Classe de Ciências

info:eu-repo/semantics/publishedVersio

Calibration of the distribution of the pair-rule proteins Even-skipped and Fushi-tarazu in the Drosophila embryo

We modelled and calibrated the distributions of the seven-stripe patterns of Even-skipped (\textit{Eve}) and Fushi-tarazu (\textit{Ftz}) pair-rule proteins along the anteroposterior axis of the Drosophila embryo, established during early development. The regulators of \textit{Eve} and \textit{Ftz} are stripe-specific enhancers from the gap family of proteins and determine the body structure of the \textit{Drosophila} larva. We achieved remarkable data matching of the \textit{Eve} stripe pattern, and the calibrated model reproduces gap gene mutation experiments. We have identified the putative repressive combinations for five \textit{Eve} enhancers, and we have explored the relationship between \textit{Eve} and \textit{Ftz} for complementary patterns. Extended work inferring the Wingless (\textit{Wg}) fourteen stripe pattern from \textit{Eve} and \textit{Ftz} enhancers has been proposed, clarifying the hierarchical structure of \textit{Drosphila}'s genetic expression network during early development before cellularisation.Comment: 15 pages, 10 figure

Equilibrium price dynamics in an overlapping-generations exchange economy

We present a continuous time overlapping generations model for an endowment Arrow-Debreu economy with an age-structured popu¬lation. For an economy with a balanced growth path, we prove that Arrow-Debreu equilibrium prices exist, and their dynamic properties are age-dependent. Our model allows for an explicit dependence of prices on critical age-specific endowment parameters. We show that, if endowments are distributed earlier than some critical age, then spec¬ulative bubbles for prices do exist

The Exact Value for European Options on a Stock Paying a Discrete Dividend

In the context of a Black-Scholes economy and with a no-arbitrage argument, we derive arbitrarily accurate lower and upper bounds for the value of European options on a stock paying a discrete dividend. Setting the option price error below the smallest monetary unity, both bounds coincide, and we obtain the exact value of the option.Comment: 14 pages,3 figure

The role of ion channels in the transmission of signals along axons

This work proposes a two-dimensional electrophysiological model for describing neuronal responses to external electric stimuli under patch-clamped conditions. Our proposed model successfully captures the key features of the Hodgkin-Huxley model, while offering improved informativeness and numerical efficiency. By analysing bifurcation diagrams from various reduced models, we describe the contributions of different ionic channels to the stability or instability of the neurones' response. We also explore the influence of various cell parameters in the neurone's spiking frequency, including the membrane capacitance and the ionic channels' conductivities and Nerst potentials. Additionally, we suggest a spatial model for the axon that effectively simulates unidirectional signal transmission along neurons unaffected by membrane potential perturbations. After analysing the characteristics of this compartmental model, including the impact of intracellular resistance and membrane capacitance on the signal's velocity, we observed considerable discrepancies between our findings and those predicted by the cable equation model for signal propagation. Moreover, our investigation reveals that when the transmission of neuronal signals occurs in multiple peaks, there is a transient variation in their wavelength and frequency, resulting in different peak velocities. Furthermore, our findings consistently demonstrate that the first peak - in some cases, the only peak observed - maintains a relatively constant velocity along the axon regardless of the stimulus intensity and is always faster than the subsequent peaks.Comment: 40 pages, 48 figure

Calibration and validation of a genetic regulatory network model describing the production of the protein Hunchback in <i>Drosophila</i> early development

We fit the parameters of a differential equations model describing the production of gap gene proteins Hunchback and Knirps along the antero-posterior axis of the embryo of \emph{Drosophila}. As initial data for the differential equations model, we take the antero-posterior distribution of the proteins Bicoid, Hunchback and Tailless at the beginning of cleavage cycle 14. We calibrate and validate the model with experimental data using single- and multi-objective evolutionary optimization techniques. In the multi-objective optimization technique, we compute the associated Pareto fronts. We analyze the cross regulation mechanism between the gap-genes protein pair Hunchback-Knirps and we show that the posterior distribution of Hunchback follow the experimental data if Hunchback is negatively regulated by the Huckebein protein. This approach enables to predict the posterior localization on the embryo of the protein Huckebein, and we validate with the experimental data the genetic regulatory network responsible for the antero-posterior distribution of the gap gene protein Hunchback. We discuss the importance of Pareto multi-objective optimization techniques in the calibration and validation of biological models.Comment: 25 pages, 10 figure