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PubMed2006

A generalized model of the repressilator.

The repressilator is a regulatory cycle of n genes where each gene represses its successor in the cycle: [see text]. The system is modelled by ODEs for an arbitrary number of identical genes and arbitrarily strong repressor binding. A detailed mathematical analysis of the dynamical behavior is provided for two model systems: (i) a repressilator with leaky transcription and single-step cooperative repressor binding, and (ii) a repressilator with auto-activation and cooperative regulator binding. Genes are assumed to be present in constant amounts, transcription and translation are modelled by single-step kinetics, and mRNAs as well as proteins are assumed to be degraded by first order reactions. Several dynamical patterns are observed: multiple steady states, periodic and aperiodic oscillations corresponding to limit cycles and heteroclinic cycles, respectively. The results of computer simulations are complemented by a detailed and complete stability analysis of all equilibria and of the heteroclinic cycle.

Binding Sites↗

PubMed2006

In vivo quantification of serotonin transporters using [(11)C]DASB and positron emission tomography in humans: modeling considerations.

Positron emission tomography (PET) studies of the serotonin transporter (5-HTT) in the human brain are increasingly using the radioligand [(11)C]N, N-dimethyl-2-(2-amino-4-cyanophenylthio) benzylamine. A variety of models have been applied to such data in several published articles; however to date, these models have not been validated with test-retest data. We recruited 11 healthy subjects and conducted two identical scans on each subject on the same day. We considered four different models (one- and two-tissue compartment kinetic models, likelihood estimation in graphical analysis (LEGA; a bias-free alternative to the graphical method), and basis pursuit) along with fast noniterative approximations to the kinetic models. We considered four different outcome measures (total volume of distribution (V(T)), binding potential with (BP) and without (BP(1)), free-fraction adjustment, and specific-to-nonspecific equilibrium partition coefficient (BP(2))). To assess the performance of each model, we compared results using six different metrics (percent difference (PD) and within-subject mean sum of squares for reproducibility, interclass coefficient for reliability, variance across subjects, identifiability based on bootstrap resampling of residuals for each method, and time stability analysis to determine minimal required scanning time). We considered analysis of both at the voxel level and at the region of interest (ROI) level and compared results from these two approaches to assess agreement. We determined that 100 mins of scanning time is adequate and that for ROI-level analysis, LEGA gives best results. Average PD is 5.51 for V(T), 20.7 for BP, 17.2 for BP(1), and 16.5 for BP(2) across all regions. For voxel-level analysis we determined that the one-tissue compartment noniterative model is best.

Adolescent↗

PubMed2004

Importance of direction of vibration on the onset of Soret-driven convection under gravity or weightlessness.

This paper considers the influence of the direction of vibration on the stability threshold of two-dimensional Soret-driven convection. The configuration is an infinite layer filled with a binary mixture, which can be heated from below or from above. The limiting case of high-frequency and small-amplitude vibration is considered for which the time-averaged formulation has been adopted. The linear stability analysis of the quasi-mechanical equilibrium shows that the problem depends on five non-dimensional parameters. These include the thermal Rayleigh number (Ra(T)), the vibrational parameter (R), the Prandtl number (Pr), the Lewis number (Le), the separation ratio (S) and the orientation of vibration with respect to the horizontal heated plate (alpha). For different sets of parameters, the bifurcation diagrams are plotted Ra(c) = f(S) and k(c) = g(S), which are the critical thermal Rayleigh and the critical wave numbers, respectively. Our results indicate that, relative to the classical case of static gravity, vibration may affect all regions in Ra(c)-S stability diagram. In the case of mono-cellular convection, by using a regular perturbation method, a closed-form relation for the critical Rayleigh number is found. Several physical situations in the presence or in the absence of gravity (micro-gravity) are discussed.

Journal Article↗

PubMed2001

Capillary instabilities in thin nematic liquid crystalline fibers.

A complete identification and characterization of three distinct capillary instabilities in nematic liquid crystal fibers is presented. Linear stability analysis of capillary instabilities in thin nematic liquid crystalline cylindrical fibers is performed by formulating and solving the governing nematocapillary equations. A representative axial nematic orientation texture is studied. The surface disturbance is expressed in normal modes, which include the azimuthal wavenumber m to take into account nonaxisymmetric modes of the disturbance. Capillary instabilities in nematic fibers reflect the anisotropic nature of liquid crystals, such as the orientation contribution to the surface elasticity and surface bending stresses. Surface gradients of bending stresses provide additional anisotropic contributions to the capillary pressure that may renormalize the classical displacement and curvature forces that exist in any fluid fiber. The exact nature (stabilizing and destabilizing) and magnitude of the renormalization of the displacement and curvature forces depend on the nematic orientation and the anisotropic contribution to the surface energy, and accordingly capillary instabilities may be axisymmetric or nonaxisymmetric, with finite or unbounded wavelengths. Thus, the classical fiber-to-droplet transformation is one of several possible instability pathways while others include surface fibrillation.

Journal Article↗

PubMed2006

Dried blood spot liquid chromatography assay for therapeutic drug monitoring of metformin.

The use of blood spot collection cards is a simple way to obtain specimens for analysis of drugs for the purpose of therapeutic drug monitoring, assessing adherence to medications and preventing toxicity in routine clinical setting. We describe the development and validation of a microanalytical technique for the determination of metformin from dried blood spots. The method is based on reversed phase high-performance liquid chromatography with ultraviolet detection. Drug recovery in the developed method was found to be more than 84%. The limits of detection and quantification were calculated to be to be 90 and 150 ng/ml, respectively. The intraday and interday precision (measured by CV%) was always less than 9%. The accuracy (measured by relative error, %) was always less than 12%. Stability analysis showed that metformin is stable for at least 2 months when stored at -70 degrees C. The small volume of blood required (10 microL), combined with the simplicity of the analytical technique makes this a useful procedure for monitoring metformin concentrations in routine clinical settings. The method is currently being applied to the analysis of blood spots taken from diabetic patients to assess adherence to medications and relationship between metformin level and metabolic control of diabetes.

Drug Monitoring↗

PubMed2007

Explicit off-line criteria for stable accurate time filtering of strongly unstable spatially extended systems.

Many contemporary problems in science involve making predictions based on partial observation of extremely complicated spatially extended systems with many degrees of freedom and physical instabilities on both large and small scales. Various new ensemble filtering strategies have been developed recently for these applications, and new mathematical issues arise. Here, explicit off-line test criteria for stable accurate discrete filtering are developed for use in the above context and mimic the classical stability analysis for finite difference schemes. First, constant coefficient partial differential equations, which are randomly forced and damped to mimic mesh scale energy spectra in the above problems are developed as off-line filtering test problems. Then mathematical analysis is used to show that under natural suitable hypothesis the time filtering algorithms for general finite difference discrete approximations to an sxs partial differential equation system with suitable observations decompose into much simpler independent s-dimensional filtering problems for each spatial wave number separately; in other test problems, such block diagonal models rigorously provide upper and lower bounds on the filtering algorithm. In this fashion, elementary off-line filtering criteria can be developed for complex spatially extended systems. The theory is illustrated for time filters by using both unstable and implicit difference scheme approximations to the stochastically forced heat equation where the combined effects of filter stability and model error are analyzed through the simpler off-line criteria.

Journal Article↗

PubMed2004

The circular topology of rhythm in asynchronous random Boolean networks.

The analysis of previously evolved rhythmic asynchronous random Boolean networks [Biosystems 59 (2001) 185] reveals common topological characteristics indicating that rhythm originates from a circular functional structure. The rhythm generating core of the network has the form of a closed ring which operates as a synchronisation substrate by supporting a travelling wave of state change; the size of the ring corresponds well with the period of oscillation. The remaining nodes in the network are either stationary or follow the activity of the ring without feeding back into it so as to form a coherent whole. Rings are typically formed early on in the evolutionary search process. Alternatively, long chains of nodes are favoured before they close upon themselves to stabilize. Analysis of asynchronous networks with de-correlated (non-rhythmic, non-stationary) attractors reveals no such common topological characteristics. These results have been obtained using statistical analysis and a specifically developed bottom-up pruning algorithm. This algorithm works from local interactions to global configuration by eliminating redundant links. The suitability of the algorithm has been confirmed by both numerical and single lesion analysis. The ring topology solution for the generation of rhythm implies that it will be harder to evolve rhythmic networks for big sizes and small periods and for bigger number of connections per node. These trends are confirmed empirically. Finally, the identified mechanisms are utilised to handcraft rhythmic networks of different periods showing that a low number of connections suffices for a large variety of rhythms. Random asynchronous update forces the evolved solutions to be highly robust maintaining their performance in the presence of intrinsic noise. The biological implications of such robust designs for molecular clocks are discussed.

Algorithms↗

PubMed2006

Linear instability of a coflowing jet under an axial electric field.

A temporal linear stability analysis is carried out for a coflowing jet with two immiscible inviscid liquids under a uniform axial electric field. According to the electrical properties of the inner and outer liquids, four cases, i.e., IDOC (inner: dielectric; outer: conductor), ICOD (inner: conductor; outer: dielectric), ICOC (inner and outer: conductor), and IDOD (inner and outer: dielectric), are considered. The analytical dimensionless dispersion relation is derived for both axisymmetric and nonaxisymmetric perturbations and is solved for axisymmetric ones. Three unstable modes, i.e., the paravaricose, parasinuous and transitional modes, are identified in the Rayleigh regime. The influences of the axial electric field, liquid electrical properties, and Weber number are studied at length. The results show that the axial electric field has a generally stabilizing effect on the unstable modes. The effects of the liquid electrical properties are quite different but all great for each case. The change of dominant mode is detected with the variation of the electric field intensity, electrical properties or Weber number. It is found that the parasinuous instability is the easiest to realize in IDOC. And the comparison with the experiment validates that the parasinuous mode is predominant in coaxial electrospray.

Journal Article↗

PubMed2006

Nonlinear instabilities and pathways of rupture in thin liquid bilayers.

A long-wave nonlinear analysis of dewetting of thin (<100 nm) liquid bilayers on solid substrates is presented. The short and the long time dynamics, interfacial morphologies, and the pathways of rupture and dewetting are studied to assess the roles of interfacial energies, film thicknesses, and viscosities. The twin interfaces (liquid-liquid and liquid-air) of bilayers under the influence of attractive van der Waals forces show a variety of dewetting pathways which, depending on the interfacial energies and film thicknesses, initially start with one of the two basic modes of instability--in-phase bending and out-of-phase squeezing. These short time modes of evolution and the extent of relative deformations at the interfaces are predicted from the linear stability analysis and verified by the nonlinear simulations. Simulations also show that in the later nonlinear regime, the intermolecular and viscous forces can profoundly modify the initial mode of instability and its growth rate leading to different pathways of dewetting and late stage morphologies. The complex late time patterns such as embedded droplets, inversion of top and bottom phases, and encapsulation of one fluid into the other are also engendered by tuning the intermolecular forces.

Chemistry, Physical↗

PubMed2001

An analysis of neural receptive field plasticity by point process adaptive filtering.

Neural receptive fields are plastic: with experience, neurons in many brain regions change their spiking responses to relevant stimuli. Analysis of receptive field plasticity from experimental measurements is crucial for understanding how neural systems adapt their representations of relevant biological information. Current analysis methods using histogram estimates of spike rate functions in nonoverlapping temporal windows do not track the evolution of receptive field plasticity on a fine time scale. Adaptive signal processing is an established engineering paradigm for estimating time-varying system parameters from experimental measurements. We present an adaptive filter algorithm for tracking neural receptive field plasticity based on point process models of spike train activity. We derive an instantaneous steepest descent algorithm by using as the criterion function the instantaneous log likelihood of a point process spike train model. We apply the point process adaptive filter algorithm in a study of spatial (place) receptive field properties of simulated and actual spike train data from rat CA1 hippocampal neurons. A stability analysis of the algorithm is sketched in the. The adaptive algorithm can update the place field parameter estimates on a millisecond time scale. It reliably tracked the migration, changes in scale, and changes in maximum firing rate characteristic of hippocampal place fields in a rat running on a linear track. Point process adaptive filtering offers an analytic method for studying the dynamics of neural receptive fields.

Adaptation, Physiological↗

PubMed1983

Repulsive stabilization in black lipid membranes. A hydrodynamic model.

A linear stability analysis is performed for a black lipid membrane. The hydrodynamic model consists of a viscous hydrocarbon film sandwiched between two aqueous phases. Attractive forces (van der Waals and electrical) and repulsive forces (steric) are expressed as body forces in the equations of fluid motion in the three phases. The steric repulsion due to overlap of the hydrocarbon chains of the lipids at small film thicknesses is described via an exponentially decaying interaction potential. The dispersion equation displays two modes of vibrations: the bending mode with the two Film surfaces transversely in phase, and the squeezing mode with the two surfaces 180 degrees out of phase. For symmetrical films, these two modes are uncoupled, and the squeezing mode (with thickness variations) is stabilized by the repulsive interactions. For nonsymmetrical films (different surface tensions, surface charges, etc.). these two modes are coupled and the asymmetry induces a shift of the marginal stability curve to shorter wavelengths.

Journal Article↗

PubMed2003

Naturally occurring Phe151Leu substitution near a conserved folding module lowers stability of glutathione transferase P1-1.

Glutathione transferases (GSTs) are a family of enzymes that detoxify electrophilic compounds, such as carcinogens or drugs, by conjugating them to glutathione. The enzymes have contributed to the understanding of protein structure, due to large differences in amino acid sequence within the family, yet similar architecture and folding. Our objective was to conduct a systematic survey of GSTP1 polymorphisms and their function. Nearly all variants detected were known polymorphisms: IVS4+13C>A; Ile105Val; Ala114Val; and g.2596T>C (Ser185Ser). However, we also found a novel Phe151Leu substitution in an African-American subject (1 out of 111). Kinetic parameters for the conjugation reaction with 1-chloro-2,4-dinitrobenzene (CDNB) were determined for the novel variant enzyme purified via heterologous expression in Escherichia coli. Five substrates were used for measurement of specific activities, including isothiocyanate compounds that occur in cruciferous vegetables (benzylisothiocyanate, phenethylisothiocyanate, and sulforaphane). Such isothiocyanate substrates are potential cancer chemopreventive agents that are conjugated by GSTs. No major change in kinetic parameters was observed. However, the half-life at 50 degrees C of the Leu 151 enzyme was reduced to 12 min, as compared to 28 min for the Phe 151 enzyme. Residue 151 is located at the N-terminus of helix alpha6 in GST motif II, surrounded by hydrophobic residues, and near the conserved "hydrophobic staple" and N-capping box motifs. These local structural elements aid in formation of helix alpha6 and promote proper folding and protein stability. Analysis of the three-dimensional structure showed that substitution of Phe 151 with Leu produces a hydrophobic cavity in the GSTP1 core, thereby destabilizing its structure. Phe151Leu represents one of the first-described allelic variations in a protein folding motif.

Amino Acid Motifs↗

PubMed2004

Self-adaptive blind source separation based on activation functions adaptation.

Independent component analysis is to extract independent signals from their linear mixtures without assuming prior knowledge of their mixing coefficients. As we know, a number of factors are likely to affect separation results in practical applications, such as the number of active sources, the distribution of source signals, and noise. The purpose of this paper to develop a general framework of blind separation from a practical point of view with special emphasis on the activation function adaptation. First, we propose the exponential generative model for probability density functions. A method of constructing an exponential generative model from the activation functions is discussed. Then, a learning algorithm is derived to update the parameters in the exponential generative model. The learning algorithm for the activation function adaptation is consistent with the one for training the demixing model. Stability analysis of the learning algorithm for the activation function is also discussed. Both theoretical analysis and simulations show that the proposed approach is universally convergent regardless of the distributions of sources. Finally, computer simulations are given to demonstrate the effectiveness and validity of the approach.

Computer Simulation↗

PubMedDate not supplied

Application of factorial design to accelerate identification of CHO growth factor requirements.

To accelerate recombinant CHO media and process development, we describe a simple approach to integrating multiple tasks associated with these processes including initial media design, serum-free adaptation, stability analysis and first generation scale-up. Factorial design techniques and normal probability chart representation of the results were first applied to identify potent parental CHO cell growth factors in a lean basal medium. These results were then applied to identify a suitable manufacturing medium from a panel of commercial and proprietary media formulations. When this approach was applied to recombinant CHO cell line, rapid adaptation of the cell line to an appropriate production medium occurred during culture expansion in the presence of the identified growth factor(s). This approach allows media component screening to be naturally integrated into the adaptation and scale-up processes since components that have little or no relative effect on cell proliferation are selected against as the "best" cultures are moved forward. The rapidity of the adaptation process allowed cell line stability studies to be initiated relatively early in the development process, thus providing preliminary stability information by the time the "outgrowing" culture could be scaled to 100-L reactors some 30 days after adaptation commenced. The application of full factorial design techniques allowed us to calculate the maximum number of interaction effects, the interpretation of which we believe can provide insights into growth factor biology.

Animals↗

PubMed2004

Analysis of the stability of multimeric proteins by effective DeltaG and effective m-values.

Analyzing the stability of a multimeric protein is challenging because of the intrinsic difficulty in handling the mathematical model for the folded multimer-unfolded monomer equilibrium. To circumvent this problem, we introduce the concept of effective stability, DeltaGeff (= -RTlnKeff), where Keff is the equilibrium constant expressed in monomer units. Analysis of the denaturant effect on DeltaGeff gives new insight into the stability of multimeric proteins. When a multimeric protein is mostly folded, the dependence of effective stability on denaturant concentration (effective m-value) is simply the m-value of its monomeric unit. However, when the protein is mostly unfolded, its stability depends on denaturant concentration with the m-value of its multimeric form. We also find that the effective m-value at the Cm is a good approximation of the apparent m-value determined by fitting the equilibrium unfolding data from multimeric proteins with a two-state monomer model. Moreover, when the m-value of a monomeric unit is estimated from its size, the effective stability of a multimeric protein can be determined simply from Cm and this estimated m-value. These simple and intuitive approaches will allow a facile analysis of the stability of multimeric proteins. These analyses are also applicable for high-throughput analysis of protein stability on a proteomic scale.

Models, Chemical↗

PubMed2003

Punctuated equilibria and 1/f noise in a biological coevolution model with individual-based dynamics.

We present a study by linear stability analysis and large-scale Monte Carlo simulations of a simple model of biological coevolution. Selection is provided through a reproduction probability that contains quenched, random interspecies interactions, while genetic variation is provided through a low mutation rate. Both selection and mutation act on individual organisms. Consistent with some current theories of macroevolutionary dynamics, the model displays intermittent, statistically self-similar behavior with punctuated equilibria. The probability density for the lifetimes of ecological communities is well approximated by a power law with exponent near -2, and the corresponding power spectral densities show 1/f noise (flicker noise) over several decades. The long-lived communities (quasisteady states) consist of a relatively small number of mutualistically interacting species, and they are surrounded by a "protection zone" of closely related genotypes that have a very low probability of invading the resident community. The extent of the protection zone affects the stability of the community in a way analogous to the height of the free-energy barrier surrounding a metastable state in a physical system. Measures of biological diversity are on average stationary with no discernible trends, even over our very long simulation runs of approximately 3.4 x 10(7) generations.

Journal Article↗

PubMed2003

Activity, stability and flexibility in glycosidases adapted to extreme thermal environments.

To elucidate the strategy of low temperature adaptation for a cold-adapted family 8 xylanase, the thermal and chemical stabilities, thermal inactivation, thermodependence of activity and conformational flexibility, as well as the thermodynamic basis of these processes, were compared with those of a thermophilic homolog. Differential scanning calorimetry, fluorescence monitoring of guanidine hydrochloride unfolding and fluorescence quenching were used, among other techniques, to show that the cold-adapted enzyme is characterized by a high activity at low temperatures, a poor stability and a high flexibility. In contrast, the thermophilic enzyme is shown to have a reduced low temperature activity, high stability and a reduced flexibility. These findings agree with the hypothesis that cold-adapted enzymes overcome the quandary imposed by low temperature environments via a global or local increase in the flexibility of their molecular edifice, with this in turn leading to a reduced stability. Analysis of the guanidine hydrochloride unfolding, as well as the thermodynamic parameters of irreversible thermal unfolding and thermal inactivation shows that the driving force for this denaturation and inactivation is a large entropy change while a low enthalpy change is implicated in the low temperature activity. A reduced number of salt-bridges are believed to be responsible for both these effects. Guanidine hydrochloride unfolding studies also indicate that both family 8 enzymes unfold via an intermediate prone to aggregation.

Adaptation, Physiological↗

PubMed2002

Temperature effects on capillary instabilities in a thin nematic liquid crystalline fiber embedded in a viscous matrix.

Linear stability analysis of capillary instabilities in a thin nematic liquid crystalline cylindrical fiber embedded in an immiscible viscous matrix is performed by formulating and solving the governing nemato-capillary equations, that include the effect of temperature on the nematic ordering as well as the effect of the nematic orientation. A representative axial nematic orientation texture with the planar easy axis at the fiber surface is studied. The surface disturbance is expressed in normal modes, which include the azimuthal wave number m to take into account non-axisymmetric modes. Capillary instabilities in nematic fibers reflect the anisotropic nature of liquid crystals, such as the ordering and orientation contributions to the surface elasticity and surface normal and bending stresses. Surface gradients of normal and bending stresses provide additional anisotropic contributions to the capillary pressure that may renormalize the classical displacement and curvature forces that exist in any fluid fiber. The exact nature (stabilizing and destabilizing) and magnitude of the renormalization of the displacement and curvature forces depend on the nematic ordering and orientation, i.e. the anisotropic contribution to the surface energy, and accordingly capillary instabilities may be axisymmetric or non-axisymmetric. In addition, when the interface curvature effects are accounted for as contributions of the work of interfacial bending and torsion to the total energy of the system, the higher-order bending moment contribution to the surface stress tensor is critical in stabilizing the fiber instabilities. For the planar easy axis, the nematic ordering contribution to the surface energy, which renormalizes the effect of the fiber shape, plays a crucial role to determine the instability mechanisms. Moreover, the unstable modes, which are most likely observed, can be driven by the dependence of surface energy on the surface area. Low-ordering fibers display the classical axisymmetric mode, since the surface energy decreases by decreasing the surface area. Decreasing temperature gives rise to the encounter with a local maximum or to monotonic increase of the characteristic length of the axisymmetric mode. Meanwhile, in the presence of high surface ordering, non-axisymmetric finite wavelength instabilities emerge, with higher modes growing faster since the surface energy decreases by increasing the surface area. As temperature decreases, the pitches of the chiral microstructures become smaller. However, this non-axisymmetric instability mechanism can be regulated by taking account of the surface bending moment, which contains higher order variations in the interface curvatures. More and more non-axisymmetric modes emerge as temperature decreases, but, at constant temperature, only a finite number of non-axisymmetric modes are unstable and a single fastest growing mode emerges with lower and higher unstable modes growing slower. For nematic fibers, the classical fiber-to-droplet transformation is one of several possible instability pathways, while others include chiral microstructures. The capillary instabilities' growth rate of a thin nematic fiber in a viscous matrix is suppressed by increasing either the fiber or matrix viscosity, but the estimated droplet sizes after fiber breakup in axisymmetric instabilities decrease with increasing the matrix viscosity.

Journal Article↗