Modelling evolutionary cell behaviour using neural networks: Application to tumour growth

In this paper, we present a modelling framework for cellular evolution that is based on the notion that a cell’s behaviour is driven by interactions with other cells and its immediate environment. We equip each cell with a phenotype that determines its behaviour and implement a decision mechanism to allow evolution of this phenotype. This decision mechanism is modelled using feed-forward neural networks, which have been suggested as suitable models of cell signalling pathways. The environmental variables are presented as inputs to the network and result in a response that corresponds to the phenotype of the cell. The response of the network is determined by the network parameters, which are subject to mutations when the cells divide. This approach is versatile as there are no restrictions on what the input or output nodes represent, they can be chosen to represent any environmental variables and behaviours that are of importance to the cell population under consideration. This framework was implemented in an individual-based model of solid tumour growth in order to investigate the impact of the tissue oxygen concentration on the growth and evolutionary dynamics of the tumour. Our results show that the oxygen concentration affects the tumour at the morphological level, but more importantly has a direct impact on the evolutionary dynamics. When the supply of oxygen is limited we observe a faster divergence away from the initial genotype, a higher population diversity and faster evolution towards aggressive phenotypes. The implementation of this framework suggests that this approach is well suited for modelling systems where evolution plays an important role and where a changing environment exerts selection pressure on the evolving population.     

In situ measurement of cell stiffness of Arabidopsis roots growing on a glass micropillar support by atomic force microscopy

Atomic force microscopy (AFM) can measure the mechanical properties of plant tissue at the cellular level, but for in situ observations, the sample must be held in place on a rigid support and it is difficult to obtain accurate data for living plants without inhibiting their growth. To investigate the dynamics of root cell stiffness during seedling growth, we circumvented these problems by using an array of glass micropillars as a support to hold an Arabidopsis thaliana root for AFM measurements without inhibiting root growth. The root elongated in the gaps between the pillars and was supported by the pillars. The AFM cantilever could contact the root for repeated measurements over the course of root growth. The elasticity of the root epidermal cells was used as an index of the stiffness. By contrast, we were not able to reliably observe roots on a smooth glass substrate because it was difficult to retain contact between the root and the cantilever without the support of the pillars. Using adhesive to fix the root on the smooth glass plane overcame this issue, but prevented root growth. The glass micropillar support allowed reproducible measurement of the spatial and temporal changes in root cell elasticity, making it possible to perform detailed AFM observations of the dynamics of root cell stiffness.     

Direct force measurement of single DNA–peptide interactions using atomic force microscopy

The selective interactions between DNA and miniature (39 residues) engineered peptide were directly measured at the single‐molecule level by using atomic force microscopy. This peptide (p007) contains an α‐helical recognition site similar to leucine zipper GCN4 and specifically recognizes the ATGAC sequence in the DNA with nanomolar affinity. The average rupture force was 42.1 pN, which is similar to the unbinding forces of the digoxigenin–antidigoxigenin complex, one of the strongest interactions in biological systems. The single linear fit of the rupture forces versus the logarithm of pulling rates showed a single energy barrier with a transition state located at 0.74 nm from the bound state. The smaller k_off compared with that of other similar systems was presumably due to the increased stability of the helical structure by putative folding residues in p007. This strong sequence‐specific DNA–peptide interaction has a potential to be utilized to prepare well‐defined mechanically stable DNA–protein hybrid nanostructures. Copyright © 2013 John Wiley & Sons, Ltd.     

Muscle force estimation in clinical gait analysis using AnyBody and OpenSim

A variety of musculoskeletal models are applied in different modelling environments for estimating muscle forces during gait. Influence of different modelling assumptions and approaches on model outputs are still not fully understood, while direct comparisons of standard approaches have been rarely undertaken. This study seeks to compare joint kinematics, joint kinetics and estimated muscle forces of two standard approaches offered in two different modelling environments (AnyBody, OpenSim). It is hypothesised that distinctive differences exist for individual muscles, while summing up synergists show general agreement. Experimental data of 10 healthy participants (28 ± 5 years, 1.72 ± 0.08 m, 69 ± 12 kg) was used for a standard static optimisation muscle force estimation routine in AnyBody and OpenSim while using two gait-specific musculoskeletal models. Statistical parameter mapping paired t-test was used to compare joint angle, moment and muscle force waveforms in Matlab. Results showed differences especially in sagittal ankle and hip angles as well as sagittal knee moments. Differences were also found for some of the muscles, especially of the triceps surae group and the biceps femoris short head, which occur as a result of different anthropometric and anatomical definitions (mass and inertia of segments, muscle properties) and scaling procedures (static vs. dynamic). Understanding these differences and their cause is crucial to operate such modelling environments in a clinical setting. Future research should focus on alternatives to classical generic musculoskeletal models (e.g. implementation of functional calibration tasks), while using experimental data reflecting normal and pathological gait to gain a better understanding of variations and divergent behaviour between approaches.     

Functional identification of biological neural networks using reservoir adaptation for point processes

The complexity of biological neural networks does not allow to directly relate their biophysical properties to the dynamics of their electrical activity. We present a reservoir computing approach for functionally identifying a biological neural network, i.e. for building an artificial system that is functionally equivalent to the reference biological network. Employing feed-forward and recurrent networks with fading memory, i.e. reservoirs, we propose a point process based learning algorithm to train the internal parameters of the reservoir and the connectivity between the reservoir and the memoryless readout neurons. Specifically, the model is an Echo State Network (ESN) with leaky integrator neurons, whose individual leakage time constants are also adapted. The proposed ESN algorithm learns a predictive model of stimulus-response relations in in vitro and simulated networks, i.e. it models their response dynamics. Receiver Operating Characteristic (ROC) curve analysis indicates that these ESNs can imitate the response signal of a reference biological network. Reservoir adaptation improved the performance of an ESN over readout-only training methods in many cases. This also held for adaptive feed-forward reservoirs, which had no recurrent dynamics. We demonstrate the predictive power of these ESNs on various tasks with cultured and simulated biological neural networks.     

Application of atomic force microscopy to the study of micromechanical properties of biological materials

Atomic force microscopy (AFM) has been used to study the micromechanical properties of biological systems. Its unique ability to function both as an imaging device and force sensor with nanometer resolution in both gaseous and liquid environments has meant that AFM has provided unique insights into the mechanical behaviour of tissues, cells and single molecules. As a surface scanning device, AFM can map properties such as adhesion and the Young's modulus of surfaces. As a force sensor and nanoindentor AFM can directly measure properties such as the Young's modulus of surfaces or the binding forces of cells. As a stress-strain gauge AFM can study the stretching of single molecules or fibres and as a nanomanipulator it can dissect biological particles such as viruses or DNA strands. The present paper reviews key research that has demonstrated the versatility of AFM and how it can be exploited to study the micromechanical behaviour of biological materials.     

Extraction of membrane proteins from a living cell surface using the atomic force microscope and covalent crosslinkers

The force curve mode of the atomic force microscope (AFM) was applied to extract intrinsic membrane proteins from the surface of live cells using AFM tips modified by amino reactive bifunctional covalent crosslinkers. The modified AFM tips were individually brought into brief contact with the living cell surface to form covalent bonds with cell surface molecules. The force curves recorded during the detachment process from the cell surface were often characterized by an extension of a few hundred nanometers followed mostly by a single step jump to the zero force level. Collection and analysis of the final rupture force revealed that the most frequent force values (of the force) were in the range of 0.4–0.6 nN. The observed rupture force most likely represented extraction events of intrinsic membrane proteins from the cell membrane because the rupture force of a covalent crosslinking system was expected to be significantly larger than 1.0 nN, and the separation force of noncovalent ligand-receptor pairs to be less than 0.2 nN, under similar experimental conditions. The transfer of cell surface proteins to the AFM tip was verified by recording characteristic force curves of protein stretching between the AFM tips used on the cell surface and a silicon surface modified with amino reactive bifunctional crosslinkers. This method will be a useful addition to bionanotechnological research for the application of AFM.     

Atomic force microscope-based single cell force spectroscopy of breast cancer cell lines: An approach for evaluating cellular invasion

The adhesiveness of cancerous cells to their neighboring cells significantly contributes to tumor progression and metastasis. The single-cell force spectroscopy (SCFS) approach was implemented to survey the cell–cell adhesion force between cancerous cells in three cancerous breast cell lines (MCF-7, T47D, and MDA-MB-231). The gene expression levels of two dominant cell adhesion markers (E-cadherin and N-cadherin) were quantified by real-time PCR. Additionally, the local stiffness of the cell bodies was measured by atomic force microscopy (AFM), and the actin cytoskeletal organization was examined by confocal microscopy. Results indicated that the adhesion force between cells was conversely correlated with their invasion potential. The highest adhesion force was observed in the MCF-7 cells. A reduction in cell–cell adhesion, which is required for the detachment of cells from the main tumor during metastasis, is partly due to the loss of E-cadherin expression and the enhanced expression of N-cadherins. The reduced adhesion was accompanied by the softening of cells, as described by the rearrangement of actin filaments through confocal microscopy observations. The softening of the cell body and the reduced cellular adhesiveness are two adaptive mechanisms through which malignant cells achieve the increased deformability, motility, and strong metastasis potential necessary for passage through endothelial junctions and positioning in host tissue. This study presented application of SCFS to survey cell phenotype transformation during cancer progression. The results can be implemented as a platform for further investigations that target the manipulation of cellular adhesiveness and stiffness as a therapeutic choice.     

Investigating the relationship between proteomic,compositional, and histologic biomarkers and cartilage biomechanics using artificial neural networks

A thorough understanding of the relationship between the biological and mechanical functions of articular cartilage is necessary to develop diagnostics and treatments for arthritic diseases. A key step in developing this understanding is the establishment of models which utilize large numbers of biomarkers to create comprehensive models of the interplay between cartilage biology and biomechanics, which will more accurately demonstrate the complex etiology and progression of tissue adaptation and degradation. It is the goal of this study to demonstrate the ability of artificial neural networks (ANNs) to utilize biomarkers to create predictive models of articular cartilage biomechanics, which will provide a basis for more sophisticated research in the future. Osteochondral plugs were collected from patients undergoing total knee arthroplasty, cultured, then analyzed to collect proteomic, compositional, and histologic biomarker data. Samples were subjected to stress relaxation testing as well as computational simulations using finite element analysis (FEA) modeling and optimization to determine key mechanical properties. The acquired data was fed into an ANN to generate a model which predicts the biomechanical properties of cartilage from given biomarkers. Using all significant inputs, the developed neural network predicted the ground substance modulus with a moderate degree of accuracy, but had difficulty predicting the collagen fiber modulus and cartilage permeability. Using only clinically attainable biomarkers, the best-performing model produced comparably accurate and more consistent predictions of all three mechanical properties. These models demonstrate the potential for ANNs to be included in clinical studies of articular cartilage.     

Measurement of cell adhesion force by vertical forcible detachment using an arrowhead nanoneedle and atomic force microscopy

The properties of substrates and extracellular matrices (ECM) are important factors governing the functions and fates of mammalian adherent cells. For example, substrate stiffness often affects cell differentiation. At focal adhesions, clustered–integrin bindings link cells mechanically to the ECM. In order to quantitate the affinity between cell and substrate, the cell adhesion force must be measured for single cells. In this study, forcible detachment of a single cell in the vertical direction using AFM was carried out, allowing breakage of the integrin–substrate bindings. An AFM tip was fabricated into an arrowhead shape to detach the cell from the substrate. Peak force observed in the recorded force curve during probe retraction was defined as the adhesion force, and was analyzed for various types of cells. Some of the cell types adhered so strongly that they could not be picked up because of plasma membrane breakage by the arrowhead probe. To address this problem, a technique to reinforce the cellular membrane with layer-by-layer nanofilms composed of fibronectin and gelatin helped to improve insertion efficiency and to prevent cell membrane rupture during the detachment process, allowing successful detachment of the cells. This method for detaching cells, involving cellular membrane reinforcement, may be beneficial for evaluating true cell adhesion forces in various cell types.     

A new training algorithm using artificial neural networks to classify gender-specific dynamic gait patterns

The aim of this study was to present a new training algorithm using artificial neural networks called multi-objective least absolute shrinkage and selection operator (MOBJ-LASSO) applied to the classification of dynamic gait patterns. The movement pattern is identified by 20 characteristics from the three components of the ground reaction force which are used as input information for the neural networks in gender-specific gait classification. The classification performance between MOBJ-LASSO (97.4%) and multi-objective algorithm (MOBJ) (97.1%) is similar, but the MOBJ-LASSO algorithm achieved more improved results than the MOBJ because it is able to eliminate the inputs and automatically select the parameters of the neural network. Thus, it is an effective tool for data mining using neural networks. From 20 inputs used for training, MOBJ-LASSO selected the first and second peaks of the vertical force and the force peak in the antero-posterior direction as the variables that classify the gait patterns of the different genders.     

Biomechanical measurement and analysis of colchicine-induced effects on cells by nanoindentation using an atomic force microscope

Colchicine is a drug commonly used for the treatment of gout, however, patients may sometimes encounter side-effects induced by taking colchicine, such as nausea, vomiting, diarrhea and kidney failure. In this regard, it is imperative to investigate the mechanism effects of colchicine on biological cells. In this paper, we present a method for the detection of mechanical properties of nephrocytes (VERO cells), hepatocytes (HL-7702 cells) and hepatoma cells (SMCC-7721 cells) in culture by atomic force microscope (AFM) to analyze the 0.1 μg/mL colchicine-induced effects on the nanoscale for two, four and six hours. Compared to the corresponding control cells, the biomechanical properties of the VERO and SMCC-7721 cells changed significantly and the HL-7702 cells did not considerably change after the treatment when considering the same time period. Based on biomechanical property analyses, the colchicine solution made the VERO and SMCC-7721 cells harder. We conclude that it is possible to reduce the division rate of the VERO cells and inhibit the metastasis of the SMCC-7721 cells. The method described here can be applied to study biomechanics of many other types of cells with different drugs. Therefore, this work provides an accurate and rapid method for drug screening and mechanical analysis of cells in medical research.     

Atomic force microscopy-based cell nanostructure for ligand-conjugated quantum dot endocytosis

While it has been well demonstrated that quantum dots (QDs) play an important role inbiological labeling both in vitro and in vivo,there is no report describing the cellular nanostructure basis ofreceptor-mediated endocytosis.Here,nanostructure evolution responses to the endocytosis of transferrin(Tf)-conjugated QDs were characterized by atomic force microscopy (AFM).AFM-based nanostructureanalysis demonstrated that the Tf-conjugated QDs were specifically and tightly bound to the cell receptorsand the nanostructure evolution is highly correlated with the cell membrane receptor-mediated transduction.Consistently,confocal microscopic and flow cytometry results have demonstrated the specificity anddynamic property of Tf-QD binding and internalization.We found that the internalization of Tf-QD is linearlyrelated to time.Moreover,while the nanoparticles on the cell membrane increased,the endocytosis was stillvery active,suggesting that QD nanoparticles did not interfere sterically with the binding and function ofreceptors.Therefore,ligand-conjugated QDs are potentially useful in biological labeling of cells at a nanometerscale.     

A neural basis for gyroscopic force measurement in the halteres of <Emphasis Type="Italic">Holorusia</Emphasis>

Dipteran flight requires rapid acquisition of mechanosensory information provided by modified hindwings known as halteres. Halteres experience torques resulting from Coriolis forces that arise during body rotations. Although biomechanical and behavioral data indicate that halteres detect Coriolis forces, there are scant data regarding neural encoding of these or any other forces. Coriolis forces arise on the haltere as it oscillates in one plane while rotating in another, and occur at oscillation frequency and twice the oscillation frequency. Using single-fiber recordings of haltere primary afferent responses to mechanical stimuli, we show that spike rate increases linearly with stimulation frequency up to 150 Hz, much higher than twice the natural oscillation frequency of 40 Hz. Furthermore, spike-timing precision is extremely high throughout the frequency range tested. These characteristics indicate that afferents respond with high speed and high precision, neural features that are useful for detecting Coriolis forces. Additionally, we found that neurons respond preferentially to specific stimulus directions, with most responding more strongly to stimulation in the orthogonal plane. Directional sensitivity, coupled with precise, high-speed encoding, suggests that haltere afferents are capable of providing information about forces occurring at the haltere base, including Coriolis forces.     

Evaluating the efficiency of enzyme accelerated CO2 capture: chemical kinetics modelling for interpreting measurement results

In this paper, the efficiency of the carbonic anhydrase (CA) enzyme in accelerating the hydration of CO₂ is evaluated using a measurement system which consists of a vessel in which a gaseous flow of mixtures of nitrogen and CO₂ is bubbled into water or water solutions containing a known quantity of CA enzyme. The pH value of the solution and the CO₂ concentration at the measurement system gas exhaust are continuously monitored. The measured CO₂ level allows for assessing the quantity of CO₂, which, subtracted from the gaseous phase, is dissolved into the liquid phase and/or hydrated to bicarbonate. The measurement procedure consists of inducing a transient and observing and modelling the different kinetics involved in the steady-state recovery with and without CA. The main contribution of this work is exploiting dynamical system theory and chemical kinetics modelling for interpreting measurement results for characterising the activity of CA enzymes. The data for model fitting are obtained from a standard bioreactor, in principle equal to standard two-phase bioreactors described in the literature, in which two different techniques can be used to move the process itself away from the steady-state, inducing transients.     

Correcting for measurement error in fractional polynomial models using Bayesian modelling and regression calibration,with an application to alcohol and mortality

Exposure measurement error can result in a biased estimate of the association between an exposure and outcome. When the exposure–outcome relationship is linear on the appropriate scale (e.g. linear, logistic) and the measurement error is classical, that is the result of random noise, the result is attenuation of the effect. When the relationship is non‐linear, measurement error distorts the true shape of the association. Regression calibration is a commonly used method for correcting for measurement error, in which each individual's unknown true exposure in the outcome regression model is replaced by its expectation conditional on the error‐prone measure and any fully measured covariates. Regression calibration is simple to execute when the exposure is untransformed in the linear predictor of the outcome regression model, but less straightforward when non‐linear transformations of the exposure are used. We describe a method for applying regression calibration in models in which a non‐linear association is modelled by transforming the exposure using a fractional polynomial model. It is shown that taking a Bayesian estimation approach is advantageous. By use of Markov chain Monte Carlo algorithms, one can sample from the distribution of the true exposure for each individual. Transformations of the sampled values can then be performed directly and used to find the expectation of the transformed exposure required for regression calibration. A simulation study shows that the proposed approach performs well. We apply the method to investigate the relationship between usual alcohol intake and subsequent all‐cause mortality using an error model that adjusts for the episodic nature of alcohol consumption.     

Novel recurrent neural network for modelling biological networks: Oscillatory p53 interaction dynamics

Understanding the control of cellular networks consisting of gene and protein interactions and their emergent properties is a central activity of Systems Biology research. For this, continuous, discrete, hybrid, and stochastic methods have been proposed. Currently, the most common approach to modelling accurate temporal dynamics of networks is ordinary differential equations (ODE). However, critical limitations of ODE models are difficulty in kinetic parameter estimation and numerical solution of a large number of equations, making them more suited to smaller systems. In this article, we introduce a novel recurrent artificial neural network (RNN) that addresses above limitations and produces a continuous model that easily estimates parameters from data, can handle a large number of molecular interactions and quantifies temporal dynamics and emergent systems properties. This RNN is based on a system of ODEs representing molecular interactions in a signalling network. Each neuron represents concentration change of one molecule represented by an ODE. Weights of the RNN correspond to kinetic parameters in the system and can be adjusted incrementally during network training. The method is applied to the p53-Mdm2 oscillation system – a crucial component of the DNA damage response pathways activated by a damage signal. Simulation results indicate that the proposed RNN can successfully represent the behaviour of the p53-Mdm2 oscillation system and solve the parameter estimation problem with high accuracy. Furthermore, we presented a modified form of the RNN that estimates parameters and captures systems dynamics from sparse data collected over relatively large time steps. We also investigate the robustness of the p53-Mdm2 system using the trained RNN under various levels of parameter perturbation to gain a greater understanding of the control of the p53-Mdm2 system. Its outcomes on robustness are consistent with the current biological knowledge of this system. As more quantitative data become available on individual proteins, the RNN would be able to refine parameter estimation and mapping of temporal dynamics of individual signalling molecules as well as signalling networks as a system. Moreover, RNN can be used to modularise large signalling networks.