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19 p.-8 fig.-1 tab., Long-duration space missions will need to rely on the use of plants in bio-regenerative life support systems (BLSSs) because these systems can produce fresh food and oxygen, reduce carbon dioxide levels, recycle metabolic waste, and purify water. In this scenario, the need for new experiments on the effects of altered gravity conditions on plant biological processes is increasing, and significant efforts should be devoted to new ideas aimed at increasing the scientific output and lowering the experimental costs. Here, we report the design of an easy-to-produce and inexpensive device conceived to analyze the effect of interaction between gravity and light on root tropisms. Each unit consisted of a polystyrene multi-slot rack with light-emitting diodes (LEDs), capable of holding Petri dishes and assembled with a particular filter-paper folding. The device was successfully used for the ROOTROPS (for root tropisms) experiment performed in the Large Diameter Centrifuge (LDC) and Random Positioning Machine (RPM) at ESA's European Space Research and Technology centre (ESTEC). During the experiments, four light treatments and six gravity conditions were factorially combined to study their effects on root orientation of Brassica oleracea seedlings. Light treatments (red, blue, and white) and a dark condition were tested under four hypergravity levels (20 g, 15 g, 10 g, 5 g), a 1 g control, and a simulated microgravity (RPM) condition. Results of validation tests showed that after 24 h, the assembled system remained unaltered, no slipping or displacement of seedlings occurred at any hypergravity treatment or on the RPM, and seedlings exhibited robust growth. Overall, the device was effective and reliable in achieving scientific goals, suggesting that it can be used for ground-based research on phototropism-gravitropism interactions. Moreover, the concepts developed can be further expanded for use in future spaceflight experiments with plants., This work was supported by the ESA-HRE CORA contract #4000127705/19/NL/PG/pt. Financial support was also provided by ESA-TEC contract #4000116223/16/NL/KML/hh to Jack J.W.A. van Loon, by Spanish Agencia Estatal de Investigación (grant RTI2018–099309-B-I00, co-funded by EU-ERDF) to F. Javier Medina, and by NASA (grant 80NSSC17K0546) to John Z. Kiss.

15 p.-6 fig., In a microgravity environment, without any gravitropic signal, plants are not able to define and establish a longitudinal growth axis. Consequently, absorption of water and nutrients by the root and exposure of leaves to sunlight for efficient photosynthesis is hindered. In these conditions, other external cues can be explored to guide the direction of organ growth. Providing a unilateral light source can guide the shoot growth, but prolonged root exposure to light causes a stress response, affecting growth and development, and also affecting the response to other environmental factors. Here, we have investigated how the protection of the root from light exposure, while the shoot is illuminated, influences the direction of root growth in microgravity. We report that the light avoidance mechanism existing in roots guides their growth towards diminishing light and helps establish the proper longitudinal seedling axis in simulated microgravity conditions. This process is regulated by flavonols, as shown in the flavonoid-accumulating mutant transparent testa 3, which shows an increased correction of the root growth direction in microgravity, when the seedling is grown with the root protected from light. This finding may improve the efficiency of water and nutrient sourcing and photosynthesis under microgravity conditions, as they exist in space, contributing to better plant fitness and biomass production in space farming enterprises, necessary for space exploration by humans., The funds for this research were provided by Agencia Estatal de Investigación of the Spanish Ministry of Science and Innovation, Grants #ESP2015-64323-R and #RTI2018-099309-B-I00 (co-funded by EU-ERDF), awarded to FJM. The clinostat was granted by the United Nations Zero-Gravity Instrument Project (ZGIP). AV was a recipient of a contract of the Spanish National Program for Young Researchers Training (BES-2016-077976).

24 p.-9 fig., Gravitropism and phototropism play a primary role in orienting root growth. Tropistic responses of roots mediated by gravity and light have been extensively investigated, and a complex mutual interaction occurs between these two tropisms. To date, most studies have been conducted in 1 g, microgravity, or simulated microgravity, whereas no studies investigated root phototropism in hypergravity. Therefore, we studied the effects of several gravity treatments with those of different light wavelengths on root growth orientation. Here, we report growth and curvature of Brassica oleracea roots under different g levels, from simulated microgravity up to 20 g, and unilateral illumination with different spectral treatments provided by light emitting diodes. Microgravity was simulated with a random positioning machine whereas hypergravity conditions were obtained using the Large Diameter Centrifuge at the laboratories of the European Space Agency in the Netherlands. Four light treatments (white light, blue light, red light, and dark) were used in this study. Overall, roots of seedlings grown in the dark were longer than those developed under unilateral light treatments, regardless of the gravity level. Unilateral blue light or white light stimulated a negative phototropism of roots under all g levels, and root curvature was not affected by either hypergravity or simulated microgravity compared to 1 g. Results also confirmed previous findings on the effect of light intensity on root curvature and highlighted the relevance of blue-light photon flux density in root phototropism. Roots illuminated with red light showed a weak curvature in simulated microgravity but not in hypergravity. Moreover, root curvature under red light was similar to dark-grown roots in all g levels, suggesting a possible involvement of surface-dependent phenomena in root skewing under either red light or dark conditions. Further studies can confirm phototropic responses of B. oleracea in the weightless environment of orbiting spacecraft. Nevertheless, according to our findings, directional lighting represents an effective stimulus to guide root growth in a wide range of gravity conditions., This work was supported by the ESA-HRE CORA contract #4000127705/19/NL/PG/pt. Financial support was also provided by ESA-TEC contract #4000116223/16/NL/KML/hh to Jack J.W.A. van Loon, by Spanish Agencia Estatal de Investigación (Grant RTI2018-099309-B-I00, co-funded by EU- ERDF) to F. Javier Medina, and by NASA (Grant 80NSSC17K0546) to John Z. Kiss.

Simulated microgravity and partial gravity research on Earth is a necessary complement to space research in real microgravity due to limitations of access to spaceflight. However, the use of ground-based facilities for reduced gravity simulation is far from simple. Microgravity simulation usually results in the need to consider secondary effects that appear in the generation of altered gravity. These secondary effects may interfere with gravity alteration in the changes observed in the biological processes under study. In addition to microgravity simulation, ground-based facilities are also capable of generating hypergravity or fractional gravity conditions whose effects on biological systems are worth being tested and compared with the results of microgravity exposure. Multiple technologies (2D clinorotation, random positioning machines, magnetic levitators, or centrifuges) and experimental hardware (different containers and substrates for seedlings or cell cultures) are available for these studies. Experimental requirements should be collectively and carefully considered in defining the optimal experimental design, taking into account that some environmental parameters, or life-support conditions, could be difficult to be provided in certain facilities. Using simulation facilities will allow us to anticipate, modify, or redefine the findings provided by the scarce available spaceflight opportunities.

14 p.-5 fig.-2 tab., Nuclear matrix constituent proteins (NMCPs), the structural components of the plant lamina, are considered to be the analogues of lamins in plants based on numerous structural and functional similarities. Current phylogenetic know-ledge suggests that, in contrast to lamins, which are widely distributed in eukaryotes, NMCPs are taxonomically re-stricted to Streptophyta. At present, most information about NMCPs comes from angiosperms, and virtually no data are available from more ancestral groups. In angiosperms, the NMCP family comprises two phylogenetic groups, NMCP1 and NMCP2, which evolved from the NMCP1 and NMCP2 progenitor genes. Based on sequence conservation and the presence of NMCP-specific domains, we determined the structure and number of NMCP genes present in different Streptophyta clades. We analysed 91 species of embryophytes and report additional NMCP sequences from mosses, liverworts, clubmosses, horsetail, ferns, gymnosperms, and Charophyta algae. Our results confirm an origin of NMCPs in Charophyta (the earliest diverging group of Streptophyta), resolve the number and structure of NMCPs in the different clades, and propose the emergence of additional NMCP homologues by whole-genome duplication events. Immunofluorescence microscopy demonstrated localization of a basal NMCP from the moss Physcomitrella patens at the nuclear envelope, suggesting a functional conservation for basal and more evolved NMCPs., This work was supported by the Spanish Ministry of Science and Innovation (BFU2010-15900) and CSIC (PIE 201020E019).

20 p.-6 fig., Clinorotation was the first method designed to simulate microgravity on ground and it remains the most common and accessible simulation procedure. However, different experimental settings, namely angular velocity, sample orientation, and distance to the rotation center produce different responses in seedlings. Here, we compare A. thaliana root responses to the two most commonly used velocities, as examples of slow and fast clinorotation, and to vertical and horizontal clinorotation. We investigate their impact on the three stages of gravitropism: statolith sedimentation, asymmetrical auxin distribution, and differential elongation. We also investigate the statocyte ultrastructure by electron microscopy. Horizontal slow clinorotation induces changes in the statocyte ultrastructure related to a stress response and internalization of the PIN-FORMED 2 (PIN2) auxin transporter in the lower endodermis, probably due to enhanced mechano-stimulation. Additionally, fast clinorotation, as predicted, is only suitable within a very limited radius from the clinorotation center and triggers directional root growth according to the direction of the centrifugal force. Our study provides a full morphological picture of the stages of graviresponse in the root tip, and it is a valuable contribution to the field of microgravity simulation by clarifying the limitations of 2D-clinostats and proposing a proper use., This research was funded by Agencia Estatal de Investigación of the Spanish Ministry of Science and Innovation, Grants #ESP2015-64323-R and #RTI2018-099309-B-I00 (co-funded by EU-ERDF), awarded to FJM. The clinostat was obtained by a Grant of the United Nations Zero-Gravity Instrument Project (ZGIP), second and third cycle calls 2014/2018 (UNOOSA), awarded to RH and FJM. AV is a recipient of a contract of the Spanish National Program for Young Researchers Training (BES-2016-077976).

The response of plants to the spaceflight environment and microgravity is still not well understood, although research has increased in this area. Even less is known about plants’ response to partial or reduced gravity levels. In the absence of the directional cues provided by the gravity vector, the plant is especially perceptive to other cues such as light. Here, we investigate the response of Arabidopsis thaliana 6-day-old seedlings to microgravity and the Mars partial gravity level during spaceflight, as well as the effects of red-light photostimulation by determining meristematic cell growth and proliferation. These experiments involve microscopic techniques together with transcriptomic studies. We demonstrate that microgravity and partial gravity trigger differential responses. The microgravity environment activates hormonal routes responsible for proliferation/growth and upregulates plastid/mitochondrial-encoded transcripts, even in the dark. In contrast, the Mars gravity level inhibits these routes and activates responses to stress factors to restore cell growth parameters only when red photostimulation is provided. This response is accompanied by upregulation of numerous transcription factors such as the environmental acclimation-related WRKY-domain family. In the long term, these discoveries can be applied in the design of bioregenerative life support systems and space farming., This research was funded by the Agencia Estatal de Investigación of the Spanish Ministry of Science an Innovation, Grants #ESP2015-64323-R and #RTI2018-099309-B-I00 (co-funded by EU-ERDF) to F.J.M., by pre-doctoral fellowships to A.M. and A.V. from the Spanish National Program for Young Researchers Training (MINECO, Ref. #BES-2013-063933, #BES-2016-077976) and the Seedling Growth Project for ISS experimentation #LSRA2009-0932/ 1177, a shared project of ESA-ELIPS Program and NASA, to F.J.M. and J.Z.K. In addition, J.Z.K. is funded by Grants NNX12A065G and 80NSSC17K0546. This research is related to the Space Omics TT funded by the ESA contract 4000131202/20/NL/PG to R.H.

25 p.-4 fig., Any space exploration initiative, such as the human presence in the Moon and Mars, must incorporate plants for life support. To enable space plant culture we need to understand how plants respond to extraterrestrial conditions, adapt to them, and compensate their deleterious effects at multiple levels. Gravity is a major difference between the terrestrial and the extraterrestrial environment. Gravitropism is the process of establishing a growth direction for plant organs according to the gravity vector. Gravity signals are sensed at specialized tissues by the motion of amyloplasts called statoliths and transduced to produce a cellular polarization capable of influencing the transport of auxin. Gravity alterations eventually result in changes in the lateral balance of auxin in the root, producing deviations of the growth direction. Under microgravity, auxin changes affect the root meristem causing increased cell proliferation and decreased cell growth. The nucleolus, the nuclear site of production of ribosomes, is a marker of this unbalance, which could alter plant development. At the molecular level, microgravity induces a reprogramming of gene expression that mostly affects plant defense systems against abiotic stresses, indicating that these categories of genes are involved in the adaptation to extraterrestrial habitats. Nevertheless, no specific genes for plant response to gravitational stress have been identified. Despite this stress, plants survive, developing until the adult stage and reproducing under microgravity conditions. A major research challenge is to identify environmental factors, such as light, which could interact, modulate, or balance the impact of gravity, contributing to the tolerance and survival of plants under spaceflight conditions. Understanding the crosstalk between light and gravity sensing will contribute to the success of the next generation agriculture in human settlements outside the Earth., Work performed in the authors’ laboratory was supported by different grants of the Spanish National Agency for Research of theSpanish Government, e.g. Grants # ESP2015-64323-R and #RTI2018-099309-B-I00 (co-funded by EU-ERDF).

30 p.-10 fig.-1 tab., Plant biology is an important area for the future of space exploration, but biological spaceflight experiments have been always constrained by the hardware capabilities. The European Modular Cultivation System (EMCS) unit was an incubator for small organisms, such as Arabidopsis thaliana, built by the European Space Agency (ESA) and was decommissioned in 2018. Here, we describe the FixBox system as add-on hardware to provide fixation capabilities to the plant growth cassettes, which, initially, were not designed to be used for that purpose. Tests were performed to ensure the successful use of this device in the EMCS facility. We also evaluate the required adaptations to the hardware, e.g., to guarantee that the reduced fluid motion in microgravity does not cause any bubbles that could impair the quality of fixation. Arabidopsis thaliana seedlings grown during spaceflight were fixed in the FixBox either in glutaraldehyde or formaldehyde. Electron microscopical images and confocal microscopy immunofluorescent localizations showed an excellent preservation of both cell ultrastructure and antigen conformation. Thus, it is possible to modify existing hardware to comply with the scientific requirements to augment the existing capabilities on board the ISS. In addition, it is also possible to reuse culture chambers from predesigned experimental containers into new modular subunits as FixBox. Similarly, we can design new hardware compatible with a novel cultivation chamber on board, such as is available in BIOLAB, to be used later with FixBox. Lessons learned for future space plant biology researchers include how to manage the number of hardware requirements and constraints on how to preserve the biological samples., This work was supported by the Agencia Estatal de Investigación of the Spanish Ministry of Science an Innovation, Grants #ESP2015–64323-R and #RTI2018–099309-B-I00 (co-funded by EU-ERDF), awarded to FJM, and by pre-doctoral fellowships to (AM), (MV) and (AV) from the Spanish National Program for Young Researchers Training (MINECO, Ref. BES-2013-063933, BES-2016-077976). This research was supported also by grants (NNX12A0656 and 80NSSC17K0546) from NASA to JZK. The Seedling Growth Project spaceflights and activities to the ISS were funded by ILSRA2009–0932/1177 of ESA-ELIPS Program. The FixBox has been built under a contract to SENER Aeroespacial SA by ESA (4000105697/12/NL/FC) to support the SG project.

We study the properties of extremal function for the Fuglede's p–modulus of a measure family Σ. Based on the recent result concerning p–modulus showing the existence of certain Borel measure n Σ on Σ, we give an interpretation of n Σ in some simple cases. In particular, we consider the case of disjoint supports and a natural family of measures associated with a double fibration.

10 p.-7 fig.-3 tab. 69th International Astronautical Congress (IAC), Bremen, Germany, 1-5 October 2018, Due to high cost and low availability of space (real microgravity) experiments, ground based facilities (GBF) simulating microgravity are commonly used. The clinostat is one of the most widely used GBF in simulation experiments. Up to date, there is no clear set of rules on how to use 2D clinostats concerning the speed of rotation. With the objective of defining the optimal settings, we have used a mathematical model and compared the physiological response of A. thaliana 5-day-old seedlings to two speeds of the 2D clinostat: low- (1 rpm) and high-speed (60 rpm) for short (1, 2, 3 hours) and long (24 h) periods of time. Seedlings were grown for five days in conditions of photoperiod, oriented according to the gravity vector. Then, they were subjected to clinorotation (1 or 60 rpm) in darkness to avoid the possible effect of light on the auxin gradients. Auxin is a phytohormone driving the physiological changes resulting in gravitropism. In a control experiment, we positioned seedlings perpendicular to the gravity vector in order to observe statoliths displacement producing changes in auxin gradient and to record the timeframe of the process, by collecting samples at defined time intervals. The gravitropic reaction of plants starts with the displacement of statoliths in columella cells. We investigated the displacement of statoliths by staining starch in these organelles with Lugol solution. Next, we observed the auxin gradient using two reporter lines: DR5::GUS and DII-Venus. The changes in the position of statoliths were observed as soon as 1 h after experiment started. In the seedlings positioned perpendicular to the gravity vector, statoliths moved from the bottom of statocytes to the side of the cells, whereas in the seedlings exposed to clinorotation they appeared dispersed in the cells, which confirmed that plants were unable to sense the direction of gravity vector. Accumulation of auxin was observed on the side of the root where gravity vector was acting after 1h in case of DII-Venus and 2 h in case of DR5::GUS. We observed quantitative changes in auxin gradient and root length in the seedlings exposed to two different speeds of clinorotation. We compared the results with previous experiments using Random Positioning Machine (RPM) and in real microgravity. We conclude that the proposed mathematical model, as well as the physiological reaction of plants, confirms that the low-speed (1 rpm) is more suitable to perform microgravity simulation experiments., Funding for this study was provided by the Spanish National Plan for Research and Development (MINECO-ERDF co-funding) Grant ESP2015-64323-R to FJM. AV is recipient of grant of the Spanish National Program for Young Researchers Training (Refs. BES-2016- 077976). Clinostat for this study was provided by ZGIP, UNOOSA. ESA Education Office supported the attendance of AV to IAC 2018.

We consider the p-modulus of a foliation on a Riemannian manifold. We study the second variation of the p-modulus, and we derive a stability condition for this variation, which we formulate as a type of the Hardy inequality with the weight depending on the geometry of the foliation. In particular, we show that foliations defined by the distance function are p-stable for any p ≥ 2 . We examine the critical points of the p-modulus of the level sets of a smooth function. This leads, via a new approach, to generalizations of the well-known result that the q-capacity of a condenser is the reciprocal of the p-modulus of the family of all hyper-surfaces separating the plates of the condenser.

We extend the Rodin's formula for $p$--modulus of the family of curves in $\mathbb{R}^n$ to arbitrary codimension. The proof relies on the formula for the $p$--modulus of family of level sets of a submersion and an algebraic lemma relating Jacobi matrices of considered maps. We state appropriate examples., 10 pages

26 p.-3 fig.-3 fig. supl.-1 tab. supl., Nuclear lamina organization is similar in metazoan and plants though the latter lack orthologs of lamins, the main components of the metazoan lamina. Current evidence suggests that Nuclear Matrix Constituent Proteins (NMCPs) are the lamin analogues in plants as these proteins share several key features: higher-order secondary structure and domain layout, subnuclear distribution, and involvement in the regulation of nuclear shape and size, as well as in higher-order chromatin organization. Previously, we studied the NMCP family in flowering plants (angiosperms), in which it comprises two phylogenetic groups: NMCP1 and NMCP2. At present, in silico information about NMCP proteins in embryophytes is relatively advanced, though very few proteins, most of them of the NMCP1 type, have been extensively studied in vivo. We previously characterized the NCMP1 protein in the monocot Allium cepa. Here, we report the key features of a second protein of this species NMCP2, which presents a conserved sequence and domain layout. Immunofluorescence and immunoelectronmicroscopy evidence co-localization of endogenous AcNMCP2 and AcNMCP1 in the lamina, while Western blotting and immunoconfocal microscopy reveal a similar pattern of expression and distribution of both NMCP proteins in different root tissues. Our results provide novel insight about endogenous NMCP2-type proteins and complete the characterization of the NMCP family in A. cepa, thus advancing the current understanding of these structural proteins constituting the plant lamina., This work was supported by the Spanish Ministry of Science and Innovation [BFU2010-15900] and the Spanish National Research Council (CSIC) [PIE 201020E019].

At present, two complementary approaches are used for in situ protein visualization in plant nuclei. Imaging of transformed fluorescent proteins is the election tool for the analysis of protein movement and interaction. However, this methodology presents several drawbacks for the identification/localization of endogenous nuclear factors, such as over-expression or mislocalization of transformed proteins. In contrast, immunocytochemistry with specific antibodies represents a powerful tool for the localization of endogenous nuclear proteins at their "native" nuclear sub-compartments. In plant cells, the cell wall hampers antibody accessibility during immunocytochemical analysis thereby reducing the effectivity of the technique, particularly in the case of lowly expressed proteins. To overcome this problem in nuclear protein immunodetection, we developed a method based on the in vitro incubation of isolated nuclei with specific antibodies followed by imaging by confocal fluorescence or electron microscopy. Here we describe the application of this methodology to the localization of Nuclear Matrix Constituent Proteins (NMCP), the plant analogs of lamins, of the monocot Allium cepa, using antibodies raised against highly conserved regions of the proteins.

At present, two complementary approaches are used for in situ protein visualization in plant nuclei. Imaging of transformed fluorescent proteins is the election tool for the analysis of protein movement and interaction. However, this methodology presents several drawbacks for the identification/localization of endogenous nuclear factors, such as over-expression or mislocalization of transformed proteins. In contrast, immunocytochemistry with specific antibodies represents a powerful tool for the localization of endogenous nuclear proteins at their “native” nuclear sub-compartments. In plant cells, the cell wall hampers antibody accessibility during immunocytochemical analysis thereby reducing the effectivity of the technique, particularly in the case of lowly expressed proteins. To overcome this problem in nuclear protein immunodetection, we developed a method based on the in vitro incubation of isolated nuclei with specific antibodies followed by imaging by confocal fluorescence or electron microscopy. Here we describe the application of this methodology to the localization of Nuclear Matrix Constituent Proteins (NMCP), the plant analogs of lamins, of the monocot Allium cepa, using antibodies raised against highly conserved regions of the proteins., We acknowledge the support from the Spanish Ministry of Science and Innovation [BFU2010-15,900] and the CSIC [PIE 201020E019].

The nucleoskeleton of plants contains a peripheral lamina (also called plamina) and, even though lamins are absent in plants, their roles are still fulfilled in plant nuclei. One of the most intriguing topics in plant biology concerns the identity of lamin protein analogues in plants. Good candidates to play lamin functions in plants are the members of the NMCP (nuclear matrix constituent protein) family, which exhibit the typical tripartite structure of lamins. This paper describes a bioinformatics analysis and classification of the NMCP family based on phylogenetic relationships, sequence similarity and the distribution of conserved regions in 76 homologues. In addition, NMCP1 in the monocot Allium cepa characterized by its sequence and structure, biochemical properties, and subnuclear distribution and alterations in its expression throughout the root were identified. The results demonstrate that these proteins exhibit many similarities to lamins (structural organization, conserved regions, subnuclear distribution, and solubility) and that they may fulfil the functions of lamins in plants. These findings significantly advance understanding of the structural proteins of the plant lamina and nucleoskeleton and provide a basis for further investigation of the protein networks forming these structures.

13 p.-4 fig.-1 tab., The nuclear lamina is a complex protein mesh attached to the inner nuclear membrane(INM),which is also associated with nuclear pore complexes.It provides mechanical support to the nucleus and nuclear envelope,and as well as facilitating the connection of the nucleoskeleton to the cytoskeleton,it is also involved in chromatin organization,gene regulation,and signaling.In metazoans,the nuclear lamina consists of a polymeric layer of lamins and other interacting proteins responsible for its association with the INM and chromatin.In plants,field emission scanning electron microscopy of nuclei,and thin section transmission electron microscopy of isolated nucleoskeletons,reveals the lamina to have a similar structure to that of metazoans.Moreover,although plants lack lamin genes and the genes encoding most lamin-binding proteins,the main functions of the lamina are fulfilled in plants.Hence,it would appear that the plant lamina is not based on lamins and that other proteins substitute for lamins in plant cells.The nuclear matrix constituent proteins are the best characterized structural proteins in the plant lamina.Although these proteins do not display strong sequence similarity to lamins,their predicted secondary structure and sub-nuclear distribution,as well as their influence on nuclear size and shape,and on heterochromatin organization,suggest they could be functional lamin analogs.In this review we shall summarize what is currently known about the organization and composition of the plant nuclear lamina and its interacting complexes,and we will discuss the activity of this structure in the plant cell and its nucleus., We acknowledge the support from the Spanish Ministry of Science and Innovation[BFU2010-15900]and the CSIC[PIE 201020E019].Malgorzata Ciska was supported by a grant from the Junta de Ampliación de Estudios (JAEPre_08_00012/JAEPre027) and by PIE201020E019.

The $p$--modulus ${\rm mod}_p(\mathcal{F})$ of a foliation $\mathcal{F}$ on a Riemannian manifold $M$ is a generalization of extremal length of plane curves introduced by L. Ahlfors. We study the variation $t\mapsto{\rm mod}_p(\mathcal{F}_t)$ of the modulus. In particular, we consider product of moduli of orthogonal foliations., 12 pages

34 p.-2 fig.-2 tab. Este artículo pertenece a la Tesis presentada por Malgorzata Ciska con título: "Caracterización de AcNMCP1 una proteína implicada en organización nuclear de plantas."(https://digital.csic.es/handle/10261/98559), Lamins are the main components of the metazoan lamina, and while the organization of the nuclear lamina of metazoans and plants is similar, there are apparently no genes encoding lamins or most lamin-binding proteins in plants. Thus, the plant lamina is not lamin-based and the proteins that form this structure are still to be characterized. Members of the plant NMCP/LINC/CRWN protein family share the typical tripartite structure of lamins, although the 2 exhibit no sequence similarity. However, given the many similarities between NMCP/LINC/CRWN proteins and lamins (structural organization, position of conserved regions, sub-nuclear distribution, solubility, and pattern of expression), these proteins are good candidates to carry out the functions of lamins in plants. Moreover, functional analysis of NMCP/LINC mutants has revealed their involvement in maintaining nuclear size and shape, another activity fulfilled by lamins. This review summarizes the current understanding of NMCP/LINC proteins and discusses future studies that will be required to demonstrate definitively that these proteins are plant analogs of lamins. © 2013 Landes Bioscience., We acknowledge support from the Spanish Ministry of Science and Innovation [BFU2010–15900] and the CSIC [PIE 201020E019]. Ciska M was supported by a grant from the Junta de Ampliación de Estudios (JAEPre_08_00012/JAEPre027) and by PIE 201020E019.