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Search results for: genre model
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Analysis of a gene expression model
PublicationWe study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the number of active binding sites, the way in which dimers bind to DNA and time delay in translation process. For a simplified model that consist of three ordinary differential equations with time delay we derive conditions for stability of the positive steady state and for the...
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Genre
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ANALYSIS OF THE p53 PROTEIN GENE EXPRESSION MODEL
PublicationWe study the asymptotic behaviour of the solutions of the p53-Mdm2 model proposed by Monk (2003). The p53 gene is crucial for cellular inhibition of the angiogenesis process, while Mdm2 is a negative regulator of the p53 tumor-suppressor. We investigate the stability of the positive steady state and perform some numerical experiments.
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Delay induced oscillations in gene expression of Hes1 protein model
PublicationW pracy został omówiony model produkcji białka Hes1. Stężenie Hes1 jest kontrolowane przez ujemne sprzężenie zwrotne wbudowane w białko i jego mRNA. Przeprowadzona analiza potwierdziła znane wyniki numeryczne, że oscylacje wywołane są przez opóźnienie. Pokazaliśmy również, że jeśli współczynnik Hilla jest większy niż 1, to istnieje krytyczna wartość opóźnienia, dla której ma miejsce bifurkacja Hopfa i pojawiają się rozwiązania...
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Hopf bifurcation in time‐delayed gene expression model with dimers
PublicationWe study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the formation of dimers (i.e., complex formed by two protein monomers), the way in which dimers bind to DNA and time delay in translation process. For the model consisting of three ordinary differential equations with time delay, we derive conditions for stability of the positive...
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Genre & Histoire
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Mathematical analysis of a generalised p53-Mdm2 protein gene expression model
PublicationWe propose the generalisation of the p53-Mdm2 protein gene expression model introduced by Monk (2003). We investigate the stability of a unique positive steady state and formulate conditions which guarantee the occurrence of the Hopf bifurcation. We show that oscillatory behaviour can be caused not only by time lag in protein transcription process, but also can be present in the model without time delay. Moreover, we investigate...
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Stability of delay induced oscillations in gene expression of Hes1 protein model
PublicationW pracy prezentowana jest matematyczna analiza modelu ekspresji genu białka Hes1. Rozważamy układ równań z dwoma opóźnieniami - w produkcji białka Hes1 oraz jego mRNA. Dowodzimy istnienia i jednoznaczności oraz nieujemności rozwiązań. Pokazujemy istnienie dokładnie jednego dodatniego stanu stacjonarnego. Wykazujemy, że stabilność stanu stacjonarnego zależy od sumy opóźnień. Podajemy warunek dostateczny na wystąpienie bifurkacji...
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Geoscientific Model Development
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The effects of p53 gene inactivation on mutant proteome expression in a human melanoma cell model
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