Browsing by Subject "Nonlinear Dynamics"

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Open Access
A cerebellar learning model of vestibulo-ocular reflex adaptation in wild-type and mutant mice.
(The Journal of neuroscience : the official journal of the Society for Neuroscience, 2014-05) Clopath, Claudia; Badura, Aleksandra; De Zeeuw, Chris I; Brunel, Nicolas
Mechanisms of cerebellar motor learning are still poorly understood. The standard Marr-Albus-Ito theory posits that learning involves plasticity at the parallel fiber to Purkinje cell synapses under control of the climbing fiber input, which provides an error signal as in classical supervised learning paradigms. However, a growing body of evidence challenges this theory, in that additional sites of plasticity appear to contribute to motor adaptation. Here, we consider phase-reversal training of the vestibulo-ocular reflex (VOR), a simple form of motor learning for which a large body of experimental data is available in wild-type and mutant mice, in which the excitability of granule cells or inhibition of Purkinje cells was affected in a cell-specific fashion. We present novel electrophysiological recordings of Purkinje cell activity measured in naive wild-type mice subjected to this VOR adaptation task. We then introduce a minimal model that consists of learning at the parallel fibers to Purkinje cells with the help of the climbing fibers. Although the minimal model reproduces the behavior of the wild-type animals and is analytically tractable, it fails at reproducing the behavior of mutant mice and the electrophysiology data. Therefore, we build a detailed model involving plasticity at the parallel fibers to Purkinje cells' synapse guided by climbing fibers, feedforward inhibition of Purkinje cells, and plasticity at the mossy fiber to vestibular nuclei neuron synapse. The detailed model reproduces both the behavioral and electrophysiological data of both the wild-type and mutant mice and allows for experimentally testable predictions.
Open Access
Association between perceived life chaos and medication adherence in a postmyocardial infarction population.
(Circulation. Cardiovascular quality and outcomes, 2013-11) Zullig, Leah L; Shaw, Ryan J; Crowley, Matthew J; Lindquist, Jennifer; Grambow, Steven C; Peterson, Eric; Shah, Bimal R; Bosworth, Hayden B
Background
The benefits of medication adherence to control cardiovascular disease (CVD) are well defined, yet multiple studies have identified poor adherence. The influence of life chaos on medication adherence is unknown. Because this is a novel application of an instrument, our preliminary objective was to understand patient factors associated with chaos. The main objective was to evaluate the extent to which an instrument designed to measure life chaos is associated with CVD-medication nonadherence.
Methods and results
Using baseline data from an ongoing randomized trial to improve postmyocardial infarction (MI) management, multivariable logistic regression identified the association between life chaos and CVD-medication nonadherence. Patients had hypertension and a myocardial infarction in the past 3 years (n=406). Nearly 43% reported CVD-medication nonadherence in the past month. In simple linear regression, the following were associated with higher life chaos: medication nonadherence (β=1.86; 95% confidence interval [CI], 0.96-2.76), female sex (β=1.22; 95% CI [0.22-2.24]), minority race (β=1.72; 95% CI [0.78-2.66]), having less than high school education (β=2.05; 95% CI [0.71-3.39]), low health literacy (β=2.06; 95% CI [0.86-3.26]), and inadequate financial status (β=1.93; 95% CI [0.87-3.00]). Being married (β=-2.09, 95% CI [-3.03 to -1.15]) was associated with lower life chaos. As chaos quartile increased, patients exhibited more nonadherence. In logistic regression, adjusting for sex, race, marital status, employment, education, health literacy, and financial status, a 1-unit life chaos increase was associated with a 7% increase (odds ratio, 1.07; 95% CI [1.02-1.12]) in odds of reporting medication nonadherence.
Conclusions
Our results suggest that life chaos may be an important determinant of medication adherence. Life chaos screenings could identify those at risk for nonadherence.
Clinical trial registration
URL: http://www.clinicaltrials.gov. Unique identifier: NCT000901277.
Open Access
Chaos in percepts?
(Biol Cybern, 1994) Richards, W; Wilson, HR; Sommer, MA
Multistability in perceptual tasks has suggested that the mechanisms underlying our percepts might be modeled as nonlinear, deterministic systems that exhibit chaotic behavior. We present evidence supporting this view, obtaining an estimate of 3.5 for the dimensionality of such a system. A surprising result is that this estimate applies for a rather diverse range of perceptual tasks.
Open Access
Control of the orientational order and nonlinear optical response of the "push-pull" chromophore RuPZn via specific incorporation into densely packed monolayer ensembles of an amphiphilic four-helix bundle peptide: characterization of the peptide-chromophore complexes.
(J Am Chem Soc, 2010-08-18) Krishnan, Venkata; Tronin, Andrey; Strzalka, Joseph; Fry, H Christopher; Therien, Michael J; Blasie, J Kent
"Push-pull" chromophores based on extended pi-electron systems have been designed to exhibit exceptionally large molecular hyperpolarizabilities. We have engineered an amphiphilic four-helix bundle peptide to vectorially incorporate such hyperpolarizable chromophores having a metalloporphyrin moiety, with high specificity into the interior core of the bundle. The amphiphilic exterior of the bundle facilitates the formation of densely packed monolayer ensembles of the vectorially oriented peptide-chromophore complexes at the liquid-gas interface. Chemical specificity designed into the ends of the bundle facilitates the subsequent covalent attachment of these monolayer ensembles onto the surface of an inorganic substrate. In this article, we describe the structural characterization of these monolayer ensembles at each stage of their fabrication for one such peptide-chromophore complex designated as AP0-RuPZn. In the accompanying article, we describe the characterization of their macroscopic nonlinear optical properties.
Open Access
Dual-energy computed tomography with advanced postimage acquisition data processing: improved determination of urinary stone composition.
(J Endourol, 2010-03) Ferrandino, MN; Pierre, SA; Simmons, WN; Paulson, EK; Albala, DM; Preminger, GM
INTRODUCTION: The characterization of urinary calculi using noninvasive methods has the potential to affect clinical management. CT remains the gold standard for diagnosis of urinary calculi, but has not reliably differentiated varying stone compositions. Dual-energy CT (DECT) has emerged as a technology to improve CT characterization of anatomic structures. This study aims to assess the ability of DECT to accurately discriminate between different types of urinary calculi in an in vitro model using novel postimage acquisition data processing techniques. METHODS: Fifty urinary calculi were assessed, of which 44 had >or=60% composition of one component. DECT was performed utilizing 64-slice multidetector CT. The attenuation profiles of the lower-energy (DECT-Low) and higher-energy (DECT-High) datasets were used to investigate whether differences could be seen between different stone compositions. RESULTS: Postimage acquisition processing allowed for identification of the main different chemical compositions of urinary calculi: brushite, calcium oxalate-calcium phosphate, struvite, cystine, and uric acid. Statistical analysis demonstrated that this processing identified all stone compositions without obvious graphical overlap. CONCLUSION: Dual-energy multidetector CT with postprocessing techniques allows for accurate discrimination among the main different subtypes of urinary calculi in an in vitro model. The ability to better detect stone composition may have implications in determining the optimum clinical treatment modality for urinary calculi from noninvasive, preprocedure radiological assessment.
Open Access
From spiking neuron models to linear-nonlinear models.
(PLoS Comput Biol, 2011-01-20) Ostojic, Srdjan; Brunel, Nicolas
Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.
Open Access
Glutamate receptor dynamics in dendritic microdomains.
(Neuron, 2008-05) Newpher, Thomas M; Ehlers, Michael D
Among diverse factors regulating excitatory synaptic transmission, the abundance of postsynaptic glutamate receptors figures prominently in molecular memory and learning-related synaptic plasticity. To allow for both long-term maintenance of synaptic transmission and acute changes in synaptic strength, the relative rates of glutamate receptor insertion and removal must be tightly regulated. Interactions with scaffolding proteins control the targeting and signaling properties of glutamate receptors within the postsynaptic membrane. In addition, extrasynaptic receptor populations control the equilibrium of receptor exchange at synapses and activate distinct signaling pathways involved in plasticity. Here, we review recent findings that have shaped our current understanding of receptor mobility between synaptic and extrasynaptic compartments at glutamatergic synapses, focusing on AMPA and NMDA receptors. We also examine the cooperative relationship between intracellular trafficking and surface diffusion of glutamate receptors that underlies the expression of learning-related synaptic plasticity.
Open Access
Inference for nonlinear epidemiological models using genealogies and time series.
(PLoS Comput Biol, 2011-08) Rasmussen, David A; Ratmann, Oliver; Koelle, Katia
Phylodynamics - the field aiming to quantitatively integrate the ecological and evolutionary dynamics of rapidly evolving populations like those of RNA viruses - increasingly relies upon coalescent approaches to infer past population dynamics from reconstructed genealogies. As sequence data have become more abundant, these approaches are beginning to be used on populations undergoing rapid and rather complex dynamics. In such cases, the simple demographic models that current phylodynamic methods employ can be limiting. First, these models are not ideal for yielding biological insight into the processes that drive the dynamics of the populations of interest. Second, these models differ in form from mechanistic and often stochastic population dynamic models that are currently widely used when fitting models to time series data. As such, their use does not allow for both genealogical data and time series data to be considered in tandem when conducting inference. Here, we present a flexible statistical framework for phylodynamic inference that goes beyond these current limitations. The framework we present employs a recently developed method known as particle MCMC to fit stochastic, nonlinear mechanistic models for complex population dynamics to gene genealogies and time series data in a Bayesian framework. We demonstrate our approach using a nonlinear Susceptible-Infected-Recovered (SIR) model for the transmission dynamics of an infectious disease and show through simulations that it provides accurate estimates of past disease dynamics and key epidemiological parameters from genealogies with or without accompanying time series data.
Open Access
Modeling endocrine control of the pituitary-ovarian axis: androgenic influence and chaotic dynamics.
(Bulletin of mathematical biology, 2014-01) Hendrix, Angelean O; Hughes, Claude L; Selgrade, James F
Mathematical models of the hypothalamus-pituitary-ovarian axis in women were first developed by Schlosser and Selgrade in 1999, with subsequent models of Harris-Clark et al. (Bull. Math. Biol. 65(1):157-173, 2003) and Pasteur and Selgrade (Understanding the dynamics of biological systems: lessons learned from integrative systems biology, Springer, London, pp. 38-58, 2011). These models produce periodic in-silico representation of luteinizing hormone (LH), follicle stimulating hormone (FSH), estradiol (E2), progesterone (P4), inhibin A (InhA), and inhibin B (InhB). Polycystic ovarian syndrome (PCOS), a leading cause of cycle irregularities, is seen as primarily a hyper-androgenic disorder. Therefore, including androgens into the model is necessary to produce simulations relevant to women with PCOS. Because testosterone (T) is the dominant female androgen, we focus our efforts on modeling pituitary feedback and inter-ovarian follicular growth properties as functions of circulating total T levels. Optimized parameters simultaneously simulate LH, FSH, E2, P4, InhA, and InhB levels of Welt et al. (J. Clin. Endocrinol. Metab. 84(1):105-111, 1999) and total T levels of Sinha-Hikim et al. (J. Clin. Endocrinol. Metab. 83(4):1312-1318, 1998). The resulting model is a system of 16 ordinary differential equations, with at least one stable periodic solution. Maciel et al. (J. Clin. Endocrinol. Metab. 89(11):5321-5327, 2004) hypothesized that retarded early follicle growth resulting in "stockpiling" of preantral follicles contributes to PCOS etiology. We present our investigations of this hypothesis and show that varying a follicular growth parameter produces preantral stockpiling and a period-doubling cascade resulting in apparent chaotic menstrual cycle behavior. The new model may allow investigators to study possible interventions returning acyclic patients to regular cycles and guide developments of individualized treatments for PCOS patients.
Open Access
Monte Carlo methods for localization of cones given multielectrode retinal ganglion cell recordings.
(Network (Bristol, England), 2013-01) Sadeghi, K; Gauthier, JL; Field, GD; Greschner, M; Agne, M; Chichilnisky, EJ; Paninski, L
It has recently become possible to identify cone photoreceptors in primate retina from multi-electrode recordings of ganglion cell spiking driven by visual stimuli of sufficiently high spatial resolution. In this paper we present a statistical approach to the problem of identifying the number, locations, and color types of the cones observed in this type of experiment. We develop an adaptive Markov Chain Monte Carlo (MCMC) method that explores the space of cone configurations, using a Linear-Nonlinear-Poisson (LNP) encoding model of ganglion cell spiking output, while analytically integrating out the functional weights between cones and ganglion cells. This method provides information about our posterior certainty about the inferred cone properties, and additionally leads to improvements in both the speed and quality of the inferred cone maps, compared to earlier "greedy" computational approaches.
Open Access
Nonlinear oscillator metamaterial model: numerical and experimental verification.
(Opt Express, 2011-04-25) Poutrina, E; Huang, D; Urzhumov, Y; Smith, DR
We verify numerically and experimentally the accuracy of an analytical model used to derive the effective nonlinear susceptibilities of a varactor-loaded split ring resonator (VLSRR) magnetic medium. For the numerical validation, a nonlinear oscillator model for the effective magnetization of the metamaterial is applied in conjunction with Maxwell equations and the two sets of equations solved numerically in the time-domain. The computed second harmonic generation (SHG) from a slab of a nonlinear material is then compared with the analytical model. The computed SHG is in excellent agreement with that predicted by the analytical model, both in terms of magnitude and spectral characteristics. Moreover, experimental measurements of the power transmitted through a fabricated VLSRR metamaterial at several power levels are also in agreement with the model, illustrating that the effective medium techniques associated with metamaterials can accurately be transitioned to nonlinear systems.
Open Access
On the distribution of firing rates in networks of cortical neurons.
(The Journal of neuroscience : the official journal of the Society for Neuroscience, 2011-11) Roxin, Alex; Brunel, Nicolas; Hansel, David; Mongillo, Gianluigi; van Vreeswijk, Carl
The distribution of in vivo average firing rates within local cortical networks has been reported to be highly skewed and long tailed. The distribution of average single-cell inputs, conversely, is expected to be Gaussian by the central limit theorem. This raises the issue of how a skewed distribution of firing rates might result from a symmetric distribution of inputs. We argue that skewed rate distributions are a signature of the nonlinearity of the in vivo f-I curve. During in vivo conditions, ongoing synaptic activity produces significant fluctuations in the membrane potential of neurons, resulting in an expansive nonlinearity of the f-I curve for low and moderate inputs. Here, we investigate the effects of single-cell and network parameters on the shape of the f-I curve and, by extension, on the distribution of firing rates in randomly connected networks.
Open Access
Storing structured sparse memories in a multi-modular cortical network model.
(Journal of computational neuroscience, 2016-04) Dubreuil, Alexis M; Brunel, Nicolas
We study the memory performance of a class of modular attractor neural networks, where modules are potentially fully-connected networks connected to each other via diluted long-range connections. On this anatomical architecture we store memory patterns of activity using a Willshaw-type learning rule. P patterns are split in categories, such that patterns of the same category activate the same set of modules. We first compute the maximal storage capacity of these networks. We then investigate their error-correction properties through an exhaustive exploration of parameter space, and identify regions where the networks behave as an associative memory device. The crucial parameters that control the retrieval abilities of the network are (1) the ratio between the number of synaptic contacts of long- and short-range origins (2) the number of categories in which a module is activated and (3) the amount of local inhibition. We discuss the relationship between our model and networks of cortical patches that have been observed in different cortical areas.
Open Access
Synaptic plasticity rules with physiological calcium levels.
(Proceedings of the National Academy of Sciences of the United States of America, 2020-12-16) Inglebert, Yanis; Aljadeff, Johnatan; Brunel, Nicolas; Debanne, Dominique
Spike-timing-dependent plasticity (STDP) is considered as a primary mechanism underlying formation of new memories during learning. Despite the growing interest in activity-dependent plasticity, it is still unclear whether synaptic plasticity rules inferred from in vitro experiments are correct in physiological conditions. The abnormally high calcium concentration used in in vitro studies of STDP suggests that in vivo plasticity rules may differ significantly from in vitro experiments, especially since STDP depends strongly on calcium for induction. We therefore studied here the influence of extracellular calcium on synaptic plasticity. Using a combination of experimental (patch-clamp recording and Ca²⁺ imaging at CA3-CA1 synapses) and theoretical approaches, we show here that the classic STDP rule in which pairs of single pre- and postsynaptic action potentials induce synaptic modifications is not valid in the physiological Ca²⁺ range. Rather, we found that these pairs of single stimuli are unable to induce any synaptic modification in 1.3 and 1.5 mM calcium and lead to depression in 1.8 mM. Plasticity can only be recovered when bursts of postsynaptic spikes are used, or when neurons fire at sufficiently high frequency. In conclusion, the STDP rule is profoundly altered in physiological Ca²⁺, but specific activity regimes restore a classical STDP profile.
Open Access
The synchronization of superparamagnetic beads driven by a micro-magnetic ratchet.
(Lab Chip, 2010-08-21) Gao, Lu; Gottron, Norman J; Virgin, Lawrence N; Yellen, Benjamin B
We present theoretical, numerical, and experimental analyses on the non-linear dynamic behavior of superparamagnetic beads exposed to a periodic array of micro-magnets and an external rotating field. The agreement between theoretical and experimental results revealed that non-linear magnetic forcing dynamics are responsible for transitions between phase-locked orbits, sub-harmonic orbits, and closed orbits, representing different mobility regimes of colloidal beads. These results suggest that the non-linear behavior can be exploited to construct a novel colloidal separation device that can achieve effectively infinite separation resolution for different types of beads, by exploiting minor differences in their bead's properties. We also identify a unique set of initial conditions, which we denote the "devil's gate" which can be used to expeditiously identify the full range of mobility for a given bead type.

Browsing by Subject "Nonlinear Dynamics"

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