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At least 235 records · Page 13

CBL aggravates Ang II-induced cardiac hypertrophy via the VHL/HIF-1α pathway

Highlights: • 1. The expression of CBL is increased in Ang II-induced cardiac hypertrophy in vitro and in vivo. • The pro-hypertrophic function of CBL on Ang II-induced myocardial hypertrophy was mediated by HIF-1α. • CBL increased HIF-1α expression via regulating VHL. • CBL decreased VHL through directly promote its ubiquitination modification. CBL (Casitas B cell lymphoma), an important ubiquitin protein ligase, is involved in protein folding, protein maturation, and proteasome-dependent protein catabolism in different cells. However, its role in cardiac hypertrophy is still unclear. In this study, we found that expression of CBL is increased in an Ang II-induced mouse cardiac hypertrophy animal model and in Ang II-treated H9C2 cells. Interference with CBL expression attenuates the degree of myocardial hypertrophy as well as the expression of hypertrophy-related genes in H9C2 cells. Further research found that CBL aggravates myocardial hypertrophy by activating HIF-1α, which is an aggravating factor for hypertrophy. The effect of CBL on promoting myocardial hypertrophy was reversed by interference with HIF-1α. Mechanistically, we found that CBL directly interacted with and degraded VHL by increasing its ubiquitination level, which is a widely accepted regulatory factor of HIF-1α. Finally, our results showed that CBL was partially dependent on degradation of VHL and that activation of HIF-1α promoted myocardial hypertrophy. Collectively, these findings suggest that strategies based on activation of the CBL/HIF-1α axis might be promising for the treatment of hypertrophic cardiomyopathy.

60 APPLIED LIFE SCIENCES↗

Stress-induced alterations in interferon production and class II histocompatibility antigen expression

Mild electric foot-shock has been shown to be a stressor that can alter immune responses. Male Lewis rats were exposed to one session of 16 5.0-s 1.6-mA foot-shocks. Production of interferon-gamma by splenocytes in response to concanavalin-A was decreased in spleens from the shocked rats compared to control spleens. Spleen cells from rats treated with nadolol, a peripherally acting beta-adrenergic receptor antagonist, and then shocked, showed dose-dependent attenuation of the suppression of interferon-gamma production. This suggests that catecholamines mediate shock-induced suppression of interferon-gamma production. The percentage of splenic mononuclear cells expressing class II histocompatibility (Ia) antigens on their surfaces from spleens of shocked rats was determined by flow cytometry. Significantly decreased class II positive mononuclear cells were present in the spleens of shocked rats in comparison to the spleens of control rats. This may reflect an alteration of cell trafficking or decreased production of class II antigens.

Non-NASA Center↗

Simulated Microgravity Regulates Gene Transcript Profiles of 2T3 Preosteoblasts: Comparison of the Random Positioning Machine and the Rotating Wall Vessel Bioreactor

Microgravity of spaceflight induces bone loss due in part to decreased bone formation by osteoblasts. We have previously examined the microgravity-induced changes in gene expression profiles in 2T3 preosteoblasts using the Random Positioning Machine (RPM) to simulate microgravity conditions. Here, we hypothesized that exposure of preosteoblasts to an independent microgravity simulator, the Rotating Wall Vessel (RWV), induces similar changes in differentiation and gene transcript profiles, resulting in a more confined list of gravi-sensitive genes that may play a role in bone formation. In comparison to static 1g controls, exposure of 2T3 cells to RWV for 3 days inhibited alkaline phosphatase activity, a marker of differentiation, and downregulated 61 genes and upregulated 45 genes by more than two-fold as shown by microarray analysis. The microarray results were confirmed with real time PCR for downregulated genes osteomodulin, bone morphogenic protein 4 (BMP4), runx2, and parathyroid hormone receptor 1. Western blot analysis validated the expression of three downregulated genes, BMP4, peroxiredoxin IV, and osteoglycin, and one upregulated gene peroxiredoxin I. Comparison of the microarrays from the RPM and the RWV studies identified 14 gravi-sensitive genes that changed in the same direction in both systems. Further comparison of our results to a published database showing gene transcript profiles of mechanically loaded mouse tibiae revealed 16 genes upregulated by the loading that were shown to be downregulated by RWV and RPM. These mechanosensitive genes identified by the comparative studies may provide novel insights into understanding the mechanisms regulating bone formation and potential targets of countermeasure against decreased bone formation both in astronauts and in general patients with musculoskeletal disorders.

Patel, Mamta J.↗

Influence of Mild Chronic Stress and Social Isolation on Acute Ozone-Induced Alterations in Stress Biomarkers and Brain-Region-Specific Gene Expression in Male Wistar–Kyoto Rats

Individuals with psychosocial stress often experience an exaggerated response to air pollutants. Ozone (O 3 ) exposure has been associated with the activation of the neuroendocrine stress-response system. We hypothesized that preexistent mild chronic stress plus social isolation (CS), or social isolation (SI) alone, would exacerbate the acute effects of O 3 exposure on the circulating adrenal-derived stress hormones, and the expression of the genes regulating glucocorticoid stress signaling via an altered stress adaptation in a brain-region-specific manner. Male Wistar–Kyoto rats (5 weeks old) were socially isolated, plus were subjected to either CS (noise, confinement, fear, uncomfortable living, hectic activity, and single housing), SI (single housing only, restricted handling and no enrichment) or no stress (NS; double housing, frequent handling and enrichment provided) for 8 weeks. The rats were then exposed to either air or O 3 (0.8 ppm for 4 h), and the samples were collected immediately after. The indicators of sympathetic and hypothalamic–pituitary axis (HPA) activation (i.e., epinephrine, corticosterone, and lymphopenia) increased with O 3 exposure, but there were no effects from CS or SI, except for the depletion of serum BDNF. CS and SI revealed small changes in brain-region-specific glucocorticoid-signaling-associated markers of gene expression in the air-exposed rats (hypothalamic Nr3c1, Nr3c2 Hsp90aa1, Hspa4 and Cnr1 inhibition in SI; hippocampal HSP90aa1 increase in SI; and inhibition of the bed nucleus of the stria terminalis (BNST) Cnr1 in CS). Gene expression across all brain regions was altered by O 3 , reflective of glucocorticoid signaling effects, such as Fkbp5 in NS, CS and SI. The SI effects on Fkbp5 were greatest for SI in BNST. O 3 increased Cnr2 expression in the hypothalamus and olfactory bulbs of the NS and SI groups. O 3 , in all stress conditions, generally inhibited the expression of Nr3c1 in all brain regions, Nr3c2 in the hippocampus and hypothalamus and Bdnf in the hippocampus. SI, in general, showed slightly greater O 3 -induced changes when compared to NS and CS. Serum metabolomics revealed increased sphingomyelins in the air-exposed SI and O 3 -exposed NS, with underlying SI dampening some of the O 3 -induced changes. These results suggest a potential link between preexistent SI and acute O 3 -induced increases in the circulating adrenal-derived stress hormones and brain-region-specific gene expression changes in glucocorticoid signaling, which may partly underlie the stress dynamic in those with long-term SI.

gene expression↗

Persistent Expression Changes of Fibrosis-Related Genes in the Lung Tissues of Rats Exposed to Lunar Dust Particles

The Moon's surface is covered by a layer of fine, potential reactive dust. Lunar dust contain about 1‐2% of very fine respirable dust (less than 3 micrometers). The habitable area of any lunar landing vehicle and outpost would inevitably be contaminated with lunar dust that could pose a health risk. The purpose of the study is to evaluate the toxicity of Apollo moon dust in rodents to assess the health risk of dust exposures to humans. One of the particular interests in the study is to evaluate dust‐induced changes of the expression of fibrosis‐related genes, and to identify specific signaling pathways involved in lunar dustinduced toxicity. F344 rats were exposed for 4 weeks (6h/d; 5d/wk) in nose‐only inhalation chambers to concentrations of 0 (control air), 2.1, 6.8, 21, and 61 milligrams per cubic meters of lunar dust. Five rats per group were euthanized at 1 day, 1 week, 1 month, and 3 months after the last inhalation exposure. The bronchoalveolar lavage fluid (BALF) was collected by lavaging with phosphate‐buffered saline (PBS). A zymosan‐induced luminolbased chemiluminescence assay was used to assess the activity of BAL cells. The lavaged lung tissue was snap frozen in LN2 and total RNA was isolated using the Qigen RNeasy kit. The expression of 84 fibrosisrelated genes were analyzed using the RT2 Profiler PCR Array technique. The expression of 18 genes of interest were further measured using real‐time PCR technique in all the samples. 10 out of 18 genes of interest showed persistently significant expression changes in the local lung tissue exposed to lunar dust, indicating a prolonged proinflammatory response. The expressions of several of these genes were dose‐ and time‐dependent and were significantly correlated with other pathological parameters. The potential signaling pathways and upstream regulators were further analyzed using IPA pathway analysis tool based on the gene expression data. The data presented in this study, for the first time, explore the molecular mechanisms of lunar dust induced toxicity, contributing not only the risk assessment for future space exploration, but also understandings of the dust‐induced toxicity in humans on earth.

Zhang, Ye↗

Immunomodulation by cannabidiol in bovine primary ruminal epithelial cells

Ruminant livestock experience a number of challenges, including high concentrate diets, weaning and transport, which can increase their risk of disorders such as ruminal acidosis, and the associated inflammation of the ruminal epithelium. Cannabidiol (CBD), a phytochemical from hemp (Cannabis sativa), is a promising target as a therapy for gastrointestinal inflammation, and may be extremely valuable as either a treatment or prophylactic. However, the effects of CBD in the the ruminant gastrointestinal tract have not been explored, in part due to the restrictions on feeding hemp to livestock. Therefore, the objective of this study was to investigate the immunomodulatory properties of CBD using a model of inflammation in primary ruminal epithelial cells (REC). In addition, CBD dose was evaluated for possible cytotoxic effects. Negative effects on cell viability were not observed when REC were exposed to 10 μM CBD. However, when the dose was increased to 50 μM for 24 h, there was a significant cytotoxic effect. When 10 μM CBD was added to culture media as treatment for inflammation induced with lipopolysaccharide (LPS), expression of genes encoding for pro-inflammatory cytokine IL1B was less compared to LPS exposure alone, and CBD resulted in a down-regulation of IL6. As a pre-treatment, prior to LPS exposure, REC had decreased expression of IL6 and CXCL10 while CBD was present in the media, but not when it was removed prior to addition of LPS. Results suggest that CBD may reduce cytokine transcription both during LPS-induced inflammation and when used preventatively, although these effects were dependent on its continued presence in the culture media. Overall, these experiments provide evidence of an immunomodulatory effect by CBD during a pro-inflammatory response in primary REC in culture.

59 BASIC BIOLOGICAL SCIENCES↗

The molecular responses of skeletal muscle satellite cells to continuous expression of IGF-1: implications for the rescue of induced muscular atrophy in aged rats

Approximately 50% of humans older than 85 years have physical frailty due to weak skeletal muscles. This indicates a need for determining mechanisms to combat this problem. A critical cellular factor for postnatal muscle growth is a population of myogenic precursor cells called satellite cells. Given the complex process of sarcopenia, it has been postulated that, at some point in this process, a limited satellite cell proliferation potential could become rate-limiting to the regrowth of old muscles. It is conceivable that if satellite cell proliferative capacity can be maintained or enhanced with advanced age, sarcopenia could potentially be delayed or prevented. Therefore, the purposes of this paper are to describe whether IGF-I can prevent muscular atrophy induced by repeated cycles of hindlimb immobilization, increase the in vitro proliferation in satellite cells from these muscles and, if so, the molecular mechanisms by which IGF-I mediates this increased proliferation. Our results provide evidence that IGF-I can enhance aged muscle regrowth possibly through increased satellite cell proliferation. The results also suggest that IGF-I enhances satellite cell proliferation by decreasing the cell cycle inhibitor, p27Kip1, through the PI3'-K/Akt pathway. These data provide molecular evidence for IGF-I's rescue effect upon aging-associated skeletal muscle atrophy.

NASA Discipline Musculoskeletal↗

Dynamic errors in a tuned flexure-mounted strapdown gyro

Motion induced errors in a tuned, flexure-mounted strapdown gyro are investigated. Analytic expressions are developed for errors induced by linear vibrations, angular motion, and detuning. Sensor-level errors (gyro drift rate) and system-level errors (navigation errors) that are stimulated by an actual dynamic motion environment are computed.

Bortz, J. E., Sr.↗

CAZymes from the thermophilic fungus Thermoascus aurantiacus are induced by C5 and C6 sugars

Abstract Background Filamentous fungi are excellent lignocellulose degraders, which they achieve through producing carbohydrate active enzymes (CAZymes). CAZyme production is highly orchestrated and gene expression analysis has greatly expanded understanding of this important biotechnological process. The thermophilic fungus Thermoascus aurantiacus secretes highly active thermostable enzymes that enable saccharifications at higher temperatures; however, the genome-wide measurements of gene expression in response to CAZyme induction are not understood. Results A fed-batch system with plant biomass-derived sugars d -xylose, l -arabinose and cellobiose established that these sugars induce CAZyme expression in T. aurantiacus . The C5 sugars induced both cellulases and hemicellulases, while cellobiose specifically induced cellulases. A minimal medium formulation was developed to enable gene expression studies of T. aurantiacus with these inducers. It was found that d-xylose and l -arabinose strongly induced a wide variety of CAZymes, auxiliary activity (AA) enzymes and carbohydrate esterases (CEs), while cellobiose facilitated lower expression of mostly cellulase genes. Furthermore, putative orthologues of different unfolded protein response genes were up-regulated during the C5 sugar feeding together with genes in the C5 sugar assimilation pathways. Conclusion This work has identified two additional CAZyme inducers for T. aurantiacus , l -arabinose and cellobiose, along with d -xylose. A combination of biochemical assays and RNA-seq measurements established that C5 sugars induce a suite of cellulases and hemicellulases, providing paths to produce broad spectrum thermotolerant enzymatic mixtures.

09 BIOMASS FUELS↗

Unilateral optic nerve transection alters light response of suprachiasmatic nucleus and intergeniculate leaflet

The suprachiasmatic nucleus (SCN), the circadian pacemaker, receives photic input directly from the retina to synchronize the pacemaker to the environment. Additionally, the intergeniculate leaflet (IGL), which innervates the SCN, is known to modulate the retinal photic input to the SCN. To further understand the role of the IGL in mediating the photic input to the SCN, this study examined the effects of unilateral optic nerve transection (UONx) on the photic response of the SCN and IGL in adult and neonatal hamsters. UONx led to an overall reduction in light-induced c-Fos expression in the SCN and IGL. The c-Fos expression was greater in the SCN ipsilateral to the remaining eye, despite a symmetrically bilateral retinohypothalamic tract projection as revealed by intraocular injection of horseradish peroxidase. In contrast, UONx led to a greater c-Fos expression in the contralateral IGL. The contralateral IGL of UONx animals also revealed more neuropeptide Y-immunoreactive neurons, while the ipsilateral SCN of these animals exhibited a denser neuropeptide Y terminal field. The neonates with UONx showed a similar pattern with a slight compensation of the photic-induced c-Fos in the SCN. This study suggests that the IGL may have an ipsilateral inhibitory effect in mediating retinal photic input to the SCN.

Non-NASA Center↗

Fluid shear-induced mechanical signaling in MC3T3-E1 osteoblasts requires cytoskeleton-integrin interactions

Mechanical stimulation of bone induces new bone formation in vivo and increases the metabolic activity and gene expression of osteoblasts in culture. We investigated the role of the actin cytoskeleton and actin-membrane interactions in the transmission of mechanical signals leading to altered gene expression in cultured MC3T3-E1 osteoblasts. Application of fluid shear to osteoblasts caused reorganization of actin filaments into contractile stress fibers and involved recruitment of beta1-integrins and alpha-actinin to focal adhesions. Fluid shear also increased expression of two proteins linked to mechanotransduction in vivo, cyclooxygenase-2 (COX-2) and the early response gene product c-fos. Inhibition of actin stress fiber development by treatment of cells with cytochalasin D, by expression of a dominant negative form of the small GTPase Rho, or by microinjection into cells of a proteolytic fragment of alpha-actinin that inhibits alpha-actinin-mediated anchoring of actin filaments to integrins at the plasma membrane each blocked fluid-shear-induced gene expression in osteoblasts. We conclude that fluid shear-induced mechanical signaling in osteoblasts leads to increased expression of COX-2 and c-Fos through a mechanism that involves reorganization of the actin cytoskeleton. Thus Rho-mediated stress fiber formation and the alpha-actinin-dependent anchorage of stress fibers to integrins in focal adhesions may promote fluid shear-induced metabolic changes in bone cells.

Non-NASA Center↗

CCAAT/enhancer-binding protein delta is a critical regulator of insulin-like growth factor-I gene transcription in osteoblasts

Insulin-like growth factor-I (IGF-I) plays a major role in promoting skeletal growth by stimulating bone cell replication and differentiation. Prostaglandin E2 and other agents that induce cAMP production enhance IGF-I gene transcription in cultured rat osteoblasts through a DNA element termed HS3D, located in the proximal part of the major rat IGF-I promoter. We previously determined that CCAAT/enhancer-binding protein delta (C/EBPdelta) is the key cAMP-stimulated regulator of IGF-I transcription in these cells and showed that it transactivates the rat IGF-I promoter through the HS3D site. We now have defined the physical-chemical properties and functional consequences of the interactions between C/EBPdelta and HS3D. C/EBPdelta, expressed in COS-7 cells or purified as a recombinant protein from Escherichia coli, bound to HS3D with an affinity at least equivalent to that of the albumin D-site, a known high affinity C/EBP binding sequence, and both DNA elements competed equally for C/EBPdelta. C/EBPdelta bound to HS3D as a dimer, with protein-DNA contact points located on guanine residues on both DNA strands within and just adjacent to the core C/EBP half-site, GCAAT, as determined by methylation interference footprinting. C/EBPdelta also formed protein-protein dimers in the absence of interactions with its DNA binding site, as indicated by results of glutaraldehyde cross-linking studies. As established by competition gel-mobility shift experiments, the conserved HS3D sequence from rat, human, and chicken also bound C/EBPdelta with similar affinity. We also found that prostaglandin E2-induced expression of reporter genes containing human IGF-I promoter 1 or four tandem copies of the human HS3D element fused to a minimal promoter and show that these effects were enhanced by a co-transfected C/EBPdelta expression plasmid. Taken together, our results provide evidence that C/EBPdelta is a critical activator of IGF-I gene transcription in osteoblasts and potentially in other cell types and species.

NASA Discipline Musculoskeletal↗

Experimental and theoretical investigation of three-dimensional turbulent boundary layers and turbulence characteristics inside an axial flow inducer passage

Analytical and experimental investigations of the characteristics of three dimensional turbulent boundary layers in a rotating helical passage of an inducer rotor are reported. Expressions are developed for the velocity profiles in the inner layer, where the viscous effects dominate, in the outer layer, where the viscous effects are small, and in the interference layer, where the end walls influence the flow. The prediction of boundary layer growth is based on the momentum integral technique. The equations derived are general enough to be valid for all turbomachinery rotors with arbitrary pressure gradients. The experimental investigations are carried out in a flat plate inducer 3 feet in diameter. The mean velocity profiles, turbulence intensities and shear stresses, wall shear stress, and limiting streamline angles are measured at various radial and chordwise locations by using rotating probes. The measurements are in general agreement with the predictions. The radial flows are well represented by an expression which includes the effect of stagger angle and radial pressure gradient. The radial flows in the rotor channel are higher than those on a single blade. The collateral region exists only very near the blade surface. The radial component of turbulence intensity is higher than the streamwise component because of the effect of rotation.

Anand, A. K.↗

Space Charge Forces analytical model for emittance compensation

Space charge forces represent main induced effects in an RF-injector that degrade the beam quality. In this scenario the laser distribution sent on the photocathode acquires an important role in the emittance compensation process, as the slice analysis shows. Starting from the preliminary studies performed on [1], a novel semi-analytical model of space charge forces is proposed in detail for bunch with arbitrary charge distribution to derive expressions of self-induced forces. The performance of the fields at low energy regime (as the field has not expired RF forces) is under present analysis, we can investigate use of this model in low charge regime. Further, the model has been bench-marked with the behavior of the distributions present in the literature and studied for new ones. It has also been applied for the study of the optimization of a C-band hybrid photoinjector now being commissioned, thus explaining the factor two reduction of the emittance observed at the exit of the gun by changing the initial distribution at the cathode.

Carillo, M.↗

A modular chromosomally integrated toolkit for ectopic gene expression in Vibrio cholerae

The ability to express genes ectopically in bacteria is essential for diverse academic and industrial applications. Two major considerations when utilizing regulated promoter systems for ectopic gene expression are (1) the ability to titrate gene expression by addition of an exogenous inducer and (2) the leakiness of the promoter element in the absence of the inducer. Here, we describe a modular chromosomally integrated platform for ectopic gene expression in Vibrio cholerae . We compare the broadly used promoter elements P tac and P BAD to versions that have an additional theophylline-responsive riboswitch (P tac -riboswitch and P BAD -riboswitch). These constructs all exhibited unimodal titratable induction of gene expression, however, max induction varied with P tac > P BAD > P BAD -riboswitch > P tac -riboswitch. We also developed a sensitive reporter system to quantify promoter leakiness and show that leakiness for P tac > P tac -riboswitch > P BAD ; while the newly developed P BAD -riboswitch exhibited no detectable leakiness. We demonstrate the utility of the tightly inducible P BAD -riboswitch construct using the dynamic activity of type IV competence pili in V. cholerae as a model system. The modular chromosomally integrated toolkit for ectopic gene expression described here should be valuable for the genetic study of V. cholerae and could be adapted for use in other species.

59 BASIC BIOLOGICAL SCIENCES↗

Overexpression of Catalase in Mitochondria Mitigates Changes in Hippocampal Cytokine Expression Following Simulated Microgravity and Isolation

Isolation on Earth can alter physiology and signaling of organs systems, including the central nervous system. Although not in complete solitude, astronauts operate in an isolated environment during spaceflight. In this study, we determined the effects of isolation and simulated microgravity solely or combined, on the inflammatory cytokine milieu of the hippocampus. Adult female wild-type mice underwent simulated microgravity by hindlimb unloading for 30 days in single or social (paired) housing. In hippocampus, simulated microgravity and isolation each regulate a discrete repertoire of cytokines associated with inflammation. Their combined effects are not additive. A model for mitochondrial reactive oxygen species (ROS) quenching via targeted overexpression of the human catalase gene to the mitochondria (MCAT mice), are protected from isolation- and/or simulated microgravity-induced changes in cytokine expression. These findings suggest a key role for mitochondrial ROS signaling in neuroinflammatory responses to spaceflight and prolonged bedrest, isolation, and confinement on Earth.

simulated microgravity↗

Dynamic and single cell characterization of a CRISPR-interference toolset in Pseudomonas putida KT2440 for β-ketoadipate production from p -coumarate

We report Pseudomonas putida KT2440 is a well-studied bacterium for the conversion of lignin-derived aromatic compounds to bioproducts. The development of advanced genetic tools in P. putida has reduced the turnaround time for hypothesis testing and enabled the construction of strains capable of producing various products of interest. Here, we evaluate an inducible CRISPR-interference (CRISPRi) toolset on fluorescent, essential, and metabolic targets. Nuclease-deficient Cas9 (dCas9) expressed with the arabinose (8K)-inducible promoter was shown to be tightly regulated across various media conditions and when targeting essential genes. In addition to bulk growth data, single cell time lapse microscopy was conducted, which revealed intrinsic heterogeneity in knockdown rate within an isoclonal population. The dynamics of knockdown were studied across genomic targets in exponentially-growing cells, revealing a universal 1.75 ± 0.38 hour quiescent phase after induction where 1.5 ± 0.35 doublings occur before a phenotypic response is observed. To demonstrate application of this CRISPRi toolset, β-ketoadipate, a monomer for performance-advantaged nylon, was produced at a 4.39 ± 0.5 g/L and yield of 0.76 ± 0.10 mol/mol from p-coumarate, a hydroxycinnamic acid that can be derived from grasses. These cultivation metrics were achieved by using the higher strength IPTG (1K)-inducible promoter to knockdown the pcaIJ operon in the βKA pathway during early exponential phase. This allowed the majority of the carbon to be shunted into the desired product while eliminating the need for a supplemental carbon and energy source to support growth and maintenance.

59 BASIC BIOLOGICAL SCIENCES↗

Pole and prime meridian expressions for Phobos and Deimos

Simple trigonometric expressions are derived for the right ascensions and declinations of the spin axes of Phobos and Deimos as well as for their prime meridians. Simple expressions are possible since both satellites are in synchronous rotation about Mars and since the orbits of both satellites are accurately modeled as precessing ellipses. Spin axis expressions reflect the offset and precession of the orbit pole about the Laplacian pole. Prime meridian expressions include orbital mean motion, long-period solar perturbations, secular acceleration, and short-period, tidally induced forced libration. These simple expressions agree with rigorous expressions to + or - 0.2 deg.

Duxbury, T. C.↗