Modeling chondrocyte patterns by elliptical cluster processes

Superficial zone chondrocytes (CHs) of human joints are spatially organized in distinct horizontal patterns. Among other factors, the type of spatial CH organization within a given articular surface depends on whether the cartilage has been derived from an intact joint or the joint is affected by osteoarthritis (OA). Furthermore, specific variations of the type of spatial organization are associated with particular states of OA. This association may prove relevant for early disease recognition based on a quantitative structural characterization of CH patterns. Therefore, we present a point process model describing the distinct morphology of CH patterns within the articular surface of intact human cartilage. This reference model for intact CH organization can be seen as a first step towards a model-based statistical diagnostic tool. Model parameters are fitted to fluorescence microscopy data by a novel statistical methodology utilizing tools from cluster and principal component analysis. This way, the complex morphology of surface CH patters is represented by a relatively small number of model parameters. We validate the point process model by comparing biologically relevant structural characteristics between the fitted model and data derived from photomicrographs of the human articular surface using techniques from spatial statistics.     

Two step mechanism of phosphate release and the mechanism of force generation in chemically skinned fibers of rabbit psoas muscle.

The elementary steps of contraction in rabbit fast twitch muscle fibers were investigated with particular emphasis on the mechanism of phosphate (Pi) binding/release, the mechanism of force generation, and the relation between them. We monitor the rate constant 2 pi b of a macroscopic exponential process (B) by imposing sinusoidal length oscillations. We find that the plot of 2 pi b vs. Pi concentration is curved. From this observation we infer that Pi released is a two step phenomenon: an isomerization followed by the actual Pi release. Our results fit well to the kinetic scheme: [formula: see text] where A = actin, M = myosin, S = MgATP (substrate), D = MgADP, P = phosphate, and Det is a composite of all the detached and weakly attached states. For our data to be consistent with this scheme, it is also necessary that step 4 (isomerization) is observed in process (B). By fitting this scheme to our data, we obtained the following kinetic constants: k4 = 56 s-1, k-4 = 129 s-1, and K5 = 0.069 mM-1, assuming that K2 = 4.9. Experiments were performed at pCa 4.82, pH 7.00, MgATP 5 mM, free ATP 5 mM, ionic strength 200 mM in K propionate medium, and at 20 degrees C. Based on these kinetic constants, we calculated the probability of each cross-bridge state as a function of Pi, and correlated this with the isometric tension. Our results indicate that all attached cross-bridges support equal amount of tension. From this, we infer that the force is generated at step 4. Detailed balance indicates that 50-65% of the free energy available from ATP hydrolysis is transformed to work at this step. For our data to be consistent with the above scheme, step 6 must be the slowest step of the cross-bridge cycle (the rate limiting step). Further, AM*D is a distinctly different state from the AMD state that is formed by adding D to the bathing solution. From our earlier ATP hydrolysis data, we estimated k6 to be 9 s-1.     

Extracting the dynamics of perceptual switching from 'noisy' behaviour: an application of hidden Markov modelling to pecking data from pigeons.

When studying animal perception, one normally has the chance of localizing perceptual events in time, that is via behavioural responses time-locked to the stimuli. With multistable stimuli, however, perceptual changes occur despite stationary stimulation. Here, the challenge is to infer these not directly observable perceptual states indirectly from the behavioural data. This estimation is complicated by the fact that an animal's performance is contaminated by errors. We propose a two-step approach to overcome this difficulty: First, one sets up a generative, stochastic model of the behavioural time series based on the relevant parameters, including the probability of errors. Second, one performs a model-based maximum-likelihood estimation on the data in order to extract the non-observable perceptual state transitions. We illustrate this methodology for data from experiments on perception of bistable apparent motion in pigeons. The observed behavioural time series is analysed and explained by a combination of a Markovian perceptual dynamics with a renewal process that governs the motor response. We propose a hidden Markov model in which non-observable states represent both the perceptual states and the states of the renewal process of the motor dynamics, while the observable states account for overt pecking performance. Showing that this constitutes an appropriate phenomenological model of the time series of observable pecking events, we use it subsequently to obtain an estimate of the internal (and thus covert) perceptual reversals. These may directly correspond to changes in the activity of mutually inhibitory populations of motion selective neurones tuned to orthogonal directions.     

Hybrid modeling in bioprocess dynamics: Structural variabilities,implementation strategies,and practical challenges

Hybrid modeling, with an appropriate blend of the mechanistic and data-driven framework, is increasingly being adopted in bioprocess modeling, model-based experimental design (digital-twin), identification of critical process parameters, and optimization. However, the development of a hybrid model from experimental data is an inherently complex workflow, involving designed experiments, selection of the data-driven process, identification of model parameters, assessment fitness, and generalization capability. Depending on the complexity of the process system and purpose, each piece of these modules can flexibly be incorporated into the puzzle. However, this extra flexibility can be a cause of concern to trace an “optimal” model structure. In this paper, the development of hybrid models in a common bioprocess system, selection of data-driven components and their mapping to states, choice of parameter identification techniques, and model quality assurance are revisited. The challenges associated with hybrid-model development, and corrective actions have also been reviewed. The review also suggests the lack of data, and code sharing in communal repositories can be a hurdle in the exploration, and expansion of those tools in a bioprocess system.     

Toward intensifying design of experiments in upstream bioprocess development: An industrial Escherichia coli feasibility study

In this study, step variations in temperature, pH, and carbon substrate feeding rate were performed within five high cell density Escherichia coli fermentations to assess whether intraexperiment step changes, can principally be used to exploit the process operation space in a design of experiment manner. A dynamic process modeling approach was adopted to determine parameter interactions. A bioreactor model was integrated with an artificial neural network that describes biomass and product formation rates as function of varied fed‐batch fermentation conditions for heterologous protein production. A model reliability measure was introduced to assess in which process region the model can be expected to predict process states accurately. It was found that the model could accurately predict process states of multiple fermentations performed at fixed conditions within the determined validity domain. The results suggest that intraexperimental variations of process conditions could be used to reduce the number of experiments by a factor, which in limit would be equivalent to the number of intraexperimental variations per experiment. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1343–1352, 2016     

Development of a dynamic continuous-discrete-continuous model describing the lag phase of individual bacterial cells

AIMS: A previous model for adaptation and growth of individual bacterial cells was not dynamic in the lag phase, and could not be used to perform simulations of growth under non-isothermal conditions. The aim of the present study was to advance this model by adding a continuous adaptation step, prior to the discrete step, to form a continuous-discrete-continuous (CDC) model. METHODS AND RESULTS: The revised model uses four parameters: N(0), initial population; N(max), maximum population; p0, mean initial individual cell physiological state; SD(p0), standard deviation of the distribution of individual physiological states. A truncated normal distribution was used to generate tables of distributions to allow fitting of the CDC model to viable count data for Listeria monocytogenes grown at 5 degrees C to 35 degrees C. The p0 values increased with increasing SD(p0) and were, on average, greater than the corresponding population physiological states (h0); p0 and h0 were equivalent for individual cells. CONCLUSION: The CDC model has improved the ability to simulate the behaviour of individual bacterial cells by using a physiological state parameter and a distribution function to handle inter-cell variability. The stages of development of this model indicate the importance of physiological state parameters over the population lag concept, and provide a potential approach for making growth models more mechanistic by incorporating actual physiological events. SIGNIFICANCE AND IMPACT OF THE STUDY: Individual cell behaviour is important in modelling bacterial growth in foods. The CDC model provides a means of improving existing growth models, and increases the value of mathematical modelling to the food industry.     

Uncertainty analysis of penicillin V production using Monte Carlo simulation

Uncertainty and variability affect economic and environmental performance in the production of biotechnology and pharmaceutical products. However, commercial process simulation software typically provides analysis that assumes deterministic rather than stochastic process parameters and thus is not capable of dealing with the complexities created by variance that arise in the decision-making process. Using the production of penicillin V as a case study, this article shows how uncertainty can be quantified and evaluated. The first step is construction of a process model, as well as analysis of its cost structure and environmental impact. The second step is identification of uncertain variables and determination of their probability distributions based on available process and literature data. Finally, Monte Carlo simulations are run to see how these uncertainties propagate through the model and affect key economic and environmental outcomes. Thus, the overall variation of these objective functions are quantified, the technical, supply chain, and market parameters that contribute most to the existing variance are identified and the differences between economic and ecological evaluation are analyzed. In our case study analysis, we show that final penicillin and biomass concentrations in the fermenter have the highest contribution to variance for both unit production cost and environmental impact. The penicillin selling price dominates return on investment variance as well as the variance for other revenue-dependent parameters.     

Definition of lipid membrane structural parameters from neutronographic experiments with the help of the strip function model.

Neutron diffraction is an effective method for investigating model and biological membranes. Yet, to obtain accurate structural information it is necessary to use deuterium labels and much time is needed to acquire experimental data as there are a large number of diffraction reflections to register. This paper offers a way to define the hydrophobic boundary position in lipid membranes with high accuracy and for this purpose it is sufficient to take into consideration three structural factors. The method is based on modeling the density of the neutron diffraction amplitude rho(x) in the direction of the bilayer plane normal by means of a strip function, but it also takes into consideration the fact that the multiplication of the strip function amplitude rho i by the step width zi-zi-1 makes the sum of neutron scattering amplitudes of the atoms included in the step region. On the basis of the analysis of a large number of experimental data for different membranes, the effectiveness of this method in the determination of the position of hydrophilic/hydrophobic boundary is demonstrated, including the case of various rho(x) modifications in the region of polar heads and also the different phase states of membranes. However, it is shown in the present paper that the strip function model is not an adequate instrument for the determination of other structural parameters of membranes.     

Biphasic folding kinetics of RNA pseudoknots and telomerase RNA activity

Using a combined master equation and kinetic cluster approach, we investigate RNA pseudoknot folding and unfolding kinetics. The energetic parameters are computed from a recently developed Vfold model for RNA secondary structure and pseudoknot folding thermodynamics. The folding kinetics theory is based on the complete conformational ensemble, including all the native-like and non-native states. The predicted folding and unfolding pathways, activation barriers, Arrhenius plots, and rate-limiting steps lead to several findings. First, for the PK5 pseudoknot, a misfolded 5' hairpin emerges as a stable kinetic trap in the folding process, and the detrapping from this misfolded state is the rate-limiting step for the overall folding process. The calculated rate constant and activation barrier agree well with the experimental data. Second, as an application of the model, we investigate the kinetic folding pathways for human telomerase RNA (hTR) pseudoknot. The predicted folding and unfolding pathways not only support the proposed role of conformational switch between hairpin and pseudoknot in hTR activity, but also reveal molecular mechanism for the conformational switch. Furthermore, for an experimentally studied hTR mutation, whose hairpin intermediate is destabilized, the model predicts a long-lived transient hairpin structure, and the switch between the transient hairpin intermediate and the native pseudoknot may be responsible for the observed hTR activity. Such finding would help resolve the apparent contradiction between the observed hTR activity and the absence of a stable hairpin.     

Implementation of chemometrics,design of experiments,and neural network analysis for prior process knowledge assessment,failure modes and effect analysis,scale-down model development,and process characterization for a chromatographic purification of Teriparatide

Process understanding and characterization forms the foundation, ensuring consistent and robust biologics manufacturing process. Using appropriate modeling tools and machine learning approaches, the process data can be monitored in real time to avoid manufacturing risks. In this article, we have outlined an approach toward implementation of chemometrics and machine learning tools (neural network analysis) to model and predict the behavior of a mixed-mode chromatography step for a biosimilar (Teriparatide) as a case study. The process development data and process knowledge was assimilated into a prior process knowledge assessment using chemometrics tools to derive important parameters critical to performance indicators (i.e., potential quality and process attributes) and to establish the severity ranking for the FMEA analysis. The characterization data of the chromatographic operation are presented alongwith the determination of the critical, key and non- key process parameters, set points, operating, process acceptance and characterized ranges. The scale-down model establishment was assessed using traditional approaches and novel approaches like batch evolution model and neural network analysis. The batch evolution model was further used to demonstrate batch monitoring through direct chromatographic data, thus demonstrating its application for continuos process verification. Assimilation of process knowledge through a structured data acquisition approach, built-in from process development to continuous process verification was demonstrated to result in a data analytics driven model that can be coupled with machine learning tools for real time process monitoring. We recommend application of these approaches with the FDA guidance on stage wise process development and validation to reduce manufacturing risks.     

Control in bioreactors showing gradients

In large-scale bioreactors gradients often occur as a result of non-ideal mixing. This phenomenon complicates design and control of large-scale bioreactors. Gradients in the oxygen concentration can be modeled with a two-compartment model of the liquid phase. Application of this model had been suggested for the control of the dissolved oxygen concentration with a batch gluconic acid fermentation process as the model system. The control system consists of a controller, an observer and a parameter estimator. In this work, the controller design is reconsidered and, in simulation experiments, the performance of the control system has been investigated. When the parameter values are known, the controller in combination with the observer works adequately. The parameter estimator, however, yields incorrect parameters, which are caused by a coupling between two parameters. This causes a deviation of the estimated states from the process states. The simulation results suggest that a priori knowledge of the parameters is required for application of the model for control and state estimation.     

Reduction-induced inhibition and Mn(II) release from the photosystem II oxygen-evolving complex by hydroquinone or NH2OH are consistent with a Mn(III)/Mn(III)/Mn(IV)/Mn(IV) oxidation state for the dark-adapted enzyme

Hydroxylamine and hydroquinone were used to probe the oxidation states of Mn in the oxygen-evolving complex of dark-adapted intact (hydroxylamine) and salt-washed (hydroquinone) photosystem II. These preparations were incubated in the dark for 24 h in the presence of increasing reductant/photosystem II ratios, and the loss of oxygen evolution activity and of Mn(II) was determined for each incubation mixture. Monte Carlo simulations of these data yielded models that provide insight into the structure, reactivity, and oxidation states of the manganese in the oxygen-evolving complex. Specifically, the data support oxidation states of Mn(III)(2)/Mn(IV)(2) for the dark stable S(1) state of the O(2)-evolving complex. Activity and Mn(II) loss data were best modeled by assuming an S(1) --> S(-)(1) conversion of intermediate probability, a S(-)(1) --> S(-)(3) reaction of high probability, and subsequent step(s) of low probability. This model predicts that photosystem II Mn clusters that have undergone an initial reduction step become more reactive toward a second reduction, followed by a slower third reduction step. Analysis of the Mn(II) release parameters used to model the data suggests that the photosystem II manganese cluster consists of three Mn atoms that exhibit a facile reactivity with both reductants, and a single Mn that is reducible but sterically trapped at or near its binding site. Activity assays indicate that intact photosystem II centers reduced to S(-)(1) can evolve oxygen upon illumination, but that these centers are inactive in preparations depleted of the extrinsic 23 and 17 kDa polypeptides. Finally, it was found that a substantial population of the tyrosine D radical is reduced by hydroxylamine, but a smaller population reacts with hydroquinone over the course of a 24 h exposure to the reductant.     

Mechanism of the binding of 2-(4'-hydroxyphenylazo)benzoic acid to bovine serum albumin

The mechanism of the binding of 2-(4'-hydroxyphenylazo)benzoic acid (HABA) to bovine serum albumin was studied by relaxation methods as well as the binding isotherm using gel chromatography. A single relaxation was observed over a wide range of HABA concentration except at the extremes of high concentration where another slow process was observed. The concentration dependence of the reciprocal relaxation time of the fast process decreased monotonically with increase in concentration of HABA at constant polymer concentration. The data were analyzed on the basis of Brown's domain structure model and were found to be consistent with a sequential binding mechanism. The azohydrazon tautomerism of HABA was identified with the intramolecular step of the complex. The activation parameters of the step, determined from the temperature dependence of the relaxation time of the fast process, showed that this step is rate limited by an enthalpy barrier in both forward and backward directions. Comparison of the activation parameters with those of other serum albumin-ligand systems suggests that there is an enthalpy-entropy compensation in the activation process of the intramolecular step with the compensation temperature at about 270 K; the enthalpy-entropy compensation is thought to be related to the hydrophobic nature of the ligand.     

Time-dependent elastic extensional RBC deformation by micropipette aspiration: redistribution of the spectrin network?

The time dependence of small elastic extensional RBC deformation by micropipette aspiration has been analyzed. This process shows two-phases which are characterized by time constants of the order of some tenths of seconds and about ten seconds, respectively. The equilibrium tongue length is reached after about 30 s. For the first, fast step we assume that the membrane model of immobilized boundaries holds, i.e., the skeleton is tightly associated with the lipid bilayer and no redistribution of the skeleton with respect to the lipid bilayer is allowed. This lipid-spectrin interaction or anchorage is characterized by some association force density. It has been shown that at a given tongue length the force generated owing to the membrane deformation and acting to redistribute the spectrin, overcomes (in some membrane area) the association force density and results in an additional increase of the sucked membrane length. Equations have been derived to describe this process. From the experimental conditions of an RBC aspiration and the determined tongue length corresponding to the second slow aspiration step, the association force density between the lipid bilayer and the spectrin network may be determined. From literature data and our own results a force density of between 40 and 50 Pa has been estimated. Offprint requests to: D. Lerche     

QUANTITATIVE GENETIC MODELING AND INFERENCE IN THE PRESENCE OF NONIGNORABLE MISSING DATA

Natural selection is typically exerted at some specific life stages. If natural selection takes place before a trait can be measured, using conventional models can cause wrong inference about population parameters. When the missing data process relates to the trait of interest, a valid inference requires explicit modeling of the missing process. We propose a joint modeling approach, a shared parameter model, to account for nonrandom missing data. It consists of an animal model for the phenotypic data and a logistic model for the missing process, linked by the additive genetic effects. A Bayesian approach is taken and inference is made using integrated nested Laplace approximations. From a simulation study we find that wrongly assuming that missing data are missing at random can result in severely biased estimates of additive genetic variance. Using real data from a wild population of Swiss barn owls Tyto alba, our model indicates that the missing individuals would display large black spots; and we conclude that genes affecting this trait are already under selection before it is expressed. Our model is a tool to correctly estimate the magnitude of both natural selection and additive genetic variance.     

The impact of phenotypic switching on glioblastoma growth and invasion

The brain tumour glioblastoma is characterised by diffuse and infiltrative growth into surrounding brain tissue. At the macroscopic level, the progression speed of a glioblastoma tumour is determined by two key factors: the cell proliferation rate and the cell migration speed. At the microscopic level, however, proliferation and migration appear to be mutually exclusive phenotypes, as indicated by recent in vivo imaging data. Here, we develop a mathematical model to analyse how the phenotypic switching between proliferative and migratory states of individual cells affects the macroscopic growth of the tumour. For this, we propose an individual-based stochastic model in which glioblastoma cells are either in a proliferative state, where they are stationary and divide, or in motile state in which they are subject to random motion. From the model we derive a continuum approximation in the form of two coupled reaction-diffusion equations, which exhibit travelling wave solutions whose speed of invasion depends on the model parameters. We propose a simple analytical method to predict progression rate from the cell-specific parameters and demonstrate that optimal glioblastoma growth depends on a non-trivial trade-off between the phenotypic switching rates. By linking cellular properties to an in vivo outcome, the model should be applicable to designing relevant cell screens for glioblastoma and cytometry-based patient prognostics.     

Mapping uncertainty and phylogenetic uncertainty in ancestral character state reconstruction: an example in the moss genus Brachytheciastrum

The evolution of species traits along a phylogeny can be examined through an increasing number of possible, but not necessarily complementary, approaches. In this paper, we assess whether deriving ancestral states of discrete morphological characters from a model whose parameters are (i) optimized by ML on a most likely tree; (II) optimized by ML onto each of a Bayesian sample of trees; and (III) sampled by a MCMC visiting the space of a Bayesian sample of trees affects the reconstruction of ancestral states in the moss genus Brachytheciastrum. In the first two methods, the choice of a single- or two-rate model and of a genetic distance (wherein branch lengths are used to determine the probabilities of change) or speciational (wherein changes are only driven by speciation events) model based upon a likelihood-ratio test strongly depended on the sampled trees. Despite these differences in model selection, reconstructions of ancestral character states were strongly correlated to each others across nodes, often at r > 0.9, for all the characters. The Bayesian approach of ancestral character state reconstruction offers, however, a series of advantages over the single-tree approach or the ML model optimization on a Bayesian sample of trees because it does not involve restricting model parameters prior to reconstructing ancestral states, but rather allows a range of model parameters and ancestral character states to be sampled according to their posterior probabilities. From the distribution of the latter, conclusions on trait evolution can be made in a more satisfactorily way than when a substantial part of the uncertainty of the results is obscured by the focus on a single set of model parameters and associated ancestral states. The reconstructions of ancestral character states in Brachytheciastrum reveal rampant parallel morphological evolution. Most species previously described based on phenetic grounds are thus resolved of polyphyletic origin. Species polyphylly has been increasingly reported among mosses, raising severe reservations regarding current species definition.     

Sensitivity Analysis of Environmental Process Modeling in a Life Cycle Context: A Case Study of Hemp Crop Production

The aim of this article is to develop a methodological approach allowing to assess the influence of parameters of one or more elementary processes in the foreground system, on the outcomes of a life cycle assessment (LCA) study. From this perspective, the method must be able to: (1) include foreground process modeling in order to avoid the assumption of proportionality between inventory data and reference flows; (2) quantify influences of foreground processes’ parameters (and, possibly, interactions between parameters); and (3) identify trends (either increasing or decreasing) for each parameter on each indicator in order to determine the most favorable direction for parametric variation. These objectives can be reached by combining foreground system modeling, a set of two different sensitivity analysis methods (each one providing different and complementary information), and LCA. The proposed method is applied to a case study of hemp‐based insulation materials for buildings. The present study will focus on the agricultural stage as a foreground system and as a first step encompassing the entire life cycle. A set of technological recommendations were identified for hemp farmers in order to reduce the crop's environmental impacts (from –11% to –89% according to the considered impact category). One of the main limitations of the approach is the need for a detailed model of the foreground process. Further, the method is, at present, rather time‐consuming. However, it offers long‐term advantages given that the higher level of model detail adds robustness to the LCA results.     

Estimating equations for a latent transition model with multiple discrete indicators

This paper proposes a two-part model for studying transitions between health states over time when multiple, discrete health indicators are available. The includes a measurement model positing underlying latent health states and a transition model between latent health states over time. Full maximum likelihood estimation procedures are computationally complex in this latent variable framework, making only a limited class of models feasible and estimation of standard errors problematic. For this reason, an estimating equations analogue of the pseudo-likelihood method for the parameters of interest, namely the transition model parameters, is considered. The finite sample properties of the proposed procedure are investigated through a simulation study and the importance of choosing strong indicators of the latent variable is demonstrated. The applicability of the methodology is illustrated with health survey data measuring disability in the elderly from the Longitudinal Study of Aging.