differences in nuclear matrix protein composition among different cell types were observed, a limited set of polypeptides common to all mouse cell types was identified. A majority of these common proteins was also present in cells from other mammalian species (i.e. rat and human). For this set of proteins, we coin the term "minimal matrix." As expected, lamin B, known to be expressed throughout differentiation, is part of the common set of peripheral nuclear matrix proteins. Lamins A and C are not because these proteins were absent from undifferentiated embryonal carcinoma cells. Since these common nuclear matrix proteins occur in all mammalian nuclear matrices analyzed so far, it is likely that they have a basic role in nuclear organization and function.     

Non-zero mean alpha oscillations revealed with computational model and empirical data

Ongoing oscillations and evoked responses are two main types of neuronal activity obtained with diverse electrophysiological recordings (EEG/MEG/iEEG/LFP). Although typically studied separately, they might in fact be closely related. One possibility to unite them is to demonstrate that neuronal oscillations have non-zero mean which predicts that stimulus- or task-triggered amplitude modulation of oscillations can contribute to the generation of evoked responses. We validated this mechanism using computational modelling and analysis of a large EEG data set. With a biophysical model, we indeed demonstrated that intracellular currents in the neuron are asymmetric and, consequently, the mean of alpha oscillations is non-zero. To understand the effect that neuronal currents exert on oscillatory mean, we varied several biophysical and morphological properties of neurons in the network, such as voltage-gated channel densities, length of dendrites, and intensity of incoming stimuli. For a very large range of model parameters, we observed evidence for non-zero mean of oscillations. Complimentary, we analysed empirical rest EEG recordings of 90 participants (50 young, 40 elderly) and, with spatio-spectral decomposition, detected at least one spatially-filtred oscillatory component of non-zero mean alpha oscillations in 93% of participants. In order to explain a complex relationship between the dynamics of amplitude-envelope and corresponding baseline shifts, we performed additional simulations with simple oscillators coupled with different time delays. We demonstrated that the extent of spatial synchronisation may obscure macroscopic estimation of alpha rhythm modulation while leaving baseline shifts unchanged. Overall, our results predict that amplitude modulation of neural oscillations should at least partially explain the generation of evoked responses. Therefore, inference about changes in evoked responses with respect to cognitive conditions, age or neuropathologies should be constructed while taking into account oscillatory neuronal dynamics.     

Temperature- and ionic strength-induced conformational changes in the lipid head group region of liposomes as suggested by zeta potential data.

Neutral liposomes composed of DMPC (dimyristoylphosphatidylcholine), DPPC (dipalmitoylphosphatidylcholine) or DSPC (distearoylphosphatidylcholine) are found to exhibit non-zero zeta potentials in an electric field even when they are dispersed in solution at pH 7.4. A model for the orientation of lipid head groups is proposed to explain the observed non-zero zeta potentials. The dependence of the zeta potential on temperature and ionic strength is analyzed via this model to obtain the information on the direction of the lipid head group in the liposome surface region. The direction of the lipid head group is found to be sensitive to the temperature and the ionic strength of the medium. At low ionic strengths, the phosphatidyl groups are located at the outer portion of the head group region. At constant temperature, as the ionic strength increases, the choline group approaches the outer region of the bilayer surface while the phosphatidyl group hides behind the surface. At the phase transition temperature of the lipid, the phosphatidyl group lies in the outer-most region of the surface and the choline group is in the inner-most region.     

Conditions for Global Dynamic Stability of a Class of Resource-Bounded Model Ecosystems

This paper studies a class of dynamical systems that model multi-species ecosystems. These systems are ‘resource bounded’ in the sense that species compete to utilize an underlying limiting resource or substrate. This boundedness means that the relevant state space can be reduced to a simplex, with coordinates representing the proportions of substrate utilized by the various species. If the vector field is inward pointing on the boundary of the simplex, the state space is forward invariant under the system flow, a requirement that can be interpreted as the presence of non-zero exogenous recruitment. We consider conditions under which these model systems have a unique interior equilibrium that is globally asymptotically stable. The systems we consider generalize classical multi-species Lotka–Volterra systems, the behaviour of which is characterized by properties of the community (or interaction) matrix. However, the more general systems considered here are not characterized by a single matrix, but rather a family of matrices. We develop a set of ‘explicit conditions’ on the basis of a notion of ‘uniform diagonal dominance’ for such a family of matrices, that allows us to extract a set of sufficient conditions for global asymptotic stability based on properties of a single, derived matrix. Examples of these explicit conditions are discussed.     

On the Population Dynamics of the Malaria Vector

A deterministic differential equation model for the population dynamics of the human malaria vector is derived and studied. Conditions for the existence and stability of a non-zero steady state vector population density are derived. These reveal that a threshold parameter, the vectorial basic reproduction number, exist and the vector can established itself in the community if and only if this parameter exceeds unity. When a non-zero steady state population density exists, it can be stable but it can also be driven to instability via a Hopf Bifurcation to periodic solutions, as a parameter is varied in parameter space. By considering a special case, an asymptotic perturbation analysis is used to derive the amplitude of the oscillating solutions for the full non-linear system. The present modelling exercise and results show that it is possible to study the population dynamics of disease vectors, and hence oscillatory behaviour as it is often observed in most indirectly transmitted infectious diseases of humans, without recourse to external seasonal forcing.     

Fast adaptive formation of orthogonalizing filters and associative memory in recurrent networks of neuron-like elements

A demonstration is given that an orthogonalizing filter for patterns is formed adaptively and very rapidly in a network of neuron-like elements with internal feedback connections. It is here assumed that the feedback gain is variable, and proportional to the correlation matrix of the output pattern vectors. The time-dependent signal transfer properties of the complete system are described by a system matrix which satisfies a matrix Bernoulli differential equation; solutions of this equation are outlined. The asymptotic value of the system matrix is shown to correspond to the orthogonal projection operator on the space that is complementary to the space spanned by all of the earlier input pattern vectors. Such a system then acts as a filter, which optimally extracts the amount that is new in an input pattern with respect to all old patterns. It also has features that are directly attributable to a distributed associative memory that is optimally selective.     

Sensitivity of predicted muscle forces to parameters of the optimization-based human leg model revealed by analytical and numerical analyses

There are different opinions in the literature on whether the cost functions: the sum of muscle stresses squared and the sum of muscle stresses cubed, can reasonably predict muscle forces in humans. One potential reason for the discrepancy in the results could be that different authors use different sets of model parameters which could substantially affect forces predicted by optimization-based models. In this study, the sensitivity of the optimal solution obtained by minimizing the above cost functions for a planar three degrees-of-freedom (DOF) model of the leg with nine muscles was investigated analytically for the quadratic function and numerically for the cubic function. Analytical results revealed that, generally, the non-zero optimal force of each muscle depends in a very complex non-linear way on moments at all three joints and moment arms and physiological cross-sectional areas (PCSAs) of all muscles. Deviations of the model parameters (moment arms and PCSAs) from their nominal values within a physiologically feasible range affected not only the magnitude of the forces predicted by both criteria, but also the number of non-zero forces in the optimal solution and the combination of muscles with non-zero predicted forces. Muscle force magnitudes calculated by both criteria were similar. They could change several times as model parameters changed, whereas patterns of muscle forces were typically not as sensitive. It is concluded that different opinions in the literature about the behavior of optimization-based models can be potentially explained by differences in employed model parameters.     

Optimality under noise: higher memory strategies for the alternating prisoner's dilemma.

The Alternating Prisoner's Dilemma is a variant of the iterated Prisoner's Dilemma in which the players alternate in the roles of actor and recipient. We searched for strategies which are "optimal" in the Alternating Prisoner's Dilemma with noise (a non-zero probability that a player's decision will be transmitted incorrectly). In order to achieve success against a variety of other strategies, a strategy must be "self-cooperating" (able to achieve mutual cooperation with its clone), "C-exploiting" (able to exploit unconditional cooperators), and "D-unexploitable" (able to resist exploitation by defectors). It must also have high evolutionary "dominance", a general measure of evolutionary performance which considers both resistance to invasion and the ability to invade other strategies. A strategy which meets these optimality criteria can evolve cooperation by invading a population of defectors and establishing a stable cooperative society. Most of the strategies commonly discussed in the Alternating Prisoner's Dilemma literature are low-memory strategies such as Tit For Tat, Pavlov, and Firm But Fair, but none of these strategies can simultaneously meet all of the optimality criteria. However, we discovered a class of higher memory "Firm Pavlov" strategies, which not only meet our stringent optimality criteria, but also achieve remarkable success in round-robin tournaments and evolutionary interactions. These higher memory strategies are friendly enough to cooperate with their clone, pragmatic enough to exploit unconditional cooperators, and wary enough to resist exploitation by defectors: they are truly "optimal under noise" in the Alternating Prisoner's Dilemma.     

Evaluation of the New MALDI Matrix 4-Chloro-α-Cyanocinnamic Acid

MALDI-TOF continues to be an important tool for many proteomic studies. Recently, a new rationally designed matrix 4-chloro-α-cyanocinnamic acid was introduced, which is reported to have superior performance as compared with the “gold standard” α-cyano-4-hydroxycinnamic acid (CHCA).¹ In this study, the performance of this new matrix, using the Shimadzu Biotech Axima TOF² (Shimadzu Biotech, Manchester, UK), was investigated. The overall sequence coverage as well as sensitivity of this matrix were compared with CHCA using standard protein tryptic digests. The performance of this matrix with labile peptides, such as phosphopeptides and 4-sulfophenyl isothiocynate-derivatized peptides, to facilitate de novo sequencing was also explored. This matrix was found to be better performing than CHCA in overall sensitivity and showed better sequence coverage at low-digest levels, partly as a result of less of a bias for arginine-containing peptides. It also showed as much as a tenfold improvement in sensitivity with labile peptides on standard stainless-steel targets. In addition, as a result of the much cooler nature of this matrix, labile peptides are readily seen intact with much less fragmentation in mass spectrometry (MS) mode. This matrix was also evaluated in the MS/MS fragmentation modes of post-source decay (PSD) and collisional-induced dissociation (CID). It was found that fragmentation occurs readily in CID, however as a result of the very cool nature of this new matrix, the PSD fragments were quite weak. This matrix promises to be an important addition to the already extensive array of MALDI matrices.