Using approximate Bayesian computation to quantify cell-cell adhesion parameters in a cell migratory process.
ABSTRACT: In this work, we implement approximate Bayesian computational methods to improve the design of a wound-healing assay used to quantify cell-cell interactions. This is important as cell-cell interactions, such as adhesion and repulsion, have been shown to play a role in cell migration. Initially, we demonstrate with a model of an unrealistic experiment that we are able to identify model parameters that describe agent motility and adhesion, given we choose appropriate summary statistics for our model data. Following this, we replace our model of an unrealistic experiment with a model representative of a practically realisable experiment. We demonstrate that, given the current (and commonly used) experimental set-up, our model parameters cannot be accurately identified using approximate Bayesian computation methods. We compare new experimental designs through simulation, and show more accurate identification of model parameters is possible by expanding the size of the domain upon which the experiment is performed, as opposed to increasing the number of experimental replicates. The results presented in this work, therefore, describe time and cost-saving alterations for a commonly performed experiment for identifying cell motility parameters. Moreover, this work will be of interest to those concerned with performing experiments that allow for the accurate identification of parameters governing cell migratory processes, especially cell migratory processes in which cell-cell adhesion or repulsion are known to play a significant role.
Project description:As olfactory receptor axons grow from the peripheral to the central nervous system (CNS) aided by olfactory ensheathing cells (OECs), the transplantation of OECs has been suggested as a plausible therapy for spinal cord lesions. The problem with this hypothesis is that OECs do not represent a single homogeneous entity, but, instead, a functionally heterogeneous population that exhibits a variety of responses, including adhesion and repulsion during cell-matrix interactions. Some studies report that the migratory properties of OECs are compromised by inhibitory molecules and potentiated by chemical gradients. In this paper, we report a system based on modified OECs carrying magnetic nanoparticles as a proof of concept experiment enabling specific studies aimed at exploring the potential of OECs in the treatment of spinal cord injuries. Our studies have confirmed that magnetized OECs (i) survive well without exhibiting stress-associated cellular responses; (ii) in vitro, their migration can be modulated by magnetic fields; and (iii) their transplantation in organotypic slices of spinal cord and peripheral nerve showed positive integration in the model. Altogether, these findings indicate the therapeutic potential of magnetized OECs for CNS injuries.
Project description:Cancer progression is associated with alternations in the cytoskeletal architecture of cells and, consequently, their mechanical properties such as stiffness. Changing the mechanics of cells enables cancer cells to migrate and invade to distant organ sites. This process, metastasis, is the main reason for cancer-related mortality. Cell migration is an essential step towards increasing the invasive potential of cells. Although many studies have shown that the migratory speed and the invasion of cells can be inversely correlated to the stiffness of cells, some other investigations indicate opposing results. In the current work, based on the strain energy stored in cells due to the contractile forces, we defined an energy-dependent term, migratory index, to approximate how changes in the mechanical properties of cells influence cell migration required for cancer progression. Cell migration involves both cell deformation and force transmission within cells. The effects of these two parameters can be represented equally by the migratory index. Our mechanical modelling and computational study show that cells depending on their shape, size and other physical parameters have a maximum migratory index taking place at a specific range of cell bulk elasticity, indicating the most favourable conditions for invasive mobility. This approximate model could be used to explain why the stiffness of cells varies during cancer progression. We believe that the stiffness of cancer or malignant cells depending on the stiffness of their normal or non-malignant counterparts is either decreased or increased to reach the critical condition in which the mobility potential of cells is approximated to be maximum.
Project description:Advanced imaging techniques generate large datasets capable of describing the structure and kinematics of tissue spreading in embryonic development, wound healing, and the progression of many diseases. These datasets can be integrated with mathematical models to infer biomechanical properties of the system, typically identifying an optimal set of parameters for an individual experiment. However, these methods offer little information on the robustness of the fit and are generally ill-suited for statistical tests of multiple experiments. To overcome this limitation and enable efficient use of large datasets in a rigorous experimental design, we use the approximate Bayesian computation rejection algorithm to construct probability density distributions that estimate model parameters for a defined theoretical model and set of experimental data. Here, we demonstrate this method with a 2D Eulerian continuum mechanical model of spreading embryonic tissue. The model is tightly integrated with quantitative image analysis of different sized embryonic tissue explants spreading on extracellular matrix (ECM) and is regulated by a small set of parameters including forces on the free edge, tissue stiffness, strength of cell-ECM adhesions, and active cell shape changes. We find statistically significant trends in key parameters that vary with initial size of the explant, e.g., for larger explants cell-ECM adhesion forces are weaker and free edge forces are stronger. Furthermore, we demonstrate that estimated parameters for one explant can be used to predict the behavior of other similarly sized explants. These predictive methods can be used to guide further experiments to better understand how collective cell migration is regulated during development.
Project description:Eph receptor and ephrin signalling has a major role in cell segregation and border formation, and may act through regulation of cell adhesion, repulsion or tension. To elucidate roles of cell repulsion and adhesion, we combined experiments in cell culture assays with quantitations of cell behaviour which are used in computer simulations. Cells expressing EphB2, or kinase-inactive EphB2 (kiEphB2), segregate and form a sharp border with ephrinB1-expressing cells, and this is disrupted by knockdown of N-cadherin. Measurements of contact inhibition of locomotion reveal that EphB2-, kiEphB2- and ephrinB1-expressing cells have strong heterotypic and weak homotypic repulsion. EphB2 cells have a transient increase in migration after heterotypic activation, which underlies a shift in the EphB2-ephrinB1 border but is not required for segregation or border sharpening. Simulations with the measured values of cell behaviour reveal that heterotypic repulsion can account for cell segregation and border sharpening, and is more efficient than decreased heterotypic adhesion. By suppressing homotypic repulsion, N-cadherin creates a sufficient difference between heterotypic and homotypic repulsion, and enables homotypic cohesion, both of which are required to sharpen borders.
Project description:The establishment of sharp boundaries is essential for segregation of embryonic tissues during development, but the underlying mechanism of cell sorting has remained unclear. Opposing hypotheses have been proposed, either based on global tissue adhesive or contractile properties or on local signalling through cell contact cues. Here we use ectoderm-mesoderm separation in Xenopus to directly evaluate the role of these various parameters. We find that ephrin-Eph-based repulsion is very effective at inducing and maintaining separation, whereas differences in adhesion or contractility have surprisingly little impact. Computer simulations support and generalise our experimental results, showing that a high heterotypic interfacial tension between tissues is key to their segregation. We propose a unifying model, in which conditions of sorting previously considered as driven by differential adhesion/tension should be viewed as suboptimal cases of heterotypic interfacial tension.The mechanisms that cause different cells to segregate into distinct tissues are unclear. Here the authors show in Xenopus that formation of a boundary between two tissues is driven by local tension along the interface rather than by global differences in adhesion or cortical contractility.
Project description:Model-based analyses of natural selection often categorize sites into a relatively small number of site classes. Forcing each site to belong to one of these classes places unrealistic constraints on the distribution of selection parameters, which can result in misleading inference due to model misspecification. We present an approximate hierarchical Bayesian method using a Markov chain Monte Carlo (MCMC) routine that ensures robustness against model misspecification by averaging over a large number of predefined site classes. This leaves the distribution of selection parameters essentially unconstrained, and also allows sites experiencing positive and purifying selection to be identified orders of magnitude faster than by existing methods. We demonstrate that popular random effects likelihood methods can produce misleading results when sites assigned to the same site class experience different levels of positive or purifying selection--an unavoidable scenario when using a small number of site classes. Our Fast Unconstrained Bayesian AppRoximation (FUBAR) is unaffected by this problem, while achieving higher power than existing unconstrained (fixed effects likelihood) methods. The speed advantage of FUBAR allows us to analyze larger data sets than other methods: We illustrate this on a large influenza hemagglutinin data set (3,142 sequences). FUBAR is available as a batch file within the latest HyPhy distribution (http://www.hyphy.org), as well as on the Datamonkey web server (http://www.datamonkey.org/).
Project description:The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C?, H?, etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain.
Project description:Semiempirical orthogonalization-corrected methods (OM1, OM2, and OM3) go beyond the standard MNDO model by explicitly including additional interactions into the Fock matrix in an approximate manner (Pauli repulsion, penetration effects, and core-valence interactions), which yields systematic improvements both for ground-state and excited-state properties. In this Article, we describe the underlying theoretical formalism of the OMx methods and their implementation in full detail, and we report all relevant OMx parameters for hydrogen, carbon, nitrogen, oxygen, and fluorine. For a standard set of mostly organic molecules commonly used in semiempirical method development, the OMx results are found to be superior to those from standard MNDO-type methods. Parametrized Grimme-type dispersion corrections can be added to OM2 and OM3 energies to provide a realistic treatment of noncovalent interaction energies, as demonstrated for the complexes in the S22 and S66×8 test sets.
Project description:Eph receptors, the largest family of receptor tyrosine kinases, control cell-cell adhesion/de-adhesion, cell morphology and cell positioning through interaction with cell surface ephrin ligands. Bi-directional signalling from the Eph and ephrin complexes on interacting cells have a significant role in controlling normal tissue development and oncogenic tissue patterning. Eph-mediated tissue patterning is based on the fine-tuned balance of adhesion and de-adhesion reactions between distinct Eph- and ephrin-expressing cell populations, and adhesion within like populations (expressing either Eph or ephrin). Here we develop a stochastic, Lagrangian model that is based on Eph/ephrin biology: incorporating independent Brownian motion to describe cell movement and a deterministic term (the drift term) to represent repulsive and adhesive interactions between neighbouring cells. Comparison between the experimental and computer simulated Eph/ephrin cell patterning events shows that the model recapitulates the dynamics of cell-cell segregation and cell cluster formation. Moreover, by modulating the term for Eph/ephrin-mediated repulsion, the model can be tuned to match the actual behaviour of cells with different levels of Eph expression or activity. Together the results of our experiments and modelling suggest that the complexity of Eph/ephrin signalling mechanisms that control cell-cell interactions can be described well by a mathematical model with a single term balancing adhesion and de-adhesion between interacting cells. This model allows reliable prediction of Eph/ephrin-dependent control of cell patterning behaviour.
Project description:West Nile virus (WNV)-a mosquito-borne arbovirus-entered the USA through New York City in 1999 and spread to the contiguous USA within three years while transitioning from epidemic outbreaks to endemic transmission. The virus is transmitted by vector competent mosquitoes and maintained in the avian populations. WNV spatial distribution is mainly determined by the movement of residential and migratory avian populations. We developed an individual-level heterogeneous network framework across the USA with the goal of understanding the long-range spatial distribution of WNV. To this end, we proposed three distance dispersal kernels model: 1) exponential-short-range dispersal, 2) power-law-long-range dispersal in all directions, and 3) power-law biased by flyway direction -long-range dispersal only along established migratory routes. To select the appropriate dispersal kernel we used the human case data and adopted a model selection framework based on approximate Bayesian computation with sequential Monte Carlo sampling (ABC-SMC). From estimated parameters, we find that the power-law biased by flyway direction kernel is the best kernel to fit WNV human case data, supporting the hypothesis of long-range WNV transmission is mainly along the migratory bird flyways. Through extensive simulation from 2014 to 2016, we proposed and tested hypothetical mitigation strategies and found that mosquito population reduction in the infected states and neighboring states is potentially cost-effective.