scholarly journals Multi-stable dynamics of the non-adiabatic repressilator

2015 ◽  
Vol 12 (104) ◽  
pp. 20141315 ◽  
Author(s):  
Ilya Potapov ◽  
Boris Zhurov ◽  
Evgeny Volkov
Keyword(s):  
Steady State ◽  
Intrinsic Noise ◽  
Stochastic Simulations ◽  
Stable Steady State ◽  
Genetic Circuits ◽  
The Times ◽  
Parameter Values ◽  
Considerable Range ◽  
Type Of Transition

The assumption of the fast binding of transcription factors (TFs) to promoters is a typical point in studies of synthetic genetic circuits functioning in bacteria. Although the assumption is effective for simplifying the models, it becomes questionable in the light of in vivo measurements of the times TF spends searching for its cognate DNA sites. We investigated the dynamics of the full idealized model of the paradigmatic genetic oscillator, the repressilator, using deterministic mathematical modelling and stochastic simulations. We found (using experimentally approved parameter values) that decreases in the TF binding rate changes the type of transition between steady state and oscillation. As a result, this gives rise to the hysteresis region in the parameter space, where both the steady state and the oscillation coexist. We further show that the hysteresis is persistent over a considerable range of the parameter values, but the presence of the oscillations is limited by the low rate of TF dimer degradation. Finally, the stochastic simulation of the model confirms the hysteresis with switching between the two attractors, resulting in highly skewed period distributions. Moreover, intrinsic noise stipulates trains of large-amplitude modulations around the stable steady state outside the hysteresis region, which makes the period distributions bimodal.

Contractile parameters and occurrence of alternans in isolated rat myocardium at supra-physiological stimulation frequency

2012 ◽  
Vol 302 (11) ◽  
pp. H2267-H2275 ◽  
Author(s):  
Jessica L. Slabaugh ◽  
Lucia Brunello ◽  
Sandor Gyorke ◽  
Paul M. L. Janssen
Keyword(s):  
Heart Rate ◽  
Steady State ◽  
Refractory Period ◽  
Striated Muscle ◽  
Stable Steady State ◽  
Maximal Heart Rate ◽  
Force Frequency ◽  
Mechanical Instability ◽  
Continuous Increase

The cardiac refractory period prevents the heart from tetanic activation that is typically used in noncardiac striated muscle tissue. To what extent the refractory period prevents successive action potentials to activate the excitation-contraction coupling process and contractile machinery at supra-physiological rates, such as those present during ventricular fibrillation, is unknown. Using multicellular trabeculae isolated from rat hearts, we studied amplitude and kinetics of contraction at rates well above the normal in vivo rat heart range. We show that even at twice the maximal heart rate of the rat, little or no mechanical instability is observed; twitch contractions are at steady state, albeit with an elevated active diastolic force. Although the amplitude of contraction increased within in vivo heart rates (positive force-frequency response), at frequencies beyond the maximal heart rate (10–30 Hz) a steady decline of contractile amplitude is observed. Not until 30 Hz do the majority of the isolated muscle preparations show mechanical alternans, where strong and weak beats alternate. Interestingly, unlike striated limb skeletal muscle, fusing of twitch contractions did not cause a continuous increase in peak force: at frequencies of 10 Hz and above, systolic force declines with relatively little elevation in diastolic force. Contractile kinetics continued to accelerate, from 1 Hz up to 30 Hz, whereas the relative speed of contraction and relaxation remained closely coupled, reflected by a singular linear relationship between the maximal and minimal derivative of force (dF/d t). We conclude that cardiac muscle can produce mechanically stable steady-state contractions at supra-physiological pacing rates, while these contractions continue to decline in amplitude and increase in diastolic force past maximal heart rate.

scholarly journals The regulatory principles of glycolysis in erythrocytes in vivo and in vitro. A minimal comprehensive model describing steady states, quasi-steady states and time-dependent processes

1976 ◽  
Vol 154 (2) ◽  
pp. 449-469 ◽  
Author(s):  
T A. Rapoport ◽  
R Heinrich ◽  
S M. Rapoport
Keyword(s):  
Steady State ◽  
Atp Synthesis ◽  
Steady States ◽  
Time Dependent ◽  
Glycolytic Flux ◽  
Stable Steady State ◽  
Time Interval ◽  
Fructose 1,6 Bisphosphate

A simple mathematical model for glycolysis in erythrocytes is presented which takes into account ATP synthesis and consumption. The system is described by four ordinary differential equations. Conditions in vivo are described by a stable steady state. The model predicts correctly the metabolite concentrations found in vivo. The parameters involved are in agreement with data on the separate steps. The metabolite changes found in pyruvate kinase-deficient erythrocytes and the species variations among erythrocytes from different animals are described satisfactorily. The roles of the enzymes in the control of metabolites and glycolytic flux are expressed in the form of a control matrix and control strengths [R. Heinrich & T.A. Rapoport (1974) Eur. J. Biochem. 42, 89-95] respectively. Erythrocytes from various species are shown to be adapted to a maximal ATP-consumption rate. The calculated eigenvalues reveal the pronounced time-hierarchy of the glycolytic reactions. Owing to the slowness of the 2,3-bisphospho-glycerate phosphatase reaction, quasi-steady states occur during the time-interval of about 0.5-2h incubation, which are defined by perturbed 2,3-bisphosphoglycerate concentrations. The theoretical predictions agree with experimental data. In the quasi-steady state the flux control is exerted almost entirely by the hexokinase-phosphofructokinase system. The model describes satisfactorily the time-dependent changes after addition of glucose to starved erythrocytes. The theoretical consequences are discussed of the conditions in vitro with lactate accumulation and the existence of a time-independent conservation quantity for the oxidized metabolites. Even in this closed system quasi-steady states occur which are characterized by approximately constant concentrations of all glycolytic metabolites except for the accumulation of lactate, fructose 1,6-bisphosphate and triose phosphate.

The Synergy between CRISPR and Chemical Engineering

2019 ◽  
Vol 19 (3) ◽  
pp. 147-171
Author(s):  
Cia-Hin Lau ◽  
Chung Tin
Keyword(s):  
Viral Vectors ◽  
Chemical Engineering ◽  
Target Genes ◽  
New Technologies ◽  
Rapid Development ◽  
Genetic Circuits ◽  
Viral Packaging ◽  
Conditional Control ◽  
Logic Operations

Gene therapy and transgenic research have advanced quickly in recent years due to the development of CRISPR technology. The rapid development of CRISPR technology has been largely benefited by chemical engineering. Firstly, chemical or synthetic substance enables spatiotemporal and conditional control of Cas9 or dCas9 activities. It prevents the leaky expression of CRISPR components, as well as minimizes toxicity and off-target effects. Multi-input logic operations and complex genetic circuits can also be implemented via multiplexed and orthogonal regulation of target genes. Secondly, rational chemical modifications to the sgRNA enhance gene editing efficiency and specificity by improving sgRNA stability and binding affinity to on-target genomic loci, and hence reducing off-target mismatches and systemic immunogenicity. Chemically-modified Cas9 mRNA is also more active and less immunogenic than the native mRNA. Thirdly, nonviral vehicles can circumvent the challenges associated with viral packaging and production through the delivery of Cas9-sgRNA ribonucleoprotein complex or large Cas9 expression plasmids. Multi-functional nanovectors enhance genome editing in vivo by overcoming multiple physiological barriers, enabling ligand-targeted cellular uptake, and blood-brain barrier crossing. Chemical engineering can also facilitate viral-based delivery by improving vector internalization, allowing tissue-specific transgene expression, and preventing inactivation of the viral vectors in vivo. This review aims to discuss how chemical engineering has helped improve existing CRISPR applications and enable new technologies for biomedical research. The usefulness, advantages, and molecular action for each chemical engineering approach are also highlighted.

scholarly journals Inducible ablation of mouse Langerhans cells diminishes but fails to abrogate contact hypersensitivity

2005 ◽  
Vol 169 (4) ◽  
pp. 569-576 ◽  
Author(s):  
Clare L. Bennett ◽  
Erwin van Rijn ◽  
Steffen Jung ◽  
Kayo Inaba ◽  
Ralph M. Steinman ◽  
...  
Keyword(s):  
Dendritic Cells ◽  
Steady State ◽  
Diphtheria Toxin ◽  
Langerhans Cells ◽  
Contact Hypersensitivity ◽  
Relative Importance ◽  
Skin Immunity

Langerhans cells (LC) form a unique subset of dendritic cells (DC) in the epidermis but so far their in vivo functions in skin immunity and tolerance could not be determined, in particular in relation to dermal DC (dDC). Here, we exploit a novel diphtheria toxin (DT) receptor (DTR)/DT-based system to achieve inducible ablation of LC without affecting the skin environment. Within 24 h after intra-peritoneal injection of DT into Langerin-DTR mice LC are completely depleted from the epidermis and only begin to return 4 wk later. LC deletion occurs by apoptosis in the absence of inflammation and, in particular, the dDC compartment is not affected. In LC-depleted mice contact hypersensitivity (CHS) responses are significantly decreased, although ear swelling still occurs indicating that dDC can mediate CHS when necessary. Our results establish Langerin-DTR mice as a unique tool to study LC function in the steady state and to explore their relative importance compared with dDC in orchestrating skin immunity and tolerance.

scholarly journals Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP

2012 ◽  
Vol 6 (3) ◽  
pp. 573-588 ◽  
Author(s):  
F. Pattyn ◽  
C. Schoof ◽  
L. Perichon ◽  
R. C. A. Hindmarsh ◽  
E. Bueler ◽  
...  
Keyword(s):  
Steady State ◽  
Adaptive Mesh Refinement ◽  
Ice Sheet ◽  
Adaptive Mesh ◽  
Stable Steady State ◽  
Fixed Grid ◽  
Approximate Analytical Solutions ◽  
Grounding Line ◽  
Intercomparison Project ◽  
Line Positions

Abstract. Predictions of marine ice-sheet behaviour require models that are able to robustly simulate grounding line migration. We present results of an intercomparison exercise for marine ice-sheet models. Verification is effected by comparison with approximate analytical solutions for flux across the grounding line using simplified geometrical configurations (no lateral variations, no effects of lateral buttressing). Unique steady state grounding line positions exist for ice sheets on a downward sloping bed, while hysteresis occurs across an overdeepened bed, and stable steady state grounding line positions only occur on the downward-sloping sections. Models based on the shallow ice approximation, which does not resolve extensional stresses, do not reproduce the approximate analytical results unless appropriate parameterizations for ice flux are imposed at the grounding line. For extensional-stress resolving "shelfy stream" models, differences between model results were mainly due to the choice of spatial discretization. Moving grid methods were found to be the most accurate at capturing grounding line evolution, since they track the grounding line explicitly. Adaptive mesh refinement can further improve accuracy, including fixed grid models that generally perform poorly at coarse resolution. Fixed grid models, with nested grid representations of the grounding line, are able to generate accurate steady state positions, but can be inaccurate over transients. Only one full-Stokes model was included in the intercomparison, and consequently the accuracy of shelfy stream models as approximations of full-Stokes models remains to be determined in detail, especially during transients.

Noradrenaline-induced calorigenesis in warm- or cold-acclimated rats. In vivo estimation of adrenoceptor concentration of noradrenaline effecting half-maximal response

1980 ◽  
Vol 58 (9) ◽  
pp. 1072-1077 ◽  
Author(s):  
Florent Depocas ◽  
Gloria Zaror-Behrens ◽  
Suzanne Lacelle
Keyword(s):  
Adipose Tissue ◽  
Steady State ◽  
Brown Adipose Tissue ◽  
Maximal Response ◽  
Brown Adipose ◽  
Acclimation Group ◽  
Arterial Plasma ◽  
State Concentration ◽  
Na Uptake

Desmethylimipramine (DMI, 1 mg DMI∙HCl kg−1) and normetanephrine (NMN, 1 μg min−1 g−0.74) were used to inhibit, respectively, neuronal and extraneuronal uptakes of noradrenaline (NA) during calorigenesis induced in barbital-sedated warm-acclimated (WA) or cold-acclimated (CA) rats by infusion of NA, a procedure which mimics the effects of NA released within calorigenic tissues in response to cold exposure. The doses of the inhibitors were selected for maximal effectiveness in potentiating calorigenic response and for minimal side effects. For rats of either acclimation group treated with DMI and NMN, with DMI only, or with neither inhibitor the doses of NA required to evoke approximately half-maximal calorigenic responses were, respectively, 0.5, 1.0, and 3.5 ng min−1 g−0.74. The corresponding steady-state concentrations of NA in arterial plasma averaged 14.3, 21.7, and 43.2 nM in the three groups of WA rats and 10.0, 14.8, and 31.9 nM in the three groups of CA rats. Reduction by NA uptake inhibitors of the circulating levels of NA necessary to stimulate calorigenesis, half-maximally, presumably in brown adipose tissue, indicates a reduction in the steepness of the NA concentration gradient between capillary plasma and synaptic clefts in that tissue. The steady-state concentration of NA in blood plasma of rats treated with DMI and NMN and infused with NA at a dose of 0.5 ng min−1 g−0.74 (~1 × 10−8 M) is a good estimate of the NA concentration required at calorigenic adrenoceptors to effect half-maximal activation. Presumably, this concentration is also an estimate of that resulting from NA released at nerve endings during cold-induced activation of nonshivering thermogenesis at half-maximal rates in brown adipose tissue.

MONETARY POLICY SWITCHING IN THE EURO AREA AND MULTIPLE STEADY STATES: AN EMPIRICAL INVESTIGATION

2016 ◽  
Vol 21 (5) ◽  
pp. 1175-1188 ◽  
Author(s):  
Gilles Dufrénot ◽  
Guillaume A. Khayat
Keyword(s):  
Steady State ◽  
Euro Area ◽  
European Central Bank ◽  
Empirical Investigation ◽  
Standard Assumption ◽  
Demand Shock ◽  
Liquidity Trap ◽  
European Central ◽  
Parameter Values ◽  
Policy Function

This paper investigates, in the case of the euro area, the standard assumption that the liquidity trap steady state, which arises from the existence of the zero lower bound on the nominal interest rate, is locally unstable. We show that the policy function of the European Central Bank (ECB) is described by a nonlinear Taylor rule. Then, using our estimations, we show that around the liquidity trap steady state the equilibrium is locally determinate for most plausible parameter values. Finally, we find that an inflation shock is more efficient than a demand shock to escape the liquidity trap steady state.

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