Protocol to prepare MUC1 glycopeptide vaccines and evaluate immunization effects in mice.

The tumor-associated mucin MUC1 is overexpressed in almost all types of epithelial tumor tissues, making it an attractive target antigen for cancer immunotherapy. Here we present a protocol to prepare MUC1 glycopeptide vaccines and to evaluate immunization effects in mice. We describe steps for synthesizing glycopeptide antigen and conjugating it with carrier protein to make vaccine candidates. We then detail procedures for mice immunization, antibody response evaluation, and cellular immune response. For complete details on the use and execution of this protocol, please refer to Cai et al.1,2.

Novel CDK19-Targeted Radiotracers: A Potential Design Strategy to Improve the Pharmacokinetics and Tumor Uptake.

Cyclin-dependent kinase 19 (CDK19) is overexpressed in prostate cancer, making it an attractive target for both imaging and therapy. Since little is known about the optimized approach for radioligands of nuclear proteins, linker optimization strategies were used to improve pharmacokinetics and tumor absorption, including the adjustment of the length, flexibility/rigidity, and hydrophilicity/lipophilicity of linkers. Molecular docking was conducted for virtual screening and followed by IC50 determination. Both BALB/c mice and P-16 xenografts were used for tissue distribution and PET/CT imaging. The ligand 68Ga-10c demonstrated high absorption in tumor 5 min after injection and sustains long-term imaging within 3 h. Furthermore, 68Ga-10c exhibited slow clearance within the tumor and was predominantly metabolized in both the liver and kidneys, showing the potential to alleviate metabolic pressure and enhance tissue safety. Therefore, the linker optimization strategy is well suited for CDK19 and provides a reference for the radioactive ligands of other nuclear targets.

Comments on "was hydrogen peroxide present before the arrival of oxygenic photosynthesis? The important role of iron(II) in the archean ocean".

Recent research has hypothesized that hydrogen peroxide (H2O2) may have emerged from abiotic geochemical processes during the Archean eon (4.0-2.5 Ga), stimulating the evolution of an enzymatic antioxidant system in early life. This eventually led to the evolution of cyanobacteria, and in turn, the accumulation of oxygen on Earth. In the latest issue of Redox Biology, Koppenol and Sies (vol. 29, no. 103012, 2024) argued against this hypothesis and suggested instead that early organisms would not have been exposed to H2O2 due to its short half-life in the ferruginous oceans of the Archean. We find these arguments to be factually incomplete because they do not consider that freshwater or some coastal marine environments during the Archean could indeed have led to H2O2 generation and accumulation. In these environments, abiotic oxidants could have interacted with early life, thus steering its evolutionary course.

Roseburia intestinalis sensitizes colorectal cancer to radiotherapy through the butyrate/OR51E1/RALB axis.

The radioresistant signature of colorectal cancer (CRC) hampers the clinical utility of radiotherapy. Here, we find that fecal microbiota transplantation (FMT) potentiates the tumoricidal effects of radiation and degrades the intertwined adverse events in azoxymethane (AOM)/dextran sodium sulfate (DSS)-induced CRC mice. FMT cumulates Roseburia intestinalis (R. intestinalis) in the gastrointestinal tract. Oral gavage of R. intestinalis assembles at the CRC site and synthetizes butyrate, sensitizing CRC to radiation and alleviating intestinal toxicity in primary and CRC hepatic metastasis mouse models. R. intestinalis-derived butyrate activates OR51E1, a G-protein-coupled receptor overexpressing in patients with rectal cancer, facilitating radiogenic autophagy in CRC cells. OR51E1 shows a positive correlation with RALB in clinical rectal cancer tissues and CRC mouse model. Blockage of OR51E1/RALB signaling restrains butyrate-elicited autophagy in irradiated CRC cells. Our findings highlight that the gut commensal bacteria R. intestinalis motivates radiation-induced autophagy to accelerate CRC cell death through the butyrate/OR51E1/RALB axis and provide a promising radiosensitizer for CRC in a pre-clinical setting.

Metagenomic insight into the pathogenic-related characteristics and resistome profiles within microbiome residing on the Angkor sandstone monuments in Cambodia.

To reveal the characteristics of indigenous microbiome including the pathogenic-related ones on Angkor monuments in Cambodia and the distribution pattern of resistome at different locations, several sites, namely Angkor Wat, Bayon of Angkor Thom, and Prasat Preah Vihear with different exposure levels to tourists were selected to conduct the metagenomic analysis in this study. The general characteristics of the microbiome on these monuments were revealed, and the association between the environmental geo-ecological feature and the indigenous microbiome was delineated. The most common microbial groups included 6 phyla, namely Acidobacteria, Actinobacteria, Gemmatimonadetes, Nitrospirae, Proteobacteria and Verrucomicrobia on the monuments, but Firmicutes and Chlamydiae were the most dominant phyla found in bats droppings. The taxonomic family of Chitinophagaceae could serve as a signature microbial group for Preah Vihear, the less visited site. More importantly, the pathogenic-related characteristics of the microbiome residing on Angkor monuments were uncovered. A set of specific antibiotic resistance genes (ARGs) with cross-niches dispersal capacity (between the environmental microbiome and the microbiome within warm blood fauna) was identified to be high by the source tracking analysis based on ARGs profile varies in this study. Among the 10 ARG-types detected in this study, 6 of them are confined to resistance mechanism of antibiotic efflux-pump. The findings of this study provide new a new direction on public health management and implication globally at archaeological sites for tourism.

Bazedoxifene analogs as potential WDHD1 degraders and antitumor agents: Synthesis, evaluation and molecular dynamics simulation studies.

DNA repair is strongly associated with tumor resistance to radiotherapy and chemotherapy. WD repeat and HMG-box DNA binding protein 1 (WDHD1) is a key adaptor for homologous recombination repair of DNA, and its overexpression is relevant to the poor prognosis of many tumor patients. We previously have identified and validated bazedoxifene (BZA), which had 60% inhibitory rate on WDHD1 in MCF7 cells at 10 µM, from the Food and Drug Administration-approved compound library. Here, we initially established the binding model of BZA, synthesized and evaluated eight BZA analogs. Further, we detailed the use of molecular dynamics simulations to provide insights into the basis for activity against WDHD1. This binding mode will be instructive for the development of new WDHD1 degraders.

Stachydrine represses the proliferation and enhances cell cycle arrest and apoptosis of breast cancer cells via PLA2G2A/DCN axis.

Considering the therapeutic efficacy of Stachydrine on breast cancer (BC), this study aims to decipher the relevant mechanism. The effects of Stachydrine on BC cell viability, proliferation and apoptosis were firstly investigated. Then, Bioinformatics was applied to sort out the candidate interacting with Stachydrine as well as its expression and downstream target in BC. Relative expressions of genes of interest as well as proliferation- and apoptosis-related factors in BC cells were quantified through quantitative reverse-transcription PCR and western blot as appropriate. As a result, Stachydrine inhibited the proliferation, down-regulated the expressions of proliferating cell nuclear antigen and CyclinD1, enhanced cell cycle arrest and apoptosis, and up-regulated the levels of Cleaved caspase-3 and Cleaved caspase-9 in BC cells. Phospholipase A2 Group IIA (PLA2G2A) was predicted as the candidate interacting with Stachydrine and to be lowly expressed in BC. PLA2G2A silencing reversed while PLA2G2A overexpression reinforced the effects of Stachydrine. Decorin (DCN) was the downstream target of PLA2G2A and also lowly expressed in BC. PLA2G2A silencing counteracted yet overexpressed PLA2G2A strengthened the promoting effects of Stachydrine on DCN level. Collectively, Stachydrine inhibits the growth of BC cells to promote cell cycle arrest and apoptosis via PLA2G2A/DCN axis.

Freeze-thaw cycles drove chemical weathering and enriched sulfates in the Burns formation at Meridiani, Mars.

Sulfate-rich sedimentary rocks explored by the Opportunity rover during its 14-year surface mission at Meridiani Planum provide an invaluable window into the thousands of sulfate deposits detected on Mars via remote sensing. Existing models explaining the formation of martian sulfates can be generally described as either bottom-up, groundwater-driven playa settings or top-down icy chemical weathering environments. Here, we propose a hybrid model involving both bottom-up and top-down processes driven by freeze-thaw cycles. Freezing leads to cryo-concentration of acidic fluids from precipitations at the surface, facilitating rapid chemical weathering despite low temperatures. Cryosuction causes the upward migration of vadose water and even groundwater with dissolved ions, resulting in the accumulation of ions in near-surface environments. Evaporation precipitates salts, but leaching separates chlorides from sulfates during the thawing period. Freeze-thaw cycles, therefore, can enrich sulfates at the surface. While freeze-thaw is more commonly understood as a mechanism of physical weathering, we suggest that it is a fundamental aspect of chemical weathering on Mars.

PRMD: an integrated database for plant RNA modifications.

The scope and function of RNA modifications in model plant systems have been extensively studied, resulting in the identification of an increasing number of novel RNA modifications in recent years. Researchers have gradually revealed that RNA modifications, especially N6-methyladenosine (m6A), which is one of the most abundant and commonly studied RNA modifications in plants, have important roles in physiological and pathological processes. These modifications alter the structure of RNA, which affects its molecular complementarity and binding to specific proteins, thereby resulting in various of physiological effects. The increasing interest in plant RNA modifications has necessitated research into RNA modifications and associated datasets. However, there is a lack of a convenient and integrated database with comprehensive annotations and intuitive visualization of plant RNA modifications. Here, we developed the Plant RNA Modification Database (PRMD; http://bioinformatics.sc.cn/PRMD and http://rnainformatics.org.cn/PRMD) to facilitate RNA modification research. This database contains information regarding 20 plant species and provides an intuitive interface for displaying information. Moreover, PRMD offers multiple tools, including RMlevelDiff, RMplantVar, RNAmodNet and Blast (for functional analyses), and mRNAbrowse, RNAlollipop, JBrowse and Integrative Genomics Viewer (for displaying data). Furthermore, PRMD is freely available, making it useful for the rapid development and promotion of research on plant RNA modifications.

SREBP inhibitors: an updated patent review for 2008-present.

INTRODUCTION: Sterol regulatory element-binding proteins (SREBPs) are a family of membrane-binding transcription factors that activate genes encoding enzymes required for cholesterol and unsaturated fatty acid synthesis. Overactivation of SREBP is related to the occurrence and development of diabetes, nonalcoholic fatty liver, tumor, and other diseases. In the past period, many SREBP inhibitors have been found. AREAS COVERED: This manuscript is a patent review of SREBP inhibitors. We searched 2008 to date for all data from the US patent database (https://www.uspto.gov/) and the European patent database (https://www.epo.org/) with 'SREBP' and 'inhibitor' as keywords and analyzed the search results. EXPERT OPINION: Both synthetic and natural SREBP inhibitors have been reported. Despite the lack of cocrystal structure of SREBP inhibitor, the mechanisms of several compounds have been clarified. Importantly, some SREBP inhibitors have been proved to have good activity in preclinical studies. As the characteristics of lipid metabolism reprogramming in cardio-cerebrovascular diseases and tumors are gradually revealed, more and more attention will be focused on SREBP.

Text Analysis via Learning Model in Teaching Ability Evaluation System for College Physical Education Teachers / Análisis de texto mediante modelo de aprendizaje en el sistema de evaluación de habilidades docentes para profesores universitarios de educación física

With the overall increase in the state's attention to quality of higher education teaching, overall teaching level for college physical education teachers has been greatly improved. However, it is influenced by traditional academic and teaching concepts, as well as school administrators do not pay attention to physical education teaching. The development for the teaching ability of college physical education teachers is still not optimistic. Therefore, paying attention to the teaching ability of physical education teachers has gradually become a practical problem that society and schools cannot ignore and must pay attention to. Among them, the evaluation for teaching ability of physical education teachers is the most important. With the reform of the Internet, there is much textual information on teaching of physical education teachers in colleges. By analyzing these texts, an evaluation of teachers' teaching ability can be obtained. This work combines this topic with a deep learning model, and proposes a text analysis model (PEAENet) for teaching ability evaluation of physical education teachers. The model first proposes an interactive multi-head attention to enhance interaction between aspect words as well as context. The attention of two aspects is calculated at the same time, including the attention of the context to the aspect word as well as aspect word attention to context. Second, this work combines Transformer's encoder structure with LSTM to obtain a more capable feature extraction module. In the label mapping stage, the label smoothing coefficient is introduced, which makes the model have stronger generalization ability.(AU)

Laparoscopic hiatal hernia repair for treating patients with massive hiatal hernia and iron-deficiency anaemia.

BACKGROUND: Massive hiatal hernias may result in extraoesophageal symptoms, including iron-deficiency anaemia. However, the role played by hiatal hernias in iron-deficiency anaemia is not clearly understood. We examined the prevalence of anaemia in patients with massive hiatal hernias and the frequency of anaemia resolution after laparoscopic hiatal hernia repair at long term follow-up. METHODS: Patients who underwent laparoscopic hiatal hernia repair from June 2008 to June 2019 were enrolled in this study. We collected the patients' demographic and clinical data from their medical records, and compared the pre-surgical and post-surgical findings (at 1 week and 3 months post-surgery). All patients with adequate documentation underwent post-surgical follow-up to evaluate improvements in clinical symptoms and signs. RESULTS: A total of 126 patients with massive hiatal hernias underwent laparoscopic hiatal hernia repair. Of these, 35 (27.8%) had iron-deficiency anaemia. Anaemia was resolution in all the patients and they had significantly reduced GERD-Q scores at 3 months postoperatively (P<0.01) .The mean follow-up period was 60 months. Iron-deficiency anaemia resolution after hiatal hernia repair was achieved in 93.9% of the patients. CONCLUSION: Anaemia is common in patients with massive hiatal hernias, and most of our patients were symptomatic because of their anaemia. Moreover, in patients with massive hiatal hernias, iron-deficiency anaemia resolution is likely after laparoscopic hiatal hernia repair.

[Research progress in prevention and treatment of radiation-induced intestinal injury by traditional Chinese medicine active components].

Radiation-induced intestinal injury(RIII), a common complication of radiotherapy for pelvic malignancies, affects the quality of life and the radiotherapy efficacy for cancer. Currently, the main clinical approaches for the prevention and treatment of RIII include drug therapy, hyperbaric oxygen therapy, and surgical treatment. Among these methods, drug therapy is cost-effective. Traditional Chinese medicine(TCM) containing a variety of active components demonstrates mild side effects and good efficacy in preventing and treating RIII. Studies have proven that TCM active components, such as flavonoids, terpenoids, phenylpropanoids, and alkaloids, can protect the intestine against RIII by inhibiting oxidative stress, regulating the expression of inflammatory cytokines, modulating the mitochondrial apoptosis pathway, adjusting intestinal flora, and suppressing cell apoptosis. These mechanisms can help alleviate the symptoms of RIII. The paper aims to provide a theoretical reference for the discovery of new drugs for the prevention and treatment of RIII by reviewing the literature on TCM active components in the last 10 years.

PET imaging of new target CDK19 in prostate cancer.

PURPOSE: Prostate-specific membrane antigen (PSMA)-positron emission tomography (PET) is a superior method to predict patients' risk of cancer progression and response to specific therapies. However, its performance is limited for neuroendocrine prostate cancer (NEPC) and PSMA-low prostate cancer cells, resulting in diagnostic blind spots. Hence, identifying novel specific targets is our aim for diagnosing those prostate cancers with low PSMA expression. METHODS: The Cancer Genome Atlas (TCGA) database and our cohorts from men with biopsy-proven high-risk metastatic prostate cancer were used to identify CDK19 and PSMA expression. PDX lines neP-09 and P-16 primary cells were used for cellular uptake and imaging mass cytometry in vitro. To evaluate in vivo CDK19-specific uptake of gallium(Ga)-68-IRM-015-DOTA, xenograft mice models and blocking assays were used. PET/CT imaging data were obtained to estimate the absorbed dose in organs. RESULTS: Our study group had reported the overexpression of a novel tissue-specific gene CDK19 in high-risk metastatic prostate cancer and CDK19 expression correlated with metastatic status and tumor staging, independently with PSMA and PSA levels. Following up on this new candidate for use in diagnostics, small molecules targeting CDK19 labeled with Ga-68 (68Ga-IRM-015-DOTA) were used for PET in this study. We found that the 68Ga-IRM-015-DOTA was specificity for prostate cancer cells, but the other cancer cells also took up little 68Ga-IRM-015-DOTA. Importantly, mouse imaging data showed that the NEPC and CRPC xenografts exhibited similar signal strength with 68Ga-IRM-015-DOTA, but 68Ga-PSMA-11 only stained the CRPC xenografts. Furthermore, target specificity was elucidated by a blocking experiment on a CDK19-bearing tumor xenograft. These data concluded that 68Ga-CDK19 PET/CT was an effective technology to detect lesions with or without PSMA in vitro, in vivo, and in the PDX model. CONCLUSION: Thus, we have generated a novel PET small molecule with predictive value for prostate cancer. The findings indicate that 68Ga-CDK19 may merit further evaluation as a predictive biomarker for PET scans in prospective cohorts and may facilitate the identification of molecular types of prostate cancer independent of PSMA.

KYNU-related transcriptome profile and clinical outcome from 2994 breast tumors.

The Catabolism of tryptophan modulates the immunosuppressive microenvironment in tumors. KYNU (Kynureninase) served as an enzyme involved in amino acid tryptophan catabolism through the kynurenine pathway. The molecular and clinical characteristics of KYNU remain unclear, and the impact of KYNU on the immune response has not been reported until now. We analyzed large-scale transcriptome data and related clinical information on 2994 breast cancer patients to characterize KYNU's role in breast cancer. There was a strong correlation between KYNU expression and major molecular and clinical characteristics, and it was more likely to be overexpressed in patients with higher malignancy subtypes. Inflammatory and immune responses were strongly correlated with KYNU. KYNU was also associated with immune modulators at the pan-cancer level, particularly its potential synergistic role with other immune checkpoints in breast cancer. KYNU expression was linked to the malignancy grade of breast cancer and predicted poorer outcomes. Tryptophan catabolism might play an important role in modulating the tumor immune microenvironment through KYNU. More significantly, KYNU might synergize with CTLA4, PDL2, IDO1, and other immune checkpoints, contributing to the development of combination cancer immunotherapy targeting KYNU and other checkpoints. As far as we are aware, this is the biggest and most thorough study describing KYNU's role in breast cancer.

An investigation of PM2.5 concentration changes in Mid-Eastern China before and after COVID-19 outbreak.

With the Chinese government revising ambient air quality standards and strengthening the monitoring and management of pollutants such as PM2.5, the concentrations of air pollutants in China have gradually decreased in recent years. Meanwhile, the strong control measures taken by the Chinese government in the face of COVID-19 in 2020 have an extremely profound impact on the reduction of pollutants in China. Therefore, investigations of pollutant concentration changes in China before and after COVID-19 outbreak are very necessary and concerning, but the number of monitoring stations is very limited, making it difficult to conduct a high spatial density investigation. In this study, we construct a modern deep learning model based on multi-source data, which includes remotely sensed AOD data products, other reanalysis element data, and ground monitoring station data. Combining satellite remote sensing techniques, we finally realize a high spital density PM2.5 concentration change investigation method, and analyze the seasonal and annual, the spatial and temporal characteristics of PM2.5 concentrations in Mid-Eastern China from 2016 to 2021 and the impact of epidemic closure and control measures on regional and provincial PM2.5 concentrations. We find that PM2.5 concentrations in Mid-Eastern China during these years is mainly characterized by "north-south superiority and central inferiority", seasonal differences are evident, with the highest in winter, the second highest in autumn and the lowest in summer, and a gradual decrease in overall concentration during the year. According to our experimental results, the annual average PM2.5 concentration decreases by 3.07 % in 2020, and decreases by 24.53 % during the shutdown period, which is probably caused by China's epidemic control measures. At the same time, some provinces with a large share of secondary industry see PM2.5 concentrations drop by more than 30 %. By 2021, PM2.5 concentrations rebound slightly, rising by 10 % in most provinces.

Protective effect of total flavonoids of Engelhardia roxburghiana Wall. leaves against radiation-induced intestinal injury in mice and its mechanism.

ETHNOPHARMACOLOGICAL RELEVANCE: Irradiation-induced intestinal injury (RIII) often occurs during radiotherapy in patients, which would result in abdominal pain, diarrhea, nausea, vomiting, and even death. Engelhardia roxburghiana Wall. leaves, a traditional Chinese herb, has unique anti-inflammatory, anti-tumor, antioxidant, and analgesic effects, is used to treat damp-heat diarrhea, hernia, and abdominal pain, and has the potential to protect against RIII. AIM OF THE STUDY: To explore the protective effects of the total flavonoids of Engelhardia roxburghiana Wall. leaves (TFERL) on RIII and provide some reference for the application of Engelhardia roxburghiana Wall. leaves in the field of radiation protection. MATERIALS AND METHODS: The effect of TFERL on the survival rate of mice was observed after a lethal radiation dose (7.2 Gy) by ionizing radiation (IR). To better observe the protective effects of the TFERL on RIII, a mice model of RIII induced by IR (13 Gy) was established. Small intestinal crypts, villi, intestinal stem cells (ISC) and the proliferation of ISC were observed by haematoxylin and eosin (H&E) and immunohistochemistry (IHC). Quantitative real-time PCR (qRT-PCR) was used to detect the expression of genes related to intestinal integrity. Superoxide dismutase (SOD), reduced glutathione (GSH), interleukin-6 (IL-6) and tumor necrosis factor-α (TNF-α) in the serum of mice were assessed. In vitro, cell models of RIII induced by IR (2, 4, 6, 8 Gy) were established. Normal human intestinal epithelial cells HIEC-6 cells were treated with TFERL/Vehicle, and the radiation protective effect of TFERL on HIEC-6 cells was detected by clone formation assay. DNA damage was detected by comet assay and immunofluorescence assay. Reactive oxygen species (ROS), cell cycle and apoptosis rate were detected by flow cytometry. Oxidative stress, apoptosis and ferroptosis-related proteins were detected by western blot. Finally, the colony formation assay was used to detect the effect of TFERL on the radiosensitivity of colorectal cancer cells. RESULTS: TFERL treatment can increase the survival rate and time of the mice after a lethal radiation dose. In the mice model of RIII induced by IR, TFERL alleviated RIII by reducing intestinal crypt/villi structural damage, increasing the number and proliferation of ISC, and maintaining the integrity of the intestinal epithelium after total abdominal irradiation. Moreover, TFERL promoted the proliferation of irradiated HIEC-6 cells, and reduced radiation-induced apoptosis and DNA damage. Mechanism studies have found that TFERL promotes the expression of NRF2 and its downstream antioxidant proteins, and silencing NRF2 resulted in the loss of radioprotection by TFERL, suggesting that TFERL exerts radiation protection by activating the NRF2 pathway. Surprisingly, TFERL reduced the number of clones of colon cancer cells after irradiation, suggesting that TFERL can increase the radiosensitivity of colon cancer cells. CONCLUSION: Our data showed that TFERL inhibited oxidative stress, reduced DNA damage, reduced apoptosis and ferroptosis, and improved IR-induced RIII. This study may offer a fresh approach to using Chinese herbs for radioprotection.

A mineral-based origin of Earth's initial hydrogen peroxide and molecular oxygen.

Terrestrial reactive oxygen species (ROS) may have played a central role in the formation of oxic environments and evolution of early life. The abiotic origin of ROS on the Archean Earth has been heavily studied, and ROS are conventionally thought to have originated from H2O/CO2 dissociation. Here, we report experiments that lead to a mineral-based source of oxygen, rather than water alone. The mechanism involves ROS generation at abraded mineral-water interfaces in various geodynamic processes (e.g., water currents and earthquakes) which are active where free electrons are created via open-shell electrons and point defects, high pressure, water/ice interactions, and combinations of these processes. The experiments reported here show that quartz or silicate minerals may produce reactive oxygen-containing sites (≡SiO•, ≡SiOO•) that initially emerge in cleaving Si-O bonds in silicates and generate ROS during contact with water. Experimental isotope-labeling experiments show that the hydroxylation of the peroxy radical (≡SiOO•) is the predominant pathway for H2O2 generation. This heterogeneous ROS production chemistry allows the transfer of oxygen atoms between water and rocks and alters their isotopic compositions. This process may be pervasive in the natural environment, and mineral-based production of H2O2 and accompanying O2 could occur on Earth and potentially on other terrestrial planets, providing initial oxidants and free oxygen, and be a component in the evolution of life and planetary habitability.

Corrigendum: Exploring the pharmacological mechanisms of icaritin against nasopharyngeal carcinoma via network pharmacology and experimental validation.

[This corrects the article DOI: 10.3389/fphar.2022.993022.].

Reachability of dimension-bounded linear systems.

In this paper, the reachability of dimension-bounded linear systems is investigated. Since state dimensions of dimension-bounded linear systems vary with time, the expression of state dimension at each time is provided. A method for judging the reachability of a given vector space $ \mathcal{V}_{r} $ is proposed. In addition, this paper proves that the $ t $-step reachable subset is a linear space, and gives a computing method. The $ t $-step reachability of a given state is verified via a rank condition. Furthermore, annihilator polynomials are discussed and employed to illustrate the relationship between the invariant space and the reachable subset after the invariant time point $ t^{\ast} $. The inclusion relation between reachable subsets at times $ t^{\ast}+i $ and $ t^{\ast}+j $ is shown via an example.