RESUMO
Single cell dendritic spine modelling methodology has been adopted to explain structural plasticity and respective change in the neuronal volume previously. However, the single cell dendrite methodology has not been employed previously to explain one of the important aspects of memory allocation i.e., Synaptic tagging and Capture (STC) hypothesis. It is difficult to relate the physical properties of STC pathways to structural changes and synaptic strength. We create a mathematical model based on earlier reported synaptic tagging networks. We built the model using Virtual Cell (VCell) software and used it to interpret experimental data and investigate the behavior and characteristics of known Synaptic tagging candidates.â¢We investigate processes associated with synaptic tagging candidates and compare them to the assumptions based on the STC hypothesis.â¢We assess the behavior of several reported synaptic tagging candidates against the requirements outlined in the synaptic tagging hypothesis.
RESUMO
The synaptic tagging and capture (STC) hypothesis not only explain the integration and association of synaptic activities, but also the formation of learning and memory. The synaptic pathways involved in the synaptic tagging and capture phenomenon are called STC pathways. The STC hypothesis provides a potential explanation of the neuronal and synaptic processes underlying the synaptic consolidation of memories. Several mechanisms and molecules have been proposed to explain the process of memory allocation and synaptic tags, respectively. However, a clear link between the STC hypothesis and memory allocation is still missing because the encoding of memories in neural circuits is mainly associated with strongly recurrently connected groups of neurons. To explore the mechanisms of potential synaptic tagging candidates and their involvement in the process of memory allocation, we develop a mathematical model for a single dendritic spine based on five essential criteria of a synaptic tag. By developing a mathematical model, we attempt to understand the roles of the potentially critical molecular networks underlying the STC and the essential attributes of a synaptic tag. We include essential memory molecules in the STC model that have been identified in earlier studies as crucial for STC pathways. CaMKII activation is critical for the setting of the initial tag; however, coordinated activities with other kinases and the biochemical pathways are necessary for the tag to be stable. PKA modulates NMDAR-mediated Ca2+ signalling. Similarly, PKA and ERK crosstalk is essential for Ca2+ - mediated protein synthesis during l-LTP. Our theoretical model explains the quantitative contribution of Tags and protein synthesis during l-LTP in synaptic strength.
Assuntos
Plasticidade Neuronal , Sinapses , Sinapses/fisiologia , Plasticidade Neuronal/fisiologia , Neurônios/fisiologia , Receptores de N-Metil-D-Aspartato/metabolismo , Modelos Teóricos , Potenciação de Longa Duração/fisiologiaRESUMO
Perfluorohexanesulfonic acid (PFHxS) is one of the persistent organic pollutants that has been recommended to be listed in Annex A of the Stockholm Convention. It has gained increasing attention in recent years due to its toxic effects. The guideline values of PFHxS are commonly associated with PFOS in various countries and regulatory agencies. In this study, multispecies bioassays were conducted to determine the ecological toxic effects of PFHxS, including plants, soil invertebrates, and soil microorganisms, which indicated the EC10/NOEC values ranged from 2.9 to 250 mg/kg. Where possible, logistic models were used to calculate the EC30 values for various endpoints. The species sensitivity distributions were employed to estimate the ecological investigation levels for PFHxS contamination in soils using toxicity results from literature and this study. The calculation using EC10/NOEC values from both literature and this study indicated a most conservative HC5 as 1.0 mg/kg (hazardous concentration for 5 % of the species being impacted). However, utilisation of EC30 values derived from this study resulted in a much higher HC5 for PFHxS in contaminated soils (13.0 mg/kg) which is at the higher end of the existing guideline values for PFOS for protecting ecological systems. The results obtained in this study can be useful in risk assessment processes to minimize any uncertainty using combined values with PFOS.
Assuntos
Poluentes do Solo , Solo , Animais , Fluorocarbonos , Invertebrados , Medição de Risco , Poluentes do Solo/análise , Poluentes do Solo/toxicidade , Ácidos SulfônicosRESUMO
The concept of 'presence' in the context of virtual reality (VR) refers to the experience of being in the virtual environment, even when one is physically situated in the real world. Therefore, it is a key parameter of assessing a VR system, based on which, improvements can be made to it. To overcome the limitations of existing methods that are based on standard questionnaires and behavioral analysis, this study proposes to investigate the suitability of biosignals of the user to derive an objective measure of presence. The proposed approach includes experiments conducted on 20 users, recording EEG, ECG and electrodermal activity (EDA) signals while experiencing custom designed VR scenarios with factors contributing to presence suppressed and unsuppressed. Mutual Information based feature selection and subsequent paired t-tests used to identify significant variations in biosignal features when each factor of presence is suppressed revealed significant (p < 0.05) differences in the mean values of EEG signal power and coherence within alpha, beta and gamma bands distributed in specific regions of the brain. Statistical features showed a significant variation with the suppression of realism factor. The variations of activity in the temporal region lead to the assumption of insula activation which may be related to the sense of presence. Therefore, the use of biosignals for an objective measurement of presence in VR systems indicates promise.
Assuntos
Mapeamento Encefálico , Realidade Virtual , Encéfalo , Córtex Cerebral , Humanos , Interface Usuário-ComputadorRESUMO
Membrane-based air separation (O2/N2) is of great importance owing to its energy efficiency as compared to conventional processes. Currently, dense polymeric membranes serve as the main pillar of industrial processes used for the generation of O2- and N2-enriched gas. However, conventional polymeric membranes often fail to meet the selectivity needs owing to the similarity in the effective diameters of O2 and N2 gases. Meanwhile, mixed-matrix membranes (MMMs) are convenient to produce high-performance membranes while keeping the advantages of polymeric materials. Here, we propose a novel MMM for O2/N2 separation, which is composed of Matrimid® 5218 (Matrimid) as the matrix, cobalt(II) phthalocyanine microparticles (CoPCMPs) as the filler, and Pluronic® F-127 (Pluronic) as the compatibilizer. By the incorporation of CoPCMPs to Matrimid, without Pluronic, interfacial defects were formed. Pluronic-treated CoPCMPs, on the other hand, enhanced O2 permeability and O2/N2 selectivity by 64% and 34%, respectively. We explain the enhancement achieved with the increase of both O2 diffusivity and O2/N2 solubility selectivity.
RESUMO
The energy-intensive ethylene/ethane separation process is a key challenge to the petrochemical industry. HKUST-1, a metal-organic framework (MOF) which possesses high accessible surface area and porosity, is utilized in mixed-matrix membrane fabrication to investigate its potential for improving the performance for C2H4/C2H6 separation. Prior to membrane fabrication and gas permeation analysis, nanocrystal HKUST-1 was first synthesized. This step is critical in order to ensure that defect-free mixed-matrix membranes can be formed. Then, polyimide-based polymers, ODPA-TMPDA and 6FDA-TMPDA, were chosen as the matrices. Our findings revealed that 20 wt% loading of HKUST-1 was capable of improving C2H4 permeability (155% for ODPA-TMPDA and 69% for 6FDA-TMPDA) without excessively sacrificing the C2H4/C2H6 selectivity. The C2H4 and C2H6 diffusivity, as well as solubility, were also improved substantially as compared to the pure polymeric membranes. Overall, our results edge near the upper bound, confirming the effectiveness of leveraging nanocrystal HKUST-1 filler for performance enhancements in mixed-matrix membranes for C2H4/C2H6 separation.
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Parabens are used as antimicrobial preservative agent in many commercial products including cosmetics and pharmaceuticals. Weak oestrogenic and antiandrogenic activities have been attributed to parabens in in vitro and in vivo studies. In this study, human spermatozoa were exposed to different concentrations of an equimolar paraben mixture containing methyl, ethyl, propyl and butylparaben as well as to methylparaben alone at a concentration that is typical of commercially available vaginal lubricants. The induction of oxidative stress and DNA damage was then assessed at different time points. Our results demonstrate that the paraben mixture was capable of stimulating the generation of mitochondrial and cytosolic reactive oxygen species (ROS), inhibiting sperm motility and viability in a dose-dependent manner. The ability of individual parabens to activate ROS generation and induce oxidative DNA damage was related to alkyl chain length. At the concentration used clinically, methylparaben inhibited sperm motility after both 2 and 5 h exposure (p < 0.05) and affected cell viability (p < 0.01) while augmenting ROS production and oxidative DNA damage. However, DNA fragmentation was not evident following methylparaben exposure. Based on these results, we conclude that, at the concentrations used in commercially available formulations, parabens may impair sperm motility, enhance the generation of mitochondrial ROS and stimulate the formation of oxidative DNA adducts. Taken together, these data underline the potential cytotoxic and genotoxic impact of such compounds in a clinical setting.
Assuntos
Parabenos/toxicidade , Conservantes Farmacêuticos/toxicidade , Espécies Reativas de Oxigênio , Espermatozoides/efeitos dos fármacos , Apoptose/efeitos dos fármacos , Adutos de DNA , Dano ao DNA/efeitos dos fármacos , Humanos , Masculino , Motilidade dos Espermatozoides/efeitos dos fármacosRESUMO
Despite advances in our understanding of the molecular basis for particular subtypes of acute myeloid leukemia (AML), effective therapy remains a challenge for many individuals suffering from this disease. A significant proportion of both pediatric and adult AML patients cannot be cured and since the upper limits of chemotherapy intensification have been reached, there is an urgent need for novel therapeutic approaches. The transcription factor c-MYB has been shown to play a central role in the development and progression of AML driven by several different oncogenes, including mixed lineage leukemia (MLL)-fusion genes. Here, we have used a c-MYB gene expression signature from MLL-rearranged AML to probe the Connectivity Map database and identified mebendazole as a c-MYB targeting drug. Mebendazole induces c-MYB degradation via the proteasome by interfering with the heat shock protein 70 (HSP70) chaperone system. Transient exposure to mebendazole is sufficient to inhibit colony formation by AML cells, but not normal cord blood-derived cells. Furthermore, mebendazole is effective at impairing AML progression in vivo in mouse xenotransplantation experiments. In the context of widespread human use of mebendazole, our data indicate that mebendazole-induced c-MYB degradation represents a safe and novel therapeutic approach for AML.
Assuntos
Leucemia Mieloide Aguda/tratamento farmacológico , Leucemia Mieloide Aguda/metabolismo , Mebendazol/farmacologia , Proteólise/efeitos dos fármacos , Proteínas Proto-Oncogênicas c-myb/metabolismo , Animais , Criança , Feminino , Humanos , Lactente , Masculino , Camundongos , Oncogenes/efeitos dos fármacos , Complexo de Endopeptidases do Proteassoma/metabolismoRESUMO
In this paper, we show how to extend our previously proposed novel continuous time Recurrent Neural Networks (RNN) approach that retains the advantage of continuous dynamics offered by Ordinary Differential Equations (ODE) while enabling parameter estimation through adaptation, to larger signalling networks using a modular approach. Specifically, the signalling network is decomposed into several sub-models based on important temporal events in the network. Each sub-model is represented by the proposed RNN and trained using data generated from the corresponding ODE model. Trained sub-models are assembled into a whole system RNN which is then subjected to systems dynamics and sensitivity analyses. The concept is illustrated by application to G1/S transition in cell cycle using Iwamoto et al. (2008) ODE model. We decomposed the G1/S network into 3 sub-models: (i) E2F transcription factor release; (ii) E2F and CycE positive feedback loop for elevating cyclin levels; and (iii) E2F and CycA negative feedback to degrade E2F. The trained sub-models accurately represented system dynamics and parameters were in good agreement with the ODE model. The whole system RNN however revealed couple of parameters contributing to compounding errors due to feedback and required refinement to sub-model 2. These related to the reversible reaction between CycE/CDK2 and p27, its inhibitor. The revised whole system RNN model very accurately matched dynamics of the ODE system. Local sensitivity analysis of the whole system model further revealed the most dominant influence of the above two parameters in perturbing G1/S transition, giving support to a recent hypothesis that the release of inhibitor p27 from Cyc/CDK complex triggers cell cycle stage transition. To make the model useful in a practical setting, we modified each RNN sub-model with a time relay switch to facilitate larger interval input data (≈20min) (original model used data for 30s or less) and retrained them that produced parameters and protein concentrations similar to the original RNN system. Results thus demonstrated the reliability of the proposed RNN method for modelling relatively large networks by modularisation for practical settings. Advantages of the method are its ability to represent accurate continuous system dynamics and ease of: parameter estimation through training with data from a practical setting, model analysis (40% faster than ODE), fine tuning parameters when more data are available, sub-model extension when new elements and/or interactions come to light and model expansion with addition of sub-models.
Assuntos
Modelos Biológicos , Redes Neurais de Computação , Transdução de Sinais , Animais , Ciclo Celular , Retroalimentação , Humanos , Reprodutibilidade dos TestesRESUMO
We have developed a 3D dry lift-off process to localize multiple types of nitrifying bacteria in polyethylene glycol diacrylate (PEGDA) cubes for enhanced nitrification, a two-step biological process that converts ammonium to nitrite and then to nitrate. Ammonia-oxidizing bacteria (AOB) is responsible for converting ammonia into nitrite, and nitrite-oxidizing bacteria (NOB) is responsible for converting nitrite to nitrate. Successful nitrification is often challenging to accomplish, in part because AOB and NOB are slow growers and highly susceptible to many organic and inorganic chemicals in wastewater. Most importantly, the transportation of chemicals among scattered bacteria is extremely inefficient and can be problematic. For example, nitrite, produced from ammonia oxidation, is toxic to AOB and can lead to the failure of nitrification. To address these challenges, we closely localize AOB and NOB in PEGDA cubes as microenvironment modules to promote synergetic interactions. The AOB is first localized in the vicinity of the surface of the PEGDA cubes that enable AOB to efficiently uptake ammonia from a liquid medium and convert it into nitrite. The produced nitrite is then efficiently transported to the NOB localized at the center of the PEGDA particle and converted into non-toxic nitrate. Additionally, the nanoscale PEGDA fibrous structures offer a protective environment for these strains, defending them from sudden toxic chemical shocks and immobilize in cubes. This engineered microenvironment cube significantly enhances nitrification and improves the overall ammonia removal rate per single AOB cell. This approach-encapsulation of multiple strains at close range in cube in order to control their interactions-not only offers a new strategy for enhancing nitrification, but also can be adapted to improve the production of fermentation products and biofuel, because microbial processes require synergetic reactions among multiple species.
Assuntos
Bactérias/efeitos dos fármacos , Bactérias/metabolismo , Reatores Biológicos/microbiologia , Nitrificação/efeitos dos fármacos , Polietilenoglicóis/farmacologia , Amônia/metabolismo , Nitritos/metabolismo , Oxirredução/efeitos dos fármacosRESUMO
Allogeneic hematopoietic stem cell transplantation (HSCT) offers the potential to cure patients with an inherited bone marrow failure syndrome (IBMFS). However, the procedure involves the risk of treatment-related mortality and may be associated with significant early and late morbidity. For these reasons, the benefits should be carefully weighed against the risks. IBMFS are rare, whereas case reports and small series in the literature illustrate highly heterogeneous practices in terms of indications for HSCT, timing, stem cell source and conditioning regimens. A consensus meeting was therefore held in Vienna in September 2012 on behalf of the European Group for Blood and Marrow Transplantation to discuss HSCT in the setting of IBMFS. This report summarizes the recommendations from this expert panel, including indications for HSCT, timing, stem cell source and conditioning regimen.
Assuntos
Transplante de Células-Tronco Hematopoéticas/métodos , Hemoglobinúria Paroxística/terapia , Condicionamento Pré-Transplante/métodos , Adolescente , Aloenxertos , Anemia Aplástica , Doenças da Medula Óssea , Transtornos da Insuficiência da Medula Óssea , Criança , Pré-Escolar , Feminino , Humanos , Lactente , MasculinoRESUMO
A synaptic protein, Ca(2+)/Calmodulin dependent protein kinase II (CaMKII), has complex state transitions and facilitates the emergence of long term potentiation (LTP), which is highly correlated to memory formation. Two of the state transitions are critical for LTP: (1) threonine 286 autophosphorylation of CaMKII; and (2) binding to N-methyl-d-aspartate receptor (NMDAR) in the postsynaptic density (PSD) to form CaMKII-NMDAR complex. Both of these state transitions retain the activity of CaMKII when the induction signal disappears which is very important for the long-lasting characteristics of LTP. However, the possible relationships between the state transitions in the emergence of LTP are not well understood. We develop a mathematical model of the formation of CaMKII-NMDAR complex with the full state transitions of CaMKII, including the autophosphorylation, based on ordinary differential equations. In addition, we formulate a probabilistic framework for the binding between CaMKII and NMDAR. The model gives accurate predictions of the behaviours of CaMKII in comparisons to the experimental observations. Using the model, we show that: (1) the formation of CaMKII-NMDAR complex is dependent not only on the binding affinity between CaMKII and NMDAR, but also on the translocation of CaMKII into PSD; and (2) the autophosphorylation is not a requirement for the formation of CaMKII-NMDAR complex, but is important for the rapid formation of CaMKII-NMDAR complex during LTP.
Assuntos
Proteína Quinase Tipo 2 Dependente de Cálcio-Calmodulina/metabolismo , Potenciação de Longa Duração/fisiologia , Memória/fisiologia , Modelos Biológicos , Receptores de N-Metil-D-Aspartato/metabolismo , Sinapses/fisiologia , Treonina/metabolismo , Proteína Quinase Tipo 2 Dependente de Cálcio-Calmodulina/química , Calmodulina/metabolismo , Fosforilação , Densidade Pós-Sináptica/metabolismo , Ligação Proteica , Conformação Proteica , Transporte ProteicoRESUMO
Experiments show that the meiotic-mitotic initiation switch in budding yeast functions robustly during the early hours of meiosis initiation. In this study, we explain these experimental observations first by understanding how this switching occurs during the early hours of meiosis by studying the temporal variation of this switch at the gene expression level. Then, we investigate the effects on this meiotic-mitotic switching from the perturbations of the most sensitive parameters in budding yeast meiosis initiation network. We use a mathematical model of meiosis initiation in budding yeast for this task and find the most sensitive group of parameters that influence the expressions of meiosis and mitosis initiators at all stages of the meiotic-mitotic switch. The results indicate that the transition region of the switch, where a double negative feedback loop between meiosis (Ime2) and mitosis (Cdk1/Cln3) initiators plays a major role, shows lower robustness. Feedback loops are frequently observed serving as a major robust adaption mechanism in many biological networks. Consequences of this less robust region appear in the transition region of the resulting switches. Most importantly, despite the differences observed in the transition region, we find that the meiotic-mitotic switch robustly maintains its main function of transition from meiosis to mitosis when the nutrients are re-supplied, against the perturbations in the sensitive parameters.
Assuntos
Meiose , Mitose , Saccharomyces cerevisiae/fisiologia , Modelos Teóricos , Saccharomyces cerevisiae/citologiaRESUMO
Synaptic plasticity, an emergent property of synaptic networks, has shown strong correlation to one of the essential functions of the brain, memory formation. Through understanding synaptic plasticity, we hope to discover the modulators and mechanisms that trigger memory formation. In this paper, we first review the well understood modulators and mechanisms underlying N-methyl-D-aspartate receptor dependent synaptic plasticity, a major form of synaptic plasticity in hippocampus, and then comment on the key mathematical modelling approaches available in the literature to understand synaptic plasticity as the integration of the established functionalities of synaptic components.
Assuntos
Encéfalo/fisiologia , Memória/fisiologia , Modelos Biológicos , Plasticidade Neuronal/fisiologia , Receptores de N-Metil-D-Aspartato/metabolismo , Transdução de Sinais/fisiologia , Biologia de Sistemas/métodos , Cálcio/metabolismo , Calmodulina/metabolismo , Humanos , Receptores de Glutamato/genética , Receptores de Glutamato/metabolismo , Biologia de Sistemas/tendênciasRESUMO
Malawi is one of the world's poorest countries, but despite this, has a dedicated paediatric oncology service. The service has been hampered by the inability to make a timely cytological diagnosis in the majority of patients. A telemedicine programme was commenced to help overcome this problem, and the results for the first 197 consecutive patients are described. The results are compared with the local reports where available. Most samples were fine needle aspirates (104/197-53%), but others included bone marrow aspirates, peripheral blood films and other fluid collections. A diagnosis was arrived at in 52% of the samples; there were 46 discordant results, 38 were when one or other of the local or distant teams were unable to make a diagnosis, and only 8 where the diagnoses of the 2 teams differed. Diagnoses were made and reports were compiled by the 'distant' team within 24â h and sent to the centre in Malawi. This simple telepathology initiative has had a positive impact on clinical management, and could be used in other less resourced centres twinned with better resourced ones.
Assuntos
Países em Desenvolvimento , Oncologia/métodos , Patologia Clínica/métodos , Pediatria/métodos , Telepatologia , Adolescente , Biópsia por Agulha Fina , Exame de Medula Óssea , Criança , Pré-Escolar , Países em Desenvolvimento/economia , Feminino , Custos de Cuidados de Saúde , Recursos em Saúde , Acessibilidade aos Serviços de Saúde , Humanos , Lactente , Malaui , Masculino , Oncologia/economia , Patologia Clínica/economia , Pediatria/economia , Valor Preditivo dos Testes , Avaliação de Programas e Projetos de Saúde , Telepatologia/economia , Fatores de TempoRESUMO
This retrospective national study compared the use of alemtuzumab-based conditioning regimens for hematopoietic SCT (HSCT) in acquired severe aplastic anemia with antithymocyte globulin (ATG)-based regimens. One hundred patients received alemtuzumab and 55 ATG-based regimens. A matched sibling donor (MSD) was used in 87 (56%), matched unrelated donor (MUD) in 60 (39%) and other related or mismatched unrelated donor (UD) in 8 (5%) patients. Engraftment failure occurred in 9% of the alemtuzumab group and 11% of the ATG group. Five-year OS was 90% for the alemtuzumab and 79% for the ATG groups, P=0.11. For UD HSCT, OS of patients was better when using alemtuzumab (88%) compared with ATG (57%), P=0.026, although smaller numbers of patients received ATG. Similar outcomes for MSD HSCT using alemtuzumab or ATG were seen (91% vs 85%, respectively, P=0.562). A lower risk of chronic GVHD (cGVHD) was observed in the alemtuzumab group (11% vs 26%, P=0.031). On multivariate analysis, use of BM as stem cell source was associated with better OS and EFS, and less acute and cGVHD; young age was associated with better EFS and lower risk of graft failure. This large study confirms successful avoidance of irradiation in the conditioning regimens for MUD HSCT patients.
Assuntos
Anemia Aplástica/terapia , Anticorpos Monoclonais Humanizados/uso terapêutico , Soro Antilinfocitário/uso terapêutico , Transplante de Medula Óssea/métodos , Transplante de Células-Tronco de Sangue Periférico/métodos , Condicionamento Pré-Transplante/métodos , Adolescente , Adulto , Idoso , Alemtuzumab , Células da Medula Óssea/citologia , Criança , Pré-Escolar , Feminino , Sobrevivência de Enxerto , Doença Enxerto-Hospedeiro , Humanos , Lactente , Masculino , Pessoa de Meia-Idade , Sistema de Registros , Estudos Retrospectivos , Fatores de Risco , Irmãos , Doadores de Tecidos , Resultado do Tratamento , Reino Unido , Adulto JovemRESUMO
Nutrients from living environment are vital for the survival and growth of any organism. Budding yeast diploid cells decide to grow by mitosis type cell division or decide to create unique, stress resistant spores by meiosis type cell division depending on the available nutrient conditions. To gain a molecular systems level understanding of the nutrient dependant switching between meiosis and mitosis initiation in diploid cells of budding yeast, we develop a theoretical model based on ordinary differential equations (ODEs) including the mitosis initiator and its relations to budding yeast meiosis initiation network. Our model accurately and qualitatively predicts the experimentally revealed temporal variations of related proteins under different nutrient conditions as well as the diverse mutant studies related to meiosis and mitosis initiation. Using this model, we show how the meiosis and mitosis initiators form an all-or-none type bistable switch in response to available nutrient level (mainly nitrogen). The transitions to and from meiosis or mitosis initiation states occur via saddle node bifurcation. This bidirectional switch helps the optimal usage of available nutrients and explains the mutually exclusive existence of meiosis and mitosis pathways.
Assuntos
Meiose/fisiologia , Mitose/fisiologia , Modelos Biológicos , Fenômenos Fisiológicos da Nutrição/fisiologia , Saccharomyces cerevisiae/fisiologia , Saccharomycetales/fisiologia , Algoritmos , Retroalimentação Fisiológica/fisiologia , Saccharomyces cerevisiae/genética , Saccharomycetales/genética , Estresse Fisiológico/fisiologiaRESUMO
After a very brief introduction to a mechanistic and statistical theory of molecular fluctuations in chemical reactions developed by Joel Keizer, we explore the robustness of a circadian rhythm model by using the theory and the exact stochastic simulation (ESS). The comparative study shows that the theory reflects the effects of the dynamics of the model on the robustness more than ESS does. Even though the theory is a macroscopic one, the robustness of the model compares well with that computed from the ESS when the system size is larger than 50. The robustness increases nonlinearly with the system size and it reaches an asymptotic value at higher system sizes. As we can expect from the dynamics of the system, the robustness is minimum near the bifurcation point and as the most sensitive parameter increases away from the bifurcation point the robustness according to the theory as well as the ESS increases and then reaches to a steady value.