Multiscale analysis of protein functions and stochastic modelling of gene transcriptional regulatory networks

Genomic and proteomic analyses have attracted a great deal of interests in biological research in recent years. Many methods have been applied to discover useful information contained in the enormous databases of genomic sequences and amino acid sequences. The results of these investigations inspire further research in biological fields in return. These biological sequences, which may be considered as multiscale sequences, have some specific features which need further efforts to characterise using more refined methods. This project aims to study some of these biological challenges with multiscale analysis methods and stochastic modelling approach. The first part of the thesis aims to cluster some unknown proteins, and classify their families as well as their structural classes. A development in proteomic analysis is concerned with the determination of protein functions. The first step in this development is to classify proteins and predict their families. This motives us to study some unknown proteins from specific families, and to cluster them into families and structural classes. We select a large number of proteins from the same families or superfamilies, and link them to simulate some unknown large proteins from these families. We use multifractal analysis and the wavelet method to capture the characteristics of these linked proteins. The simulation results show that the method is valid for the classification of large proteins. The second part of the thesis aims to explore the relationship of proteins based on a layered comparison with their components. Many methods are based on homology of proteins because the resemblance at the protein sequence level normally indicates the similarity of functions and structures. However, some proteins may have similar functions with low sequential identity. We consider protein sequences at detail level to investigate the problem of comparison of proteins. The comparison is based on the empirical mode decomposition (EMD), and protein sequences are detected with the intrinsic mode functions. A measure of similarity is introduced with a new cross-correlation formula. The similarity results show that the EMD is useful for detection of functional relationships of proteins. The third part of the thesis aims to investigate the transcriptional regulatory network of yeast cell cycle via stochastic differential equations. As the investigation of genome-wide gene expressions has become a focus in genomic analysis, researchers have tried to understand the mechanisms of the yeast genome for many years. How cells control gene expressions still needs further investigation. We use a stochastic differential equation to model the expression profile of a target gene. We modify the model with a Gaussian membership function. For each target gene, a transcriptional rate is obtained, and the estimated transcriptional rate is also calculated with the information from five possible transcriptional regulators. Some regulators of these target genes are verified with the related references. With these results, we construct a transcriptional regulatory network for the genes from the yeast Saccharomyces cerevisiae. The construction of transcriptional regulatory network is useful for detecting more mechanisms of the yeast cell cycle.

Multiscale analysis of factors that affect the distribution of sharks throughout the northern Gulf of Mexico

Identification of the spatial scale at which marine communities are organized is critical to proper management, yet this is particularly difficult to determine for highly migratory species like sharks. We used shark catch data collected during 2006–09 from fishery-independent bottom-longline surveys, as well as biotic and abiotic explanatory data to identify the factors that affect the distribution of coastal sharks at 2 spatial scales in the northern Gulf of Mexico. Centered principal component analyses (PCAs) were used to visualize the patterns that characterize shark distributions at small (Alabama and Mississippi coast) and large (northern Gulf of Mexico) spatial scales. Environmental data on temperature, salinity, dissolved oxygen (DO), depth, fish and crustacean biomass, and chlorophyll-a (chl-a) concentration were analyzed with normed PCAs at both spatial scales. The relationships between values of shark catch per unit of effort (CPUE) and environmental factors were then analyzed at each scale with co-inertia analysis (COIA). Results from COIA indicated that the degree of agreement between the structure of the environmental and shark data sets was relatively higher at the small spatial scale than at the large one. CPUE of Blacktip Shark (Carcharhinus limbatus) was related positively with crustacean biomass at both spatial scales. Similarly, CPUE of Atlantic Sharpnose Shark (Rhizoprionodon terraenovae) was related positively with chl-a concentration and negatively with DO at both spatial scales. Conversely, distribution of Blacknose Shark (C. acronotus) displayed a contrasting relationship with depth at the 2 scales considered. Our results indicate that the factors influencing the distribution of sharks in the northern Gulf of Mexico are species specific but generally transcend the spatial boundaries used in our analyses.

Linear multiscale analysis and finite element validation of stretching and bending dominated lattice materials

The paper presents a multiscale procedure for the linear analysis of components made of lattice materials. The method allows the analysis of both pin-jointed and rigid-jointed microtruss materials with arbitrary topology of the unit cell. At the macroscopic level, the procedure enables to determine the lattice stiffness, while at the microscopic level the internal forces in the lattice elements are expressed in terms of the macroscopic strain applied to the lattice component. A numeric validation of the method is described. The procedure is completely automated and can be easily used within an optimization framework to find the optimal geometric parameters of a given lattice material. © 2011 Elsevier Ltd. All rights reserved.

Multiscale Analysis of Topographic Surface Roughness in the Midland Valley, Scotland

Surface roughness is an important geomorphological variable which has been used in the Earth and planetary sciences to infer material properties, current/past processes, and the time elapsed since formation. No single definition exists; however, within the context of geomorphometry, we use surface roughness as an expression of the variability of a topographic surface at a given scale, where the scale of analysis is determined by the size of the landforms or geomorphic features of interest. Six techniques for the calculation of surface roughness were selected for an assessment of the parameter`s behavior at different spatial scales and data-set resolutions. Area ratio operated independently of scale, providing consistent results across spatial resolutions. Vector dispersion produced results with increasing roughness and homogenization of terrain at coarser resolutions and larger window sizes. Standard deviation of residual topography highlighted local features and did not detect regional relief. Standard deviation of elevation correctly identified breaks of slope and was good at detecting regional relief. Standard deviation of slope (SD(slope)) also correctly identified smooth sloping areas and breaks of slope, providing the best results for geomorphological analysis. Standard deviation of profile curvature identified the breaks of slope, although not as strongly as SD(slope), and it is sensitive to noise and spurious data. In general, SD(slope) offered good performance at a variety of scales, while the simplicity of calculation is perhaps its single greatest benefit.

Multiscale analysis of the mechanical behavior of needle-punched nonwoven fabrics

Los fieltros son una familia de materiales textiles constituidos por una red desordenada de fibras conectadas por medio de enlaces térmicos, químicos o mecánicos. Presentan menor rigidez y resistencia (al igual que un menor coste de procesado) que sus homólogos tejidos, pero mayor deformabilidad y capacidad de absorción de energía. Los fieltros se emplean en diversas aplicaciones en ingeniería tales como aislamiento térmico, geotextiles, láminas ignífugas, filtración y absorción de agua, impacto balístico, etc. En particular, los fieltros punzonados fabricados con fibras de alta resistencia presentan una excelente resistencia frente a impacto balístico, ofreciendo las mismas prestaciones que los materiales tejidos con un tercio de la densidad areal. Sin embargo, se sabe muy poco acerca de los mecanismos de deformación y fallo a nivel microscópico, ni sobre como influyen en las propiedades mecánicas del material. Esta carencia de conocimiento dificulta la optimización del comportamiento mecánico de estos materiales y también limita el desarrollo de modelos constitutivos basados en mecanismos físicos, que puedan ser útiles en el diseño de componentes estructurales. En esta tesis doctoral se ha llevado a cabo un estudio minucioso con el fin de determinar los mecanismos de deformación y las propiedades mecánicas de fieltros punzonados fabricados con fibras de polietileno de ultra alto peso molecular. Los procesos de deformación y disipación de energía se han caracterizado en detalle por medio de una combinación de técnicas experimentales (ensayos mecánicos macroscópicos a velocidades de deformación cuasi-estáticas y dinámicas, impacto balístico, ensayos de extracción de una o múltiples fibras, microscopía óptica, tomografía computarizada de rayos X y difracción de rayos X de gran ángulo) que proporcionan información de los mecanismos dominantes a distintas escalas. Los ensayos mecánicos macroscópicos muestran que el fieltro presenta una resistencia y ductilidad excepcionales. El estado inicial de las fibras es curvado, y la carga se transmite por el fieltro a través de una red aleatoria e isótropa de nudos creada por el proceso de punzonamiento, resultando en la formación de una red activa de fibra. La rotación y el estirado de las fibras activas es seguido por el deslizamiento y extracción de la fibra de los puntos de anclaje mecánico. La mayor parte de la resistencia y la energía disipada es proporcionada por la extracción de las fibras activas de los nudos, y la fractura final tiene lugar como consecuencia del desenredo total de la red en una sección dada donde la deformación macroscópica se localiza. No obstante, aunque la distribución inicial de la orientación de las fibras es isótropa, las propiedades mecánicas resultantes (en términos de rigidez, resistencia y energía absorbida) son muy anisótropas. Los ensayos de extracción de múltiples fibras en diferentes orientaciones muestran que la estructura de los nudos conecta más fibras en la dirección transversal en comparación con la dirección de la máquina. La mejor interconectividad de las fibras a lo largo de la dirección transversal da lugar a una esqueleto activo de fibras más denso, mejorando las propiedades mecánicas. En términos de afinidad, los fieltros deformados a lo largo de la dirección transversal exhiben deformación afín (la deformación macroscópica transfiere directamente a las fibras por el material circundante), mientras que el fieltro deformado a lo largo de la dirección de la máquina presenta deformación no afín, y la mayor parte de la deformación macroscópica no es transmitida a las fibras. A partir de estas observaciones experimentales, se ha desarrollado un modelo constitutivo para fieltros punzonados confinados por enlaces mecánicos. El modelo considera los efectos de la deformación no afín, la conectividad anisótropa inducida durante el punzonamiento, la curvatura y re-orientación de la fibra, así como el desenredo y extracción de la fibra de los nudos. El modelo proporciona la respuesta de un mesodominio del material correspondiente al volumen asociado a un elemento finito, y se divide en dos bloques. El primer bloque representa el comportamiento de la red y establece la relación entre el gradiente de deformación macroscópico y la respuesta microscópica, obtenido a partir de la integración de la respuesta de las fibras en el mesodominio. El segundo bloque describe el comportamiento de la fibra, teniendo en cuenta las características de la deformación de cada familia de fibras en el mesodominio, incluyendo deformación no afín, estiramiento, deslizamiento y extracción. En la medida de lo posible, se ha asignado un significado físico claro a los parámetros del modelo, por lo que se pueden identificar por medio de ensayos independientes. Las simulaciones numéricas basadas en el modelo se adecúan a los resultados experimentales de ensayos cuasi-estáticos y balísticos desde el punto de vista de la respuesta mecánica macroscópica y de los micromecanismos de deformación. Además, suministran información adicional sobre la influencia de las características microstructurales (orientación de la fibra, conectividad de la fibra anisótropa, afinidad, etc) en el comportamiento mecánico de los fieltros punzonados. Nonwoven fabrics are a class of textile material made up of a disordered fiber network linked by either thermal, chemical or mechanical bonds. They present lower stiffness and strength (as well as processing cost) than the woven counterparts but much higher deformability and energy absorption capability and are used in many different engineering applications (including thermal insulation, geotextiles, fireproof layers, filtration and water absorption, ballistic impact, etc). In particular, needle-punched nonwoven fabrics manufactured with high strength fibers present an excellent performance for ballistic protection, providing the same ballistic protection with one third of the areal weight as compared to dry woven fabrics. Nevertheless, very little is known about their deformation and fracture micromechanisms at the microscopic level and how they contribute to the macroscopic mechanical properties. This lack of knowledge hinders the optimization of their mechanical performance and also limits the development of physically-based models of the mechanical behavior that can be used in the design of structural components with these materials. In this thesis, a thorough study was carried out to ascertain the micromechanisms of deformation and the mechanical properties of a needle-punched nonwoven fabric made up by ultra high molecular weight polyethylene fibers. The deformation and energy dissipation processes were characterized in detail by a combination of experimental techniques (macroscopic mechanical tests at quasi-static and high strain rates, ballistic impact, single fiber and multi fiber pull-out tests, optical microscopy, X-ray computed tomography and wide angle X-ray diffraction) that provided information of the dominant mechanisms at different length scales. The macroscopic mechanical tests showed that the nonwoven fabric presented an outstanding strength and energy absorption capacity. It was found that fibers were initially curved and the load was transferred within the fabric through the random and isotropic network of knots created by needlepunching, leading to the formation of an active fiber network. Uncurling and stretching of the active fibers was followed by fiber sliding and pull-out from the entanglement points. Most of the strength and energy dissipation was provided by the extraction of the active fibers from the knots and final fracture occurred by the total disentanglement of the fiber network in a given section at which the macroscopic deformation was localized. However, although the initial fiber orientation distribution was isotropic, the mechanical properties (in terms of stiffness, strength and energy absorption) were highly anisotropic. Pull-out tests of multiple fibers at different orientations showed that structure of the knots connected more fibers in the transverse direction as compared with the machine direction. The better fiber interconnection along the transverse direction led to a denser active fiber skeleton, enhancing the mechanical response. In terms of affinity, fabrics deformed along the transverse direction essentially displayed affine deformation {i.e. the macroscopic strain was directly transferred to the fibers by the surrounding fabric, while fabrics deformed along the machine direction underwent non-affine deformation, and most of the macroscopic strain was not transferred to the fibers. Based on these experimental observations, a constitutive model for the mechanical behavior of the mechanically-entangled nonwoven fiber network was developed. The model accounted for the effects of non-affine deformation, anisotropic connectivity induced by the entanglement points, fiber uncurling and re-orientation as well as fiber disentanglement and pull-out from the knots. The model provided the constitutive response for a mesodomain of the fabric corresponding to the volume associated to a finite element and is divided in two blocks. The first one was the network model which established the relationship between the macroscopic deformation gradient and the microscopic response obtained by integrating the response of the fibers in the mesodomain. The second one was the fiber model, which took into account the deformation features of each set of fibers in the mesodomain, including non-affinity, uncurling, pull-out and disentanglement. As far as possible, a clear physical meaning is given to the model parameters, so they can be identified by means of independent tests. The numerical simulations based on the model were in very good agreement with the experimental results of in-plane and ballistic mechanical response of the fabrics in terms of the macroscopic mechanical response and of the micromechanisms of deformation. In addition, it provided additional information about the influence of the microstructural features (fiber orientation, anisotropic fiber connectivity, affinity) on the mechanical performance of mechanically-entangled nonwoven fabrics.

Multiscale Analysis for Field-Effect Penetration through Two-Dimensional Materials

Gate-tunable two-dimensional (2D) materials-based quantum capacitors (QCs) and van der Waals heterostructures involve tuning transport or optoelectronic characteristics by the field effect. Recent studies have attributed the observed gate-tunable characteristics to the change of the Fermi level in the first 2D layer adjacent to the dielectrics, whereas the penetration of the field effect through the one-molecule-thick material is often ignored or oversimplified. Here, we present a multiscale theoretical approach that combines first-principles electronic structure calculations and the Poisson–Boltzmann equation methods to model penetration of the field effect through graphene in a metal–oxide–graphene–semiconductor (MOGS) QC, including quantifying the degree of “transparency” for graphene two-dimensional electron gas (2DEG) to an electric displacement field. We find that the space charge density in the semiconductor layer can be modulated by gating in a nonlinear manner, forming an accumulation or inversion layer at the semiconductor/graphene interface. The degree of transparency is determined by the combined effect of graphene quantum capacitance and the semiconductor capacitance, which allows us to predict the ranking for a variety of monolayer 2D materials according to their transparency to an electric displacement field as follows: graphene > silicene > germanene > WS2 > WTe2 > WSe2 > MoS2 > phosphorene > MoSe2 > MoTe2, when the majority carrier is electron. Our findings reveal a general picture of operation modes and design rules for the 2D-materials-based QCs.

Fiedler trees for multiscale surface analysis

In this work we introduce a new hierarchical surface decomposition method for multiscale analysis of surface meshes. In contrast to other multiresolution methods, our approach relies on spectral properties of the surface to build a binary hierarchical decomposition. Namely, we utilize the first nontrivial eigenfunction of the Laplace-Beltrami operator to recursively decompose the surface. For this reason we coin our surface decomposition the Fiedler tree. Using the Fiedler tree ensures a number of attractive properties, including: mesh-independent decomposition, well-formed and nearly equi-areal surface patches, and noise robustness. We show how the evenly distributed patches can be exploited for generating multiresolution high quality uniform meshes. Additionally, our decomposition permits a natural means for carrying out wavelet methods, resulting in an intuitive method for producing feature-sensitive meshes at multiple scales. Published by Elsevier Ltd.

Multiscale study on hydrogen mobility in metallic fusion divertor material

For achieving efficient fusion energy production, the plasma-facing wall materials of the fusion reactor should ensure long time operation. In the next step fusion device, ITER, the first wall region facing the highest heat and particle load, i.e. the divertor area, will mainly consist of tiles based on tungsten. During the reactor operation, the tungsten material is slowly but inevitably saturated with tritium. Tritium is the relatively short-lived hydrogen isotope used in the fusion reaction. The amount of tritium retained in the wall materials should be minimized and its recycling back to the plasma must be unrestrained, otherwise it cannot be used for fueling the plasma. A very expensive and thus economically not viable solution is to replace the first walls quite often. A better solution is to heat the walls to temperatures where tritium is released. Unfortunately, the exact mechanisms of hydrogen release in tungsten are not known. In this thesis both experimental and computational methods have been used for studying the release and retention of hydrogen in tungsten. The experimental work consists of hydrogen implantations into pure polycrystalline tungsten, the determination of the hydrogen concentrations using ion beam analyses (IBA) and monitoring the out-diffused hydrogen gas with thermodesorption spectrometry (TDS) as the tungsten samples are heated at elevated temperatures. Combining IBA methods with TDS, the retained amount of hydrogen is obtained as well as the temperatures needed for the hydrogen release. With computational methods the hydrogen-defect interactions and implantation-induced irradiation damage can be examined at the atomic level. The method of multiscale modelling combines the results obtained from computational methodologies applicable at different length and time scales. Electron density functional theory calculations were used for determining the energetics of the elementary processes of hydrogen in tungsten, such as diffusivity and trapping to vacancies and surfaces. Results from the energetics of pure tungsten defects were used in the development of an classical bond-order potential for describing the tungsten defects to be used in molecular dynamics simulations. The developed potential was utilized in determination of the defect clustering and annihilation properties. These results were further employed in binary collision and rate theory calculations to determine the evolution of large defect clusters that trap hydrogen in the course of implantation. The computational results for the defect and trapped hydrogen concentrations were successfully compared with the experimental results. With the aforedescribed multiscale analysis the experimental results within this thesis and found in the literature were explained both quantitatively and qualitatively.

Multi-scale analysis of AFM tip and surface interactions

Thoroughly understanding AFM tip-surface interactions is crucial for many experimental studies and applications. It is important to realize that despite its simple appearance, the system of tip and sample surface involves multiscale interactions. In fact, the system is governed by a combination of molecular force (like the van der Waals force), its macroscopic representations (such as surface force) and gravitational force (a macroscopic force). Hence, in the system, various length scales are operative, from sub-nanoscale (at the molecular level) to the macroscopic scale. By integrating molecular forces into continuum equations, we performed a multiscale analysis and revealed the nonlocality effect between a tip and a rough solid surface and the mechanism governing liquid surface deformation and jumping. The results have several significant implications for practical applications. For instance, nonlocality may affect the measurement accuracy of surface morphology. At the critical state of liquid surface jump, the ratio of the gap between a tip and a liquid dome (delta) over the dome height (y(o)) is approximately (n-4) (for a large tip), which depends on the power law exponent n of the molecular interaction energy. These findings demonstrate that the multiscale analysis is not only useful but also necessary in the understanding of practical phenomena involving molecular forces. (c) 2007 Elsevier Ltd. All rights reserved.

A computer vision approach to quantify leaf anatomical plasticity: A case study on gochnatia polymorpha (less.) cabrera

Inferences about leaf anatomical characteristics had largely been made by manually measuring diverse leaf regions, such as cuticle, epidermis and parenchyma to evaluate differences caused by environmental variables. Here we tested an approach for data acquisition and analysis in ecological quantitative leaf anatomy studies based on computer vision and pattern recognition methods. A case study was conducted on Gochnatia polymorpha (Less.) Cabrera (Asteraceae), a Neotropical savanna tree species that has high phenotypic plasticity. We obtained digital images of cross-sections of its leaves developed under different light conditions (sun vs. shade), different seasons (dry vs. wet) and in different soil types (oxysoil vs. hydromorphic soil), and analyzed several visual attributes, such as color, texture and tissues thickness in a perpendicular plane from microscopic images. The experimental results demonstrated that computational analysis is capable of distinguishing anatomical alterations in microscope images obtained from individuals growing in different environmental conditions. The methods presented here offer an alternative way to determine leaf anatomical differences. © 2013 Elsevier B.V.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Petrographic image analysis and understanding

This study considers the application of image analysis in petrography and investigates the possibilities for advancing existing techniques by introducing feature extraction and analysis capabilities of a higher level than those currently employed. The aim is to construct relevant, useful descriptions of crystal form and inter-crystal relations in polycrystalline igneous rock sections. Such descriptions cannot be derived until the `ownership' of boundaries between adjacent crystals has been established: this is the fundamental problem of crystal boundary assignment. An analysis of this problem establishes key image features which reveal boundary ownership; a set of explicit analysis rules is presented. A petrographic image analysis scheme based on these principles is outlined and the implementation of key components of the scheme considered. An algorithm for the extraction and symbolic representation of image structural information is developed. A new multiscale analysis algorithm which produces a hierarchical description of the linear and near-linear structure on a contour is presented in detail. Novel techniques for symmetry analysis are developed. The analyses considered contribute both to the solution of the boundary assignment problem and to the construction of geologically useful descriptions of crystal form. The analysis scheme which is developed employs grouping principles such as collinearity, parallelism, symmetry and continuity, so providing a link between this study and more general work in perceptual grouping and intermediate level computer vision. Consequently, the techniques developed in this study may be expected to find wider application beyond the petrographic domain.

Brain-derived neurotrophic factor enhances the hippocampal expression of key postsynaptic proteins in vivo including the monocarboxylate transporter MCT2.

Brain-derived neurotrophic factor (BDNF) promotes synaptic plasticity via an enhancement in expression of specific synaptic proteins. Recent results suggest that the neuronal monocarboxylate transporter MCT2 is a postsynaptic protein critically involved in synaptic plasticity and long-term memory. To investigate in vivo whether BDNF can modulate the expression of MCT2 as well as other proteins involved in synaptic plasticity, acute injection of BDNF was performed in mouse dorsal hippocampal CA1 area. Using immunohistochemistry, it was found that MCT2 expression was enhanced in part of the CA1 area and in the dentate gyrus 6 h after a single intrahippocampal injection of BDNF. Similarly, expression of the immediate early genes Arc and Zif268 was enhanced in the same hippocampal areas, in accordance with their role in synaptic plasticity. Immunoblot analysis confirmed the significant enhancement in MCT2 protein expression. In contrast, no changes were observed for the glial monocarboxylate transporters MCT1 and MCT4. When other synaptic proteins were investigated, it was found that postsynaptic density 95 (PSD95) and glutamate receptor 2 (GluR2) protein levels were significantly enhanced while no effect could be detected for synaptophysin, synaptosomal-associated protein 25 (SNAP25), αCaMKII and GluR1. These results demonstrate that MCT2 expression can be upregulated together with other key postsynaptic proteins in vivo under conditions related to synaptic plasticity, further suggesting the importance of energetics for memory formation.

Symmetry breaking, mixing, instability, and low frequency variability in a minimal Lorenz-like system

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of O(Ec−1) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/f3/2 power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.