Computational methods for yeast prion curing curves

If the chemical guanidine hydrochloride is added to a dividing culture of yeast cells in which some of the protein Sup35p is in its prion form, the proportion of cells that carry replicating units of the prion, termed propagons, decreases gradually over time. Stochastic models to describe this process of ‘curing’ have been developed in earlier work. The present paper investigates the use of numerical methods of Laplace transform inversion to calculate curing curves and contrasts this with an alternative, more direct, approach that involves numerical integration. Transform inversion is found to provide a much more efficient computational approach that allows different models to be investigated with minimal programming effort. The method is used to investigate the robustness of the curing curve to changes in the assumed distribution of cell generation times. Matlab code is available for carrying out the calculations.     

A New Approach to Epithelial Isotonic Fluid Transport: An Osmosensor Feedback Model

A model for control of the transport rate and osmolarity of epithelial fluid (isotonic transport) is presented by using an analogy with the control of temperature and flow rate in a shower. The model brings recent findings and theory concerning the role of aquaporins in epithelia together with measurements of epithelial paracellular flow into a single scheme. It is not based upon osmotic equilibration across the epithelium but rather on the function of aquaporins as osmotic sensors that control the tonicity of the transported fluid by mixing cellular and paracellular flows, which may be regarded individually as hyper- and hypo-tonic fluids, to achieve near-isotonicity. The system is built on a simple feedback loop and the quasi-isotonic behavior is robust to the precise values of most parameters. Although the two flows are separate, the overall fluid transport rate is governed by the rate of salt pumping through the cell. The model explains many things: how cell pumping and paracellular flow can be coupled via control of the tight junctions; how osmolarity is controlled without depending upon the precise magnitude of membrane osmotic permeability; and why many epithelia have different aquaporins at the two membranes.The model reproduces all the salient features of epithelial fluid transport seen over many years but also indicates novel behavior that may provide a subject for future research and serve to distinguish it from other schemes such as simple osmotic equilibration. Isotonic transport is freed from constraints due to limited permeability of the membranes and the precise geometry of the system. It achieves near-isotonicity in epithelia in which partial water transport by co-transporters may be present, and shows apparent electro-osmotic effects. The model has been developed with a minimum of parameters, some of which require measurement, but the model is flexible enough for the basic idea to be extended both to complex systems of water and salt transport that still await a clear explanation, such as intestine and airway, and to systems that may lack aquaporins or use other sensors.     

A central role for cell osmolarity in isotonic fluid transport across epithelia

Previous theoretical models for solute-solvent coupling in epithelia that dealt only with the intercellular channel did not predict isotonic transport except when very high cell membrane permeabilities were assumed. To study this issue, we have developed the formalisms for osmotic equilibration at an alternative location, the apical cell membrane (including its adjacent unstirred layer), which are somewhat simpler than those for the channel. Much as in other models, we confirm that only rather unrealistically high values of the cell membrane permeability lead to isotonic transport. We have also found, however, that isotonic transport can occur at much lower values of the cell membrane permeability if the concentration within the cell differs slightly from that in the ambient medium. This emphasizes the importance of incorporating the intracellular concentration as an integral part to any transport model, such as in the present apical membrane version of local osmosis.     

Creatine and creatinine transport in old and young human red blood cells

The time course of creatine influx or efflux as measured in populations of red cells or red cell ghosts with normal age distribution does not follow simple two-compartment kinetics. This suggests that the contributions of individual cells to transport as measured in the populations as a whole are not uniform. In agreement with this inference, fractionation of red cell populations with respect to cell age shows that transport in young cells is considerably faster than in old cells.The dependence of creatine transport on creatine concentration in the medium follows an equation that can be interpreted to represent a super-imposition of a saturable component (apparent K_m = 0.02 mM) and another component that cannot be saturated up to a creatine concentration of 5.0 mM. In contrast to the non-saturable component, the saturable component depends on the energy metabolism of the cell and can be inhibited by β-guanidinopropionic acid and the proteolytic enzyme pronase. This latter finding suggests that the saturable component represents active transport that is mediated by a transport protein. The non-saturable component is little, if at all, dependent on cell age while the saturable component is higher in young cells than in old cells. Phloretin inhibits both components of creatine flux, but the maximal inhibition that can be achieved at high concentration is only 70–80%.Under the experimental conditions used for the study of creatine transport, creatinine equilibration between cells and medium follows the kinetics expected for a steady-state two-compartment system. Creatinine flux is proportional to creatine concentration over the concentration range studied (up to 5 mM). It cannot be inhibited by β-guanidinopropionic acid or pronase.     

Entropy effects on the ion-diffusion rate in transmembrane protein channels

We treat the transport of univalent cations through pore-like protein channels in biological membranes analytically, using two models (A + B) for the channel and the ion-channel interaction. A Lennard-Jones-type repulsion between the ions and the pore wall is introduced. We also include Van der Waals- and coulomb-type interactions between polar ligands of the pore-forming protein (e.g., carbonyl groups directed towards the axis of the channel) and the migrating particles. In model A, the polar groups are assumed to occur in pairs of dipoles pointing in opposite directions (as in the gramicidin A channel), while in model B the channel is treated as a pore with a radially isotropic charge distribution. In both models the ion-channel interaction leads to the occurrence of periodic potentials, corresponding to quasi-equilibrium and transition state sites of the ion in the pore. The diffusion rate can be calculated employing rate-theoretical concepts on the basis of microscopic parameters. It is demonstrated that the anomaly (inversion of the normal mass effect) for the transport rates of different ions can be related to differences in the activation entropy. The latter quantity is estimated analytically for both models. As a test, we performed numerical calculations with parameters based on the gramicidin A model. The results are in good agreement with experimental data and data from computer simulations. This shows that simple analytic expressions are well suited for predicting trends in the ionic conductivity of protein channels on the basis of microscopic interactions.     

Descriptive parameter evaluation in mammalian cell culture

Several methods exist for assessing population growth and protein productivity in mammalian cell culture. These methods were critically examined here, based on experiments with two hybridoma cell lines. It is shown that mammalian cell culture parameters must be evaluated on the same basis. In batch culture mode most data is obtained on a cumulative basis (protein product titre, substrate concentration, metabolic byproduct concentration). A simple numerical integration technique can be employed to convert cell concentration data to a cumulative basis (cell-hours). The hybridoma lines used in this study included a nutritionally non-fastidious line producing low levels of MAb and a nutritionally fastidious hybridoma with high productivity. In both cases the cell-hour approach was the most appropriate means of expressing the relationship between protein productivity and cell population dynamics. The cell-hour approach could be used as the basis for all metabolic population parameter evaluations. This method has the potential to be used successfully for both prediction and optimization purposes. This revised version was published online in August 2006 with corrections to the Cover Date.     

Comparing a discrete and continuum model of the intestinal crypt

The integration of processes at different scales is a key problem in the modelling of cell populations. Owing to increased computational resources and the accumulation of data at the cellular and subcellular scales, the use of discrete, cell-level models, which are typically solved using numerical simulations, has become prominent. One of the merits of this approach is that important biological factors, such as cell heterogeneity and noise, can be easily incorporated. However, it can be difficult to efficiently draw generalizations from the simulation results, as, often, many simulation runs are required to investigate model behaviour in typically large parameter spaces. In some cases, discrete cell-level models can be coarse-grained, yielding continuum models whose analysis can lead to the development of insight into the underlying simulations. In this paper we apply such an approach to the case of a discrete model of cell dynamics in the intestinal crypt. An analysis of the resulting continuum model demonstrates that there is a limited region of parameter space within which steady-state (and hence biologically realistic) solutions exist. Continuum model predictions show good agreement with corresponding results from the underlying simulations and experimental data taken from murine intestinal crypts.     

Heat transport mechanisms in vascular tissues: a model comparison

We have conducted a parametric comparison of three different vascular models for describing heat transport in tissue. Analytical and numerical methods were used to predict the gross temperature distribution throughout the tissue and the small-scale temperature gradients associated with thermally significant blood vessels. The models are: an array of unidirectional vessels, an array of countercurrent vessels, and a set of large vessels feeding small vessels which then drain into large vessels. We show that three continuum formulations of bioheat transfer (directed perfusion, effective conductivity, and a temperature-dependent heat sink) are limiting cases of the vascular models with respect to the thermal equilibration length of the vessels. When this length is comparable to the width of the heated region of tissue, the local temperature changes near the vessels can be comparable to the gross temperature elevation. These results are important to the use of thermal techniques used to measure the blood perfusion rate and in the treatment of cancer with local hyperthermia.     

Towards building the silicon cell: a modular approach

Systems Biology aims to understand quantitatively how properties of biological systems can be understood as functions of the characteristics of, and interactions between their macromolecular components. Whereas, traditional biochemistry focused on isolation and characterization of cellular components, the challenge for Systems Biology lies in integration of this knowledge and the knowledge about molecular interactions. Computer models play an important role in this integration. We here discuss an approach with which we aim to link kinetic models on small parts of metabolism together, so as to form detailed kinetic models of larger chunks of metabolism, and ultimately of the entire living cell. Specifically, we will discuss techniques that can be used to model a sub-network in isolation of a larger network of which it is a part, while still maintaining the dynamics of the larger complete network. We will start by outlining the JWS online system, the silicon cell project, and the type of models we propose. JWS online is a model repository, which can be used for the storage, simulation and analysis of kinetic models. We advocate to integrate a top-down approach, where measurements on the complete system are used to derive fluxes in a detailed structural model, with a bottom-up approach, consisting of the integration of molecular mechanism-based detailed kinetic models into the structural model.     

D-glucose permeability in river lamprey (Lampetra fluviatilis) and carp (Cyprinus carpio) erythrocytes.

1. The transport of 3-O-methyl-D-glucose (3-OMG) in lamprey and carp erythrocytes was studied. 2. In lamprey erythrocytes the half-time for the equilibration of 3-OMG was fast, approx. 8 min. In contrast, the erythrocytes of carp were almost impermeable to 3-OMG, with a half-time for equilibration of 14.2 hr. 3. 3-OMG was taken up by lamprey erythrocytes both by facilitated diffusion and simple diffusion. The presence of carrier-mediated transport was indicated by saturation kinetics and by inhibition by phloretin. The Km and Vm of the saturable component of 3-OMG transport were 1.6 mmol/l and 12.4 mmol/kg packed cells/hr. 4. Since the 3-OMG transport in carp erythrocytes showed no sign of saturation kinetics, it appears to proceed by simple diffusion only. 5. These results suggest that, as for most other teleost fish so far studied, low glucose permeability is insufficient to maintain normal energy metabolism in carp erythrocytes. In contrast, in agnathans facilitated glucose transport seems to be quite effective.     

Solution of large compartmental models using numerical transform inversion

Compartmental models of biological or physical systems are often described by a system of “stiff” differential equations. In this paper an algorithm for solving a system with linear coefficients is presented that employs numerical inversion of the Laplace transform of the model equations. The inversion algorithms and Gear's backward differentiation method are compared for two stiff test problems and a differential system governing a 27-compartment model of bile acid transport and metabolism. The inversion algorithm is reliable, requires modest computation time on a desktop computer and provides better accuracy than Gear's method, especially for the extremely stiff example.     

General tissue mass transfer model for cryopreservation applications

Successful cryopreservation of complex specimens, such as tissues and organs, would greatly benefit both the medical and scientific research fields. Vitrification is one of the most promising techniques for complex specimen cryopreservation, but toxicity remains a major challenge because of the high concentration of cryoprotectants (CPAs) needed to vitrify. Our group has approached this problem using mathematical optimization to design less toxic CPA equilibration methods for cells. To extend this approach to tissues, an appropriate mass transfer model is required. Fick’s law is commonly used, but this simple modeling framework does not account for the complexity of mass transfer in tissues, such as the effects of fixed charges, tissue size changes, and the interplay between cell membrane transport and transport through the extracellular fluid. Here, we propose a general model for mass transfer in tissues that accounts for all of these phenomena. To create this model, we augmented a previously published acellular model of mass transfer in articular cartilage to account for the effects of cells. We show that the model can accurately predict changes in CPA concentration and tissue size for both articular cartilage and pancreatic islets, tissue types with vastly different properties.     

Analytical Integration Procedures for the Derivation of Risk-Based Generic Assessment Criteria for Soil

Risk assessment models commonly used in contaminated sites employ a simple integration procedure by only partially combining exposure pathways from surface soil with vapor pathways from subsurface soil being excluded in the combination. The simplified approach can approximate the integrated generic assessment criteria only when there is a dominant exposure pathway. But these models are often based on a simple partitioning of a chemical in soil between the sorbed, dissolved, and vapor phases without consideration of the presence of non-aqueous phase liquid, and critically fail to consider non-soil background exposure for non-carcinogenic compounds. As a result, the generic assessment criteria derived may not be considered protective of human health. This article describes analytical integration procedures for the derivation of the generic assessment criteria that consider non-soil background exposure while limiting the average daily exposure for vapor pathways calculated from soil saturation limits. Significance of consideration of soil saturation limits for the derivation of the generic assessment criteria using an integrated approach is illustrated for organic compounds having varied levels of background exposure and soil saturations. The analytical integration procedures for the derivation of the soil generic assessment criteria under the linear chemical partition approach are also reviewed aiming to provide a single source of complete integration procedures for the derivation of the integrated generic assessment criteria.     

Simple model for encoding natural images by retinal ganglion cells with nonlinear spatial integration

A central goal in sensory neuroscience is to understand the neuronal signal processing involved in the encoding of natural stimuli. A critical step towards this goal is the development of successful computational encoding models. For ganglion cells in the vertebrate retina, the development of satisfactory models for responses to natural visual scenes is an ongoing challenge. Standard models typically apply linear integration of visual stimuli over space, yet many ganglion cells are known to show nonlinear spatial integration, in particular when stimulated with contrast-reversing gratings. We here study the influence of spatial nonlinearities in the encoding of natural images by ganglion cells, using multielectrode-array recordings from isolated salamander and mouse retinas. We assess how responses to natural images depend on first- and second-order statistics of spatial patterns inside the receptive field. This leads us to a simple extension of current standard ganglion cell models. We show that taking not only the weighted average of light intensity inside the receptive field into account but also its variance over space can partly account for nonlinear integration and substantially improve response predictions of responses to novel images. For salamander ganglion cells, we find that response predictions for cell classes with large receptive fields profit most from including spatial contrast information. Finally, we demonstrate how this model framework can be used to assess the spatial scale of nonlinear integration. Our results underscore that nonlinear spatial stimulus integration translates to stimulation with natural images. Furthermore, the introduced model framework provides a simple, yet powerful extension of standard models and may serve as a benchmark for the development of more detailed models of the nonlinear structure of receptive fields.     

A Simple Illustration of the Failure of PQL,IRREML and APHL as Approximate ML Methods for Mixed Models for Binary Data

Evaluation of the likelihood in mixed models for non-normal data, e.g. dependent binary data, involves high dimensional integration, which offers severe numerical problems. Penalized quasi-likelihood, iterative re-weighted restricted maximum likelihood and adjusted profile h-likelihood estimation are methods which avoid numerical integration. They will be derived by approximation of the maximum likelihood equations. For binary data, these estimation procedures may yield seriously biased estimates for components of variance, intra-class correlation or heritability. An analytical evaluation of a simple example illustrates how very critical the approximations can be for the performance of the variance component estimators.     

The influence of transport on the kinetics of binding to surface receptors: application to cells and BIAcore

Accurate estimation of biomolecular reaction rates from binding data, when ligands in solution bind to receptors on the surfaces of cells or biosensors, requires an understanding of the contributions of both molecular transport and reaction. Efficient estimation of parameters requires relatively simple models. In this review, we give conditions under which various transport effects are negligible and identify simple binding models that incorporate the effects of transport, when transport cannot be neglected. We consider effects of diffusion of ligands to cell or biosensor surfaces, flow in a BIAcore biosensor, and distribution of receptors in a dextran layer above the sensor surface. We also give conditions under which soluble receptors can be expected to compete effectively with surface-bound receptors.     

Hypothesis testing via integrated computer modeling and digital fluorescence microscopy

Computational modeling has the potential to add an entirely new approach to hypothesis testing in yeast cell biology. Here, we present a method for seamless integration of computational modeling with quantitative digital fluorescence microscopy. This integration is accomplished by developing computational models based on hypotheses for underlying cellular processes that may give rise to experimentally observed fluorescent protein localization patterns. Simulated fluorescence images are generated from the computational models of underlying cellular processes via a "model-convolution" process. These simulated images can then be directly compared to experimental fluorescence images in order to test the model. This method provides a framework for rigorous hypothesis testing in yeast cell biology via integrated mathematical modeling and digital fluorescence microscopy.     

Tailoring broadband inversion pulses for MAS Solid state NMR

A simple approach is demonstrated for designing optimised broadband inversion pulses for MAS solid state NMR studies of biological systems. The method involves a two step numerical optimisation procedure and takes into account experimental requirements such as the pulse length, resonance offset range and extent of H₁ inhomogeneity compensation needed. A simulated annealing protocol is used initially to find appropriate values for the parameters that define the well known tanh/tan adiabatic pulse such that a satisfactory spin inversion is achieved with minimum RF field strength. This information is then used in the subsequent stage of refinement where the RF pulse characteristics are further tailored via a local optimisation procedure without imposing any restrictions on the amplitude and frequency modulation profiles. We demonstrate that this approach constitutes a generally applicable tool for obtaining pulses with good inversion characteristics. At moderate MAS frequencies the efficacy of the method is experimentally demonstrated for generating double-quantum NMR spectra via the zero-quantum dipolar recoupling scheme RFDR.     

D-Glucose uptake in fish hepatocytes: mediated by transporter in rainbow trout (Oncorhynchus mykiss), but only by diffusion in prespawning lamprey (Lampetra fluviatilis) and in RTH-149 cell line

The transport of D-glucose into rainbow trout (Oncorhynchus mykiss) and river lamprey (Lampetra fluviatilis) hepatocytes, as well as into rainbow trout hepatoblastoma cell line RTH-149 was studied using tracer methods. The half-time for D-glucose equilibration was 15 s for rainbow trout. The half-times for the non-metabolizable D-glucose analog, 3-O-methyl-D-glucose equilibration were 8 s, 37 s and 38 s for rainbow trout, lamprey and RTH-149 cells, respectively. The 3-O-methyl-D-glucose was taken up by rainbow trout hepatocytes by facilitated diffusion in addition to simple diffusion. The uptake showed saturation kinetics with the K(m) of 37 mM and V(max) of 62 mmol kg(-1) cells min(-1). The uptake was sensitive to phloretin and cytochalasin B, but not affected by ouabain. The 3-O-methyl-D-glucose uptake by lamprey hepatocytes and RTH-149 cells showed no indication of saturation up to 160 mM, and was not affected by phloretin, cytochalasin B or ouabain, which suggests the mode of transport to be by passive diffusion. However, immunocytochemical stainings revealed the existence of mammalian type GLUT1 and GLUT2 transporters in all cells studied. The lack of a functioning carrier-mediated glucose uptake in lamprey hepatocytes might be due to its physiological state (prespawning starvation). The minor 3-O-methyl-D-glucose uptake into RTH-149 cells compared to freshly isolated rainbow trout hepatocytes might reflect low metabolic activity of the cell lines. Under the conditions applied the RTH-149 cell line is no suitable in vitro model for glucose transport in fish cells.