Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport.

Auxin is a well-studied plant hormone, the spatial distribution of which remains incompletely understood. Here, we investigate the effects of cell growth and divisions on the dynamics of auxin patterning, using a combination of mathematical modelling and experimental observations. In contrast to most prior work, models are not designed or tuned with the aim to produce a specific auxin pattern. Instead, we use well-established techniques from dynamical systems theory to uncover and classify ranges of auxin patterns as exhaustively as possible as parameters are varied. Previous work using these techniques has shown how a multitude of stable auxin patterns may coexist, each attainable from a specific ensemble of initial conditions. When a key parameter spans a range of values, these steady patterns form a geometric curve with successive folds, often nicknamed a snaking diagram. As we introduce growth and cell division into a one-dimensional model of auxin distribution, we observe new behaviour which can be explained in terms of this diagram. Cell growth changes the shape of the snaking diagram, and this corresponds in turn to deformations in the patterns of auxin distribution. As divisions occur this can lead to abrupt creation or annihilation of auxin peaks. We term this phenomenon 'snake-jumping'. Under rhythmic cell divisions, we show how this can lead to stable oscillations of auxin. We also show that this requires a high level of synchronisation between cell divisions. Using 18 hour time-lapse imaging of the auxin reporter DII:Venus in roots of Arabidopsis thaliana, we show auxin fluctuates greatly, both in terms of amplitude and periodicity, consistent with the snake-jumping events observed with non-synchronised cell divisions. Periodic signals downstream of the auxin signalling pathway have previously been recorded in plant roots. The present work shows that auxin alone is unlikely to play the role of a pacemaker in this context.

Positive Linear Relationship between Nucleophosmin Protein Expression and the Viral Load in HPV-Associated Oropharyngeal Squamous Cell Carcinoma: A Possible Tool for Stratification of Patients.

Most oropharyngeal squamous cell carcinomas (OPSCCs) are human papillomavirus (HPV)-associated, high-risk (HR) cancers that show a better response to chemoradiotherapy and are associated with improved survival. Nucleophosmin (NPM, also called NPM1/B23) is a nucleolar phosphoprotein that plays different roles within the cell, such as ribosomal synthesis, cell cycle regulation, DNA damage repair and centrosome duplication. NPM is also known as an activator of inflammatory pathways. An increase in NPM expression has been observed in vitro in E6/E7 overexpressing cells and is involved in HPV assembly. In this retrospective study, we investigated the relationship between the immunohistochemical (IHC) expression of NPM and HR-HPV viral load, assayed by RNAScope in situ hybridization (ISH), in ten patients with histologically confirmed p16-positive OPSCC. Our findings show that there is a positive correlation between NPM expression and HR-HPV mRNA (Rs = 0.70, p = 0.03), and a linear regression (r2 = 0.55; p = 0.01). These data support the hypothesis that NPM IHC, together with HPV RNAScope, could be used as a predictor of transcriptionally active HPV presence and tumor progression, which is useful for therapy decisions. This study includes a small cohort of patients and, cannot report conclusive findings. Further studies with large series of patients are needed to support our hypothesis.

Cross-scale excitability in networks of quadratic integrate-and-fire neurons.

From the action potentials of neurons and cardiac cells to the amplification of calcium signals in oocytes, excitability is a hallmark of many biological signalling processes. In recent years, excitability in single cells has been related to multiple-timescale dynamics through canards, special solutions which determine the effective thresholds of the all-or-none responses. However, the emergence of excitability in large populations remains an open problem. Here, we show that the mechanism of excitability in large networks and mean-field descriptions of coupled quadratic integrate-and-fire (QIF) cells mirrors that of the individual components. We initially exploit the Ott-Antonsen ansatz to derive low-dimensional dynamics for the coupled network and use it to describe the structure of canards via slow periodic forcing. We demonstrate that the thresholds for onset and offset of population firing can be found in the same way as those of the single cell. We combine theoretical analysis and numerical computations to develop a novel and comprehensive framework for excitability in large populations, applicable not only to models amenable to Ott-Antonsen reduction, but also to networks without a closed-form mean-field limit, in particular sparse networks.

Laccase Mediator Cocktail System as a Sustainable Skin Whitening Agent for Deep Eumelanin Decolorization.

The overproduction of eumelanin leads to a panel of unaesthetic hyper-pigmented skin diseases, including melasma and age spots. The treatment of these diseases often requires the use of tyrosinase inhibitors, which act as skin whitening agents by inhibiting the synthesis of eumelanin, with harmful side effects. We report here that laccase from Trametes versicolor in association with a cocktail of natural phenol redox mediators efficiently degraded eumelanin from Sepia officinalis, offering an alternative procedure to traditional whitening agents. Redox mediators showed a synergistic effect with respect to their single-mediator counterpart, highlighting the beneficial role of the cocktail system. The pro-oxidant DHICA sub-units of eumelanin were degraded better than the DHI counterpart, as monitored by the formation of pyrrole-2,3,5-tricarboxylic acid (PTCA) and pyrrole-2,3-dicarboxylic acid (PDCA) degradation products. The most effective laccase-mediated cocktail system was successively applied in a two-component prototype of a topical whitening cream, showing high degradative efficacy against eumelanin.

Extracellular Nucleophosmin Is Increased in Psoriasis and Correlates With the Determinants of Cardiovascular Diseases.

We previously showed that genotoxic stress induced an active extracellular release of nucleophosmin (NPM) in human cardiac mesenchymal progenitor cells, and that serum deprivation provokes NPM secretion from human endothelial cells, eliciting inflammation via nuclear factor kappa B (NF-kB) transcriptional activation. In this study, we wanted to determine whether NPM was similarly modulated in the skin and plasma of psoriatic patients (Pso). We found that NPM was induced in 6 skin biopsies compared to 6 normal skin biopsies and was markedly increased in lesional (LS) vs. non-lesional skin (NLS) biopsies. Moreover, NPM was also increased at the transcriptional levels in LS vs. NLS. Both the innate stimuli, such as lipopolysaccharides and Poly inositol-cytosine and adaptive stimuli, that is, cytokine mix, were able to induce the extracellular release of NPM in immortalized keratinocytes and human skin fibroblasts in the absence of cytotoxicity. Interestingly, NPM interacts with Toll-like receptor (TLR)4 in these cells and activates an NF-kB-dependent inflammatory pathway upregulating interleukin IL-6 and COX-2 gene expression. Finally, circulating NPM was increased in the plasma of 29 Pso compared to 29 healthy controls, and positively correlates with psoriasis area severity index (PASI) and with determinants of cardiovascular diseases (CVDs), such as pulse wave velocity, systolic pressure, and left ventricular mass. Furthermore, NPM positively correlates with miR-200c circulating levels, which we previously showed to increase in Pso and correlate with CVD progression. Our data show that circulating miR-200c is physically associated with extracellular NPM, which most probably is responsible for its extracellular release and protection upon cytokine mix via a TLR4-mechanism. In conclusion, NPM is increased in psoriasis both in the skin and plasma and might be considered a novel biologic target to counteract chronic inflammation associated with CVD risk.

Modelling the emergence of cities and urban patterning using coupled integro-differential equations.

Human residential population distributions show patterns of higher density clustering around local services such as shops and places of employment, displaying characteristic length scales; Fourier transforms and spatial autocorrelation show the length scale between UK cities is around 45 km. We use integro-differential equations to model the spatio-temporal dynamics of population and service density under the assumption that they benefit from spatial proximity, captured via spatial weight kernels. The system tends towards a well-mixed homogeneous state or a spatial pattern. Linear stability analysis around the homogeneous steady state predicts a modelled length-scale consistent with that observed in the data. Moreover, we show that spatial instability occurs only for perturbations with a sufficiently long wavelength and only where there is a sufficiently strong dependence of service potential on population density. Within urban centres, competition for space may cause services and population to be out of phase with one another, occupying separate parcels of land. By introducing competition, along with a preference for population to be located near, but not too near, to high service density areas, secondary out-of-phase patterns occur within the model, at a higher density and with a shorter length scale than in phase patterning. Thus, we show that a small set of core behavioural ingredients can generate aggregations of populations and services, and pattern formation within cities, with length scales consistent with real-world data. The analysis and results are valid across a wide range of parameter values and functional forms in the model.

Green and Scalable Preparation of Colloidal Suspension of Lignin Nanoparticles and Its Application in Eco-friendly Sunscreen Formulations.

Lignin nanoparticles (LNPs) are applied in several industrial applications. The nanoprecipitation of LNPs is fast and inexpensive but currently still limited to the use of hazardous organic solvents, making it difficult to apply them on a large scale. Here, we report a scalable nanoprecipitation procedure for the preparation of colloidal lignin nanoparticles (cLNPs) by the use of the green solvents dimethylisosorbide and isopropylidene glycerol. Irrespective of the experimental conditions, cLNPs showed higher UV absorbing properties and radical scavenging activity than parent LNPs and raw lignin. cLNPs were successively used in the preparation of eco-friendly sunscreen formulations (SPF 15, 30, and 50+, as evaluated by the COLIPA assay), which showed high UV-shielding activity even in the absence of synthetic boosters (microplastics) and physical filters (TiO2 and ZnO). Biological assays on human HaCaT keratinocytes and human skin equivalents demonstrated the absence of cytotoxicity and genotoxicity, associated with an optimal protection of the skin from UV-A damage.

A dynamic neural field model of continuous input integration.

The ability of neural systems to turn transient inputs into persistent changes in activity is thought to be a fundamental requirement for higher cognitive functions. In continuous attractor networks frequently used to model working memory or decision making tasks, the persistent activity settles to a stable pattern with the stereotyped shape of a "bump" independent of integration time or input strength. Here, we investigate a new bump attractor model in which the bump width and amplitude not only reflect qualitative and quantitative characteristics of a preceding input but also the continuous integration of evidence over longer timescales. The model is formalized by two coupled dynamic field equations of Amari-type which combine recurrent interactions mediated by a Mexican-hat connectivity with local feedback mechanisms that balance excitation and inhibition. We analyze the existence, stability and bifurcation structure of single and multi-bump solutions and discuss the relevance of their input dependence to modeling cognitive functions. We then systematically compare the pattern formation process of the two-field model with the classical Amari model. The results reveal that the balanced local feedback mechanisms facilitate the encoding and maintenance of multi-item memories. The existence of stable subthreshold bumps suggests that different to the Amari model, the suppression effect of neighboring bumps in the range of lateral competition may not lead to a complete loss of information. Moreover, bumps with larger amplitude are less vulnerable to noise-induced drifts and distance-dependent interaction effects resulting in more faithful memory representations over time.

Enhanced NAMPT-Mediated NAD Salvage Pathway Contributes to Psoriasis Pathogenesis by Amplifying Epithelial Auto-Inflammatory Circuits.

Dysregulated cross-talk between immune cells and epithelial compartments is responsible for the onset and amplification of pathogenic auto-inflammatory circuits occurring in psoriasis. NAMPT-mediated NAD salvage pathway has been recently described as an immunometabolic route having inflammatory function in several disorders, including arthritis and inflammatory bowel diseases. To date, the role of NAD salvage pathway has not been explored in the skin of patients affected by psoriasis. Here, we show that NAD content is enhanced in lesional skin of psoriatic patients and is associated to high NAMPT transcriptional levels. The latter are drastically reduced in psoriatic skin following treatment with the anti-IL-17A biologics secukinumab. We provide evidence that NAMPT-mediated NAD+ metabolism fuels the immune responses executed by resident skin cells in psoriatic skin. In particular, intracellular NAMPT, strongly induced by Th1/Th17-cytokines, acts on keratinocytes by inducing hyper-proliferation and impairing their terminal differentiation. Furthermore, NAMPT-mediated NAD+ boosting synergizes with psoriasis-related cytokines in the upregulation of inflammatory chemokines important for neutrophil and Th1/Th17 cell recruitment. In addition, extracellular NAMPT, abundantly released by keratinocytes and dermal fibroblasts, acts in a paracrine manner on endothelial cells by inducing their proliferation and migration, as well as the expression of ICAM-1 membrane molecule and chemokines important for leukocyte recruitment into inflamed skin. In conclusion, our results showed that NAMPT-mediated NAD salvage pathway contributes to psoriasis pathogenic processes by amplifying epithelial auto-inflammatory responses in psoriasis.

Doxorubicin induces an alarmin-like TLR4-dependent autocrine/paracrine action of Nucleophosmin in human cardiac mesenchymal progenitor cells.

BACKGROUND: Doxorubicin (Dox) is an anti-cancer anthracycline drug that causes double-stranded DNA breaks. It is highly effective against several types of tumours; however, it also has adverse effects on regenerative populations of normal cells, such as human cardiac mesenchymal progenitor cells (hCmPCs), and its clinical use is limited by cardiotoxicity. Another known effect of Dox is nucleolar disruption, which triggers the ubiquitously expressed nucleolar phosphoprotein Nucleophosmin (NPM) to be released from the nucleolus into the cell, where it participates in the orchestration of cellular stress responses. NPM has also been observed in the extracellular space in response to different stress stimuli; however, the mechanism behind this and its functional implications are as yet largely unexplored. The aim of this study was to establish whether Dox could elicit NPM secretion in the extracellular space and to elucidate the mechanism of secretion and the effect of extracellular NPM on hCmPCs. RESULTS: We found that following the double-strand break formation in hCmPCs caused by Dox, NPM was rapidly secreted in the extracellular space by an active mechanism, in the absence of either apoptosis or necrosis. Extracellular release of NPM was similarly seen in response to ultraviolet radiation (UV). Furthermore, we observed an increase of NPM levels in the plasma of Dox-treated mice; thus, NPM release also occurred in vivo. The treatment of hCmPCs with extracellular recombinant NPM induced a decrease of cell proliferation and a response mediated through the Toll-like receptor (TLR)4. We demonstrated that NPM binds to TLR4, and via TLR4, and nuclear factor kappa B (NFkB) activation/nuclear translocation, exerts proinflammatory functions by inducing IL-6 and COX-2 gene expression. Finally, we found that in hCmPCs, NPM secretion could be driven by an autophagy-dependent unconventional mechanism that requires TLR4, since TLR4 inhibition dramatically reduced Dox-induced secretion. CONCLUSIONS: We hypothesise that the extracellular release of NPM could be a general response to DNA damage since it can be elicited by either a chemical agent such as Dox or a physical genotoxic stressor such as UV radiation. Following genotoxic stress, NPM acts similarly to an alarmin in hCmPCs, being rapidly secreted and promoting cell cycle arrest and a TLR4/NFκB-dependent inflammatory response.

The Nucleolar Protein Nucleophosmin Is Physiologically Secreted by Endothelial Cells in Response to Stress Exerting Proangiogenic Activity Both In Vitro and In Vivo.

Nucleophosmin (NPM), a nucleolar multifunctional phosphoprotein, acts as a stress sensor in different cell types. NPM can be actively secreted by inflammatory cells, however its biology on endothelium remains unexplored. In this study, we show for the first time that NPM is secreted by human vein endothelial cells (HUVEC) in the early response to serum deprivation and that NPM acts as a pro-inflammatory and angiogenic molecule both in vitro and in vivo. Accordingly, 24 h of serum starvation condition induced NPM relocalization from the nucleus to cytoplasm. Interestingly, NPM was increasingly excreted in HUVEC-derived conditioned media in a time dependent fashion upon stress conditions up to 24 h. The secretion of NPM was unrelated to cell necrosis within 24 h. The treatment with exogenous and recombinant NPM (rNPM) enhanced migration as well as the Intercellular Adhesion Molecule 1 (ICAM-1) but not Vascular cell adhesion protein 1 (VCAM-1) expression and it did not affect cell proliferation. Notably, in vitro tube formation by Matrigel assay was significantly increased in HUVEC treated with rNPM compared to controls. This result was confirmed by the in vivo injection of Matrigel plug assay upon stimulation with rNPM, displaying significant enhanced number of functional capillaries in the plugs. The stimulation with rNPM in HUVEC was also associated to the increased expression of master genes regulating angiogenesis and migration, including Vascular Endothelial Growth Factor-A (VEGF-A), Hepatocyte Growth Factor (HGF), Stromal derived factor-1 (SDF-1), Fibroblast growth factor-2 (FGF-2), Platelet Derived Growth Factor-B (PDGF-B), and Matrix metallopeptidase 9 (MMP9). Our study demonstrates for the first time that NPM is physiologically secreted by somatic cells under stress condition and in the absence of cell necrosis. The analysis of the biological effects induced by NPM mainly related to a pro-angiogenic and inflammatory activity might suggest an important autocrine/paracrine role for NPM in the regulation of both phenomena.

Nano-Structured Lignin as Green Antioxidant and UV Shielding Ingredient for Sunscreen Applications.

Green, biocompatible, and biodegradable antioxidants represent a milestone in cosmetic and cosmeceutical applications. Lignin is the most abundant polyphenol in nature, recovered as a low-cost waste from the pulp and paper industry and biorefinery. This polymer is characterized by beneficial physical and chemical properties which are improved at the nanoscale level due to the emergence of antioxidant and UV shielding activities. Here we review the use of lignin nanoparticles in cosmetic and cosmeceutical applications, focusing on sunscreen and antiaging formulations. Advances in the technology for the preparation of lignin nanoparticles are described highlighting structure activity relationships.

Bumps and oscillons in networks of spiking neurons.

We study localized patterns in an exact mean-field description of a spatially extended network of quadratic integrate-and-fire neurons. We investigate conditions for the existence and stability of localized solutions, so-called bumps, and give an analytic estimate for the parameter range, where these solutions exist in parameter space, when one or more microscopic network parameters are varied. We develop Galerkin methods for the model equations, which enable numerical bifurcation analysis of stationary and time-periodic spatially extended solutions. We study the emergence of patterns composed of multiple bumps, which are arranged in a snake-and-ladder bifurcation structure if a homogeneous or heterogeneous synaptic kernel is suitably chosen. Furthermore, we examine time-periodic, spatially localized solutions (oscillons) in the presence of external forcing, and in autonomous, recurrently coupled excitatory and inhibitory networks. In both cases, we observe period-doubling cascades leading to chaotic oscillations.

Brain-wave equation incorporating axodendritic connectivity.

We introduce an integral model of a two-dimensional neural field that includes a third dimension representing space along a dendritic tree that can incorporate realistic patterns of axodendritic connectivity. For natural choices of this connectivity we show how to construct an equivalent brain-wave partial differential equation that allows for efficient numerical simulation of the model. This is used to highlight the effects that passive dendritic properties can have on the speed and shape of large scale traveling cortical waves.

Enzyme-Lignin Nanocapsules Are Sustainable Catalysts and Vehicles for the Preparation of Unique Polyvalent Bioinks.

Reactive lignin nanocapsules catalyze a pigmentation reaction to furnish an innovative type of sustainable polyvalent bioink. In this nanodevice, the pigment, vehicle, binder, and additive are included in a single confined spherical space. Bioinks with different shades of color, black, gray, yellow-like, pink-like, and red/brown hues, have been prepared by selecting the reactants and the pigmentation process. Lignin nanocapsules play multiple functions in the support and activation of the enzyme necessary for the synthesis of pigments. Lignin nanocapsules protected the melanin pigment from alkaline and UV-degradation treatment.

Next-generation neural field model: The evolution of synchrony within patterns and waves.

Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the neural tissue operates in a near synchronous regime, and hence, cannot account for changes in the underlying synchrony of patterns. It is customary to use spiking neural network models when examining within population synchronization. Unfortunately, these high-dimensional models are notoriously hard to obtain insight from. In this paper, we consider a network of θ-neurons, which has recently been shown to admit an exact mean-field description in the absence of a spatial component. We show that the inclusion of space and a realistic synapse model leads to a reduced model that has many of the features of a standard neural field model coupled to a further dynamical equation that describes the evolution of network synchrony. Both Turing instability analysis and numerical continuation software are used to explore the existence and stability of spatiotemporal patterns in the system. In particular, we show that this new model can support states above and beyond those seen in a standard neural field model. These states are typified by structures within bumps and waves showing the dynamic evolution of population synchrony.

Cardiomyocyte cell cycle dynamics and proliferation revealed through cardiac-specific transgenesis of fluorescent ubiquitinated cell cycle indicator (FUCCI).

RATIONALE: Understanding and manipulating the cardiomyocyte cell cycle has been the focus of decades of research, however the ultimate goal of activating mitotic activity in adult mammalian cardiomyocytes remains elusive and controversial. The relentless pursuit of controlling cardiomyocyte mitosis has been complicated and obfuscated by a multitude of indices used as evidence of cardiomyocyte cell cycle activity that lack clear identification of cardiomyocyte "proliferation" versus cell cycle progression, endoreplication, endomitosis, and even DNA damage. Unambiguous appreciation of the complexity of cardiomyocyte replication that avoids oversimplification and misinterpretation is desperately needed. OBJECTIVE: Track cardiomyocyte cell cycle activity and authenticate fidelity of proliferation markers as indicators of de novo cardiomyogenesis in post-mitotic cardiomyocytes. METHODS AND RESULTS: Cardiomyocytes expressing the FUCCI construct driven by the α-myosin heavy chain promoter were readily and uniformly detected through the myocardium of transgenic mice. Cardiomyocyte cell cycle activity peaks at postnatal day 2 and rapidly declines thereafter with almost all cardiomyocytes arrested at the G1/S cell cycle transition. Myocardial infarction injury in adult hearts prompts transient small increases in myocytes progressing through cell cycle without concurrent mitotic activity, indicating lack of cardiomyogenesis. In comparison, cardiomyogenic activity during early postnatal development correlated with coincidence of FUCCI and cKit+ cells that were undetectable in the adult myocardium. CONCLUSIONS: Cardiomyocyte-specific expression of Fluorescence Ubiquitination-based Cell Cycle Indicators (FUCCI) reveals previously unappreciated aspects of cardiomyocyte cell cycle arrest and biological activity in postnatal development and in response to pathologic damage. Compared to many other methods and model systems, the FUCCI transgenic (FUCCI-Tg) mouse represents a valuable tool to unambiguously track cell cycle and proliferation of the entire cardiomyocyte population in the adult murine heart. FUCCI-Tg provides a desperately needed novel approach in the armamentarium of tools to validate cardiomyocyte proliferative activity that will reveal cell cycle progression, discriminate between cycle progression, DNA replication, and proliferation, and provide important insight for enhancing cardiomyocyte proliferation in the context of adult myocardial tissue.

Network mechanisms underlying the role of oscillations in cognitive tasks.

Oscillatory activity robustly correlates with task demands during many cognitive tasks. However, not only are the network mechanisms underlying the generation of these rhythms poorly understood, but it is also still unknown to what extent they may play a functional role, as opposed to being a mere epiphenomenon. Here we study the mechanisms underlying the influence of oscillatory drive on network dynamics related to cognitive processing in simple working memory (WM), and memory recall tasks. Specifically, we investigate how the frequency of oscillatory input interacts with the intrinsic dynamics in networks of recurrently coupled spiking neurons to cause changes of state: the neuronal correlates of the corresponding cognitive process. We find that slow oscillations, in the delta and theta band, are effective in activating network states associated with memory recall. On the other hand, faster oscillations, in the beta range, can serve to clear memory states by resonantly driving transient bouts of spike synchrony which destabilize the activity. We leverage a recently derived set of exact mean-field equations for networks of quadratic integrate-and-fire neurons to systematically study the bifurcation structure in the periodically forced spiking network. Interestingly, we find that the oscillatory signals which are most effective in allowing flexible switching between network states are not smooth, pure sinusoids, but rather burst-like, with a sharp onset. We show that such periodic bursts themselves readily arise spontaneously in networks of excitatory and inhibitory neurons, and that the burst frequency can be tuned via changes in tonic drive. Finally, we show that oscillations in the gamma range can actually stabilize WM states which otherwise would not persist.

Capturing the Dynamics of a Hybrid Multiscale Cancer Model with a Continuum Model.

Cancer is a complex disease involving processes at spatial scales from subcellular, like cell signalling, to tissue scale, such as vascular network formation. A number of multiscale models have been developed to study the dynamics that emerge from the coupling between the intracellular, cellular and tissue scales. Here, we develop a continuum partial differential equation model to capture the dynamics of a particular multiscale model (a hybrid cellular automaton with discrete cells, diffusible factors and an explicit vascular network). The purpose is to test under which circumstances such a continuum model gives equivalent predictions to the original multiscale model, in the knowledge that the system details are known, and differences in model results can be explained in terms of model features (rather than unknown experimental confounding factors). The continuum model qualitatively replicates the dynamics from the multiscale model, with certain discrepancies observed owing to the differences in the modelling of certain processes. The continuum model admits travelling wave solutions for normal tissue growth and tumour invasion, with similar behaviour observed in the multiscale model. However, the continuum model enables us to analyse the spatially homogeneous steady states of the system, and hence to analyse these waves in more detail. We show that the tumour microenvironmental effects from the multiscale model mean that tumour invasion exhibits a so-called pushed wave when the carrying capacity for tumour cell proliferation is less than the total cell density at the tumour wave front. These pushed waves of tumour invasion propagate by triggering apoptosis of normal cells at the wave front. Otherwise, numerical evidence suggests that the wave speed can be predicted from linear analysis about the normal tissue steady state.