Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area

Protein Pattern Formation

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in \textit{E. coli} whose biological function is to ensure precise cell division. Cell polarization, a prerequisite for processes such as stem cell differentiation and cell polarity in yeast, is also mediated by a diffusion-reaction process. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Under which conditions spatio-temporal patterns emerge, and how these patterns are regulated by biochemical and geometrical factors are major aspects of current research. Here we review recent theoretical and experimental advances in the field of intracellular pattern formation, focusing on general design principles and fundamental physical mechanisms.Comment: 17 pages, 14 figures, review articl

Thermal inactivation and conformational lock studies on glucose oxidase

In this study, the dissociative thermal inactivation and conformational lock theories are applied for the homodimeric enzyme glucose oxidase (GOD) in order to analyze its structure. For this purpose, the rate of activity reduction of glucose oxidase is studied at various temperatures using b-D-glucose as the substrate by incubation of enzyme at various temperatures in the wide range between 40 and 70 �C using UV–Vis spectrophotometry. It was observed that in the two ranges of temperatures, the enzyme has two different forms. In relatively low temperatures, the enzyme is in its dimeric state and has normal activity. In high temperatures, the activity almost disappears and it aggregates. The above achievements are confirmed by dynamic light scattering. The experimental parameter ‘‘n’’ as the obvious number of conformational locks at the dimer interface of glucose oxidase is obtained by kinetic data, and the value is near to two. To confirm the above results, the X-ray crystallography structure of the enzyme, GOD (pdb, 1gal), was also studied. The secondary and tertiary structures of the enzyme to track the thermal inactivation were studied by circular dichroism and fluorescence spectroscopy, respectively. We proposed a mechanism model for thermal inactivation of GOD based on the absence of the monomeric form of the enzyme by circular dichroism and fluorescence spectroscopy

The interplay of intrinsic and extrinsic bounded noises in genetic networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises

Measurements of Deuteron Photodisintegration up to 4.0 GeV

The first measurements of the differential cross section for the d(gamma,p)n reaction up to 4.0 GeV were performed at Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab. We report the cross sections at the proton center-of-mass angles of 36, 52, 69 and 89 degrees. These results are in reasonable agreement with previous measurements at lower energy. The 89 and 69 degree data show constituent-counting-rule behavior up to 4.0 GeV photon energy. The 36 and 52 degree data disagree with the counting rule behavior. The quantum chromodynamics (QCD) model of nuclear reactions involving reduced amplitudes disagrees with the present data.Comment: 5 pages (REVTeX), 1 figure (postscript

Spin Structure of the Proton from Polarized Inclusive Deep-Inelastic Muon-Proton Scattering

We have measured the spin-dependent structure function $g_1^p$ in inclusive deep-inelastic scattering of polarized muons off polarized protons, in the kinematic range $0.003 < x < 0.7$ and $1 GeV^2 < Q^2 < 60 GeV^2$. A next-to-leading order QCD analysis is used to evolve the measured $g_1^p(x,Q^2)$ to a fixed $Q^2_0$. The first moment of $g_1^p$ at $Q^2_0 = 10 GeV^2$ is $\Gamma^p = 0.136\pm 0.013(stat.) \pm 0.009(syst.)\pm 0.005(evol.)$. This result is below the prediction of the Ellis-Jaffe sum rule by more than two standard deviations. The singlet axial charge $a_0$ is found to be $0.28 \pm 0.16$. In the Adler-Bardeen factorization scheme, $\Delta g \simeq 2$ is required to bring $\Delta \Sigma$ in agreement with the Quark-Parton Model. A combined analysis of all available proton and deuteron data confirms the Bjorken sum rule.Comment: 33 pages, 22 figures, uses ReVTex and smc.sty. submitted to Physical Review

Two body photodisintegration of the deuteron up to 2.8 GeV

Measurements were performed for the photodisintegration cross section of the deuteron for photon energies from 1.6 to 2.8 GeV and center-of-mass angles from 37° to 90°. The measured energy dependence of the cross section at θ_(cm)=90° is in agreement with the constituent counting rules

Wild-Type Phosphoribosylpyrophosphate Synthase (PRS) from Mycobacterium tuberculosis: A Bacterial Class II PRS?

The 5-phospho-α-D-ribose 1-diphosphate (PRPP) metabolite plays essential roles in several biosynthetic pathways, including histidine, tryptophan, nucleotides, and, in mycobacteria, cell wall precursors. PRPP is synthesized from α-D-ribose 5-phosphate (R5P) and ATP by the Mycobacterium tuberculosis prsA gene product, phosphoribosylpyrophosphate synthase (MtPRS). Here, we report amplification, cloning, expression and purification of wild-type MtPRS. Glutaraldehyde cross-linking results suggest that MtPRS predominates as a hexamer, presenting varied oligomeric states due to distinct ligand binding. MtPRS activity measurements were carried out by a novel coupled continuous spectrophotometric assay. MtPRS enzyme activity could be detected in the absence of Pi. ADP, GDP and UMP inhibit MtPRS activity. Steady-state kinetics results indicate that MtPRS has broad substrate specificity, being able to accept ATP, GTP, CTP, and UTP as diphosphoryl group donors. Fluorescence spectroscopy data suggest that the enzyme mechanism for purine diphosphoryl donors follows a random order of substrate addition, and for pyrimidine diphosphoryl donors follows an ordered mechanism of substrate addition in which R5P binds first to free enzyme. An ordered mechanism for product dissociation is followed by MtPRS, in which PRPP is the first product to be released followed by the nucleoside monophosphate products to yield free enzyme for the next round of catalysis. The broad specificity for diphosphoryl group donors and detection of enzyme activity in the absence of Pi would suggest that MtPRS belongs to Class II PRS proteins. On the other hand, the hexameric quaternary structure and allosteric ADP inhibition would place MtPRS in Class I PRSs. Further data are needed to classify MtPRS as belonging to a particular family of PRS proteins. The data here presented should help augment our understanding of MtPRS mode of action. Current efforts are toward experimental structure determination of MtPRS to provide a solid foundation for the rational design of specific inhibitors of this enzyme

Burden of Illness and Quality of Life in Tuberous Sclerosis Complex: Findings From the TOSCA Study

Research on tuberous sclerosis complex (TSC) to date has focused mainly on the physical manifestations of the disease. In contrast, the psychosocial impact of TSC has received far less attention. The aim of this study was therefore to examine the impact of TSC on health, quality of life (QoL), and psychosocial well-being of individuals with TSC and their families. Questionnaires with disease-specific questions on burden of illness (BOI) and validated QoL questionnaires were used. After completion of additional informed consent, we included 143 individuals who participated in the TOSCA (TuberOus SClerosis registry to increase disease Awareness) study. Our results highlighted the substantial burden of TSC on the personal lives of individuals with TSC and their families. Nearly half of the patients experienced negative progress in their education or career due to TSC (42.1%), as well as many of their caregivers (17.6% employed; 58.8% unemployed). Most caregivers (76.5%) indicated that TSC affected family life, and social and working relationships. Further, well-coordinated care was lacking: a smooth transition from pediatric to adult care was mentioned by only 36.8% of adult patients, and financial, social, and psychological support in 21.1, 0, and 7.9%, respectively. In addition, the moderate rates of pain/discomfort (35%) and anxiety/depression (43.4%) reported across all ages and levels of disease demonstrate the high BOI and low QoL in this vulnerable population