Comparing methods for modelling spreading cell fronts

Spreading cell fronts play an essential role in many physiological processes. Classically, models of this process are based on the Fisher-Kolmogorov equation; however, such continuum representations are not always suitable as they do not explicitly represent behaviour at the level of individual cells. Additionally, many models examine only the large time asymptotic behaviour, where a travelling wave front with a constant speed has been established. Many experiments, such as a scratch assay, never display this asymptotic behaviour, and in these cases the transient behaviour must be taken into account. We examine the transient and asymptotic behaviour of moving cell fronts using techniques that go beyond the continuum approximation via a volume-excluding birth-migration process on a regular one-dimensional lattice. We approximate the averaged discrete results using three methods: (i) mean-field, (ii) pair-wise, and (iii) one-hole approximations. We discuss the performace of these methods, in comparison to the averaged discrete results, for a range of parameter space, examining both the transient and asymptotic behaviours. The one-hole approximation, based on techniques from statistical physics, is not capable of predicting transient behaviour but provides excellent agreement with the asymptotic behaviour of the averaged discrete results, provided that cells are proliferating fast enough relative to their rate of migration. The mean-field and pair-wise approximations give indistinguishable asymptotic results, which agree with the averaged discrete results when cells are migrating much more rapidly than they are proliferating. The pair-wise approximation performs better in the transient region than does the mean-field, despite having the same asymptotic behaviour. Our results show that each approximation only works in specific situations, thus we must be careful to use a suitable approximation for a given system, otherwise inaccurate predictions could be made.

Distinguishing between mechanisms of cell aggregation using pair-correlation functions

Many cell types form clumps or aggregates when cultured in vitro through a variety of mechanisms including rapid cell proliferation, chemotaxis, or direct cell-to-cell contact. In this paper we develop an agent-based model to explore the formation of aggregates in cultures where cells are initially distributed uniformly, at random, on a two-dimensional substrate. Our model includes unbiased random cell motion, together with two mechanisms which can produce cell aggregates: (i) rapid cell proliferation, and (ii) a biased cell motility mechanism where cells can sense other cells within a finite range, and will tend to move towards areas with higher numbers of cells. We then introduce a pair-correlation function which allows us to quantify aspects of the spatial patterns produced by our agent-based model. In particular, these pair-correlation functions are able to detect differences between domains populated uniformly at random (i.e. at the exclusion complete spatial randomness (ECSR) state) and those where the proliferation and biased motion rules have been employed - even when such differences are not obvious to the naked eye. The pair-correlation function can also detect the emergence of a characteristic inter-aggregate distance which occurs when the biased motion mechanism is dominant, and is not observed when cell proliferation is the main mechanism of aggregate formation. This suggests that applying the pair-correlation function to experimental images of cell aggregates may provide information about the mechanism associated with observed aggregates. As a proof of concept, we perform such analysis for images of cancer cell aggregates, which are known to be associated with rapid proliferation. The results of our analysis are consistent with the predictions of the proliferation-based simulations, which supports the potential usefulness of pair correlation functions for providing insight into the mechanisms of aggregate formation.

A simple model for the establishment of tick-borne pathogens of Ixodes scapularis : a global sensitivity analysis of R0

The basic reproduction number of a pathogen, R 0, determines whether a pathogen will spread (R0>1R 0>1), when introduced into a fully susceptible population or fade out (R0<1R 0<1), because infected hosts do not, on average, replace themselves. In this paper we develop a simple mechanistic model for the basic reproduction number for a group of tick-borne pathogens that wholly, or almost wholly, depend on horizontal transmission to and from vertebrate hosts. This group includes the causative agent of Lyme disease, Borrelia burgdorferi, and the causative agent of human babesiosis, Babesia microti, for which transmission between co-feeding ticks and vertical transmission from adult female ticks are both negligible. The model has only 19 parameters, all of which have a clear biological interpretation and can be estimated from laboratory or field data. The model takes into account the transmission efficiency from the vertebrate host as a function of the days since infection, in part because of the potential for this dynamic to interact with tick phenology, which is also included in the model. This sets the model apart from previous, similar models for R0 for tick-borne pathogens. We then define parameter ranges for the 19 parameters using estimates from the literature, as well as laboratory and field data, and perform a global sensitivity analysis of the model. This enables us to rank the importance of the parameters in terms of their contribution to the observed variation in R0. We conclude that the transmission efficiency from the vertebrate host to Ixodes scapularis ticks, the survival rate of Ixodes scapularis from fed larva to feeding nymph, and the fraction of nymphs finding a competent host, are the most influential factors for R0. This contrasts with other vector borne pathogens where it is usually the abundance of the vector or host, or the vector-to-host ratio, that determine conditions for emergence. These results are a step towards a better understanding of the geographical expansion of currently emerging horizontally transmitted tick-borne pathogens such as Babesia microti, as well as providing a firmer scientific basis for targeted use of acaricide or the application of wildlife vaccines that are currently in development.

Are in vitro estimates of cell diffusivity and cell proliferation rate sensitive to assay geometry?

Cells respond to various biochemical and physical cues during wound–healing and tumour progression. In vitro assays used to study these processes are typically conducted in one particular geometry and it is unclear how the assay geometry affects the capacity of cell populations to spread, or whether the relevant mechanisms, such as cell motility and cell proliferation, are somehow sensitive to the geometry of the assay. In this work we use a circular barrier assay to characterise the spreading of cell populations in two different geometries. Assay 1 describes a tumour–like geometry where a cell population spreads outwards into an open space. Assay 2 describes a wound–like geometry where a cell population spreads inwards to close a void. We use a combination of discrete and continuum mathematical models and automated image processing methods to obtain independent estimates of the effective cell diffusivity, D, and the effective cell proliferation rate, λ. Using our parameterised mathematical model we confirm that our estimates of D and λ accurately predict the time–evolution of the location of the leading edge and the cell density profiles for both assay 1 and assay 2. Our work suggests that the effective cell diffusivity is up to 50% lower for assay 2 compared to assay 1, whereas the effective cell proliferation rate is up to 30% lower for assay 2 compared to assay 1.

Critical dependence of blood-borne biomarker concentrations on the half-lives of their carrier proteins

Until recently, the low-abundance (LA) range of the serum proteome was an unexplored reservoir of diagnostic information. Today it is increasingly appreciated that a diagnostic goldmine of LA biomarkers resides in the blood stream in complexed association with more abundant higher molecular weight carrier proteins such as albumin and immunoglobulins. As we now look to the possibility of harvesting these LA biomarkers more efficiently through engineered nano-scale particles, mathematical approaches are needed in order to reveal the mechanisms by which blood carrier proteins act as molecular 'mops' for LA diagnostic cargo, and the functional relationships between bound LA biomarker concentrations and other variables of interest such as biomarker intravasation and clearance rates and protein half-lives in the bloodstream. Here we show, by simple mathematical modeling, how the relative abundance of large carrier proteins and their longer half-lives in the bloodstream work together to amplify the total blood concentration of these tiny biomarkers. The analysis further suggests that alterations in the production of biomarkers lead to gradual rather than immediate changes in biomarker levels in the blood circulation. The model analysis also points to the characteristics of artificial nano-particles that would render them more efficient harvesters of tumor biomarkers in the circulation, opening up possibilities for the early detection of curable disease, rather than simply better detection of advanced disease.

A computational model for BMP movement in sea urchin embryos

Bone morphogen proteins (BMPs) are distributed along a dorsal-ventral (DV) gradient in many developing embryos. The spatial distribution of this signaling ligand is critical for correct DV axis specification. In various species, BMP expression is spatially localized, and BMP gradient formation relies on BMP transport, which in turn requires interactions with the extracellular proteins Short gastrulation/Chordin (Chd) and Twisted gastrulation (Tsg). These binding interactions promote BMP movement and concomitantly inhibit BMP signaling. The protease Tolloid (Tld) cleaves Chd, which releases BMP from the complex and permits it to bind the BMP receptor and signal. In sea urchin embryos, BMP is produced in the ventral ectoderm, but signals in the dorsal ectoderm. The transport of BMP from the ventral ectoderm to the dorsal ectoderm in sea urchin embryos is not understood. Therefore, using information from a series of experiments, we adapt the mathematical model of Mizutani et al. (2005) and embed it as the reaction part of a one-dimensional reaction–diffusion model. We use it to study aspects of this transport process in sea urchin embryos. We demonstrate that the receptor-bound BMP concentration exhibits dorsally centered peaks of the same type as those observed experimentally when the ternary transport complex (Chd-Tsg-BMP) forms relatively quickly and BMP receptor binding is relatively slow. Similarly, dorsally centered peaks are created when the diffusivities of BMP, Chd, and Chd-Tsg are relatively low and that of Chd-Tsg-BMP is relatively high, and the model dynamics also suggest that Tld is a principal regulator of the system. At the end of this paper, we briefly compare the observed dynamics in the sea urchin model to a version that applies to the fly embryo, and we find that the same conditions can account for BMP transport in the two types of embryos only if Tld levels are reduced in sea urchin compared to fly.

Cell type-dependent, infection-induced, aberrant DNA methylation in gastric cancer

Epigenetic changes correspond to heritable modifications of the chromatin structure, which do not involve any alteration of the DNA sequence but nonetheless affect gene expression. These mechanisms play an important role in cell differentiation, but aberrant occurrences are also associated with a number of diseases, including cancer and neural development disorders. In particular, aberrant DNA methylation induced by H. Pylori has been found to be a significant risk factor in gastric cancer. To investigate the sensitivity of different genes and cell types to this infection, a computational model of methylation in gastric crypts is developed. In this article, we review existing results from physical experiments and outline their limitations, before presenting the computational model and investigating the influence of its parameters.

Common psychotic symptoms can be explained by the theory of ecological perception

The symptoms of psychiatric illness are diverse, as are the causes of the illnesses that cause them. Yet, regardless of the heterogeneity of cause and presentation, a great deal of symptoms can be explained by the failure of a single perceptual function – the reprocessing of ecological perception. It is a central tenet of the ecological theory of perception that we perceive opportunities to act. It has also been found that perception automatically causes actions and thoughts to occur unless this primary action pathway is inhibited. Inhibition allows perceptions to be reprocessed into more appropriate alternative actions and thoughts. Reprocessing of this kind takes place over the entire frontal lobe and it renders action optional. Choice about what action to take (if any) is the basis for the feeling of autonomy and ultimately for the sense-of-self. When thoughts and actions occur automatically (without choice) they appear to originate outside of the self, thereby providing prima facie evidence for some of the bizarre delusions that define schizophrenia such as delusional misidentification, delusions of control and Cotard’s delusion. Automatic actions and thoughts are triggered by residual stimulation whenever reprocessing is insufficient to balance automatic excitatory cues (for whatever reason). These may not be noticed if they are neutral and therefore unimportant whereas actions and thoughts with a positive bias are desirable. Responses to negative stimulus, on the other hand, are always unwelcome, because the actions that are triggered will carry the negative bias. Automatic thoughts may include spontaneous positive feelings of love and joy, but automatic negative thoughts and visualisations are experienced as hallucinations. Not only do these feel like they emerge from elsewhere but they carry a negative bias (they are most commonly critical, rude and are irrationally paranoid). Automatic positive actions may include laughter and smiling and these are welcome. Automatic behaviours that carry a negative bias, however, are unwelcome and like hallucinations, occur without a sense of choice. These include crying, stereotypies, perseveration, ataxia, utilization and imitation behaviours and catatonia.

A two-stage SVM method to predict membrane protein types by incorporating amino acid classifications and physicochemical properties into a general form of Chou's PseAAC

Membrane proteins play important roles in many biochemical processes and are also attractive targets of drug discovery for various diseases. The elucidation of membrane protein types provides clues for understanding the structure and function of proteins. Recently we developed a novel system for predicting protein subnuclear localizations. In this paper, we propose a simplified version of our system for predicting membrane protein types directly from primary protein structures, which incorporates amino acid classifications and physicochemical properties into a general form of pseudo-amino acid composition. In this simplified system, we will design a two-stage multi-class support vector machine combined with a two-step optimal feature selection process, which proves very effective in our experiments. The performance of the present method is evaluated on two benchmark datasets consisting of five types of membrane proteins. The overall accuracies of prediction for five types are 93.25% and 96.61% via the jackknife test and independent dataset test, respectively. These results indicate that our method is effective and valuable for predicting membrane protein types. A web server for the proposed method is available at http://www.juemengt.com/jcc/memty_page.php

A model to explain specific cellular communications and cellular harmony: - a hypothesis of coupled cells and interactive coupling molecules

Background The various cell types and their relative numbers in multicellular organisms are controlled by growth factors and related extracellular molecules which affect genetic expression pathways. However, these substances may have both/either inhibitory and/or stimulatory effects on cell division and cell differentiation depending on the cellular environment. It is not known how cells respond to these substances in such an ambiguous way. Many cellular effects have been investigated and reported using cell culture from cancer cell lines in an effort to define normal cellular behaviour using these abnormal cells. A model is offered to explain the harmony of cellular life in multicellular organisms involving interacting extracellular substances. Methods A basic model was proposed based on asymmetric cell division and evidence to support the hypothetical model was accumulated from the literature. In particular, relevant evidence was selected for the Insulin-Like Growth Factor system from the published data, especially from certain cell lines, to support the model. The evidence has been selective in an attempt to provide a picture of normal cellular responses, derived from the cell lines. Results The formation of a pair of coupled cells by asymmetric cell division is an integral part of the model as is the interaction of couplet molecules derived from these cells. Each couplet cell will have a receptor to measure the amount of the couplet molecule produced by the other cell; each cell will be receptor-positive or receptor-negative for the respective receptors. The couplet molecules will form a binary complex whose level is also measured by the cell. The hypothesis is heavily supported by selective collection of circumstantial evidence and by some direct evidence. The basic model can be expanded to other cellular interactions. Conclusions These couplet cells and interacting couplet molecules can be viewed as a mechanism that provides a controlled and balanced division-of-labour between the two progeny cells, and, in turn, their progeny. The presence or absence of a particular receptor for a couplet molecule will define a cell type and the presence or absence of many such receptors will define the cell types of the progeny within cell lineages.

Nonlinear Enzyme Kinetics Can Lead to High Metabolic Flux Control Coefficients: Implications for the Evolution of Dominance

In a classic study, Kacser & Burns (1981, Genetics 97, 639-666) demonstrated that given certain plausible assumptions, the flux in a metabolic pathway was more or less indifferent to the activity of any of the enzymes in the pathway taken singly. It was inferred from this that the observed dominance of most wild-type alleles with respect to loss-of-function mutations did not require an adaptive, meaning selectionist, explanation. Cornish-Bowden (1987, J. theor. Biol. 125, 333-338) showed that the Kacser-Burns inference was not valid when substrate concentrations were large relative to the relevant Michaelis constants. We find that in a randomly constructed functional pathway, even when substrate levels are small, one can expect high values of control coefficients for metabolic flux in the presence of significant nonlinearities as exemplified by enzymes with Hill coefficients ranging from two to six, or by the existence of oscillatory loops. Under these conditions the flux can be quite sensitive to changes in enzyme activity as might be caused by inactivating one of the two alleles in a diploid. Therefore, the phenomenon of dominance cannot be a trivial ''default'' consequence of physiology but must be intimately linked to the manner in which metabolic networks have been moulded by natural selection.

On the moulding of population viscosity by natural selection

In this paper, we explore the conjoint evolution of dispersal and social behaviour. The model investigated is of a population distributed over a number of sites each with a carrying capacity of two adults and an episode of dispersal in the juvenile stage. The fertilities are governed by whether an individual and its neighbour are selfish or co-operative. It is shown that the best dispersal strategy for the co-operative genotype always involves lower levels of dispersal; and further that ecological conditions favouring low levels of dispersal increase the selective advantage of a co-operative genotype. Given this positive feedback, we suggest that in any taxon viscosity and co-operativity will tend to be correlated and bimodally distributed. Hence we predict the existence of two kinds of animal societies; viscous and co-operative (e.g. quasi-social wasps such as Mischocyttarus), and non-viscous and selfish (e.g. communal sphecid wasps such as Cerceris), and relatively few social groups with intermediate levels of co-operativity and viscosity. We also suggest that when one of the two sexes disperses, it will be the sex with lower potential for co-operative behaviour.

On evolutionarily stable compositions of populations of interacting genotypes.

Consider an organism in which the genetic fitness of an individual depends to a large extent on its social interactions. Assuming the genotypes to differ only in the choice of strategies they adopt in social interactions, and equating the variation in genetic fitness to the mean payoff to an individual averaged over all possible encounters, we develop a dynamical model for the evolution of genotypic frequencies in such a population. Such a system is characterised by frequency dependent selection, and depending on the initial composition, the population evolves towards one of several possible compositions. We term as evolutionarily stable compositions (ESC) any such composition towards which a population can evolve and which is stable against small fluctuations in the frequencies of existing genotypes as well as to invasions by any other postulated genotype. We state the necessary and sufficient conditions for the identification of all possible ESC's for any number of interacting genotypes. Our results conform to those derived earlier in connection with the concept of evolutionarily stable strategies only in the case of two interacting genotypes; when more than two genotypes interact the conditions under which various ESC's exist become far richer. We consider interactions with mixed strategists and show that in a conflict with pure strategists the optimal mixed strategist will be the only one to ultimately survive. We illustrate our approach by considering the specific case of a primitively social wasp.

Modelling the movement of interacting cell populations: A moment dynamics approach

Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.