Enhancement of Biodiesel Production via Ultrasound Technology: A Mathematical Study.

Biodiesel is one of the alternative renewable energy sources that has received a lot of attention since it is clean, green energy. Different sources can be used for the production of biodiesel, but the most appropriate and economical method relies on the transesterification of methanol with the nonedible vegetable oil from the fruit of the Jatropha curcas plant. Molar ratio, vessel diameter, catalyst concentration, and ultrasound all have a substantial influence on the synthesis of biodiesel by the transesterification process. Among these factors, the diameter of the vessel and the ultrasonic effect through mass transfer limitations have a significant impact on successful reaction completion. In this research work, we have developed a mathematical model to analyze the three-step transesterification process and side saponification reaction in the presence of a potassium hydroxide catalyst. The model considers the influence of mixing intensity variations, including ultrasound, on the mass transfer in different phases. The mass transfer rate is calculated using the modified Dittus-Boelter correlation. An optimal control approach through the minimum principle by Pontryagin is applied to maximize the production of biodiesel at minimal cost. The novelty of this research, which we have derived from our analytical as well as numerical results, considering industrial processes, is that more than 97% biodiesel yield conversion is to be obtained at 50 kHz ultrasound frequency, a 6:1 methanol-to-Jatropha-oil molar ratio, and 1 m of vessel diameter within 50 min using optimal control theory.

Role of ATP Hydrolysis and Product Release in the Translocation Mechanism of SARS-CoV-2 NSP13.

In response to the emergence of COVID-19, caused by SARS-CoV-2, there has been a growing interest in understanding the functional mechanisms of the viral proteins to aid in the development of new therapeutics. Nonstructural protein 13 (nsp13) helicase is an attractive target for antivirals because it is essential for viral replication and has a low mutation rate, yet the structural mechanisms by which this enzyme binds and hydrolyzes ATP to cause unidirectional RNA translocation remain elusive. Using Gaussian accelerated molecular dynamics (GaMD), we generated comprehensive conformational ensembles of all substrate states along the ATP-dependent cycle. Shape-GMM clustering of the protein yields four protein conformations that describe an opening and closing of both the ATP pocket and the RNA cleft that is achieved through a combination of conformational selection and induction along the ATP hydrolysis cycle. Furthermore, three protein-RNA conformations are observed that implicate motifs Ia, IV, and V as playing a pivotal role in an ATP-dependent inchworm translocation mechanism. Finally, based on a linear discriminant analysis of protein conformations, we identify L405 as a pivotal residue for the opening and closing mechanism and propose a L405D mutation as a way to disrupt translocation. This research enhances our understanding of nsp13's role in viral replication and could contribute to the development of antiviral strategies.

Estrogen-induced reactive oxygen species, through epigenetic reprogramming, causes increased growth in breast cancer cells.

Despite the progress made in cancer diagnosis and treatment, breast cancer remains the second leading cause of cancer-related death among the women. Exposure to elevated levels of endogenous estrogen or environmental estrogenic chemicals is an important risk factor for breast cancer. Estrogen metabolites and ROS generated during estrogen metabolism are known to play a critical role in estrogen carcinogenesis. However, the molecular mechanisms through which estrogen-induced ROS regulate gene expression is not clear. Epigenetic changes of DNA methylation and histone modifications are known to regulate genes expression. Therefore, the objective of this study was to evaluate whether estrogen-induced ROS, through aberrant expression of epigenetic regulatory genes and epigenetic reprogramming, causes growth of breast cancer cells. Estrogen responsive MCF-7 and T47D human breast cancer cells were exposed to natural estrogen 17 beta-estradiol (E2) and synthetic estrogen Diethylstilbestrol (DES) both alone and in combination with antioxidant N-acetyl cysteine. Effects of NAC-mediated scavenging of estrogen-induced ROS on cell growth, gene expression, and histone modifications were measured. The result of MTT and cell cycle analysis revealed significant abrogation of E2 and DES-induced growth by scavenging ROS through NAC. E2 and DES caused significant changes in expression of epigenetic regulatory genes for DNA methylation and histone modifications as well as changes in both gene activating and repressive marks in the Histone H3. NAC restored the expression of epigenetic regulatory genes and changes in histone marks. Novel findings of this study suggest that estrogen can induce growth of breast cancer cells through ROS-dependent regulation of epigenetic regulatory genes and epigenetic reprogramming of histone marks.

Motif-VI Loop Acts as a Nucleotide Valve in the West Nile Virus NS3 Helicase.

The flavivirus NS3 helicase (NS3h), a highly conserved protein, plays a pivotal role in virus replication and thus represents a potential drug target for flavivirus pathogenesis. NS3h utilizes nucleotide triphosphate, such as ATP, for hydrolysis energy (ATPase) to translocate on single-stranded nucleic acids, which is an important step in the unwinding of double-stranded nucleic acids. The intermediate states along the ATP binding and hydrolysis cycle, as well as the conformational changes between these states, represent important yet difficult-to-identify targets for potential inhibitors. We use extensive molecular dynamics simulations of apo, ATP, ADP+Pi, and ADP bound to WNV NS3h+ssRNA to model the conformational ensembles along this cycle. Energetic and structural clustering analyses on these trajectories depict a clear trend of differential enthalpic affinity of NS3h with ADP, demonstrating a probable mechanism of hydrolysis turnover regulated by the motif-VI loop (MVIL). These findings were experimentally corroborated using viral replicons encoding three mutations at the D471 position. Replication assays using these mutants demonstrated a substantial reduction in viral replication compared to the wild-type. Molecular simulations of the D471 mutants in the apo state indicate a shift in MVIL populations favoring either a closed or open 'valve' conformation, affecting ATP entry or stabilization, respectively. Combining our molecular modeling with experimental evidence highlights a conformation-dependent role for MVIL as a 'valve' for the ATP-pocket, presenting a promising target for antiviral development.

Epigallocatechin-3-gallate attenuates arsenic-induced fibrogenic changes in human kidney epithelial cells through reversal of epigenetic aberrations and antioxidant activities.

Renal fibrosis is a pathogenic intermediate stage of chronic kidney disease (CKD). Nephrotoxicants including arsenic can cause kidney fibrosis through induction of oxidative stress and epigenetic aberrations. Epigallocatechin-3-gallate (EGCG), a green tea polyphenol, is known to have antioxidant and epigenetic modulation properties. Whether EGCG, through its antioxidant and epigenetic modulating activities, can attenuate fibrogenesis is not known. Therefore, the objective of this study was to determine whether EGCG can attenuate arsenic-induced acute injury and long-term exposure associated fibrogenicity in kidney epithelial cells. To address this question, two human kidney epithelial cell lines Caki-1 and HK-2 exposed to arsenic for both acute and long-term durations were treated with EGCG. The protective effect of EGCG on arsenic-induced cytotoxicity and fibrogenicity were evaluated by measuring the cell growth, reactive oxygen species (ROS) production, genes expression, and epigenetic changes in histone marks. Results revealed that EGCG has a protective effect in arsenic-induced acute cytotoxicity in these cells. EGCG scavenges the increased levels of ROS in arsenic exposed cells. Aberrant expression of fibrogenic genes in arsenic exposed cells were restored by EGCG. Abrogation of arsenic-induced fibrogenic changes was also associated with EGCG-mediated restoration of arsenic-induced aberrant expression of epigenetic regulatory proteins and histone marks. Novel findings of this study suggest that EGCG, through its antioxidant and epigenetic modulation capacities, has protective effects against arsenic-induced cytotoxicity and fibrogenic changes in kidney epithelial cells.

The Role of ATP Hydrolysis and Product Release in the Translocation Mechanism of SARS-CoV-2 NSP13.

In response to the emergence of COVID-19, caused by SARS-CoV-2, there has been a growing interest in understanding the functional mechanisms of the viral proteins to aid in the development of new therapeutics. Non-structural protein 13 (Nsp13) helicase is an attractive target for antivirals because it is essential for viral replication and has a low mutation rate; yet, the structural mechanisms by which this enzyme binds and hydrolyzes ATP to cause unidirectional RNA translocation remain elusive. Using Gaussian accelerated molecular dynamics (GaMD), we generated a comprehensive conformational ensemble of all substrate states along the ATP-dependent cycle. ShapeGMM clustering of the protein yields four protein conformations that describe an opening and closing of both the ATP pocket and RNA cleft. This opening and closing is achieved through a combination of conformational selection and induction along the ATP cycle. Furthermore, three protein-RNA conformations are observed that implicate motifs Ia, IV, and V as playing a pivotal role in an ATP-dependent inchworm translocation mechanism. Finally, based on a linear discriminant analysis of protein conformations, we identify L405 as a pivotal residue for the opening and closing mechanism and propose a L405D mutation as a way of testing our proposed mechanism. This research enhances our understanding of nsp13's role in viral replication and could contribute to the development of antiviral strategies.

Epigenetic mechanism of therapeutic resistance and potential of epigenetic therapeutics in chemorefractory prostate cancer.

Prostate cancer is the second leading cause of cancer death among men in the United States. Depending upon the histopathological subtypes of prostate cancers, various therapeutic options, such as androgen deprivation therapy (ADT), androgen receptor signaling inhibitors (ARSI), immunotherapy, and chemotherapy, are available to treat prostate cancer. While these therapeutics are effective in the initial stages during treatments, the tumors subsequently develop resistance to these therapies. Despite all the progress made so far, therapeutic resistance remains a major challenge in the treatment of prostate cancer. Although various mechanisms have been reported for the resistance development in prostate cancer, altered expression of genes either directly or indirectly involved in drug response pathways is a common event. In addition to the genetic basis of gene regulation such as mutations and gene amplifications, epigenetic alterations involved in the aberrant expression of genes have frequently been shown to be associated not only with cancer initiation and progression but also with therapeutic resistance development. There are several review articles compiling reports on genetic mechanisms involved in therapeutic resistance in prostate cancer. However, epigenetic mechanisms for the therapeutic resistance development in prostate cancer have not yet been summarized in a review article. Therefore, the objective of this article is to compile various reports and provide a comprehensive review of the epigenetic aberrations, and aberrant expression of genes by epigenetic mechanisms involved in CRPCs and therapeutic resistance development in prostate cancer. Additionally, the potential of epigenetic-based therapeutics in the treatment of chemorefractory prostate cancer as evidenced by clinical trials has also been discussed.

Critical observation of WHO recommended multidrug therapy on the disease leprosy through mathematical study.

Leprosy is a skin disease and it is characterized by a disorder of the peripheral nervous system which occurs due to the infection of Schwann cells. In this research article, we have formulated a four-dimensional ODE-based mathematical model which consists of the densities of healthy Schwann cells, infected Schwann cells, M. leprae bacteria, and the concentration of multidrug therapy (MDT). This work primarily aims on exploring the dynamical changes and interrelations of the system cell populations during the disease progression. Also, evaluating a critical value of the drug efficacy rate of MDT remains our key focus in this article so that a safe drug dose regimen for leprosy can be framed more effectively and realistically. We have examined the stability scenario of different equilibria and the occurrence of Hopf-bifurcation for the densities of our system cell populations with respect to the drug efficacy rate of MDT to gain insight on the precise impact of the efficiency rate on both the infected Schwann cell and the bacterial populations. Also, a necessary transversality condition for the occurrence of the bifurcation has been established. Our analytical and numerical investigations in this research work precisely explores that the process of demyelination, nerve regeneration, and infection of the healthy Schwann cells are the three most crucial factors in the leprosy pathogenesis and to control the M. leprae-induced infection of Schwann cells successfully, a more flexible version of MDT regime with efficacy rate varying in the range η∈(0.025,0.059) for 100-120 days in PB cases and 300 days in MB cases obtained in this research article should be applied. All of our analytical outcomes have been verified through numerical simulations and compared with some existing clinical findings.

Effects of External Perturbations on Protein Systems: A Microscopic View.

Protein folding can be viewed as the origami engineering of biology resulting from the long process of evolution. Even decades after its recognition, research efforts worldwide focus on demystifying molecular factors that underlie protein structure-function relationships; this is particularly relevant in the era of proteopathic disease. A complex co-occurrence of different physicochemical factors such as temperature, pressure, solvent, cosolvent, macromolecular crowding, confinement, and mutations that represent realistic biological environments are known to modulate the folding process and protein stability in unique ways. In the current review, we have contextually summarized the substantial efforts in unveiling individual effects of these perturbative factors, with major attention toward bottom-up approaches. Moreover, we briefly present some of the biotechnological applications of the insights derived from these studies over various applications including pharmaceuticals, biofuels, cryopreservation, and novel materials. Finally, we conclude by summarizing the challenges in studying the combined effects of multifactorial perturbations in protein folding and refer to complementary advances in experiment and computational techniques that lend insights to the emergent challenges.

Chronic coexposure to arsenic and estrogen potentiates genotoxic estrogen metabolic pathway and hypermethylation of DNA glycosylase MBD4 in human prostate epithelial cells.

BACKGROUND: Previously we reported that arsenic and estrogen cause synergistic effects in the neoplastic transformation of human prostate epithelial cells. In addition to receptor-mediated pathways, DNA-reactive estrogen metabolites have also been shown to play a critical role in mutagenicity and carcinogenicity. Both estrogen and arsenic are known prostate carcinogens, however, the effect of coexposure to these two chemicals on genes involved in estrogen metabolism is not known. Therefore, the objective of this study was to evaluate the role of arsenic and estrogen coexposure on the expression of estrogen receptors and estrogen metabolism-associated genes. Earlier, we also reported the synergistic effect of arsenic and estrogen on decreased expression of MBD4 genes that play an important role in DNA repair through its DNA glycosylase activity. To further understand the mechanism, the promoter methylation of this gene was also analyzed. METHODS: Total RNA and protein were isolated from RWPE-1 human prostate epithelial cells that were coexposed to arsenic and estrogen for a chronic duration (6 months). The expression of estrogen receptors, estrogen metabolism associated phase I genes (CYP 1A1, 1A2, 3A4, and 1B1) and phase II gene catechol-O-methyltransferase (COMT), as well as antioxidant MnSOD, were analyzed either at the RNA level by quantitative reverse transcriptase-polymerase chain reaction or at the protein level by western blot. Promoter methylation of MBD4 was analyzed by pyrosequencing. RESULTS: Expression of MnSOD and phase I genes that convert E2 into genotoxic metabolites 2-OH-E2 and 4-OH-E2 were significantly increased, whereas the expression of phase II gene COMT that detoxifies estrogen metabolites was significantly decreased in arsenic and estrogen coexposed cells. MBD4 promoter was hypermethylated in arsenic and estrogen coexposed cells. Coexposure to arsenic and estrogen has synergistic effects on the expression of these genes as well as in MBD4 promoter hypermethylation. CONCLUSIONS: These novel findings suggest that coexposure to arsenic and estrogen acts synergistically in the activation of not only the estrogen receptors but also the genes associated with genotoxic estrogen metabolism and epigenetic inactivation of DNA glycosylase MBD4. Together, these genetic and epigenetic aberrations provide the molecular basis for the potentiation of carcinogenicity of arsenic and estrogen coexposure in prostate epithelial cells.

Dynamical Manifestations of Supercooling in Amyloid Hydration.

The effect of extreme temperature on amyloidogenic species remains sparsely explored. In a recent study (J. Phys. Chem. Lett., 2019, 10, (10)), we employed exhaustive molecular dynamics simulations to explore the cold thermal response of a putative small amyloid oligomer and to elicit the role of solvent modulation. Herein, we investigate the dynamical response of the hydration waters of the oligomer within the supercooled states. Using NMR-based formalism, we delineate the entropic response in terms of the side-chain conformational entropy that corroborates the weakening of the hydrophobic core with lowering of temperature. The translational dynamics of the protein and hydration waters reveal the coupling of protein dynamical fluctuations with solvent dynamics under supercooled conditions. Probing the translational motion as a space-time correlation indicates glassy dynamics exhibited by hydration waters in the supercooled regime. Caging of the water molecules with lowering of temperature and the resultant hopping dynamics are reflected in the longer ß-relaxation timescales of translational motion. Furthermore, we utilized mode-coupling theory (MCT) and derived the ideal glass transition temperature from translational and rotational dynamics, around ∼196 and 209 K, respectively. Interestingly, rotational motion in the supercooled regime deviates from the MCT law, exhibits Arrhenius motion, and marks a fragile-to-strong crossover at 227 K. The low-frequency vibrational modes also coincide with the dynamical transition. This exposition lends dynamical insights into the hydration coupling of an amyloid aggregate under cryogenic conditions.

Hydroxy-Porphyrin as an Effective, Endogenous Molecular Clamp during Early Stages of Amyloid Fibrillization.

Amyloid fibril formation of proteins is of great concern in neurodegenerative disease and can be detrimental to the storage and stability of biologics. Recent evidence suggests that insulin fibril formation reduces the efficacy of type II diabetes management and may lead to several complications. To develop anti-amyloidogenic compounds of endogenous origin, we have utilized the hydrogen bond anchoring, π stacking ability of porphyrin, and investigated its role on the inhibition of insulin amyloid formation. We report that hydroxylation and metal removal from the heme moiety yields an excellent inhibitor of insulin fibril formation. Thioflavin T, tyrosine fluorescence, Circular Dichorism (CD) spectroscopy, Field emission scanning electron microscopy (FESEM) and molecular dynamics (MD) simulation studies suggest that hematoporphyrin (HP) having hydrogen bonding ability on both sides is a superior inhibitor compared to hemin and protoporphyrin (PP). Experiments with hen egg white lysozyme (HEWL) amyloid fibril formation also validated the efficacy of endogenous porphyrin based small molecules. Our results will help to decipher a general therapeutic strategy to counter amyloidogenesis.

Hydration of a small protein under carbon nanotube confinement: Adsorbed substates induce selective separation of the dynamical response.

The co-involvement of biological molecules and nanomaterials has increasingly come to the fore in modern-day applications. While the "bio-nano" (BN) interface presents physico-chemical characteristics that are manifestly different from those observed in isotropic bulk conditions, the underlying molecular reasons remain little understood; this is especially true of anomalies in interfacial hydration. In this paper, we leverage atomistic simulations to study differential adsorption characteristics of a small protein on the inner (concave) surface of a single-walled carbon nanotube whose diameter exceeds dimensions conducive to single-file water movement. Our findings indicate that the extent of adsorption is decided by the degree of foldedness of the protein conformational substate. Importantly, we find that partially folded substates, but not the natively folded one, induce reorganization of the protein hydration layer into an inner layer water closer to the nanotube axis and an outer layer water in the interstitial space near the nanotube walls. Further analyses reveal sharp dynamical differences between water molecules in the two layers as observed in the onset of increased heterogeneity in rotational relaxation and the enhanced deviation from Fickian behavior. The vibrational density of states reveals that the dynamical distinctions are correlated with differences in crucial bands in the power spectra. The current results set the stage for further systematic studies of various BN interfaces vis-à-vis control of hydration properties.

Disulfide Reduction Allosterically Destabilizes the ß-Ladder Subdomain Assembly within the NS1 Dimer of ZIKV.

The Zika virus (ZIKV) was responsible for a recent debilitating epidemic that till date has no cure. A potential way to reduce ZIKV virulence is to limit the action of the nonstructural proteins involved in its viral replication. One such protein, NS1, encoded as a monomer by the viral genome, plays a major role via symmetric oligomerization. We examine the homodimeric structure of the dominant ß-ladder segment of NS1 with extensive all atom molecular dynamics. We find it stably bounded by two spatially separated interaction clusters (C1 and C2) with significant differences in the nature of their interactions. Four pairs of distal, intramonomeric disulfide bonds are found to be coupled to the stability, local structure, and wettability of the interfacial region. Symmetric reduction of the intramonomeric disulfides triggers marked dynamical heterogeneity, interfacial wettability, and asymmetric salt-bridging propensity. Harnessing the model-free Lipari-Szabo based formalism for estimation of conformational entropy (Sconf), we find clear signatures of heterogeneity in the monomeric conformational entropies. The observed asymmetry, very small in the unperturbed state, expands significantly in the reduced states. This allosteric effect is most noticeable in the electrostatically bound C2 cluster that underlies the greatest stability in the unperturbed state. Allosteric induction of conformational and thermodynamic asymmetry is expected to affect the pathways leading to symmetric higher-ordered oligomerization, and thereby affect crucial replication pathways.

Stromal ß-catenin activation impacts nephron progenitor differentiation in the developing kidney and may contribute to Wilms tumor.

Wilms' tumor (WT) morphologically resembles the embryonic kidney, consisting of blastema, epithelial and stromal components, suggesting tumors arise from the dysregulation of normal development. ß-Catenin activation is observed in a significant proportion of WTs; however, much remains to be understood about how it contributes to tumorigenesis. Although activating ß-catenin mutations are observed in both blastema and stromal components of WT, current models assume that activation in the blastemal lineage is causal. Paradoxically, studies performed in mice suggest that activation of ß-catenin in the nephrogenic lineage results in loss of nephron progenitor cell (NPC) renewal, a phenotype opposite to WT. Here, we show that activation of ß-catenin in the stromal lineage non-autonomously prevents the differentiation of NPCs. Comparisons of the transcriptomes of kidneys expressing an activated allele of ß-catenin in the stromal or nephron progenitor cells reveals that human WT more closely resembles the stromal-lineage mutants. These findings suggest that stromal ß-catenin activation results in histological and molecular features of human WT, providing insights into how alterations in the stromal microenvironment may play an active role in tumorigenesis.

A vivid cytokines interaction model on psoriasis with the effect of impulse biologic (TNF-α inhibitor) therapy.

Psoriasis is a chronic skin condition that produces plaques of condensed, scaling skin due to excessively rapid proliferation of keratinocytes. During the disease progression, keratinocyte proliferation is influenced by many immune cells and cytokines. This article deals with a five dimensional deterministic model, which has been derived using quasi-steady-state approximation for describing the dynamics of psoriasis in various cytokines environment. Equilibrium analysis of the system shows that either the system converges to a stable steady state or exhibits a periodic oscillation depending upon system parameters. Finally, introducing a one dimensional impulsive system, we have determined the perfect dose and perfect dosing interval for biologic (TNF-α inhibitor) therapy to control the hyper-proliferation of keratinocytes. We have studied the effect of TNF-α inhibitor by considering both perfect and imperfect dosing during the inductive phase. The maximum possible number of drug holidays and the minimal number of doses that must subsequently be taken while avoiding drug resistance have been calculated for imperfect dosing. Since, psoriasis is non-curable but treatable disease, so the aim is to investigate the minimum dose with highest efficacy and proper dosing interval of TNF-α inhibitor for a psoriatic patient. Through numerical simulations, we have given a detailed prediction about the maximum drug holidays, tolerable for a patient, without loss of previous drug effects. Our theoretical predictions and numerical outcomes may be useful in guiding the design of future clinical trials.

Cosolvent Impurities in SWCNT Nanochannel Confinement: Length Dependence of Water Dynamics Investigated with Atomistic Simulations.

The advent of nanotechnology has seen a growing interest in the nature of fluid flow and transport under nanoconfinement. The present study leverages fully atomistic molecular dynamics (MD) simulations to study the effect of nanochannel length and intrusion of molecules of the organic solvent, hexafluoro-2-propanol (HFIP), on the dynamical characteristics of water within it. Favorable interactions of HFIP with the nanochannels comprised of single-walled carbon nanotubes traps them over time scales greater than 100 ns, and confinement confers small but distinguishable spatial redistribution between neighboring HFIP pairs. Water molecules within the nanochannels show clear signatures of dynamical slowdown relative to bulk water even for pure systems. The presence of HFIP causes further rotational and translational slowdown in waters when the nanochannel dimension falls below a critical length of 30 Å. The enhanced slowdown in the presence of HFIP is quantified from characteristic relaxation parameters and diffusion coefficients in the absence and presence of HFIP. It is finally seen that the net flow of water between the ends of the nanochannel shows a decreasing dependence with nanochannel length only when the number of HFIP molecules is small. These results lend insights into devising ways of modulating solvent properties within nanochannels with cosolvent impurities.

Biological pest control using a model-based robust feedback.

Biological control is the artificial manipulation of natural enemies of a pest for its regulation to densities below a threshold for economic damage. The authors address the biological control of a class of pest population models using a model-based robust feedback approach. The proposed control framework is based on a recursive cascade control scheme exploiting the chained form of pest population models and the use of virtual inputs. The robust feedback is formulated considering the non-linear model uncertainties via a simple and intuitive control design. Numerical results on three pest biological control problems show that the proposed model-based robust feedback can regulate the pest population at the desired reference via the manipulation of a biological control action despite model uncertainties.

Mathematical insights on psoriasis regulation: Role of Th1 and Th2 cells.

Psoriasis is an autoimmune disorder, characterized by hyper-proli-feration of Keratinocytes for the abnormal activation of T Cells, Dendritic Cells (DCs) and cytokine signaling. Interaction of DCs and T Cells enable T Cell to differentiate into Type 1 (Th1), Type 2 (Th2) helper T Cell depending on cytokine release. Hyper-proliferation of Keratinocytes may occur due to over expression of pro-inflammatory cytokines secreted by Th1-Cells viz. Interferon gamma (IFN-γ), Transforming growth factor beta (TGF-ß) and Tumor necrosis factor alpha (TNF-α) etc. Deregulation of epidermal happens due to signaling of anti-inflammatory cytokines like Interleukin 10 (IL-10), Interleukin 4 (IL-4) etc., released by Th2-Cells. In this article, we have constructed a set of nonlinear differential equations involving the above cell population for better understanding the impact of cytokines on Psoriasis. System is analyzed introducing therapeutic agent (Biologic / IL-10) for reducing the hyper-proliferation of Keratinocytes. Effect of Biologic is used as a surrogate of control parameter to reduce the psoriatic lesions. We also studied its effect both in continuous and impulsive dosing method. Our study reveals that impulsive dosing is more applicable compare with continuous dosing to prevent Psoriasis.

Human immunodeficiency virus/acquired immune deficiency syndrome: Using drug from mathematical perceptive.

Entry of acquired immune deficiency syndrome virus into the host immune cell involves the participation of various components of host and viral cell unit. These components may be categorized as attachment of the viral surface envelope protein subunit, gp120, to the CD4(+) receptor and chemokine coreceptors, CCR5 and CXCR4, present on T cell surface. The viral fusion protein, gp41, the second cleaved subunit of Env undergoes reconfiguration and the membrane fusion reaction itself. Since the CD4(+) T cell population is actively involved; the ultimate outcome of human immunodeficiency virus infection is total collapse of the host immune system. Mathematical modeling of the stages in viral membrane protein-host cell receptor-coreceptor interaction and the effect of antibody vaccine on the viral entry into the susceptible host cell has been carried out using as impulsive differential equations. We have studied the effect of antibody vaccination and determined analytically the threshold value of drug dosage and dosing interval for optimum levels of infection. We have also investigated the effect of perfect adherence of drug dose on the immune cell count in extreme cases and observed that systematic drug dosage of the immune cells leads to longer and improved lives.