La Llave Research Articles

Methoxylated Flavones from Casimiroa edulis La Llave Suppress MMP9 Expression via Inhibition of the JAK/STAT3 Pathway and TNFα-Dependent Pathways.

Matrix metalloproteinase 9 (MMP9), an MMP isozyme, plays a crucial role in tumor progression by degrading basement membranes. It has therefore been proposed that the pharmacological inhibition of MMP9 expression or activity could inhibit tumor metastasis. We previously isolated two novel methoxylated flavones, casedulones A and B, from the leaves and/or roots of Casimiroa edulis La Llave and determined that these casedulones have antitumor activity that acts via the reduction of MMP9. Here, we examined how these casedulones suppress lipopolysaccharide (LPS)-induced MMP9 expression in human monocytic THP-1 cells. The casedulones suppressed the LPS-induced signal transducer and activator of transcription 3 (STAT3) pathway, which participates in MMP9 induction. In addition, AG490 and S3I-201, inhibitors of Janus kinase (JAK) and STAT3, suppressed LPS-mediated MMP9 induction, suggesting that the casedulones suppressed MMP9 induction through the inhibition of JAK/STAT3 pathways. Based on the findings that cycloheximide, an inhibitor of de novo protein synthesis, completely inhibited LPS-mediated MMP9 induction, the role of de novo proteins in MMP9 induction was further investigated. We found that the casedulones inhibited the induction of interleukin-6 (IL-6), a key inflammatory cytokine that participates in STAT3 activation. Moreover, tumor necrosis factor-α (TNFα)-mediated MMP9 induction was significantly suppressed in the presence of the casedulones. Taken together, these findings suggest that casedulones inhibit the IL-6/STAT3 and TNFα pathways, which all involve LPS-mediated MMP9 induction.

Asymptotically quasiperiodic solutions for time-dependent Hamiltonians

Dynamical systems subject to perturbations that decay over time are relevant in describing many physical models, e.g. when considering the effect of a laser pulse on a molecule, in epidemiological studies, and celestial mechanics. For this purpose, we consider time-dependent Hamiltonian vector fields that are the sum of two components. The first has an invariant torus supporting quasiperiodic solutions, and the second decays as time tends to infinity. The time decay is modelled by functions satisfying suitable conditions verified by a proper polynomial decay in time. We prove the existence of orbits converging as time tends to infinity to the quasiperiodic solutions associated with the unperturbed system. The proof of this result relies on a new strategy based on a refined analysis of the Banach spaces and the functionals involved in the resolution of suitable nonlinear invariant equations. This result is proved for finite differentiable and real-analytic Hamiltonians. Analogous statements for time-dependent vector fields on the torus are also obtained as a corollary. These results extend a previous work of Canadell and de la Llave, where only exponential decay in time is considered. The relaxation of the decay in time makes the results in the present paper suited for applications in many physical problems, such as celestial dynamics.

Asymptotic motions converging to arbitrary dynamics for time-dependent Hamiltonians

Dynamical systems subject to perturbations that decay over time are relevant in the description of many physical models, e.g. when considering the effect of a laser pulse on a molecule, in epidemiological studies, as well as in celestial mechanics. For this reason, we consider a Hamiltonian dynamical system having an invariant torus supporting arbitrary dynamics, and we study its evolution under a perturbation decaying exponentially over time. By applying a strategy based on a refined analysis of the Banach spaces and functionals involved in the resolution of suitable non-linear invariant equations, we show the existence of orbits converging in time to the arbitrary motions associated with the unperturbed system. As a corollary, an analogous statement for time-dependent vector fields on the torus is also obtained. This result extends to the important case of arbitrary Hamiltonian dynamics a previous work of Canadell and de la Llave where only asymptotic quasi-periodic motions were considered.

Micro-Morphology characterization and HS-SPME-GC-MS Analysis of Floral parts of Quararibea funebris (La Llave) Vischer, traditionally known as Rosita de Cacao.

The flowers of Quararibea funebris are used to make a traditional drink called tejate, to which they add aroma, flavor and consistency. The study aims to profile the morphoanatomy of the floral parts of Q. funebris and analyze the changes in its volatile chemical composition during the drying process from 0 to 180 days by HS-SPME-GC-MS. The calyx, corolla, androecium, and gynoecium have distinct characteristics, such as non-glandular fused stellate trichomes, calcium oxalate crystals, and large secretory ducts. Histochemical localization reveals the presence of mucilage and total lipids in all parts of the flower. The chemical analysis of the essential oil, extracted from the flowers, showed that transfarnesol and geraniol were the most abundant compounds, with a yield of 0.04 %. HS-SPME analysis indicated that fresh flowers had a more complex composition than dried ones. In total, 31 components were identified. Nonanal and geranyl acetone were found to be distinctive components of dried flowers. Microscopic examination helps in identifying and authenticating raw materials and also reveals the presence of secretory ducts in all floral parts, which is a distinctive feature. The chemical profile of volatiles provides an important parameter for the evaluation of the quality of Rosita de Cacao raw materials.

Secondary Embryogenesis of Linaloe in Temporary Immersion Bioreactor-Type RITA®.

The linaloe [Bursera linanoe (La Llave) Rzed, Calderon and Medina] is an endemic species of Mexico, representative of the low deciduous forest of the states of Guerrero, Puebla, Morelos, and Oaxaca, and has been of great economic importance for the people, mainly for the artisanal use of its aromatic wood that is used to make boxes, trunks, and furniture that are manufactured in Olinala, Guerrero, Mexico; and industrial, thanks to the fine aroma of its essential oil (linalool), which is used in the manufacture of perfumes and pharmaceuticals. Overexploitation has endangered the species in recent years, and propagation by seed and/or cuttings has produced very poor results compared to those obtained with other recalcitrant Bursera species. The protection of endangered species makes urgent the need to propose new alternatives for its propagation. Somatic embryogenesis is a reliable and feasible technique, including induction, maintenance, multiplication, and maturation of embryos, often in semisolid culture media; however, the recent use of liquid media has allowed semi-automation in temporary immersion bioreactors, for example, the RITA® system, which favors both the multiplication rate and the final conversion to seedlings.

Historical record of the problem of the natural repopulation of the linaloe Bursera linanoe (La Llave) Rzedowski, Calderón & Medina

The linaloe it is a tree that produces a fine resin. Produces essential chemical, aromatic, cosmetic, pharmaceutical, and industrialcompounds of high commercial value, only grows in Mexico, in the middle portions of the Papaloapan and Balsas River basins.The excessive use of its wood and its fruit to obtain essential oil, the destruction of the low forest where it lives, disorderly grazingand some environmental and biological constraints have generated an excessively low, discontinuous and sparse naturalrepopulation. The study of the causes of this threatening scenario is scarce and discouraging, insufficient to propose appropriatesolutions. This motivated the present analysis of silvicultural conditions, present regeneration and basic aspects of reproductivebiology in three natural populations from Oaxaca, Puebla and Guerrero. Very few trees ha-1 (36 to 45) were found, with fewfemales (35%). Diameters ranged from 5 to 35 cm, with maximum heights from 10 to 14 m. The regeneration in Chiautla was 21individuals ha⁻¹, while in Los Cués and Xalitla no regeneration was found. When reviewing the reproductive biological factors ofthe species, it was observed that the stages of flowering, fruiting and seed dispersal are seriously limited by low rainfall and theoccurrence of these in short, rare and irregular pulses. The flowering potential is high and increases with the diameter of the femaletrees, but the conversion of flowers to full and viable fruits produced is limited by the rainfall regime. Germination is notablydecimated by the frugivorous activity of birds and mammals. The new plants are trampled and browsed by livestock and wildmammals. The simultaneous occurrence of some or all of the limitations dangerously endangers populations. Assisted propagationis suggested to guarantee the permanence of the species.

Topological shadowing methods in arnold diffusion: weak torsion and multiple time scales

Consider a map which possesses a normally hyperbolic invariant manifold of any even dimension with transverse homoclinic channels. We develop a topological shadowing argument to prove the existence of Arnold diffusion along the invariant manifold, shadowing some iterations of the inner dynamics carried by the invariant manifold and the outer dynamics induced by the stable and unstable foliations. In doing so, we generalise an idea of Gidea and de la Llave (2006 Discrete Contin. Dyn. Syst. 14 295), based on the method of correctly aligned windows and a so-called transversality-torsion argument. Our proof permits that the dynamics on the invariant manifold satisfy only a non-uniform twist condition, and, most importantly for applications, that the splitting of separatrices be small in certain directions and thus the associated drift in actions very slow; diffusion occurs in the directions of the manifold having non-small splitting. Furthermore we provide estimates for the diffusion time.

Two new methoxylated flavones isolated from Casimiroa edulis La Llave and their MMP-9 inhibitory activity

Casimiroa edulis La Llave is known to contain unusual 5,6-dimethoxyflavones bearing a variously oxygenated B-ring. Phytochemical investigation of the leaves and the roots of C. edulis achieved the isolation of two new methoxylated flavones, named casedulones A (1) and B (2), together with 12 known analogues. Their unique structures were established with the aid of spectral analyses and total syntheses. Pre-treatment with 20 µM of 1 and 2 suppressed MMP-9 expression in LPS-mediated THP-1 cells, indicating that the characteristic flavonoids in C. edulis could be potential anti-angiogenics for cancer prevention.

The Thermodynamic Formalism and the Central Limit Theorem for Stochastic Perturbations of Circle Maps with a Break

Let $T\in C^{2+\varepsilon}(S^{1}\setminus\{x_{b}\})$, $\varepsilon>0$, be an orientation preserving circle homeomorphism with rotation number $\rho_{T}=[k_{1},k_{2},\ldots,k_{m},1,1,\ldots]$, $m\geq 1$, and a single break point $x_{b}$. Stochastic perturbations $\overline{z}_{n+1}=T(\overline{z}_{n})+\sigma\xi_{n+1}$, $\overline{z}_{0}:=z\in S^{1}$ of critical circle maps have been studied some time ago by Diaz-Espinoza and de la Llave, who showed for the resulting sum of random variables a central limit theorem and its rate of convergence. Their approach used the renormalization group technique. We will use here Sinai’s et al. thermodynamic formalism approach, generalised to circle maps with a break point by Dzhalilov et al., to extend the above results to circle homemorphisms with a break point. This and the sequence of dynamical partitions allows us, following earlier work of Vul at al., to establish a symbolic dynamics for any point ${z\in S^{1}}$ and to define a transfer operator whose leading eigenvalue can be used to bound the Lyapunov function. To prove the central limit theorem and its convergence rate we decompose the stochastic sequence via a Taylor expansion in the variables $\xi_{i}$ into the linear term $L_{n}(z_{0})=\xi_{n}+\sum\limits_{k=1}^{n-1}\xi_{k}\prod\limits_{j=k}^{n-1}T^{% \prime}(z_{j})$, ${z_{0}\in S^{1}}$ and a higher order term, which is possible in a neighbourhood $A_{k}^{n}$ of the points $z_{k}$, ${k\leq n-1}$, not containing the break points of $T^{n}$. For this we construct for a certain sequence $\{n_{m}\}$ a series of neighbourhoods $A_{k}^{n_{m}}$ of the points $z_{k}$ which do not contain any break point of the map $T^{q_{n_{m}}}$, $q_{n_{m}}$ the first return times of $T$. The proof of our results follows from the proof of the central limit theorem for the linearized process.

Knowledge and attitudes of physicians in caring for transgender and transsexual patients

Abstract Background Currently, care for the community of transgender and transsexual patients has been specialized in different countries of the European Union, thereby favoring better medical care for this community of patients, however, in countries like Mexico there is still no these spaces, thereby favoring the lack of dignified treatment. Objective To determine the correlation between knowledge and attitudes of doctors in the care of transgender and transsexual patients in doctors from the State of Veracruz Ignacio de la Llave. Material and methods A cross-sectional, prospective, observational, analytical and correlational study was carried out. Doctors from the state of Veracruz were included and the tests of ‘Knowledge about transsexuality' and ‘evaluation of attitudes towards the transgender and transsexual community' (Cronbach's alpha of 0.75 and 0.85) were applied by means of electronic surveys, being selected by non-probability sampling. Results 359 doctors were included, of which 201 (56%) were men, with Catholic religion in 197 (54.4%) of the cases, cisgender in 333 (92.8%), hetero sexual 296 (82.5%) with older age. frequent between 23 to 29 years (56.3%). The correlation between the level of knowledge about transsexuality and the scale of attitude towards the transgender community was -0.08, while that of the level of knowledge about transsexuality and the scale of attitude towards the transgender community was -0.39. The Catholic religion, being a biological man, and being heterosexual showed values of p < 0.05 with respect to the presence of prejudices for the transgender and transsexual community. Conclusions There is no correlation between knowledge about transsexuality and the attitude towards this group by the doctors of the state of Veracruz. Key messages There is no correlation between knowledge about transsexuality and the attitude towards this group by the doctors of the state of Veracruz. To practice the catholic religion, being a biological man, and being heterosexual its associated to the presence of prejudices for the transgender and transsexual community.

Pollination success in three tropical dry forest orchid species from Mexico: insights from floral display, visitation rates, and flower micromorphology

Background: Despite long-lasting efforts to disentangle the drivers of orchid pollination, pollination success in tropical dry forest orchids remains largely unknown.
 Questions and hypothesis: How successful are pollination in three tropical dry forest orchids? How is pollination influenced by floral display and floral rewards (as suggested by floral micromorphology)? We hypothesized a positive effect of floral display on pollinia removal and deposition rates.
 Studied species: Barkeria whartoniana (C. Schweinf.) Soto Arenas, Clowesia dodsoniana E. Aguirre, and Cyrtopodium macrobulbon (La Llave & Lex.) G.A. Romero & Carnevali.
 Study site and dates: Nizanda (Oaxaca), Mexico; flowering periods of 2013 and 2014.
 Methods: We calculated pollinia removal and deposition rates, identified floral visitors and analyzed flower microstructure to search for structures potentially producing rewards. Floral display was measured through number of open flowers, and number and length of inflorescences, and its effect on pollination success was assessed through linear modeling.
 Results: Pollinia removal rates were higher than deposition rates, and floral display was related to pollination success in C. dodsoniana only. Visitation rates were low for the three species and most visitors were not true pollinators. The three species possess potentially secreting structures, but for B. whartoniana and C. macrobulbon these rewards are likely part of the pollinator deception mechanism.
 Conclusions: The generalized low pollination success implies the need for high population densities of both interacting parts. We emphasize the need for integrated evaluations of different aspects of the plant-pollinator interaction.

Multiple timescales and the parametrisation method in geometric singular perturbation theory

We present a novel method for computing slow manifolds and their fast fibre bundles in geometric singular perturbation problems. This coordinate-independent method is inspired by the parametrisation method introduced by Cabré, Fontich and de la Llave. By iteratively solving a so-called conjugacy equation, our method simultaneously computes parametrisations of slow manifolds and fast fibre bundles, as well as the dynamics on these objects, to arbitrarily high degrees of accuracy. We show the power of this top-down method for the study of systems with multiple (i.e. three or more) timescales. In particular, we highlight the emergence of hidden timescales and show how our method can uncover these surprising multiple timescale structures. We also apply our parametrisation method to several reaction network problems.

Does the African Citrus psyllid, Trioza erytreae (Del Guercio) (Hemiptera: Triozidae), Represent a Phytosanitary Threat to the Citrus Industry in Mexico?

Simple SummaryThe African citrus psyllid, Trioza erytreae (Del Guercio) (Hemiptera: Triozidae) is an invasive species for citrus crops. In its native range is the main vector of Candidatus Liberibacter africanus (CLaf), a pathogen that causes huanglongbing (HLB). For Mexico, T. erytreae could threat the citrus industry in a potential invasion but until now, the best chances to prevent its damage is analyzing if the country has the ecological conditions suitable for this psyllid. In this study we used the ecological niche modeling approach to explore which areas in Mexico has the environmental suitability for the T. erytreae establishment. Additionally, the potential role of an alternate host, Casimiroa edulis La Llave (Rutaceae), and five points of entry into the country, in the potential T. erytreae dispersion were analyzed. Mexico citrus areas has a wide environmental suitability for T. erytreae, including the main federal entity (Veracruz). The natural distribution of C. edulis matches with the T. erytreae environmental suitability and citrus areas, and could expand its distribution across the country. For preventive monitoring strategies, the port of Veracruz is a vital point for phytosanitary agencies, because of its proximity to citrus areas.The African citrus psyllid, Trioza erytreae (Del Guercio) (Hemiptera: Triozidae), is a vector of Candidatus Liberibacter africanus (CLaf), a pathogen that causes huanglongbing (HLB) in Africa. Trioza erytreae has invaded areas of Asia and Europe and has threatened citrus production due to its biological habits and the transmission of CLaf. Mexico is a country where citrus production has a vital role from the economic and social point of view. Therefore, ecological niche modeling (ENM) was used to determine if Mexico has the environmental availability that will allow T. erytreae invasion. We analyzed whether or not the distribution of Casimiroa edulis La Llave (Rutaceae) in the country could be a factor that enables the dispersal of T. eytreae. The environmental connectivity between five points of entry into the country (two ports and three airports) was explored to determine possible routes of dispersal of T. erytrae. The results showed that Mexico has wide availability for the invasion of the African citrus psyllid, which coincides with essential citrus areas of the country and with the distribution of C. edulis. Of the entry points studied, the Port of Veracruz showed nearby areas with environmental connectivity. Preventive monitoring measures for T. erytreae in Mexico should focus on Veracruz state because it has an entry point, ideal environmental availability, citrus areas, and specimens of C. edulis.

Variability and genetic structure of Anastrepha ludens Loew (Diptera: Tephritidae) populations from Mexico

The Mexican fruit fly, Anastrepha ludens (Loew) (Diptera: Tephritidae), is the most devastating pest of citrus in Mexico. Knowledge of the genetic relationships and structure of Mexican A. ludens populations is limited. The aim of this research was to characterize the genetic variability and structure of the Mexican fruit fly by using AFLP markers (three EcoRI/MseI primer combinations). The specimens were collected from three hosts, namely, Casimiroa edulis La Llave & Lex [white sapote], Casimiroa greggii (S. Watson) F. Chiang [yellow chapote], and Citrus X paradisi (Macfad.) [grapefruit], at four locations in the states of Veracruz (Teocelo and Jalapa), Nuevo Leon (El Jarro), and Tamaulipas (Troncones) in Mexico. A high polymorphism percentage (80.4%) allowed the differentiation of individuals from different A. ludens populations, and high intraspecies genetic variability (DI = 78.4%) was detected. The A. ludens populations clustered into two groups: group one included flies from Veracruz [grapefruit, Jalapa] and Nuevo Leon [yellow chapote, El Jarro], and group two included populations from Tamaulipas [yellow chapote, Troncones] and Veracruz [white sapote, Teocelo]. The populations from group one were from locations at lower altitudes (750 m above sea level), which had warmer (22 °C average temperature) and more humid (1470 mm of annual precipitation) climatic conditions than those of group two (1600 m, 18 °C and 965 mm). Both population structure and very high genetic differentiation (FST > 0.38) associated with geographical and/or host origin were found in A. ludens from Mexico. The genetic differentiation in Mexican A. ludens populations suggests reduced gene flow and reproductive isolation resulting either from habitat fragmentation and genetic drift or from natural selection for specific environmental (climate, geography, pest management strategies) or host (chemistry, phenology) condition. Genetic analysis could increase the success of Anastrepha control programs by improving knowledge of host-parasitoid population genetics, allowing matching of parasitoid species to their preferred pest populations.

Mexico ants: incidence and abundance along the Nearctic-Neotropical interface.

Mexico is one of the most biodiverse countries in the world, with an important proportion of endemism mainly because of the convergence of the Nearctic and Neotropical biogeographic regions, which generate great diversity and species turnover at different spatial scales. However, most of our knowledge of the Mexican ant biota is limited to a few well-studied taxa, and we lack a comprehensive synthesis of ant biodiversity information. For instance, most of the knowledge available in the literature on Mexican ant fauna refers only to species lists by states, or is focused on only a few regions of the country, which prevents the study of several basic and applied aspects of ants, from diversity and distribution to conservation. Our aims in this data paper are therefore (1) to compile all the information available regarding ants across the Mexican territory, and (2) to identify major patterns in the gathered data set and geographic gaps in order to direct future sampling efforts. All records were obtained from raw data, including both unpublished and published information. After exhaustive filtering and updating information and synonyms, we compiled a total of 21,731 records for 887 ant species distributed throughout Mexico from 1894 to 2018. These records were concentrated mainly in the states of Chiapas (n=6,902, 32.76%) and Veracruz de Ignacio de la Llave (n=4,329, 19.92%), which together comprise half the records. The subfamily with the highest number of records was Myrmicinae (n=10,458 records, 48.12%), followed by Formicinae (n=3,284, 15.11%) and Ponerinae (n=1,914, 8.8%). Most ant records were collected in the Neotropical region of the country (n=12,646, 58.19%), followed by the Mexican transition zone (n=5,237, 24.09%) and the Nearctic region (n=3,848, 17.72%). Native species comprised 95.46% of the records (n=20,745). To the best of our knowledge, this is the most complete data set available to date in the literature for the country. We hope that this compilation will encourage researchers to explore different aspects of the population and community research of ants at different spatial scales, and to aid in the establishment of conservation policies and actions. There are no copyright restrictions. Please cite this data paper when using its data for publications or teaching events.

The parameterization method for center manifolds

In this paper, we present a generalization of the parameterization method, introduced by Cabré, Fontich and De la Llave, to center manifolds associated to non-hyperbolic fixed points of discrete dynamical systems. As a byproduct, we find a new proof for the existence and regularity of center manifolds. However, in contrast to the classical center manifold theorem, our parameterization method will simultaneously obtain the center manifold and its conjugate center dynamical system. Furthermore, we will provide bounds on the error between approximations of the center manifold and the actual center manifold, as well as bounds for the error in the conjugate dynamical system.

One-Dimensional Symmetry for the Solutions of a Three-Dimensional Water Wave Problem

We prove a one-dimensional symmetry result for a weighted Dirichlet-to-Neumann problem arising in a model for water waves in dimensions 2 and 3. More precisely, we prove that stable solutions in dimension 2 and minimizers and monotone solutions in dimension 3 depend on only one Euclidean variable. Monotone solutions in the 2-dimensional case without weights were studied in de la Llave and Valdinoci (Math Res Lett 16(5):909–918, 2009). In our paper, a crucial ingredient in the proof is given by an energy estimate for minimizers obtained via a comparison argument.

Ethics and the Public Function: Evaluation of Legislative Effectiveness in Mexico

This paper addresses the study of the ethics of responsibility in the legislative function of the Chamber of Deputies of the H. Congress of the Union, from the perspective of evaluating the work of federal deputies, and seeks to answer the following question: Is the work of the Federal Deputies in the Chamber of Deputies efficient? The purpose is how to measure and evaluate the performance in the legislative function of the Federal Deputies? and with that, to approach to identify if is the work performed by these public representatives efficient and ethical? The work is integrated in three parts. The first is the concept of the ethics of responsibility and the legislative function. In the second section, the proposal of an indicator to measure legislative efficiency is presented and the case of the federal deputies of the LXI Legislature representing the State of Veracruz of Ignacio de la Llave is analyzed. Finally, the third part presents a proposal for citizen action based on information on legislative efficiency and the need to demand compliance with ethical responsibility in the legislative function. As important conclusions of the evaluation of the legislative efficiency of the federal deputies of the LXI Legislature, it shows at least two important results: i) The legislative effectiveness index (IEL) shows very low levels, both at the plenary level of the Chamber of Deputies, as at the level of the study group of federal deputies representing the State of Veracruz. ii) In both cases, they show a very high legislative lag index. An alternative is the citizen's demand for ethical compliance with responsibility in the legislative function when knowing the evaluation of results, which serves as a reference to identify scenarios of political choice based on results.

First documented record of Amazilia tzacatl (de la Llave, 1893) (Aves, Trochilidae) in the Colombian Orinoco region and comments of its distribution at the eastern Andes

First documented record of Amazilia tzacatl (de la Llave, 1893) (Aves, Trochilidae) in the Colombian Orinoco region and comments of its distribution at the eastern Andes

Bootstrap for Local Rigidity of Anosov Automorphisms on the 3-Torus

We establish a strong form of local rigidity for hyperbolic automorphisms of the 3-torus with real spectrum. Namely, let \({L:\mathbb{T}^3\to\mathbb{T}^3}\) be a hyperbolic automorphism of the 3-torus with real spectrum and let f be a C 1 small perturbation of L. Then f is smoothly (\({C^\infty}\)) conjugate to L if and only if obstructions to C 1 conjugacy given by the eigenvalues at periodic points of f vanish. By combining our result and a local rigidity result of Kalinin and Sadovskaya (Ergod Theory Dyn Syst 29:117–136, 2009) for conformal automorphisms this completes the local rigidity program for hyperbolic automorphisms in dimension 3. Our work extends de la Llave–Marco–Moriyon 2-dimensional local rigidity theory (Commun Math Phys 109:368–378, 1987; Ergod Theory Dyn Syst 17(3):649–662, 1997; Commun Math Phys 109(4):681–689, 1987).