Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtolitres. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small sub-cellular compartment. This is achieved by applying a mesoscopic version of the quasi-steady state assumption to the exact Fokker-Planck equation associated with the Poisson Representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing sub-cellular volume, decreasing Michaelis-Menten constants and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.Comment: 13 pages, 4 figures; published in The Journal of Chemical Physic

How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?

The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order $\Omega^{-3/2}$ for reaction systems which do not obey detailed balance and at least accurate to order $\Omega^{-2}$ for systems obeying detailed balance, where $\Omega$ is the characteristic size of the system. Hence the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order $\Omega^{-1/2}$ and variance estimates accurate to order $\Omega^{-3/2}$. This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.Comment: 39 pages, 3 figures, accepted for publication in J. Chem. Phy

Impaired Representation of Time in Schizophrenia Is Linked to Positive Symptoms and Cognitive Demand

Time processing critically relies on the mesencephalic dopamine system and striato-prefrontal projections and has thus been suggested to play a key role in schizophrenia. Previous studies have provided evidence for an acceleration of the internal clock in schizophrenia that may be linked to dopaminergic pathology. The present study aimed to assess the relationship between altered time processing in schizophrenia and symptom manifestation in 22 patients and 22 controls. Subjects were required to estimate the time needed for a visual stimulus to complete a horizontal movement towards a target position on trials of varying cognitive demand. It was hypothesized that patients – compared to controls – would be less accurate at estimating the movement time, and that this effect would be modulated by symptom manifestation and task difficulty. In line with the notion of an accelerated internal clock due to dopaminergic dysregulation, particularly patients with severe positive symptoms were expected to underestimate movement time. However, if altered time perception in schizophrenia was better explained in terms of cognitive deficits, patients with severe negative symptoms should be specifically impaired, while generally, task performance should correlate with measures of processing speed and cognitive flexibility. Patients underestimated movement time on more demanding trials, although there was no link to disease-related cognitive dysfunction. Task performance was modulated by symptom manifestation. Impaired estimation of movement time was significantly correlated with PANSS positive symptom scores, with higher positive symptom scores associated with stronger underestimation of movement time. The present data thus support the notion of a deficit in anticipatory and predictive mechanisms in schizophrenia that is modulated both by symptom manifestation and by cognitive demand

‘‘Lozenge’’ contour plots in scattering from polymer networks

We present a consistent explanation for the appearance of “lozenge” shapes in contour plots of the two dimensional scattering intensity from stretched polymer networks. By explicitly averaging over quenched variables in a tube model, we show that lozenge patterns arise as a result of chain material that is not directly deformed by the stretch. We obtain excellent agreement with experimental data

Aberrant network connectivity during error processing in patients with schizophrenia

BACKGROUND: Neuroimaging methods have pointed to deficits in the interaction of large-scale brain networks in patients with schizophrenia. Abnormal connectivity of the right anterior insula (AI), a central hub of the salience network, is frequently reported and may underlie patients’ deficits in adaptive salience processing and cognitive control. While most previous studies used resting state approaches, we examined right AI interactions in a task-based fMRI study. METHODS: Patients with schizophrenia and healthy controls performed an adaptive version of the Eriksen Flanker task that was specifically designed to ensure a comparable number of errors between groups. RESULTS: We included 27 patients with schizophrenia and 27 healthy controls in our study. The between-groups comparison replicated the classic finding of reduced activation in the midcingulate cortex (MCC) in patients with schizophrenia during the commission of errors while controlling for confounding factors, such as task performance and error frequency, which have been neglected in many previous studies. Subsequent psychophysiological interaction analysis revealed aberrant functional connectivity (FC) between the right AI and regions in the inferior frontal gyrus and temporoparietal junction. Additionally, FC between the MCC and the dorsolateral prefrontal cortex was reduced. LIMITATIONS: As we examined a sample of medicated patients, effects of antipsychotic medication may have influenced our results. CONCLUSION: Overall, it appears that schizophrenia is associated with impairment of networks associated with detection of errors, refocusing of attention, superordinate guiding of cognitive control and their respective coordination

Particle entrapment as a feedback effect

We consider a suspension of polarizable particles under the action of traveling wave dielectrophoresis (DEP) and focus on particle induced effects. In a situation where the particles are driven by the DEP force, but no external forces are exerted on the fluid, the joint motion of the particles can induce a steady fluid flow, which leads to particle entrapment. This feedback effect is proven to be non-negligible even for small volume concentration of particles.Comment: 4 pages, 4 figures, submitte

The role of inhibitory feedback for information processing in thalamocortical circuits

The information transfer in the thalamus is blocked dynamically during sleep, in conjunction with the occurence of spindle waves. As the theoretical understanding of the mechanism remains incomplete, we analyze two modeling approaches for a recent experiment by Le Masson {\sl et al}. on the thalamocortical loop. In a first step, we use a conductance-based neuron model to reproduce the experiment computationally. In a second step, we model the same system by using an extended Hindmarsh-Rose model, and compare the results with the conductance-based model. In the framework of both models, we investigate the influence of inhibitory feedback on the information transfer in a typical thalamocortical oscillator. We find that our extended Hindmarsh-Rose neuron model, which is computationally less costly and thus siutable for large-scale simulations, reproduces the experiment better than the conductance-based model. Further, in agreement with the experiment of Le Masson {\sl et al}., inhibitory feedback leads to stable self-sustained oscillations which mask the incoming input, and thereby reduce the information transfer significantly.Comment: 16 pages, 15eps figures included. To appear in Physical Review

Size quantization effects in InAs self-assembled quantum dots

3 páginas, 3 figuras. PACS: 73.21.-b; 78.55.Cr; 78.66.Fd; 72.40.+w; 68.35.Ct; 73.40.KpWe study size quantization effects in InAs self-assembled quantum dots (QDs) that are embedded in GaAs. Using capacitance, photoluminescence and photovoltage spectroscopy, we correlate the measured quantized level energies with the quantum dot sizes and densities obtained from transmission electron microscopy. With increasing dot size, we observe a strong redshift of the QD features in all our data. In the capacitance spectra, a band gap renormalization of the two-dimensional wetting layer system appears when the first excited QD state crosses the wetting layer ground state. The relative size dependence and absolute energetic position of the QD transitions determined with photoluminescence provide some information about the influence of lateral confinement and height of the QD.This work was supported by QUEST, a NSF science and technology center (Grant No. DMR91-20007), the Alexander von Humboldt Foundation (KHS), and the Brazilian agency CNPq (GMR).Peer reviewe

Identificación y análisis de los recursos económicos asignados a la segunda locomotora. Evolución, aciertos y desaciertos

Con la elaboración del presente documento, se pretende identificar y analizar los recursos económicos asignados a una de las locomotoras del gobierno del presidente Juan Manuel Santos en el marco de su plan de desarrollo Prosperidad para todos y el impacto social de esta asignación de recursos en el agro Colombiano, Así mismo evaluar el cumplimiento de dicha política publica y la generación de bienestar social en la población."With the production of the present document, one tries to identify and to analyze the economic resources assigned to one of the locomotives of the government of the president Juan Manuel Santos in the frame of his plan of development "" Prosperity for all "" and the social impact of this assignment of resources in the Colombian agro, Likewise to evaluate the fulfillment of the above mentioned politics publishes and the generation of social well-being in the population.

converging evidence from an intermediate phenotype approach

Representing a phylogenetically old and very basic mechanism of inhibitory neurotransmission, glycine receptors have been implicated in the modulation of behavioral components underlying defensive responding toward threat. As one of the first findings being confirmed by genome-wide association studies for the phenotype of panic disorder and agoraphobia, allelic variation in a gene coding for the glycine receptor beta subunit (GLRB) has recently been associated with increased neural fear network activation and enhanced acoustic startle reflexes. On the basis of two independent healthy control samples, we here aimed to further explore the functional significance of the GLRB genotype (rs7688285) by employing an intermediate phenotype approach. We focused on the phenotype of defensive system reactivity across the levels of brain function, structure, and physiology. Converging evidence across both samples was found for increased neurofunctional activation in the (anterior) insular cortex in GLRB risk allele carriers and altered fear conditioning as a function of genotype. The robustness of GLRB effects is demonstrated by consistent findings across different experimental fear conditioning paradigms and recording sites. Altogether, findings provide translational evidence for glycine neurotransmission as a modulator of the brain’s evolutionary old dynamic defensive system and provide further support for a strong, biologically plausible candidate intermediate phenotype of defensive reactivity. As such, glycine-dependent neurotransmission may open up new avenues for mechanistic research on the etiopathogenesis of fear and anxiety disorders