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The leaves of many trees emit volatile organic compounds (abbreviated as BVOCs), which protect them from various damages, such as herbivory, pathogens, and heat stress. For example, isoprene is highly volatile and is known to enhance the resistance to heat stress. In this study, we analyze the optimal seasonal schedule for producing isoprene in leaves to mitigate damage. We assume that photosynthetic rate, heat stress, and the stress-suppressing effect of isoprene may vary throughout the season. We seek the seasonal schedule of isoprene production that maximizes the total net photosynthesis using Pontryagin's maximum principle. The isoprene production rate is determined by the changing balance between the cost and benefit of enhanced leaf protection over time. If heat stress peaks in midsummer, isoprene production can reach its highest levels during the summer. However, if a large portion of leaves is lost due to heat stress in a short period, the optimal schedule involves peaking isoprene production after the peak of heat stress. Both high photosynthetic rate and high isoprene volatility in midsummer make the peak of isoprene production in spring. These results can be clearly understood by distinguishing immediate impacts and the impacts of future expectations.
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Butadienos , Hemiterpenos , Fotosíntesis , Hojas de la Planta , Estaciones del Año , Compuestos Orgánicos Volátiles , Butadienos/metabolismo , Butadienos/análisis , Hemiterpenos/metabolismo , Compuestos Orgánicos Volátiles/análisis , Compuestos Orgánicos Volátiles/metabolismo , Hojas de la Planta/metabolismo , Árboles/metabolismo , Respuesta al Choque Térmico , Pentanos/metabolismo , Pentanos/análisisRESUMEN
Understanding host behavioral change in response to epidemics is important to forecast the disease dynamics. To predict the behavioral change relevant to the epidemic situation (e.g., the number of reported cases), we need to know the epidemic situation at the moment of decision, which is difficult to identify from the records of actually performed human mobility. In this study, the largest travel accommodation reservation data covering half of the existed accommodations in Japan was analyzed to observe decision-making timings and how it responded to the changing epidemic situation during Japan's Coronavirus Disease 2019 until February 2023. To this end, we measured mobility avoidance index proposed in Ito et al., 2022 to indicate people's decision of mobility avoidance and quantified it using the time-series of the accommodation booking/cancellation data. We observed matches of the peak dates of the mobility avoidance and the number of reported cases, and mobility avoidance changed proportional to the logarithmic number of reported cases. We also found that the slope of mobility avoidance against the change of the logarithmic number of reported cases were similar among the epidemic waves, while the intercept of that was much reduced as the first epidemic wave passed by. People measure the intensity of epidemic by logarithm of the number of reported cases. The sensitivity of their response is established during the first wave and the people's response became weakened after the first experience, as if the number of reported cases were multiplied by a constant small factor.
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COVID-19 , Epidemias , Humanos , COVID-19/epidemiología , SARS-CoV-2 , Japón/epidemiología , PredicciónRESUMEN
Background/Aim: Inflammation and nutrition-based biomarkers, such as the neutrophil/lymphocyte ratio (NLR), platelet/lymphocyte ratio (PLR), lymphocyte/monocyte ratio (LMR), C-reactive protein/albumin ratio (CAR), prognostic nutritional index (PNI), systemic immune inflammation index (SII), and systemic inflammation response index (SIRI), have prognostic value for several types of malignancies. Markers that precisely reflect the prognosis of patients with head and neck cancers (HNCs) treated with immune-checkpoint inhibitors remain unclear. This retrospective study aimed to investigate the prognostic value of hematological markers before and after treatment with nivolumab in patients with recurrent or metastatic HNC (RM-HNC). Patients and Methods: We evaluated the clinical data of 44 patients with recurrent/metastatic head and neck squamous cell carcinoma treated with nivolumab between April 2017 and April 2023 at Shinshu University Hospital. Values of hematological biomarkers (NLR, LMR, PLR, CAR, PNI, SII, and SIRI) were calculated before and 4-6 weeks after nivolumab initiation. Receiver operating characteristic curves were constructed to determine the cutoff values of pre- and post-treatment markers for overall survival (OS) and progression-free survival (PFS). Results: Among all pre- and post-treatment markers, post-treatment NLR showed the highest area under the curve (AUC=0.702). A high post-treatment NLR (cutoff value, 4.01) was associated with a poor OS (p=0.027) and a tendency for shorter PFS (p=0.117). Multivariate analysis showed that a high post-treatment NLR was significantly associated with poor OS (p=0.026). Conclusion: A high post-treatment NLR was associated with poor response to nivolumab in head and neck cancers.
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Some viruses exhibit "rebound" when the administration of antiviral drugs is discontinued. Viral rebound caused by resistance mutations or latent reservoirs has been studied mathematically. In this study, we investigated the viral rebound due to other causes. Since immunity is weaker during antiviral treatment than without the treatment, drug discontinuation may lead to an increase in the viral load. We analyzed the dynamics of the number of virus-infected cells, cytotoxic T lymphocytes, and memory cells and identified the conditions under which the viral load increased upon drug discontinuation. If drug is administered for an extended period, a viral rebound occurs when the ratio of viral growth rate in the absence to that in the presence of the antiviral drug exceeds the "rebound threshold." We analyzed how the rebound threshold depended on the patient's conditions and the type of treatment. Mathematical and numerical analyses revealed that rebound after discontinuation was more likely to occur when the drug effectively reduced viral proliferation, drug discontinuation was delayed, and the processes activating immune responses directly were stronger than those occurring indirectly through immune memory formation. We discussed additional reasons for drugs to cause viral rebound more likely.
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Infecciones por VIH , Humanos , Preparaciones Farmacéuticas , Linfocitos T CD4-Positivos , Resistencia a Medicamentos , Carga ViralRESUMEN
Although anti-programmed death-1 (PD-1) antibody therapy improves the prognosis in patients with head and neck squamous cell carcinoma (HNSCC), some patients exhibit disease progression even after showing a good response to the treatment initially because of acquired resistance. Here, we aimed to reveal the dynamic changes in the tumor and tumor microenvironment (TME) in a 77-year-old man diagnosed with oral squamous cell carcinoma who developed acquired resistance after the administration of nivolumab using spatial transcriptomics. The results showed that, before immunotherapy, the activated pathways in the tumor area were mainly related to the cancer immune system, including antigen processing cross-presentation, interferon-gamma signaling, and the innate immune system. After immunotherapy, the activated pathways were mainly related to epigenetic modification, including RMTs methylate histone arginine and HDAC deacetylates histones. Before immunotherapy, the activated pathways in the TME were mainly related to the metabolism of proteins, including SRP-dependent co-translational protein targeting the membrane. After immunotherapy, the activated pathways in the TME were related to sensory perception and signal transduction. Our study revealed that epigenetic-modification-related pathways were mainly activated after establishing acquired resistance, suggesting that epigenetic modification in the tumor may prevent cancer immune system activation via the anti-PD-1 antibody.
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Carcinoma de Células Escamosas , Neoplasias de Cabeza y Cuello , Neoplasias de la Boca , Masculino , Humanos , Anciano , Carcinoma de Células Escamosas/tratamiento farmacológico , Carcinoma de Células Escamosas/genética , Neoplasias de la Boca/tratamiento farmacológico , Neoplasias de la Boca/genética , Microambiente Tumoral , Transcriptoma , Inmunoterapia/métodos , Carcinoma de Células Escamosas de Cabeza y CuelloRESUMEN
We study the effects of the immune system on multiple cancer colonies. When cancer cells proliferate, cytotoxic T lymphocytes (CTLs) reactive to the cancer-specific antigens are activated, suppressing the growth of cancer colonies. The immune reaction activated by a large cancer colony may suppress and eliminate smaller colonies. However, cancer cells mitigate immune reactions by slowing down the activation of CTLs in dendritic cells with regulatory T cells and by inactivating CTLs attacking cancer cells with immune checkpoints. If cancer cells strongly suppress the immune reaction, the system may become bistable, where both the cancer-dominated and immunity-dominated states are locally stable. We study several models differing in the distance between colonies and the migration speeds of CTLs and regulatory T cells. We examine how the domains of attraction for multiple equilibria change with parameters. Nonlinear cancer-immunity dynamics may produce a sharp transition from a state with a small number of colonies and strong immunity to one with many colonies and weak immunity, resulting in the rapid emergence of many cancer colonies in the same organ or metastatic sites.
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A high mutation rate of the RNA virus results in the emergence of novel mutants that may escape the immunity activated by the original (wild-type) strain. However, many of them go extinct because of the stochasticity due to the small initial number of infected cells. In a previous paper, we studied the probability of escaping stochastic extinction when the novel mutant has a faster rate of infection and when it is resistant to a drug that suppresses the wild-type virus. In this study, we examine the effect of escaping the immune reaction of the host. Based on a continuous-time branching process with time-dependent rates, we conclude the chance for a mutant strain to be established [Formula: see text] decreases with time [Formula: see text] since the wild-type infection when the mutant is produced. The number of novel mutants that can escape extinction risk has a peak soon after the wild-type infection. The number of novel escape mutations produced per patient in the early phase of host infection is small both for very strong and very weak immune responses, and it attains its maximum value when immune activity is of an intermediate strength.
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Modelos Biológicos , Virus , Humanos , Conceptos Matemáticos , Virus/genética , Probabilidad , Tasa de Mutación , MutaciónRESUMEN
We review several mathematical models and concepts in developmental biology that have been established over the last decade. (1) Feedback vertex set: Ascidian embryos contain cells of seven types, and cell fate is controlled by ~100 interacting genes. The "feedback vertex set" of the directed graph of the gene regulatory network consists of a small number of genes. By experimentally manipulating them, we can differentiate cells into any cell type. (2) Tissue deformation: Describing morphological changes in tissues and relating them to gene expression and other cellular processes is key in understanding morphogenesis. Expansion and anisotropy of the tissue are described by a "deformation tensor" at each location. A study on chick limb bud formation revealed that both the volume growth rate and anisotropy in deformation differed significantly between locations and stages. (3) Mechanobiology: Forces operating on each cell may alter cell shape and gene expression, which may subsequently exert forces on their surroundings. Measurements of force, tissue shape, and gene expression help us understand autonomous tissue deformation. (4) Adaptive design of development: An optimal growth schedule in fluctuating environments explains the growth response to starvation in Drosophila larvae. Adaptive placement of morphogen sources makes development robust to noises.
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Drosophila , Organogénesis , Animales , Morfogénesis/fisiología , Diferenciación Celular , Organogénesis/fisiología , Modelos BiológicosRESUMEN
This study aimed to investigate the prognostic value of hematological biomarkers measured before and after treatment in patients with head and neck cancer (HNC). This study reviewed 124 patients with HNC who received chemoradiotherapy. Hematological biomarkers assessed before and after treatment were investigated. The pretreatment C-reactive protein/albumin ratio (pre-CAR) and post-treatment prognostic nutritional index (post-PNI) showed the highest area under the curve with cutoff values of 0.0945 and 34.9, respectively. Patients in the high pre-CAR group showed significantly worse prognosis than those in the low pre-CAR group with respect to the progression-free survival (PFS) (3-year PFS: 44.8% vs. 76.8%, p < 0.001) and overall survival (OS) (3-year OS: 65.8% vs. 94.0%, p < 0.001). Patients in the low post-PNI group showed significantly worse prognosis than those in the high post-PNI group with respect to the PFS (3-year PFS: 58.6% vs. 77.4%, p = 0.013) and OS (3-year OS: 75.2% vs. 96.9%, p = 0.019). Multivariate analysis revealed that advanced N stage (p = 0.008), high pre-CAR (p = 0.024), and low post-PNI (p = 0.034) were significantly associated with poorer OS. We suggest that the evaluation of hematological markers before and after treatment is useful for predicting disease progression and survival.
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Neoplasias de Cabeza y Cuello , Evaluación Nutricional , Humanos , Pronóstico , Biomarcadores , Quimioradioterapia , Neoplasias de Cabeza y Cuello/terapia , Estudios RetrospectivosRESUMEN
Genomic sequencing revealed that somatic mutations cause a genetic differentiation of the cells in a single tree. We studied a mathematical model for stem cell proliferation in the shoot apical meristem (SAM). We evaluated the phylogenetic distance between cells sampled from different portions of a shoot, indicating their genetic difference due to mutations accumulated during shoot elongation. The plant tissue has cell walls that suppress the exchange of location between cells. This leads to the genetic differentiation of cells according to the angle around the shoot and a larger genetic variance among cells in the body. The assumptions are as follows: stem cells in the SAM normally undergo asymmetric cell division, producing successor stem cells and differentiated cells. Occasionally, a stem cell fails to leave its successor stem cell and the vacancy is filled by the duplication of one of the nearest neighbor stem cells. A mathematical analysis revealed the following: the genetic diversity of cells sampled at the same position along the shoot increases with the distance from the base of the shoot. Stem cells hold a larger variation if they are replaced only by the nearest neighbors. The coalescent length between two cells increases not only with the difference in the position along the shoot but also in the angle around the shoot axis. The dynamics of stem cells at the SAM determine the genetic pattern of the entire shoot.
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Proteínas de Arabidopsis , Meristema , Meristema/genética , Meristema/metabolismo , Brotes de la Planta/genética , Brotes de la Planta/metabolismo , Filogenia , Células Madre/metabolismo , Estructuras Genéticas , Regulación de la Expresión Génica de las Plantas , Proteínas de Arabidopsis/genéticaRESUMEN
Marine animals show diverse and flexible sexual systems. Here, we review several advancements of theoretical studies made in the last decade. (i) Sex change in coral fishes is often accompanied by a long break in reproductive activity. The delay can be shortened by retaining the inactive gonad for the opposite sex. (ii) Barnacles adopt diverse sexual patterns. The game model was analysed assuming that newly settled larvae choose either growth or immediate reproduction and large individuals adjust male-female investments. (iii) Some parasitic barnacles produce larvae with sexual size dimorphism and others produce larvae with the sex determined after settlement on hosts. (iv) In some fish and many reptiles, sex is determined by the temperature experienced as eggs. The dynamics of sex hormones were studied when the enzymatic reaction rates were followed by the Arrhenius equation. The FMF pattern (male at intermediates temperature; female both at high and low temperatures) required some reactions with enhanced temperature dependence at higher temperatures. The game model provides a useful framework for understanding diverse sexual patterns if we incorporate various constraints, such as unpredictability, cost of trait change and social situations. For further developments, we need to consider constraints imposed by physiological and molecular mechanisms.
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Modelos Teóricos , Thoracica , Animales , Femenino , Masculino , Reproducción/fisiología , Peces/fisiología , Caracteres Sexuales , Larva , Thoracica/fisiologíaRESUMEN
Treatment of synchronous multiple primary cancers is clinically difficult. We report four cases of synchronous primary cancers, including advanced and metastatic non-small cell lung cancer (NSCLCs) highly positive for programmed death ligand-1 (PD-L1) expression and initially treated with pembrolizumab. Pembrolizumab was efficacious in 2 patients with NSCLC lesions, followed by chemoradiotherapy for esophageal cancer (case 1) and chemotherapy for gastric cancer (case 2). Both cancers in case 1 showed a complete response for 3 years, while progression of the accompanying gastric cancer resulted in mortality at 20 months in case 2. Both NSCLC and gastric cancer in case 3 failed to respond to pembrolizumab, but the accompanying laryngeal cancer in case 4 showed a complete response, and cytotoxic chemotherapy for NSCLC was continued for 18.0 months. Our clinical experience suggests that pembrolizumab is a useful therapeutic approach for patients with synchronous cancers, including NSCLC that highly expresses PD-L1.
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Carcinoma de Pulmón de Células no Pequeñas , Neoplasias Pulmonares , Neoplasias Gástricas , Humanos , Carcinoma de Pulmón de Células no Pequeñas/tratamiento farmacológico , Carcinoma de Pulmón de Células no Pequeñas/patología , Antígeno B7-H1/metabolismo , Neoplasias Pulmonares/tratamiento farmacológico , Neoplasias Pulmonares/patologíaRESUMEN
INTRODUCTION: Sarcopenia, characterized by low skeletal muscle mass, and the outcome of cancer therapy are closely related based on recent research. This study aimed to evaluate the correlation between skeletal muscle mass and prognosis in head and neck cancer (HNC) patients. METHODS: In this study, 51 male patients with HNC treated nonsurgically between January 2016 and April 2018 at Shinshu University Hospital were evaluated. Skeletal muscle mass was assessed using bioelectrical impedance analysis, and the skeletal mass index (SMI) was calculated to classify the patients. RESULTS: The low-SMI group had a significantly worse overall survival (OS) than the normal-SMI group (3-year OS: 72.0% vs. 93.0%, p = 0.014), and there was a trend toward worse progression-free survival (PFS) in the low-SMI group (3-year PFS: 49.6% vs. 79.3%, p = 0.064). Multivariate analysis also showed that low SMI (p = 0.04) and severe N stage (p = 0.009) were significantly associated with poorer OS. CONCLUSION: The pretreatment assessment of SMI using bioelectrical impedance analysis is useful for identifying patients with poor prognoses. To improve the treatment outcome in HNC, we need to think of the intervention, such as cancer rehabilitation and nutritional support, during or before treatment, especially for patients with low SMI.
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Neoplasias de Cabeza y Cuello , Sarcopenia , Humanos , Masculino , Músculo Esquelético/patología , Sarcopenia/terapia , Pronóstico , Neoplasias de Cabeza y Cuello/terapia , Neoplasias de Cabeza y Cuello/patología , Resultado del Tratamiento , Estudios RetrospectivosRESUMEN
The coronavirus (SARS-CoV-2) exhibited waves of infection in 2020 and 2021 in Japan. The number of infected had multiple distinct peaks at intervals of several months. One possible process causing these waves of infection is people switching their activities in response to the prevalence of infection. In this paper, we present a simple model for the coupling of social and epidemiological dynamics. The assumptions are as follows. Each person switches between active and restrained states. Active people move more often to crowded areas, interact with each other, and suffer a higher rate of infection than people in the restrained state. The rate of transition from restrained to active states is enhanced by the fraction of currently active people (conformity), whereas the rate of backward transition is enhanced by the abundance of infected people (risk avoidance). The model may show transient or sustained oscillations, initial-condition dependence, and various bifurcations. The infection is maintained at a low level if the recovery rate is between the maximum and minimum levels of the force of infection. In addition, waves of infection may emerge instead of converging to the stationary abundance of infected people if both conformity and risk avoidance of people are strong.
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COVID-19 , SARS-CoV-2 , Humanos , COVID-19/epidemiología , JapónRESUMEN
Thyroglossal duct cysts (TGDC) are the most common type of congenital neck masses, which generally present in young adults. We present a rare case of a giant TGDC in a 77-year-old patient who required atypical perioperative management. The patient presented with a large soft mass on his anterior neck. Computed tomography showed a lobulated cystic mass measuring 18 × 16 cm, extending from the tongue base to the inferior level of the clavicle. Because difficult intubation was expected, the cyst was punctured and most of the fluid was drained prior to surgery. The swelling of the tongue base was remarkably reduced, and intubation was performed safely. The cyst was extracted using the Sistrunk procedure and tracheotomy was performed. Histopathological examination confirmed the diagnosis of TGDC. Preoperative volume reduction of the cyst and tracheotomy should be considered for oral intubation and postoperative airway management, respectively, in patients with large TGDC.
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BACKGROUND: Nivolumab, a programmed death-1 antibody, is an immune checkpoint inhibitor approved in Japan in March 2017 for the treatment of recurrent or metastatic head and neck cancers (RM-HNCs) after platinum drug administration. This study aimed to evaluate the effectiveness and safety of nivolumab and to determine the prognostic factors affecting the treatment outcome, in a real-world setting in Japanese RM-HNCs. METHODS: Forty-six patients with RM-HNCs treated with nivolumab between April 2017 and April 2021 at Shinshu University Hospital were retrospectively assessed in this cohort study. RESULTS: The overall response rate was 17.4%, and the disease control rate was 41.3%. The median first and second progression-free survival (PFS1 and PFS2) were 2.6 and 10.3 months, respectively. The median overall survival (OS) was 14.8 months. Multivariate analysis showed that performance status (PS) (p = 0.003) and a decrease in neutrophil-lymphocyte ratio (NLR) (p = 0.02) were significantly associated with a better OS, and a decrease in NLR (p = 0.035) was associated with a better PFS2. CONCLUSIONS: This study is the first report of PFS2 in RM-HNCs treated with nivolumab; the long PFS2 may contribute to prolonged OS. We propose that the PS and a decrease in NLR could be useful clinical prognostic markers of nivolumab therapy, which can easily be evaluated in the clinical setting.
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Antineoplásicos Inmunológicos , Neoplasias de Cabeza y Cuello , Antineoplásicos Inmunológicos/efectos adversos , Estudios de Cohortes , Neoplasias de Cabeza y Cuello/tratamiento farmacológico , Humanos , Recurrencia Local de Neoplasia/tratamiento farmacológico , Nivolumab/uso terapéutico , Estudios RetrospectivosRESUMEN
Fish live in water with a different osmotic pressure from that in the body. Their gills have chloride cells that transport ions to maintain an appropriate level of osmotic pressure in the body. The direction of ion transport is different between seawater and freshwater. There are two types of chloride cells that specialize in unidirectional transport and generalist cells that can switch their function quickly in response to environmental salinity. In species that experience salinity changes throughout life (euryhaline species), individuals may replace some chloride cells with cells of different types upon a sudden change in environmental salinity. In this paper, we develop a dynamic optimization model for the chloride cell composition of an individual living in an environment with randomly fluctuating salinity. The optimal solution is to minimize the sum of the workload of chloride cells in coping with the difference in osmotic pressure, the maintenance cost, and the temporal cost due to environmental change. The optimal fraction of generalist chloride cells increases with the frequency of salinity changes and the time needed for new cells to be fully functional but decreases with excess maintenance cost.
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Cloruros , Osmorregulación , Animales , Cloruros/metabolismo , Branquias/metabolismo , Osmorregulación/fisiología , Salinidad , Agua de Mar , Equilibrio HidroelectrolíticoRESUMEN
Many marine invertebrates have a benthic adult life with planktonic long feeding larval stages (planktotrophy). In other species, planktonic larvae do not eat, and after a rather short period, they settle and initiate their benthic stages (lecithotrophy). Still other species skip planktonic larval stages altogether, and adults produce benthic offspring (direct development). In this paper, we develop an evolutionary game among different life-cycle types and examine the conditions for each life-cycle type to win in a seasonal environment. The growth rate and mortality of benthic individuals are the same among all three life-cycle types, the local habitat (patches) for benthic individuals have a finite longevity, and adults may engage in a limited dispersal just before breeding. Planktotrophy evolves if the planktonic stages are more efficient in terms of biomass gain than benthic life. Otherwise, lecithotrophy or direct development should evolve. Among them, direct development is more advantageous than lecithotrophy if the cost of having planktonic larvae is large, the habitat for benthic individuals is stable, and adults engage in some dispersal.
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Evolución Biológica , Estadios del Ciclo de Vida , Animales , Organismos Acuáticos , Humanos , Invertebrados , LarvaRESUMEN
After infecting a host, a viral strain may increase rapidly within the body and produce mutants with a faster proliferation rate than the virus itself. However, most of the mutants become extinct because of the stochasticity caused by the small number of infected cells. In addition, the mean growth rate of a mutant strain decreases with time because the number of susceptible target cells is reduced by the original strain. In this study, we calculated the fraction of mutants that can escape stochastic extinction, based on a continuous-time branching process with a time-dependent growth rate. We analyzed two cases differing in the mode of viral transmission: (1) an infected cell transmits the virus through cell-to-cell contact with a susceptible target cell; (2) an infected cell releases numerous free viral particles that subsequently infect susceptible target cells. The chance for a mutant strain to be established decreases with time after infection of the original type, and it may oscillate before convergence at the stationary value. We then calculated the probability of escaping stochastic extinction for a drug-resistant mutant when a patient received an antiviral drug that suppressed the original strain. Combining the rate of mutant production from the original strain and the chance of escaping stochastic extinction, the number of emerging drug-resistant mutations may have two peaks: one soon after the infection of the original type and the second at the start of antiviral drug administration.
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Virus , Antivirales/farmacología , Resistencia a Medicamentos , Humanos , Mutación , Probabilidad , Procesos EstocásticosRESUMEN
In some species of separate sexes, males present a nuptial gift containing nutrition to their mate. Producing a large nuptial gift is a considerable cost to the male, but it may improve his siring success if the female reduces the likelihood to accept another male after receiving a large gift. The female may receive a direct benefit by accepting another male who provides an additional nuptial gift. Additionally, the female may receive an indirect fitness benefit via laying offspring sired by a male who is able to produce a large nuptial gift. We formalized the multivariate quantitative genetics model describing the coevolution of the size of nuptial gift produced by the male (x) and the female's propensity to engage in remating (y). We analyzed the model focusing two cases: [1] remating females receive no indirect fitness benefit, but enjoy direct benefit of nutrition; and [2] remating females receive no direct benefit, but enjoy an indirect fitness benefit due to a positive genetic correlation of x and y, which is possible if random mutations tend to make males produce small nuptial gifts. In both cases, the stable evolutionary equilibrium with neither nuptial gift nor remating (x-=y-=0) always exists. Another stable equilibrium may exist in which male produces nuptial gifts (x->0) and female engage in multiple mating (y->0). We discussed implications to the sexual conflict.