Intracellular Dynamics of HIV Infection

Early studies of HIV infection dynamics suggested that virus-producing HIV-infected cells had an average half-life of approximately 1 day. However, whether this average behavior is reflective of the dynamics of individual infected cells is unclear. Here, we use HIV-enhanced green fluorescent protein (EGFP) constructs and flow cytometry sorting to explore the dynamics of cell infection, viral protein production, and cell death in vitro. By following the numbers of productively infected cells expressing EGFP over time, we show that infected cell death slows down over time. Although infected cell death in vivo could be very different, our results suggest that the constant decay of cell numbers observed in vivo during antiretroviral treatment could reflect a balance of cell death and delayed viral protein production. We observe no correlation between viral protein production and death rate of productively infected cells, showing that viral protein production is not likely to be the sole determinant of the death of HIV-infected cells. Finally, we show that all observed features can be reproduced by a simple model in which infected cells have broad distributions of productive life spans, times to start viral protein production, and viral protein production rates. This broad spectrum of the level and timing of viral protein production provides new insights into the behavior and characteristics of HIV-infected cells.     

The effect of correlations on the population dynamics of lymphocytes

Recent studies of the population dynamics of a system of lymphocytes in an in vitro immune response have reported strong correlations in cell division times, both between parents and their progeny, and between those of sibling cells. The data also show a high level of correlation in the ultimate number of divisions achieved by cells within the same clone. Such correlations are often ignored in mathematical models of cell dynamics as they violate a standard assumption in the theory of branching processes, that of the statistical independence of cells. In this article we present a model in which these correlations can be incorporated, and have used this model to study the effect of these correlations on the population dynamics of a system of cells. We found that correlation in the division times between parents and their progeny can alter the mean population size of clones within the system, while all of the correlations can affect the variance in the sizes of different clones. The model was then applied to experimental data obtained from time-lapse video microscopy of a system of CpG stimulated B lymphocytes and it was found that inclusion of the correct correlation structure is necessary to accurately reproduce the observed population dynamics. We conclude that correlations in the dynamics of cells within an ensemble will affect the population dynamics of the system, and the effects will become more pronounced as the number of divisions increases.     

Kinetic metabolic modelling for the control of plant cells cytoplasmic phosphate

A previously developed kinetic metabolic model for plant metabolism was used in a context of identification and control of intracellular phosphate (Pi) dynamics. Experimental data from batch flask cultures of Eschscholtiza californica cells was used to calibrate the model parameters for the slow dynamics (growth, nutrition, anabolic pathways, etc.). Perturbation experiments were performed using a perfusion small-scale bioreactor monitored by in vivo³¹P NMR. Parameter identification for Pi metabolism was done by measuring the cells dynamic response to different inputs for extracellular Pi (two pulse-response experiments and a step-response experiment). The calibrated model can describe Pi translocation between the cellular pools (vacuole and cytoplasm). The effect of intracellular Pi management on ATP/ADP and phosphomonoesters concentrations is also described by the model. The calibrated model is then used to develop a control strategy on the cytoplasmic Pi pool. From the identification of the systems dynamics, a proportional-integral controller was designed and tuned. The closed-loop control was implemented in the small-scale NMR bioreactor and experimental results were in accordance with model predictions. Thus, the calibrated model is able to predict cellular behaviour for phosphate metabolism and it was demonstrated that it is possible to control the intracellular level of cytoplasmic Pi in plant cells.     

Prediction and elucidation of the population dynamics of Microcystis spp. in Lake Dianchi (China) by means of artificial neural networks

Lake Dianchi is a shallow and turbid lake, located in Southwest China. Since 1985, Lake Dianchi has experienced severe cyanabacterial blooms (dominated by Microcystis spp.). In extreme cases, the algal cell densities have exceeded three billion cells per liter. To predict and elucidate the population dynamics of Microcystis spp. in Lake Dianchi, a neural network based model was developed. The correlation coefficient (R²) between the predicted algal concentrations by the model and the observed values was 0.911. Sensitivity analysis was performed to clarify the algal dynamics to the changes of environmental factors. The results of a sensitivity analysis of the neural network model suggested that small increases in pH could cause significantly reduced algal abundance. Further investigations on raw data showed that the response of Microcystis spp. concentration to pH increase was dependent on algal biomass and pH level. When Microcystis spp. population and pH were moderate or low, the response of Microcystis spp. population would be more likely to be positive in Lake Dianchi; contrarily, Microcystis spp. population in Lake Dianchi would be more likely to show negative response to pH increase when Microcystis spp. population and pH were high. The paper concluded that the extremely high concentration of algal population and high pH could explain the distinctive response of Microcystis spp. population to + 1 SD (standard deviation) pH increase in Lake Dianchi. And the paper also elucidated the algal dynamics to changes of other environmental factors. One SD increase of water temperature (WT) had strongest positive relationship with Microcystis spp. biomass. Chemical oxygen demand (COD) and total phosphorus (TP) had strong positive effect on Microcystis spp. abundance while total nitrogen (TN), biological oxygen demand in five days (BOD₅), and dissolved oxygen had only weak relationship with Microcystis spp. concentration. And transparency (Tr) had moderate positive relationship with Microcystis spp. concentration.     

Biological features and population density forecasts of the beet webworm Pyrausta sticticalis L. (Lepidoptera, Pyraustidae) in the period of low population density of the pest in Krasnodar Territory

Population dynamics of the beet webworm Pyrausta sticticalis L. was studied in 2003–2005 in Krasnodar Territory (Slavyansk-on-Kuban District) during the period of low population density of the pest. In the period examined, the adult death rate was high, fecundity was low; the low rate of hatchability and high rate of mortality was typical of larvae reared in the laboratory. Analysis of life tables has demonstrated that the observed population density of adults could be explained only by a constant flow of migrants. Low viability of insects from the local population could be explained by the infection with pathogenic microorganisms, including viruses of the Polyhedrosis and Granulosi groups of Baculovirus, and microsporidia, including Nosema sticticalis and Microsporidium sp. Reproduction of the pest can also be influenced by unfavorable weather conditions reducing population density in the subsequent generation. It is demonstrated that the model of the beet webworm population density dynamics based on indices of female fertility, changes in the offspring viability, and the rate of infection with microsporidia is more reliable than models based only on meteorological factors.     

Inferring Diffusion Dynamics from FCS in Heterogeneous Nuclear Environments

Fluorescence correlation spectroscopy (FCS) is a noninvasive technique that probes the diffusion dynamics of proteins down to single-molecule sensitivity in living cells. Critical mechanistic insight is often drawn from FCS experiments by fitting the resulting time-intensity correlation function, G(t), to known diffusion models. When simple models fail, the complex diffusion dynamics of proteins within heterogeneous cellular environments can be fit to anomalous diffusion models with adjustable anomalous exponents. Here, we take a different approach. We use the maximum entropy method to show—first using synthetic data—that a model for proteins diffusing while stochastically binding/unbinding to various affinity sites in living cells gives rise to a G(t) that could otherwise be equally well fit using anomalous diffusion models. We explain the mechanistic insight derived from our method. In particular, using real FCS data, we describe how the effects of cell crowding and binding to affinity sites manifest themselves in the behavior of G(t). Our focus is on the diffusive behavior of an engineered protein in 1) the heterochromatin region of the cell’s nucleus as well as 2) in the cell’s cytoplasm and 3) in solution. The protein consists of the basic region-leucine zipper (BZip) domain of the CCAAT/enhancer-binding protein (C/EBP) fused to fluorescent proteins.     

Pluripotency,Differentiation, and Reprogramming: A Gene Expression Dynamics Model with Epigenetic Feedback Regulation

Embryonic stem cells exhibit pluripotency: they can differentiate into all types of somatic cells. Pluripotent genes such as Oct4 and Nanog are activated in the pluripotent state, and their expression decreases during cell differentiation. Inversely, expression of differentiation genes such as Gata6 and Gata4 is promoted during differentiation. The gene regulatory network controlling the expression of these genes has been described, and slower-scale epigenetic modifications have been uncovered. Although the differentiation of pluripotent stem cells is normally irreversible, reprogramming of cells can be experimentally manipulated to regain pluripotency via overexpression of certain genes. Despite these experimental advances, the dynamics and mechanisms of differentiation and reprogramming are not yet fully understood. Based on recent experimental findings, we constructed a simple gene regulatory network including pluripotent and differentiation genes, and we demonstrated the existence of pluripotent and differentiated states from the resultant dynamical-systems model. Two differentiation mechanisms, interaction-induced switching from an expression oscillatory state and noise-assisted transition between bistable stationary states, were tested in the model. The former was found to be relevant to the differentiation process. We also introduced variables representing epigenetic modifications, which controlled the threshold for gene expression. By assuming positive feedback between expression levels and the epigenetic variables, we observed differentiation in expression dynamics. Additionally, with numerical reprogramming experiments for differentiated cells, we showed that pluripotency was recovered in cells by imposing overexpression of two pluripotent genes and external factors to control expression of differentiation genes. Interestingly, these factors were consistent with the four Yamanaka factors, Oct4, Sox2, Klf4, and Myc, which were necessary for the establishment of induced pluripotent stem cells. These results, based on a gene regulatory network and expression dynamics, contribute to our wider understanding of pluripotency, differentiation, and reprogramming of cells, and they provide a fresh viewpoint on robustness and control during development.     

Modeling somatic evolution in tumorigenesis

Tumorigenesis in humans is thought to be a multistep process where certain mutations confer a selective advantage, allowing lineages derived from the mutated cell to outcompete other cells. Although molecular cell biology has substantially advanced cancer research, our understanding of the evolutionary dynamics that govern tumorigenesis is limited. This paper analyzes the computational implications of cancer progression presented by Hanahan and Weinberg in The Hallmarks of Cancer. We model the complexities of tumor progression as a small set of underlying rules that govern the transformation of normal cells to tumor cells. The rules are implemented in a stochastic multistep model. The model predicts that (i) early-onset cancers proceed through a different sequence of mutation acquisition than late-onset cancers; (ii) tumor heterogeneity varies with acquisition of genetic instability, mutation pathway, and selective pressures during tumorigenesis; (iii) there exists an optimal initial telomere length which lowers cancer incidence and raises time of cancer onset; and (iv) the ability to initiate angiogenesis is an important stage-setting mutation, which is often exploited by other cells. The model offers insight into how the sequence of acquired mutations affects the timing and cellular makeup of the resulting tumor and how the cellular-level population dynamics drive neoplastic evolution.     

Targeting TMPRSS2 and Cathepsin B/L together may be synergistic against SARS-CoV-2 infection

The entry of SARS-CoV-2 into target cells requires the activation of its surface spike protein, S, by host proteases. The host serine protease TMPRSS2 and cysteine proteases Cathepsin B/L can activate S, making two independent entry pathways accessible to SARS-CoV-2. Blocking the proteases prevents SARS-CoV-2 entry in vitro. This blockade may be achieved in vivo through ‘repurposing’ drugs, a potential treatment option for COVID-19 that is now in clinical trials. Here, we found, surprisingly, that drugs targeting the two pathways, although independent, could display strong synergy in blocking virus entry. We predicted this synergy first using a mathematical model of SARS-CoV-2 entry and dynamics in vitro. The model considered the two pathways explicitly, let the entry efficiency through a pathway depend on the corresponding protease expression level, which varied across cells, and let inhibitors compromise the efficiency in a dose-dependent manner. The synergy predicted was novel and arose from effects of the drugs at both the single cell and the cell population levels. Validating our predictions, available in vitro data on SARS-CoV-2 and SARS-CoV entry displayed this synergy. Further, analysing the data using our model, we estimated the relative usage of the two pathways and found it to vary widely across cell lines, suggesting that targeting both pathways in vivo may be important and synergistic given the broad tissue tropism of SARS-CoV-2. Our findings provide insights into SARS-CoV-2 entry into target cells and may help improve the deployability of drug combinations targeting host proteases required for the entry.     

The Drosophila spectraplakin Short stop regulates focal adhesion dynamics by cross-linking microtubules and actin

The spectraplakin family of proteins includes ACF7/MACF1 and BPAG1/dystonin in mammals, VAB-10 in Caenorhabditis elegans, Magellan in zebrafish, and Short stop (Shot), the sole Drosophila member. Spectraplakins are giant cytoskeletal proteins that cross-link actin, microtubules, and intermediate filaments, coordinating the activity of the entire cytoskeleton. We examined the role of Shot during cell migration using two systems: the in vitro migration of Drosophila tissue culture cells and in vivo through border cell migration. RNA interference (RNAi) depletion of Shot increases the rate of random cell migration in Drosophila tissue culture cells as well as the rate of wound closure during scratch-wound assays. This increase in cell migration prompted us to analyze focal adhesion dynamics. We found that the rates of focal adhesion assembly and disassembly were faster in Shot-depleted cells, leading to faster adhesion turnover that could underlie the increased migration speeds. This regulation of focal adhesion dynamics may be dependent on Shot being in an open confirmation. Using Drosophila border cells as an in vivo model for cell migration, we found that RNAi depletion led to precocious border cell migration. Collectively, these results suggest that spectraplakins not only function to cross-link the cytoskeleton but may regulate cell–matrix adhesion.     

Time-Lapse Imaging of Red Blood Cell Invasion by the Rodent Malaria Parasite Plasmodium yoelii

In order to propagate within the mammalian host, malaria parasites must invade red blood cells (RBCs). This process offers a window of opportunity in which to target the parasite with drugs or vaccines. However, most of the studies relating to RBC invasion have analyzed the molecular interactions of parasite proteins with host cells under static conditions, and the dynamics of these interactions remain largely unstudied. Time-lapse imaging of RBC invasion is a powerful technique to investigate cell invasion and has been reported for Plasmodium knowlesi and Plasmodium falciparum. However, experimental modification of genetic loci is laborious and time consuming for these species. We have established a system of time-lapse imaging for the rodent malaria parasite Plasmodium yoelii, for which modification of genetic loci is quicker and simpler. We compared the kinetics of RBC invasion by P. yoelii with that of P. falciparum and found that the overall kinetics during invasion were similar, with some exceptions. The most striking of these differences is that, following egress from the RBC, the shape of P. yoelii merozoites gradually changes from flat elongated ovals to spherical bodies, a process taking about 60 sec. During this period merozoites were able to attach to and deform the RBC membrane, but were not able to reorient and invade. We propose that this morphological change of P. yoelii merozoites may be related to the secretion or activation of invasion-related proteins. Thus the P. yoelii merozoite appears to be an excellent model to analyze the molecular dynamics of RBC invasion, particularly during the morphological transition phase, which could serve as an expanded window that cannot be observed in P. falciparum.     

A Theoretical Model of Jigsaw-Puzzle Pattern Formation by Plant Leaf Epidermal Cells

Plant leaf epidermal cells exhibit a jigsaw puzzle–like pattern that is generated by interdigitation of the cell wall during leaf development. The contribution of two ROP GTPases, ROP2 and ROP6, to the cytoskeletal dynamics that regulate epidermal cell wall interdigitation has already been examined; however, how interactions between these molecules result in pattern formation remains to be elucidated. Here, we propose a simple interface equation model that incorporates both the cell wall remodeling activity of ROP GTPases and the diffusible signaling molecules by which they are regulated. This model successfully reproduces pattern formation observed in vivo, and explains the counterintuitive experimental results of decreased cellulose production and increased thickness. Our model also reproduces the dynamics of three-way cell wall junctions. Therefore, this model provides a possible mechanism for cell wall interdigitation formation in vivo.     

In Silico Geobacter sulfurreducens Metabolism and Its Representation in Reactive Transport Models

Microbial activity governs elemental cycling and the transformation of many anthropogenic substances in aqueous environments. Through the development of a dynamic cell model of the well-characterized, versatile, and abundant Geobacter sulfurreducens, we showed that a kinetic representation of key components of cell metabolism matched microbial growth dynamics observed in chemostat experiments under various environmental conditions and led to results similar to those from a comprehensive flux balance model. Coupling the kinetic cell model to its environment by expressing substrate uptake rates depending on intra- and extracellular substrate concentrations, two-dimensional reactive transport simulations of an aquifer were performed. They illustrated that a proper representation of growth efficiency as a function of substrate availability is a determining factor for the spatial distribution of microbial populations in a porous medium. It was shown that simplified model representations of microbial dynamics in the subsurface that only depended on extracellular conditions could be derived by properly parameterizing emerging properties of the kinetic cell model.     

Dynamics of Telomeres and Promyelocytic Leukemia Nuclear Bodies in a Telomerase-negative Human Cell Line

Telomerase-negative tumor cells maintain their telomeres via an alternative lengthening of telomeres (ALT) mechanism. This process involves the association of telomeres with promyelocytic leukemia nuclear bodies (PML-NBs). Here, the mobility of both telomeres and PML-NBs as well as their interactions were studied in human U2OS osteosarcoma cells, in which the ALT pathway is active. A U2OS cell line was constructed that had lac operator repeats stably integrated adjacent to the telomeres of chromosomes 6q, 11p, and 12q. By fluorescence microscopy of autofluorescent LacI repressor bound to the lacO arrays the telomere mobility during interphase was traced and correlated with the telomere repeat length. A confined diffusion model was derived that describes telomere dynamics in the nucleus on the time scale from seconds to hours. Two telomere groups were identified that differed with respect to the nuclear space accessible to them. Furthermore, translocations of PML-NBs relative to telomeres and their complexes with telomeres were evaluated. Based on these studies, a model is proposed in which the shortening of telomeres results in an increased mobility that could facilitate the formation of complexes between telomeres and PML-NBs.     

Establishment of Mammary Gland Model In Vitro: Culture and Evaluation of a Yak Mammary Epithelial Cell Line

This study aimed to establish yak mammary epithelial cells (YMECs) for an in vitro model of yak mammary gland biology. The primary culture of YMECs was obtained from mammary gland tissues of lactating yak and then characterized using immunocytochemistry, RT-PCR, and western blot analysis. Whether foreign genes could be transfected into the YMECs were examined by transfecting the EGFP gene into the cells. Finally, the effect of Staphylococcus aureus infection on YMECs was determined. The established YMECs retained the mammary epithelial cell characteristics. A spontaneously immortalized yak mammary epithelial cell line was established and could be continuously subcultured for more than 60 passages without senescence. The EGFP gene was successfully transferred into the YMECs, and the transfected cells could be maintained for a long duration in the culture by continuous subculturing. The cells expressed more antimicrobial peptides upon S.aureus invasion. Therefore, the established cell line could be considered a model system to understand yak mammary gland biology.     

The fission yeast transforming acidic coiled coil-related protein Mia1p/Alp7p is required for formation and maintenance of persistent microtubule-organizing centers at the nuclear envelope

Microtubule-organizing centers (MTOCs) concentrate microtubule nucleation, attachment and bundling factors and thus restrict formation of microtubule arrays in spatial and temporal manner. How MTOCs occur remains an exciting question in cell biology. Here, we show that the transforming acidic coiled coil–related protein Mia1p/Alp7p functions in emergence of large MTOCs in interphase fission yeast cells. We found that Mia1p was a microtubule-binding protein that preferentially localized to the minus ends of microtubules and was associated with the sites of microtubule attachment to the nuclear envelope. Cells lacking Mia1p exhibited less microtubule bundles. Microtubules could be nucleated and bundled but were frequently released from the nucleation sites in mia1Δ cells. Mia1p was required for stability of microtubule bundles and persistent use of nucleation sites both in interphase and postanaphase array dynamics. The γ-tubulin–rich material was not organized in large perinuclear or microtubule-associated structures in mia1Δ cells. Interestingly, absence of microtubules in dividing wild-type cells prevented appearance of large γ-tubulin–rich MTOC structures in daughters. When microtubule polymerization was allowed, MTOCs were efficiently assembled de novo. We propose a model where MTOC emergence is a self-organizing process requiring the continuous association of microtubules with nucleation sites.     

Evolution of taxis responses in virtual bacteria: non-adaptive dynamics

Bacteria are able to sense and respond to a variety of external stimuli, with responses that vary from stimuli to stimuli and from species to species. The best-understood is chemotaxis in the model organism Escherichia coli, where the dynamics and the structure of the underlying pathway are well characterised. It is not clear, however, how well this detailed knowledge applies to mechanisms mediating responses to other stimuli or to pathways in other species. Furthermore, there is increasing experimental evidence that bacteria integrate responses from different stimuli to generate a coherent taxis response. We currently lack a full understanding of the different pathway structures and dynamics and how this integration is achieved. In order to explore different pathway structures and dynamics that can underlie taxis responses in bacteria, we perform a computational simulation of the evolution of taxis. This approach starts with a population of virtual bacteria that move in a virtual environment based on the dynamics of the simple biochemical pathways they harbour. As mutations lead to changes in pathway structure and dynamics, bacteria better able to localise with favourable conditions gain a selective advantage. We find that a certain dynamics evolves consistently under different model assumptions and environments. These dynamics, which we call non-adaptive dynamics, directly couple tumbling probability of the cell to increasing stimuli. Dynamics that are adaptive under a wide range of conditions, as seen in the chemotaxis pathway of E. coli, do not evolve in these evolutionary simulations. However, we find that stimulus scarcity and fluctuations during evolution results in complex pathway dynamics that result both in adaptive and non-adaptive dynamics depending on basal stimuli levels. Further analyses of evolved pathway structures show that effective taxis dynamics can be mediated with as few as two components. The non-adaptive dynamics mediating taxis responses provide an explanation for experimental observations made in mutant strains of E. coli and in wild-type Rhodobacter sphaeroides that could not be explained with standard models. We speculate that such dynamics exist in other bacteria as well and play a role linking the metabolic state of the cell and the taxis response. The simplicity of mechanisms mediating such dynamics makes them a candidate precursor of more complex taxis responses involving adaptation. This study suggests a strong link between stimulus conditions during evolution and evolved pathway dynamics. When evolution was simulated under conditions of scarce and fluctuating stimulus conditions, the evolved pathway contained features of both adaptive and non-adaptive dynamics, suggesting that these two types of dynamics can have different advantages under distinct environmental circumstances.     

The dynamics of acute malaria infections. I. Effect of the parasite's red blood cell preference

What determines the dynamics of parasite and anaemia during acute primary malaria infections? Why do some strains of malaria reach higher densities and cause greater anaemia than others? The conventional view is that the fastest replicating parasites reach the highest densities and cause the greatest loss of red blood cells (RBCs). Other current hypotheses suggest that the maximum parasite density is achieved by strains that either elicit the weakest immune responses or infect the youngest RBCs (reticulocytes). Yet another hypothesis is a simple resource limitation model where the peak parasite density and the maximum anaemia (percentage loss of RBCs) during the acute phase of infection equal the fraction of RBCs that the malaria parasite can infect. We discriminate between these hypotheses by developing a mathematical model of acute malaria infections and confronting it with experimental data from the rodent malaria parasite Plasmodium chabaudi. We show that the resource limitation model can explain the initial dynamics of infection of mice with different strains of this parasite. We further test the model by showing that without modification it closely reproduces the dynamics of competing strains in mixed infections of mice with these strains of P. chabaudi. Our results suggest that a simple resource limitation is capable of capturing the basic features of the dynamics of both parasite and RBC loss during acute malaria infections of mice with P. chabaudi, suggesting that it might be worth exploring if similar results might hold for other acute malaria infections, including those of humans.