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PubMed2005

The mechanism distinguishability problem in biochemical kinetics: the single-enzyme, single-substrate reaction as a case study.

A theoretical analysis of the distinguishability problem of two rival models of the single enzyme-single substrate reaction, the Michaelis-Menten and Henri mechanisms, is presented. We also outline a general approach for analysing the structural indistinguishability between two mechanisms. The approach involves constructing, if possible, a smooth mapping between the two candidate models. Evans et al. [N.D. Evans, M.J. Chappell, M.J. Chapman, K.R. Godfrey, Structural indistinguishability between uncontrolled (autonomous) nonlinear analytic systems, Automatica 40 (2004) 1947-1953] have shown that if, in addition, either of the mechanisms satisfies a particular criterion then such a transformation always exists when the models are indistinguishable from their experimentally observable outputs. The approach is applied to the single enzyme-single substrate reaction mechanism. In principle, mechanisms can be distinguished using this analysis, but we show that our ability to distinguish mechanistic models depends both on the precise measurements made, and on our knowledge of the system prior to performing the kinetics experiments.

Enzymes↗

PubMed2004

Ultrasonically assisted turning of aviation materials: simulations and experimental study.

Ultrasonically assisted turning of modern aviation materials is conducted with ultrasonic vibration (frequency f approximately 20 kHz, amplitude a approximately 15 microm) superimposed on the cutting tool movement. An autoresonant control system is used to maintain the stable nonlinear resonant mode of vibration throughout the cutting process. Experimental comparison of roughness and roundness for workpieces machined conventionally and with the superimposed ultrasonic vibration, results of high-speed filming of the turning process and nanoindentation analyses of the microstructure of the machined material are presented. The suggested finite-element model provides numerical comparison between conventional and ultrasonic turning of Inconel 718 in terms of stress/strain state, cutting forces and contact conditions at the workpiece/tool interface.

Journal Article↗

PubMed1993

Population genetics and structure of Buryats from the Lake Baikal Region of Siberia.

Genetic polymorphisms of blood groups, serum proteins, red cell enzymes, PTC tasting, and cerumen types are reported for five Mongoloid populations of Buryats from the Lake Baikal region of Siberia (Russia). These groups are characterized by relatively high frequencies of alleles ABO*B, RH*D, cerumen D, GC*1F, ACP1*B, ESD*2, and PGD*C. Significant genetic heterogeneity between populations was demonstrated for the loci RH, MN, cerumen, PGD, ABO, GC, GLO, TF, and PGM1. Genetic distance analyses using five loci revealed a lower level of genetic microdifferentiation within the Buryat populations compared with other native Siberian groups. The distribution of gene markers in Buryats is similar to that found in neighboring Central Asian groups, such as the Yakuts and the Mongols. Intrapopulational analyses of the five Buryat subdivisions, based on R matrix and rii, indicate that one of the subdivisions is reproductively more isolated than the others and that two of the communities have received considerable gene flow. A nonlinear relationship was demonstrated between geographic and genetic distances of Buryat population subdivisions.

Adolescent↗

PubMed2026

Exploring the dose-response relationship between prenatal exercise and postpartum depression: A systematic review and meta-analysis of randomized controlled trials.

IMPORTANCE: Postpartum depression (PPD) is a hidden and widespread global public health crisis affecting millions of mothers and infants annually. Prenatal exercise is a potentially accessible nonpharmacological strategy for PPD prevention, but its optimal dose remains uncertain. OBJECTIVE: To explore the dose-response relationship between prenatal exercise and the incidence of PPD through meta-analysis of randomized controlled trials (RCTs). DATA SOURCES: Systematic searches were conducted in PubMed, Embase, Web of Science, and Cochrane Library using MeSH terms and keywords related to "pregnant women," "prenatal exercise," and "postpartum depression," up to June 23, 2025. STUDY SELECTION: RCTs included examined prenatal exercise interventions in pregnant women without a history of depression, with PPD incidence reported using validated depression scales (such as EPDS, CES-D). Non-RCT studies, duplicate publications, and studies with insufficient data were excluded. DATA EXTRACTION AND SYNTHESIS: Two researchers independently extracted data according to the PRISMA guidelines. A random-effects model was used to pool odds ratios (OR) and their 95% confidence intervals (CI). Linear and nonlinear dose-response models were employed to analyze and evaluate the relationship between exercise dose (measured in METs-min/week) and the incidence of PPD. MAIN OUTCOME(S) AND MEASURE(S): The primary outcome is the incidence of PPD, analyzing its relationship with prenatal exercise dose. RESULTS: Eight RCTs involving 2231 pregnant women were included. The pooled analysis showed that prenatal exercise was associated with a potential reduction in PPD incidence, although the overall effect did not reach statistical significance (OR=0.58, 95% CI [0.33, 1.02]). In dose-stratified analysis, exercise doses ≥500 METs-min/week were associated with significantly lower PPD incidence (OR=0.44, 95% CI [0.24, 0.78]). Subgroup analyses suggested trends toward greater benefits among women aged ≥30 years and those initiating exercise between 14 and 28 weeks of gestation; however, subgroup differences did not reach statistical significance. The linear dose-response trend did not reach statistical significance (p = 0.0533), and neither the overall spline association (p = 0.1704) nor the test for nonlinearity (p = 0.6361) was statistically significant. CONCLUSIONS AND RELEVANCE: Prenatal exercise may be associated with a lower risk of PPD, but the overall pooled effect did not reach statistical significance. Findings concerning ≥500 METs-min/week and the apparent flattening of the dose-response curve should be considered exploratory and require confirmation in larger trials.

Humans↗

PubMed2005

Early-stage visual processing and cortical amplification deficits in schizophrenia.

BACKGROUND: Patients with schizophrenia show deficits in early-stage visual processing, potentially reflecting dysfunction of the magnocellular visual pathway. The magnocellular system operates normally in a nonlinear amplification mode mediated by glutamatergic (N-methyl-D-aspartate) receptors. Investigating magnocellular dysfunction in schizophrenia therefore permits evaluation of underlying etiologic hypotheses. OBJECTIVES: To evaluate magnocellular dysfunction in schizophrenia, relative to known neurochemical and neuroanatomical substrates, and to examine relationships between electrophysiological and behavioral measures of visual pathway dysfunction and relationships with higher cognitive deficits. DESIGN, SETTING, AND PARTICIPANTS: Between-group study at an inpatient state psychiatric hospital and outpatient county psychiatric facilities. Thirty-three patients met DSM-IV criteria for schizophrenia or schizoaffective disorder, and 21 nonpsychiatric volunteers of similar ages composed the control group. MAIN OUTCOME MEASURES: (1) Magnocellular and parvocellular evoked potentials, analyzed using nonlinear (Michaelis-Menten) and linear contrast gain approaches; (2) behavioral contrast sensitivity measures; (3) white matter integrity; (4) visual and nonvisual neuropsychological measures, and (5) clinical symptom and community functioning measures. RESULTS: Patients generated evoked potentials that were significantly reduced in response to magnocellular-biased, but not parvocellular-biased, stimuli (P = .001). Michaelis-Menten analyses demonstrated reduced contrast gain of the magnocellular system (P = .001). Patients showed decreased contrast sensitivity to magnocellular-biased stimuli (P<.001). Evoked potential deficits were significantly related to decreased white matter integrity in the optic radiations (P<.03). Evoked potential deficits predicted impaired contrast sensitivity (P = .002), which was in turn related to deficits in complex visual processing (P< or =.04). Both evoked potential (P< or =.04) and contrast sensitivity (P = .01) measures significantly predicted community functioning. CONCLUSIONS: These findings confirm the existence of early-stage visual processing dysfunction in schizophrenia and provide the first evidence that such deficits are due to decreased nonlinear signal amplification, consistent with glutamatergic theories. Neuroimaging studies support the hypothesis of dysfunction within low-level visual pathways involving thalamocortical radiations. Deficits in early-stage visual processing significantly predict higher cognitive deficits.

Adult↗

PubMed2005

Structural and dynamical analyses of the kinase network derived from the transpath database.

We analyze the structural design and the dynamical properties of a protein kinase network derived from the Transpath database. We consider structural properties, such as feedback cycles, pathway lengths, fraction of shortest pathways and crosstalk. Dynamic characteristics of the network are analyzed by using nonlinear differential equations with a special focus on kinase amplitudes and signal propagation times. Comparison with random networks shows that the cellular kinase network exhibits special features which might be a result of natural selection. In particular, the Transpath network contains no cycles, and input kinases and output kinases are generally connected by shortest signalling routes. Moreover, it displays a characteristic spectrum of cross-talk between different pathways.

Algorithms↗

PubMed2005

Parameterization of the shape of intracranial saccular aneurysms using Legendre polynomials.

Our recent studies of the nonlinear mechanics of saccular aneurysms suggest that it is unlikely that these lesions enlarge or rupture via material (limit point) or dynamic (resonance) instabilities. Rather, there is a growing body of evidence from both vascular biology and biomechanical analyses that implicate mechanosensitive growth and remodeling processes. There is, therefore, a pressing need to quantify regional multiaxial wall stresses which, because of the membrane-like behavior of many aneurysms, necessitates better information on the applied loads and regional surface curvatures. Herein, we present and illustrate a method whereby regional curvatures can be estimated easily for sub-classes of human aneurysms based on clinically available data from magnetic resonance angiography (MRA). Whereas Legendre polynomials are used to illustrate this approach, different functions may prove useful for different sub-classes of lesions.

Algorithms↗

PubMed2005

Thin-film theories for two-phase reactive flow models of active cell motion.

The aim of this paper is to develop a broadly-applicable and self-consistent thin-film biphasic modelling framework for the full crawling cycle of a single animal cell. A hierarchy of thin-film two-phase 'reactive flow' models is derived; between them these cover a wide range of biologically relevant parameter regimes. The mathematical properties and biological implications of the resulting systems of high-order nonlinear degenerate parabolic-elliptic evolution equations are investigated. Linear-stability arguments suggest the formation of highly localized regions of high or low network density associated with small irregular oscillations or 'ruffling' of the plasma membrane. Local analyses at the contact line identify the classes of admissible contact-line conditions, through which we study for the first time the effect on the cell-scale motion of the 'mesoscopic' contact-line physics, which consists of the chemical and mechanical mechanisms for protrusive and retractive force generation near the outer cell periphery. One of the formulations is used to develop a minimal model for cell body translocation over a thin pseudopod, which predicts that myosin-driven contraction is not essential for rapid translocation. An analytic prediction for the translocation speed is given in terms of the network viscosity and slip coefficient (a parameter measuring the adhesion strength), of the membrane tension and of the thicknesses of the pseudopod and actin cortex; this is in good agreement with the translocation speed of osteoblasts on biomaterial substrates commonly used for orthopaedic implants. Limitations of the modelling approach and directions for future work are outlined.

Actins↗

PubMed2006

Influence of density dependence on predator-prey seabird interactions at large spatio-temporal scales.

Theoretical investigations of competitive dynamics have noted that numbers of predator and prey influence each other. However, few empirical studies have demonstrated how a life-history trait of the prey (such as fecundity) can be affected simultaneously by its own density and the density of predators. For instance, density dependence can reduce fecundity with increasing number of prey, while inverse density dependence or Allee effects may occur especially when the prey is a social organism. Here we analysed an intraguild predator-prey system of two seabird species at a large spatio-temporal scale. As expected, we found that fecundity of prey was negatively affected by predator density. Nevertheless, fecundity of prey also increased nonlinearly with its own density and strikingly with the prey-predator ratio. Small groups of prey were probably not able to defend their nests especially against large number of predators. At the highest prey densities (i.e. when anti-predator strategies should be most efficient), prey fecundity also lowered, suggesting the appearance of density dependence mediated by food competition. Allee effects and density dependence occurred across a broad range of population sizes of both the prey and the predator at several local populations facing different ecological environments.

Animals↗

PubMed2002

Homo- and heterochiral alkylzinc fencholates: linear or nonlinear effects in dialkylzinc additions to benzaldehyde.

Scalemic mixtures of chiral anisyl fenchols with different ortho-substituents (X) in the anisyl moieties [X = H (1), Me (2), SiMe3 (3) and tBu (4)] are employed as pre-catalysts in enantioselective additions of diethylzinc to benzaldehyde. While a remarkable asymmetric depletion is apparent for X = H and Me, a linear relationship between the enantiomeric purity of the chiral source and the product 1-phenylpropanol is observed for X = SiMe3 and tBu. X-ray single crystal analyses show that racemic methylzinc fencholates obtained from 1 (X = H) and 2 (X = Me) yield homochiral dimeric complexes, while for 3 (X = SiMe3) and 4 (X = tBu) the heterochiral dimeric alkylzinc structures are formed. The enantiopure fenchols 1-4 all yield homochiral dimeric methylzinc complexes. Computed relative energies of homo- and heterochiral fencholate dimers with X = H and Me reveal an intrinsic preference for the formation of the homochiral dimers, consistent with the observed negative NLE. In contrast, similar stabilities are computed for homo- and heterochiral complexes of ligands 3 (X = SiMe3) and 4 (X = tBu), in agreement with the absence of a nonlinear effect for bulky ortho-subsituents.

Journal Article↗

PubMed2000

Modeling of dose-response-time data: four examples of estimating the turnover parameters and generating kinetic functions from response profiles.

The most common approach to in vivo pharmacokinetic and pharmacodynamic modeling involves sequential analysis of the plasma concentration versus time and then response versus time data, such that the plasma kinetic model provides an independent function, driving the dynamics. However, response versus time data, even in the absence of measured drug concentrations, inherently contain useful information about the turnover characteristics of response (turnover rate, half-life of response), the drug's biophase kinetics (F, half-life) as well as the pharmacodynamic characteristics (potency, intrinsic activity). Previous analyses have assumed linear kinetics, linear dynamics, no time lag between kinetics and dynamics (single-valued response), and time constant parameters. However, this report demonstrates that the drug effect can be indirect (antinociception, cortisol/adrenocorticotropin (ACTH), body temperature), display nonlinear kinetics, display feedback mechanisms (nonstationarity, cortiso/ACTH) and exhibit hysteresis with the drug levels in the biophase (antinociception, body temperature). It is also demonstrated that crucial determinants of the success of modeling dose-response-time data are the dose selection, multiple dosing, and to some extent different input rates and routes. This report exemplifies the possibility of assigning kinetic forcing functions in pharmacodynamic modeling in both preclinical and clinical studies for the purpose of characterizing (discrimination between turnover and drug-specific parameters) response data and optimizing subsequent clinical protocols, and for identification of inter-individual differences.

Animals↗

PubMed2006

Synchronization of coupled nonidentical genetic oscillators.

The study of the collective dynamics of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic oscillators are biochemical networks, which can generally be modelled as nonlinear dynamic systems. We show in this paper that many genetic oscillators can be transformed into Lur'e form by exploiting the special structure of biological systems. By using a control theory approach, we provide a theoretical method for analysing the synchronization of coupled nonidentical genetic oscillators. Sufficient conditions for the synchronization as well as the estimation of the bound of the synchronization error are also obtained. To demonstrate the effectiveness of our theoretical results, a population of genetic oscillators based on the Goodwin model are adopted as numerical examples.

Biological Clocks↗

PubMed1987

Demographic variation and survival in discrete population models.

Persistence and extinction attributes of a discrete population model are explored on both a finite and an infinite time horizon. For a first-order autonomous nonlinear difference equation, a classification is found of when, for each positive integer N, trajectories go to extinction at time N. The dynamic complexity that is known to permeate difference-equation models is also present in the survival analyses developed here. Also found is an interesting decomposition of the continuum of initial population sizes into intervals where populations are persistent at time N and intervals leading to extinction at time n less than or equal to N.

Animals↗

PubMed2003

Finite element analysis of cervical spinal instability under physiologic loading.

The definition of cervical spinal instability has been a subject of considerable debate and has not been clearly established. Stability of the motion segment is provided by ligaments, facet joints, and disc, which restrict range of movement. Moreover, permanent damage to one of the stabilizing structures alters the roles of the other two. Although many studies have been conducted to investigate cervical injuries, to date there are only limited finite element investigations reported in the literature on the biomechanical response of the cervical spine in these respects. A comprehensive, geometric, nonlinear finite element model of the lower cervical spine has been successfully developed and validated under compression, anterior-posterior shear, and sagittal moments. Injury studies were done by varying each spinal component independently from the validated model. Seven analyses were conducted for each injury simulation (model without ligaments, model without facets, model without facets and ligaments, and model without disc nucleus). Results indicate that the role of the ligaments in resisting anterior and posterior shear and flexion and axial rotation moments is important. Under other physiologic loading (anterior-posterior shear, flexion-extension, lateral bending, and axial rotation), the disc nucleus is responsible for the initial stiffness of the cervical spine. The results also highlight the importance of facets in resisting compression at higher loads, anterior shear, extension, lateral bending, and torsion. The results provide new insight through injury simulation into the role of the various spinal components in providing cervical spinal stability. These findings seem to correlate well with experimental results as well as with common clinical experience.

Cervical Vertebrae↗

PubMed2004

Lifetimes of flame balls dragged by model turbulent flows: Role of velocity gradient fluctuations.

An isolated combustion spot-known as a flame ball (FB)-is considered while it is advected by a turbulent flow of a lean premixture of such a light fuel as hydrogen. A Batchelor approximation for the surrounding Lagrangian flow is made. This in principle gives one an access to the FB lifetime t(life) and to its response to the ambiant Lagrangian rate-of-strain tensor g(t), by means of a nonlinear and forced integro-differential equation for the current FB radius. For a diagonal g(t) deduced from random Markov processes of the Ornstein-Uhlenbeck type, or linearly filtered versions thereof, extensive numerical simulations and approximate theoretical analyses agree that (i) flame balls can definitely live for much longer than their time of spontaneous expansion/collapse; (ii) large enough values of t(life) are compatible with Poisson statistics; (iii) the variations of with the characteristics of g(t) mirror the latter's statistics, more precisely that of trace(g(2)). Open problems, dealing with a nondiagonal g(t), ignition-related transients and/or collective effects, finally are evoked.

Journal Article↗

PubMed1994

Nonlinear dynamic processes in open single enzyme systems.

Chemical oscillations are predicted theoretically in single enzyme systems open to substrate containing a regulatory enzyme, which shows a slow substrate activation. The time-evolution of the system is well described by two ordinary differential equations. The conditions for oscillations or overshoot phenomena of the substrate concentration were analysed by numerical simulation. The existence of damped oscillations or overshoot phenomena in a regulatory enzyme reaction, open to substrate, has been proved experimentally in the pyruvate decarboxylase reaction and in the pyruvate dehydrogenase reaction. In both cases the concentration of the substrate pyruvate shows a strongly damped oscillation in a concentration range below the Km-value.

Binding Sites↗

PubMed1993

Determination of rate and equilibrium binding constants for macromolecular interactions using surface plasmon resonance: use of nonlinear least squares analysis methods.

Surface plasmon resonance (SPR) is a label-free, real time, optical detection method which has recently been commercialized as the BIAcore (Pharmacia). The technique relies on the immobilization of one of the interactants, the ligand, onto a dextran-coated gold surface. The second interactant, the ligate, is then injected across the surface and the interaction of the soluble ligate with the immobilized ligand is observed continuously and directly. The process of dissociation of bound ligate may also be observed directly after the sample plug has traversed the layer. Thus, the data generated contain information on the kinetic rate and equilibrium binding constants for the interaction under investigation. Historically, data from this instrument have been analyzed in terms of linear transformations of the primary data and requires that data from several ligate concentrations be analyzed to determine a single value for the association and dissociation rate constants. Here we discuss the analysis of untransformed BIAcore data by nonlinear least squares methods. The primary data are analyzed according to the integrated rate equations which describe the kinetics of the interaction of soluble ligate with immobilized ligand and the dissociation of the formed complex from the surface, respectively. Such analyses allow the direct determination of the association and dissociation rate constants for each binding experiment and, further, allow the analysis of data over a wider concentration range with lower associated errors compared to previously described methods. Through the use of modeling these interactions, we also demonstrate the limitations in determining the dissociation rate constant from the association phase of the interaction, thereby requiring that the dissociation process be analyzed. Indeed, the dissociation phase should be analyzed first to yield a relatively precise and unambiguous value of the dissociation rate constant, kd, which can then be used to constrain the analysis of the association phase to yield a better estimate of the association rate constant, k(a). We further demonstrate that, at least for the interaction investigated, the apparent rate and equilibrium binding constants determined using SPR are concentration independent and can be determined with good reproducibility.

Animals↗

PubMed1989

Noise effects in an electronic model of a single neuron.

We consider a simple electronic circuit model of a single neuron. The neuron is assumed to be driven by an external signal comprising constant (dc) and random components. In addition, the nonlinearity parameter in the circuit is assumed to fluctuate, thereby giving rise to critical behavior including the onset of hysteresis phenomena even for system parameter values that would not otherwise support such behavior. This "noise-induced critical behavior" is analysed, in the long time limit, through a study of the probability density function describing the neural response.

Animals↗