Some novel techniques of parameter estimation for the dynamical models in biological systems

Inverse problems based on using experimental data to estimate unknown parameters of a system often arise in biological and chaotic systems. In this paper, we consider parameter estimation in systems biology involving linear and non-linear complex dynamical models, including the Michaelis–Menten enzyme kinetic system, a dynamical model of competence induction in Bacillus subtilis bacteria and a model of feedback bypass in B. subtilis bacteria. We propose some novel techniques for inverse problems. Firstly, we establish an approximation of a non-linear differential algebraic equation that corresponds to the given biological systems. Secondly, we use the Picard contraction mapping, collage methods and numerical integration techniques to convert the parameter estimation into a minimization problem of the parameters. We propose two optimization techniques: a grid approximation method and a modified hybrid Nelder–Mead simplex search and particle swarm optimization (MH-NMSS-PSO) for non-linear parameter estimation. The two techniques are used for parameter estimation in a model of competence induction in B. subtilis bacteria with noisy data. The MH-NMSS-PSO scheme is applied to a dynamical model of competence induction in B. subtilis bacteria based on experimental data and the model for feedback bypass. Numerical results demonstrate the effectiveness of our approach.

Development of a colorimetric assay for heparanase activity suitable for kinetic analysis and inhibitor screening

The role that heparanase plays during metastasis and angiogenesis in tumors makes it an attractive target for cancer therapeutics. Despite this enzyme’s significance, most of the assays developed to measure its activity are complex. Moreover, they usually rely on labeling variable preparations of the natural substrate heparan sulfate, making comparisons across studies precarious. To overcome these problems, we have developed a convenient assay based on the cleavage of the synthetic heparin oligosaccharide fondaparinux. The assay measures the appearance of the disaccharide product of heparanase-catalyzed fondaparinux cleavage colorimetrically using the tetrazolium salt WST-1. Because this assay has a homogeneous substrate with a single point of cleavage, the kinetics of the enzyme can be reliably characterized, giving a Km of 46 μM and a kcat of 3.5 s−1 with fondaparinux as substrate. The inhibition of heparanase by the published inhibitor, PI-88, was also studied, and a Ki of 7.9 nM was determined. The simplicity and robustness of this method, should, not only greatly assist routine assay of heparanase activity but also could be adapted for high-throughput screening of compound libraries, with the data generated being directly comparable across studies.

Modulation of the SHBG signalling axis

Sex hormone-binding globulin (SHBG) is a homodimeric plasma glycoprotein that is the major sex steroid carrier-protein in the bloodstream and functions also as a key regulator of steroid bioavailability within target tissues, such as the prostate. Additionally, SHBG binds to prostatic cell membranes via the putative and unidentified SHBG receptor (RSHBG), activating a signal transduction pathway implicated in stimulating both proliferation and expression of prostate specific antigen (PSA) in prostate cell lines in vitro. A yeast-two hybrid assay suggested an interaction between SHBG and kallikrein-related protease (KLK) 4, which is a serine protease implicated in the progression of prostate cancer. The potential interaction between these two proteins was investigated in this PhD thesis to determine whether SHBG is a proteolytic substrate of KLK4 and other members of the KLK family including KLK3/PSA, KLK7 and KLK14. Furthermore, the effects from SHBG proteolytic degradation on SHBG-regulated steroid bioavailability and the activation of the putative RSHBG signal transduction pathway were examined in the LNCaP prostate cancer cell line. SHBG was found to be a proteolytic substrate of the trypsin-like KLK4 and KLK14 in vitro, yielding several proteolysis fragments. Both chymotrypsin-like PSA and KLK7 displayed insignificant proteolytic activity against SHBG. The kinetic parameters of SHBG proteolysis by KLK4 and KLK14 demonstrate a strong enzyme-substrate binding capacity, possessing a Km of 1.2 ± 0.7 µM and 2.1 ± 0.6 µM respectively. The catalytic efficiencies (kcat/Km) of KLK4 and KLK14 proteolysis of SHBG were 1.6 x 104 M-1s-1 and 3.8 x 104 M-1s-1 respectively, which were comparable to parameters previously reported for peptide substrates. N-terminal sequencing of the fragments revealed cleavage near the junction of the N- and C-terminal laminin globulin-like (G-like) domains of SHBG, resulting in the division of the two globulins and ultimately the full degradation of these fragments by KLK4 and KLK14 over time. Proteolytic fragments that may retain steroid binding were rapidly degraded by both proteases, while fragments containing residues beyond the steroid binding pocket were less degraded over the same period of time. Degradation of SHBG was inhibited by the divalent metal cations calcium and zinc for KLK4, and calcium, zinc and magnesium for KLK14. The human secreted serine protease inhibitors (serpins), α1-antitrypsin and α2-antiplasmin, inhibited KLK4 and KLK14 proteolysis of SHBG; α1-antichymotrypsin inhibited KLK4 but not KLK14 activity. The inhibition by these serpins was comparable and in some cases more effective than general trypsin protease inhibitors such as aprotinin and phenylmethanesulfonyl fluoride (PMSF). The binding of 5α-dihydrotestosterone (DHT) to SHBG modulated interactions with KLK4 and KLK14. Steroid-free SHBG was more readily digested by both enzymes than DHT-bound SHBG. Moreover, a binding interaction exists between SHBG and pro-KLK4 and pro-KLK14, with DHT strengthening the binding to pro-KLK4 only. The inhibition of androgen uptake by cultured prostate cancer cells, mediated by SHBG steroid-binding, was examined to assess whether SHBG proteolysis by KLK4 and KLK14 modulated this process. Proteolytic digestion eliminated the ability of SHBG to inhibit the uptake of DHT from conditioned media into LNCaP cells. Therefore, the proteolysis of SHBG by KLK4 and KLK14 increased steroid bioavailability in vitro, leading to an increased uptake of androgens by prostate cancer cells. Interestingly, different transcriptional responses of PSA and KLK2, which are androgen-regulated genes, to DHT-bounsd SHBG treatment were observed between low and high passage number LNCaP cells (lpLNCaP and hpLNCaP respectively). HpLNCaP cells treated with DHT-bound SHBG demonstrated a significant synergistic upregulation of PSA and KLK2 above DHT or SHBG treatment alone, which is similar to previously reported downstream responses from RSHBG-mediated signaling activation. As this result was not seen in lpLNCaP cells, only hpLNCaP cells were further investigated to examine the modulation of potential RSHBG activity by KLK4 and KLK14 proteolysis of SHBG. Contrary to reported results, no increase in intracellular cAMP was observed in hpLNCaP cells when treated with SHBG in the presence and absence of either DHT or estradiol. As a result, the modulation of RSHBG-mediated signaling activation could not be determined. Finally, the identification of the RSHBG from both breast (MCF-7) and prostate cancer (LNCaP) cell lines was attempted. Fluorescently labeled peptides corresponding to the putative receptor binding domain (RBD) of SHBG were shown to be internalized by MCF-7 cells. Crosslinking of the RBD peptide to the cell surfaces of both MCF-7 and LNCaP cells, demonstrated the interaction of the peptide with several targets. These targets were then captured using RBD peptides synthesized onto a hydrophilic scaffold and analysed by mass spectrometry. The samples captured by the RBD peptide returned statistically significantly matches for cytokeratin 8, 18 and 19 as well as microtubule-actin crosslinking factor 1, which may indicate a novel interaction between SHBG and these proteins, but ultimately failed to detect a membrane receptor potentially responsible for the putative RSHBG-mediated signaling. This PhD project has reported the proteolytic processing of SHBG by two members of the kallikrein family, KLK4 and KLK14. The effect of SHBG proteolysis by KLK4 and KLK14 on RSHBG-mediated signaling activation was unable to be determined as the reported signal transduction pathway was not activated after treatment with SHBG, in combination with either DHT or estradiol. However, the digestion of SHBG by these two proteases positively regulated androgen bioavailability to prostate cancer cells in vitro. The increased uptake of androgens is deleterious in prostate cancer due to the promotion of proliferation, metastasis, invasion and the inhibition of apoptosis. The increased bioavailability of androgens, from SHBG proteolysis by KLK4 and KLK14, may therefore promote both carcinogenesis and progression of prostate cancer. Finally, this information may contribute to the development of therapeutic treatment strategies for prostate cancer by inhibiting the proteolysis of SHBG, by KLK4 and KLK14, to prevent the increased uptake of androgens by hormone-dependent cancerous tissues.

A differential kinetic spectrophotometric method for determination of three sulphanilamide artificial sweeteners with the aid of chemometrics

A simple and sensitive spectrophotometric method for the simultaneous determination of acesulfame-K, sodium cyclamate and saccharin sodium sweeteners in foodstuff samples has been researched and developed. This analytical method relies on the different kinetic rates of the analytes in their oxidative reaction with KMnO4 to produce the green manganate product in an alkaline solution. As the kinetic rates of acesulfame-K, sodium cyclamate and saccharin sodium were similar and their kinetic data seriously overlapped, chemometrics methods, such as partial least squares (PLS), principal component regression (PCR) and classical least squares (CLS), were applied to resolve the kinetic data. The results showed that the PLS prediction model performed somewhat better. The proposed method was then applied for the determination of the three sweeteners in foodstuff samples, and the results compared well with those obtained by the reference HPLC method.

Simultaneous kinetic-spectrophotometric determination of maltol and ethyl maltol in food samples by using chemometrics

A fast and accurate procedure has been researched and developed for the simultaneous determination of maltol and ethyl maltol, based on their reaction with iron(III) in the presence of o-phenanthroline in sulfuric acid medium. This reaction was the basis for an indirect kinetic spectrophotometric method, which followed the development of the pink ferroin product (λmax = 524 nm). The kinetic data were collected in the 370–900 nm range over 0–30 s. The optimized method indicates that individual analytes followed Beer’s law in the concentration range of 4.0–76.0 mg L−1 for both maltol and ethyl maltol. The LOD values of 1.6 mg L−1 for maltol and 1.4 mg L−1 for ethyl maltol agree well with those obtained by the alternative high performance liquid chromatography with ultraviolet detection (HPLC-UV). Three chemometrics methods, principal component regression (PCR), partial least squares (PLS) and principal component analysis–radial basis function–artificial neural networks (PC–RBF–ANN), were used to resolve the measured data with small kinetic differences between the two analytes as reflected by the development of the pink ferroin product. All three performed satisfactorily in the case of the synthetic verification samples, and in their application for the prediction of the analytes in several food products. The figures of merit for the analytes based on the multivariate models agreed well with those from the alternative HPLC-UV method involving the same samples.

Simultaneous kinetic spectrophotometric determination of norfloxacin and rifampicin in pharmaceutical formulation and human urine samples by use of chemometrics approaches

A kinetic spectrophotometric method with aid of chemometrics is proposed for the simultaneous determination of norfloxacin and rifampicin in mixtures. The proposed method was applied for the simultaneous determination of these two compounds in pharmaceutical formulation and human urine samples, and the results obtained are similar to those obtained by high performance liquid chromatography.

Multicomponent kinetic spectrophotometric determination of pefloxacin and norfloxacin in pharmaceutical preparations and human plasma samples with the aid of chemometrics

A spectrophotometric method for the simultaneous determination of the important pharmaceuticals, pefloxacin and its structurally similar metabolite, norfloxacin, is described for the first time. The analysis is based on the monitoring of a kinetic spectrophotometric reaction of the two analytes with potassium permanganate as the oxidant. The measurement of the reaction process followed the absorbance decrease of potassium permanganate at 526 nm, and the accompanying increase of the product, potassium manganate, at 608 nm. It was essential to use multivariate calibrations to overcome severe spectral overlaps and similarities in reaction kinetics. Calibration curves for the individual analytes showed linear relationships over the concentration ranges of 1.0–11.5 mg L−1 at 526 and 608 nm for pefloxacin, and 0.15–1.8 mg L−1 at 526 and 608 nm for norfloxacin. Various multivariate calibration models were applied, at the two analytical wavelengths, for the simultaneous prediction of the two analytes including classical least squares (CLS), principal component regression (PCR), partial least squares (PLS), radial basis function-artificial neural network (RBF-ANN) and principal component-radial basis function-artificial neural network (PC-RBF-ANN). PLS and PC-RBF-ANN calibrations with the data collected at 526 nm, were the preferred methods—%RPET not, vert, similar 5, and LODs for pefloxacin and norfloxacin of 0.36 and 0.06 mg L−1, respectively. Then, the proposed method was applied successfully for the simultaneous determination of pefloxacin and norfloxacin present in pharmaceutical and human plasma samples. The results compared well with those from the alternative analysis by HPLC.