Journal of Theoretical Biology最新文献

{"title":"Range-limited Heaps’ law for functional DNA words in the human genome","authors":"Wentian Li ,&nbsp;Yannis Almirantis ,&nbsp;Astero Provata","doi":"10.1016/j.jtbi.2024.111878","DOIUrl":"10.1016/j.jtbi.2024.111878","url":null,"abstract":"<div><p>Heaps’ or Herdan-Heaps’ law is a linguistic law describing the relationship between the vocabulary/dictionary size (type) and word counts (token) to be a power-law function. Its existence in genomes with certain definition of DNA words is unclear partly because the dictionary size in genome could be much smaller than that in a human language. We define a DNA word as a coding region in a genome that codes for a protein domain. Using human chromosomes and chromosome arms as individual samples, we establish the existence of Heaps’ law in the human genome within limited range. Our definition of words in a genomic or proteomic context is different from other definitions such as over-represented k-mers which are much shorter in length. Although an approximate power-law distribution of protein domain sizes due to gene duplication and the related Zipf’s law is well known, their translation to the Heaps’ law in DNA words is not automatic. Several other animal genomes are shown herein also to exhibit range-limited Heaps’ law with our definition of DNA words, though with various exponents. When tokens were randomly sampled and sample sizes reach to the maximum level, a deviation from the Heaps’ law was observed, but a quadratic regression in log–log type-token plot fits the data perfectly. Investigation of type-token plot and its regression coefficients could provide an alternative narrative of reusage and redundancy of protein domains as well as creation of new protein domains from a linguistic perspective.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141433402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrigendum to “From the Price equation to the selection gradient in class-structured populations: A quasi-equilibrium route” [J. Theor. Biol. 447 (2018) 178–189]","authors":"Sébastien Lion","doi":"10.1016/j.jtbi.2024.111873","DOIUrl":"https://doi.org/10.1016/j.jtbi.2024.111873","url":null,"abstract":"","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324001577/pdfft?md5=dfad351749022dd305140874fde4741a&pid=1-s2.0-S0022519324001577-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141322912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evaluating infectious disease outbreak potential and mitigation effectiveness on cruise ships","authors":"Rahele Mosleh ,&nbsp;Mortaza Baky-Haskuee ,&nbsp;Abbas Ghasemi ,&nbsp;Martin Grunnill ,&nbsp;Julien Arino ,&nbsp;Mohammadali Tofighi ,&nbsp;Edward W. Thommes ,&nbsp;Jianhong Wu","doi":"10.1016/j.jtbi.2024.111875","DOIUrl":"10.1016/j.jtbi.2024.111875","url":null,"abstract":"<div><p>The cruise ship sector is a major part of the tourism industry, and an estimated over 30 million passengers are transformed worldwide each year. Cruise ships bring diverse populations into proximity for many days, facilitating the transmission of respiratory illnesses. The objective of this study is to develop a modeling framework to inform the development of viable disease risk management policies and measures to control disease outbreaks on cruises. Our model, parameterized and calibrated using the data of the COVID-19 outbreak on the Diamond Princess cruise ship in 2020, is used to assess the impact of the mitigation measures such as mask wearing, vaccination, on-board and pre-traveling testing measures. Our results indicate mask wearing in public places as the cheapest and most affordable measure can drop the number of cumulative confirmed cases by almost 50%. This measure along with the vaccination by declining the number of the cumulative confirmed cases by more than 94% is the most effective measure to control outbreaks on cruises. According to our findings, outbreaks are more predominant in the passenger population than the crew members, however, the protection measures are more beneficial if they are applied by both crew members and passengers. Regarding the testing measure, pre-traveling testing is more functional than the on-board testing to control outbreaks on cruises.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324001590/pdfft?md5=b56ebf5c3bd43d73cfa96d4a4d0e87b3&pid=1-s2.0-S0022519324001590-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141332525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Assessing dengue risk globally using non-Markovian models","authors":"Aram Vajdi ,&nbsp;Lee W. Cohnstaedt ,&nbsp;Caterina M. Scoglio","doi":"10.1016/j.jtbi.2024.111865","DOIUrl":"10.1016/j.jtbi.2024.111865","url":null,"abstract":"<div><p>Dengue is a vector-borne disease transmitted by <em>Aedes</em> mosquitoes. The worldwide spread of these mosquitoes and the increasing disease burden have emphasized the need for a spatio-temporal risk map capable of assessing dengue outbreak conditions and quantifying the outbreak risk. Given that the life cycle of <em>Aedes</em> mosquitoes is strongly influenced by habitat temperature, numerous studies have utilized temperature-dependent development rates of these mosquitoes to construct virus transmission and outbreak risk models. In this study, we contribute to existing research by developing a mechanistic model for the mosquito life cycle that accurately captures its non-Markovian nature. Beginning with integral equations to track the mosquito population across different life cycle stages, we demonstrate how to derive the corresponding differential equations using phase-type distributions. This approach can be further applied to similar non-Markovian processes that are currently described with less accurate Markovian models. By fitting the model to data on human dengue cases, we estimate several model parameters, allowing the development of a global spatiotemporal dengue risk map. This risk model employs temperature and precipitation data to assess the environmental suitability for dengue outbreaks in a given area.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141187136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling the heterogeneous apoptotic response of caspase-mediated signaling in tumor cells","authors":"Diamond S. Mangrum ,&nbsp;Stacey D. Finley","doi":"10.1016/j.jtbi.2024.111857","DOIUrl":"10.1016/j.jtbi.2024.111857","url":null,"abstract":"<div><p>Resisting apoptosis is a hallmark of cancer. For this reason, it may be possible to force cancer cells to die by targeting components along the apoptotic signaling pathway. However, apoptosis signaling is challenging to understand due to dynamic and complex behaviors of ligands, receptors, and intracellular signaling components in response to cancer therapy. In this work, we forecast the apoptotic response based on the combined impact of these features. We expanded a previously established mathematical model of caspase-mediated apoptosis to include extracellular activation and receptor dynamics. In addition, three potential threshold values of caspase-3 necessary for the activation of apoptosis were selected to forecast which cells become apoptotic over time. We first vary ligand and receptor levels with the number of intracellular signaling proteins remaining consistent. Then, we vary the intracellular protein molecules in each simulated tumor cell to forecast the response of a heterogeneous population. By leveraging the benefits of computational modeling, we investigate the combined effect of several factors on the onset of apoptosis. This work provides quantitative insights for how the apoptotic signaling response can be forecasted, and precisely triggered, amongst heterogeneous cells via extracellular activation.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324001383/pdfft?md5=86b3428602a72bef72e546b875e4174b&pid=1-s2.0-S0022519324001383-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141133713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The influence of circadian rhythms on CD8+ T cell activation upon vaccination: A mathematical modeling perspective","authors":"Nasri Balit ,&nbsp;Nicolas Cermakian ,&nbsp;Anmar Khadra","doi":"10.1016/j.jtbi.2024.111852","DOIUrl":"10.1016/j.jtbi.2024.111852","url":null,"abstract":"<div><p>Circadian rhythms have been implicated in the modulation of many physiological processes, including those associated with the immune system. For example, these rhythms influence CD8<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cell responses within the adaptive immune system. The mechanism underlying this immune-circadian interaction, however, remains unclear, particularly in the context of vaccination. Here, we devise a molecularly-explicit gene regulatory network model of early signaling in the naïve CD8<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cell activation pathway, comprised of three axes (or subsystems) labeled ZAP70, LAT and CD28, to elucidate the molecular details of this immune-circadian mechanism and its relation to vaccination. This is done by coupling the model to a periodic forcing function to identify the molecular players targeted by circadian rhythms, and analyzing how these rhythms subsequently affect CD8<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cell activation under differing levels of T cell receptor (TCR) phosphorylation, which we designate as vaccine load. By performing both bifurcation and parameter sensitivity analyses on the model at the single cell and ensemble levels, we find that applying periodic forcing on molecular targets within the ZAP70 axis is sufficient to create a day–night discrepancy in CD8<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cell activation in a manner that is dependent on the bistable switch inherent in CD8<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cell early signaling. We also demonstrate that the resulting CD8<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cell activation is dependent on the strength of the periodic coupling as well as on the level of TCR phosphorylation. Our results show that this day–night discrepancy is not transmitted to certain downstream molecules within the LAT subsystem, such as mTORC1, suggesting a secondary, independent circadian regulation on that protein complex. We also corroborate experimental results by showing that the circadian regulation of CD8<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cell primarily acts at a baseline, pre-vaccination state, playing a facilitating role in priming CD8<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cells to vaccine inputs according to the time of day. By applying an ensemble level analysis using bifurcation theory and by including several hypothesized molecular targets of this circadian rhythm, we further demonstrate an increased variability between CD8<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cells (due to heterogeneity) induced by its circadian regulation, which may allow an ensemble of CD8<span><math><msup><mrow></mrow><m","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324001334/pdfft?md5=123b5b70e6458f80bb31adaabf38cbc5&pid=1-s2.0-S0022519324001334-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141144662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effect of migrations on synchrony in host-parasitoid system","authors":"Appilineni Kushal ,&nbsp;Alan Hastings","doi":"10.1016/j.jtbi.2024.111855","DOIUrl":"10.1016/j.jtbi.2024.111855","url":null,"abstract":"<div><p>Insect outbreaks can cause large scale defoliation of forest trees or destruction of crops, leading to ecosystem degradation and economic losses. Some outbreaks occur simultaneously across large geographic scales and some outbreaks occur periodically every few years across space. Parasitoids are a natural enemy of these defoliators and could help mitigate these pest outbreaks. A holistic understanding of the host-parasitoid interactions in a spatial context would thus enhance our ability to understand, predict and prevent these outbreaks. We use a discrete time deterministic model of the host parasitoid system with populations migrating between 2 patches to elucidate features of spatial host outbreaks. We show that whenever populations persist indefinitely, host outbreaks in both patches can occur alternatively (out of phase) at low migration between patches whereas host outbreaks always occur simultaneously (in phase) in both patches at high migration between patches. We show that our results are robust across a large range of parameters across different modelling approaches used typically to model intraspecific competition among hosts and parasitism, in the host-parasitoid literature. We give an analytical expression for the period of oscillations when the migration is low <em>i.e.</em>, when host outbreaks in both patches are out of phase, show it is in agreement with numerical results. We end our paper by showing that we get the same results whether we include the biologically rooted formulations from May et al. (1981) or a general cellular automata model with qualitative rules.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141094583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Biomathematical modeling of fatigue due to sleep inertia","authors":"Mark E. McCauley ,&nbsp;Peter McCauley ,&nbsp;Leonid V. Kalachev ,&nbsp;Samantha M. Riedy ,&nbsp;Siobhan Banks ,&nbsp;Adrian J. Ecker ,&nbsp;David F. Dinges ,&nbsp;Hans P.A. Van Dongen","doi":"10.1016/j.jtbi.2024.111851","DOIUrl":"10.1016/j.jtbi.2024.111851","url":null,"abstract":"<div><p>Biomathematical models of fatigue capture the physiology of sleep/wake regulation and circadian rhythmicity to predict changes in neurobehavioral functioning over time. We used a biomathematical model of fatigue linked to the adenosinergic neuromodulator/receptor system in the brain as a framework to predict sleep inertia, that is, the transient neurobehavioral impairment experienced immediately after awakening. Based on evidence of an adenosinergic basis for sleep inertia, we expanded the biomathematical model with novel differential equations to predict the propensity for sleep inertia during sleep and its manifestation after awakening. Using datasets from large laboratory studies of sleep loss and circadian misalignment, we calibrated the model by fitting just two new parameters and then validated the model’s predictions against independent data. The expanded model was found to predict the magnitude and time course of sleep inertia with generally high accuracy. Analysis of the model’s dynamics revealed a bifurcation in the predicted manifestation of sleep inertia in sustained sleep restriction paradigms, which reflects the observed escalation of the magnitude of sleep inertia in scenarios with sleep restriction to less than ∼ 4 h per day. Another emergent property of the model involves a rapid increase in the predicted propensity for sleep inertia in the early part of sleep followed by a gradual decline in the later part of the sleep period, which matches what would be expected based on the adenosinergic regulation of non-rapid eye movement (NREM) sleep and its known influence on sleep inertia. These dynamic behaviors provide confidence in the validity of our approach and underscore the predictive potential of the model. The expanded model provides a useful tool for predicting sleep inertia and managing impairment in 24/7 settings where people may need to perform critical tasks immediately after awakening, such as on-demand operations in safety and security, emergency response, and health care.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141089120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"How do productivity gradient and diffusion shape patterns in a plant–herbivore grazing system?","authors":"Sounov Marick ,&nbsp;Fugo Takasu ,&nbsp;Nandadulal Bairagi","doi":"10.1016/j.jtbi.2024.111856","DOIUrl":"10.1016/j.jtbi.2024.111856","url":null,"abstract":"<div><p>Natural systems show heterogeneous patchy distributions of vegetation over large landscapes. Reaction–diffusion systems can demonstrate such heterogeneity of species distributions. Here, we analyse a reaction–diffusion model of plant–herbivore interactions in two-dimensional space to illustrate non-homogeneous distributions of plants and herbivores. The non-spatial system shows bottom-up control, where herbivore density is low under low and high primary productivity but increased at intermediate productivity. In addition, the non-spatial system provides bistability between a dense vegetation state devoid of herbivores and a coexisting state of plants and herbivores. In the spatiotemporal model, we give analytical conditions of occurring diffusion-driven (Turing) instability, where a novel point in our model is the relative dispersal of herbivores, which represents the movement of herbivores from a higher to a lower vegetation state in addition to the self-diffusion of both species. It is shown that heterogeneity in the population distribution does not occur if the relative dispersal of herbivores is low, but it appears in the opposite case. Due to bistability in the underlying non-spatial system, the spatiotemporal model produces initial value-dependent patterns. The two initial values make different patterns despite having the same primary productivity and relative dispersal rate. As productivity increases with a given relative herbivore dispersal, pattern transition occurs from a blend of stripes and spots of low vegetation state to a predominantly low-density vegetation state with smaller patches of densely vegetated states with one initial value. On the contrary, a discernible change in vegetation patterns from cold spots in the dense vegetation to hot stripes in the primarily low-vegetated state is noticed under the other initial population value. Furthermore, the population distributions of plants and herbivores in the entire domain after a long period are heterogeneous for both initial values, provided the relative herbivore dispersal is substantial. We estimated mean population densities to observe species fitness in the whole domain under variable productivity. When productivity is high, the mean population density of plants may go up or down, depending on the herbivore’s relative dispersal rate. In contrast to the bottom-up control dynamics of the non-spatial system, the system exhibits a top-down control under high relative dispersal, where the herbivore regulates vegetation growth under high productivity. On the other hand, herbivores are extinct under high productivity if the relative dispersal is low.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141082409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Flow modeling and structural characterization in fungal pellets","authors":"J. Sánchez-Vargas ,&nbsp;F.J. Valdés-Parada ,&nbsp;L. Peraza-Reyes ,&nbsp;D. Lasseux ,&nbsp;M.A. Trujillo-Roldán","doi":"10.1016/j.jtbi.2024.111853","DOIUrl":"10.1016/j.jtbi.2024.111853","url":null,"abstract":"<div><p>Fungal pellets are hierarchical systems that can be found in an ample variety of applications. Modeling transport phenomena in this type of systems is a challenging but necessary task to provide knowledge-based processes that improve the outcome of their biotechnological applications. In this work, an upscaled model for total mass and momentum transport in fungal pellets is implemented and analyzed, using elements of the volume averaging and adjoint homogenization methods departing from the governing equations at the microscale in the intracellular and extracellular phases. The biomass is assumed to be composed of a non-Newtonian fluid and the organelles impervious to momentum transport are modeled as a rigid solid phase. The upscaled equations contain effective-medium coefficients, which are predicted from the solution of adjoint closure problems in a three-dimensional periodic domains representative of the microstructure. The construction of these domains was performed for <em>Laccaria trichodermophora</em> based on observations of actual biological structures. The upscaled model was validated with direct numerical simulations in homogeneous portions of the pellets core. It is shown that no significant differences are observed when the dolipores are open or closed to fluid flow. By comparing the predictions of the average velocity in the extracellular phase resulting from the upscaled model with those from the classical Darcy equation (<em>i.e.</em>, assuming that the biomass is a solid phase) the contribution of the intracellular fluid phase was evidenced. This work sets the foundations for further studies dedicated to transport phenomena in this type of systems.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324001346/pdfft?md5=5ddbb5be4ce6b442d72971519d621c36&pid=1-s2.0-S0022519324001346-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141072364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}