Mathematical model for HIV dynamics in HIV-specific helper cells

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

Oriented Tailoring of Plastic Antibodies for Prostate Specific Antigen and Application of the Imprinted Material as Ionophore in Potentiometric Detection

Prostate Specific Antigen (PSA) is the biomarker of choice for screening prostate cancer throughout the population, with PSA values above 10 ng/mL pointing out a high probability of associated cancer1. According to the most recent World Health Organization (WHO) data, prostate cancer is the commonest form of cancer in men in Europe2. Early detection of prostate cancer is thus very important and is currently made by screening PSA in men over 45 years old, combined with other alterations in serum and urine parameters. PSA is a glycoprotein with a molecular mass of approximately 32 kDa consisting of one polypeptide chain, which is produced by the secretory epithelium of human prostate. Currently, the standard methods available for PSA screening are immunoassays like Enzyme-Linked Immunoabsorbent Assay (ELISA). These methods are highly sensitive and specific for the detection of PSA, but they require expensive laboratory facilities and high qualify personal resources. Other highly sensitive and specific methods for the detection of PSA have also become available and are in its majority immunobiosensors1,3-5, relying on antibodies. Less expensive methods producing quicker responses are thus needed, which may be achieved by synthesizing artificial antibodies by means of molecular imprinting techniques. These should also be coupled to simple and low cost devices, such as those of the potentiometric kind, one approach that has been proven successful6. Potentiometric sensors offer the advantage of selectivity and portability for use in point-of-care and have been widely recognized as potential analytical tools in this field. The inherent method is simple, precise, accurate and inexpensive regarding reagent consumption and equipment involved. Thus, this work proposes a new plastic antibody for PSA, designed over the surface of graphene layers extracted from graphite. Charged monomers were used to enable an oriented tailoring of the PSA rebinding sites. Uncharged monomers were used as control. These materials were used as ionophores in conventional solid-contact graphite electrodes. The obtained results showed that the imprinted materials displayed a selective response to PSA. The electrodes with charged monomers showed a more stable and sensitive response, with an average slope of -44.2 mV/decade and a detection limit of 5.8X10-11 mol/L (2 ng/mL). The corresponding non-imprinted sensors showed smaller sensitivity, with average slopes of -24.8 mV/decade. The best sensors were successfully applied to the analysis of serum samples, with percentage recoveries of 106.5% and relatives errors of 6.5%.