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1.  Curcumin mediates chemosensitization to 5-fluorouracil through miRNA-induced suppression of epithelial-to-mesenchymal transition in chemoresistant colorectal cancer 
Carcinogenesis  2015;36(3):355-367.
Summary
Curcumin appears to sensitize chemotherapy drugs to cancer, but the mechanism is unclear. We demonstrated in 5FU resistant colorectal cell lines that curcumin attenuates drug resistance through inhibition of EMT via upregulation of EMT suppressive miRNAs.
Resistance to cytotoxic chemotherapy is a major cause of mortality in colorectal cancer (CRC) patients. Chemoresistance has been linked primarily to a subset of cancer cells undergoing epithelial–mesenchymal transition (EMT). Curcumin, a botanical with antitumorigenic properties, has been shown to enhance sensitivity of cancer cells to chemotherapeutic drugs, but the molecular mechanisms underlying this phenomenon remain unclear. Effects of curcumin and 5-fluorouracil (5FU) individually, and in combination, were examined in parental and 5FU resistant (5FUR) cell lines. We performed a series of growth proliferation and apoptosis assays in 2D and 3D cell cultures. Furthermore, we identified and analyzed the expression pattern of a subset of putative EMT-suppressive microRNAs (miRNAs) and their downstream target genes regulated by curcumin. Chemosensitizing effects of curcumin were validated in a xenograft mouse model. Combined treatment with curcumin and 5FU enhanced cellular apoptosis and inhibited proliferation in both parental and 5FUR cells, whereas 5FU alone was ineffective in 5FUR cells. A group of EMT-suppressive miRNAs were upregulated by curcumin treatment in 5FUR cells. Curcumin suppressed EMT in 5FUR cells by downregulating BMI1, SUZ12 and EZH2 transcripts, key mediators of cancer stemness-related polycomb repressive complex subunits. Using a xenograft and mathematical models, we further demonstrated that curcumin sensitized 5FU to suppress tumor growth. We provide novel mechanistic evidence for curcumin-mediated sensitization to 5FU-related chemoresistance through suppression of EMT in 5FUR cells via upregulation of EMT-suppressive miRNAs. This study highlights the potential therapeutic usefulness of curcumin as an adjunct in patients with chemoresistant advanced CRC.
doi:10.1093/carcin/bgv006
PMCID: PMC4400529  PMID: 25653233
2.  Nearest-Neighbor Interactions, Habitat Fragmentation, and the Persistence of Host-Pathogen Systems 
The American naturalist  2013;182(3):E94-E111.
Spatial interactions are known to promote stability and persistence in enemy-victim interactions if instability and extinction occur in well-mixed settings. We investigate the effect of spatial interactions in the opposite case, where populations can persist in well-mixed systems. A stochastic agent-based model of host-pathogen dynamics is considered that describes nearest-neighbor interactions in an undivided habitat. Contrary to previous notions, we find that in this setting, spatial interactions in fact promote extinction. The reason is that, in contrast to the mass-action system, the outcome of the nearest-neighbor model is governed by dynamics in small “local neighborhoods.” This is an abstraction that describes interactions in a minimal grid consisting of an individual plus its nearest neighbors. The small size of this characteristic scale accounts for the higher extinction probabilities. Hence, nearest-neighbor interactions in a continuous habitat lead to outcomes reminiscent of a fragmented habitat, which is underlined further with a metapopulation model that explicitly assumes habitat fragmentation. Beyond host-pathogen dynamics, axiomatic modeling shows that our results hold for generic enemy-victim interactions under specified assumptions. These results are used to interpret a set of published experiments that provide a first step toward model testing and are discussed in the context of the literature.
doi:10.1086/671185
PMCID: PMC4762454  PMID: 23933732
mathematical models; nearest neighbor interactions; habitat fragmentation; agent-based model; metapopulation model
3.  Contribution of HIV-1 genomes that do not integrate to the basic reproductive ratio of the virus 
Journal of theoretical biology  2014;367:222-229.
Recent experimental data indicate that HIV-1 DNA that fails to integrate (from now on called uDNA) can by itself successfully produce infectious offspring virions in resting T cells that become activated after infection. This scenario is likely important at the initial stages of the infection. We use mathematical models to calculate the relative contribution of unintegrated and integrated viral DNA to the basic reproductive ratio of the virus, R0, and the models are parameterized with preliminary data. This is done in the context of both free virus spread and transmission of the virus through virological synapses. For free virus transmission, we find that under preliminary parameter estimates, uDNA might contribute about 20% to the total R0. This requires that a single copy of uDNA can successfully replicate. If the presence of more than one uDNA copy is required for replication, uDNA does not contribute to R0. For synaptic transmission, uDNA can contribute to R0 regardless of the number of uDNA copies required for replication. The larger the number of viruses that are successfully transmitted per synapse, however, the lower the contribution of uDNA to R0 because this increases the chances that at least one virus integrates. Using available parameter values, uDNA can maximally contribute 20% to R0 in this case. We argue that the contribution of uDNA to virus reproduction might also be important for continued low level replication of HIV-1 in the presence of integrase inhibitor therapy. Assuming a 20% contribution of uDNA to the overall R0, our calculations suggest that R0=1.6 in the absence of virus integration. While these are rough estimates based on preliminary data that are currently available, this analysis provides a framework for future experimental work which should directly measure key parameters.
doi:10.1016/j.jtbi.2014.12.004
PMCID: PMC4361409  PMID: 25496730
4.  Timing of CD8 T cell effector responses in viral infections 
Royal Society Open Science  2016;3(2):150661.
CD8 T cell or cytotoxic T lymphocyte (CTL) responses are an important branch of the immune system in the fight against viral infections. The dynamics of anti-viral CTL responses have been characterized in some detail, both experimentally and with mathematical models. An interesting experimental observation concerns the timing of CTL responses. A recent study reported that in pneumonia virus of mice the effector CTL tended to arrive in the lung only after maximal virus loads had been achieved, an observation that seems at first counterintuitive because prevention of pathology would require earlier CTL-mediated activity. A delay in CTL-mediated effector activity has also been quoted as a possible explanation for the difficulties associated with CTL-based vaccines. This paper uses mathematical models to show that in specific parameter regimes, delayed CTL effector activity can be advantageous for the host in the sense that it can increase the chances of virus clearance. The increased ability of the CTL to clear the infection, however, is predicted to come at the cost of acute pathology, giving rise to a trade-off, which is discussed in the light of evolutionary processes. This work provides a theoretical basis for understanding the described experimental observations.
doi:10.1098/rsos.150661
PMCID: PMC4785989  PMID: 26998338
virus dynamics; cytotoxic T lymphocyte dynamics; CD8 T cells; mathematical models; delay
5.  Telomeres open a window on stem cell division 
eLife  null;5:e12481.
Measuring the length distribution of telomeres can reveal information about biological processes that are otherwise difficult to analyze experimentally.
doi:10.7554/eLife.12481
PMCID: PMC4744181  PMID: 26807592
telomere length distribution; stem cells; mathematical modelling; hematopoiesis; self renewal; personalised medicine; Human
6.  HIV-1 latency and virus production from unintegrated genomes following direct infection of resting CD4 T cells 
Retrovirology  2016;13:1.
Background
HIV-1 integration is prone to a high rate of failure, resulting in the accumulation of unintegrated viral genomes (uDNA) in vivo and in vitro. uDNA can be transcriptionally active, and circularized uDNA genomes are biochemically stable in non-proliferating cells. Resting, non-proliferating CD4 T cells are prime targets of HIV-1 infection and latently infected resting CD4 T cells are the major barrier to HIV cure. Our prior studies demonstrated that uDNA generates infectious virions when T cell activation follows rather than precedes infection.
Results
Here, we characterize in primary resting CD4 T cells the dynamics of integrated and unintegrated virus expression, genome persistence and sensitivity to latency reversing agents. Unintegrated HIV-1 was abundant in directly infected resting CD4 T cells. Maximal gene expression from uDNA was delayed compared with integrated HIV-1 and was less toxic, resulting in uDNA enrichment over time relative to integrated proviruses. Inhibiting integration with raltegravir shunted the generation of durable latency from integrated to unintegrated genomes. Latent uDNA was activated to de novo virus production by latency reversing agents that also activated latent integrated proviruses, including PKC activators, histone deacetylase inhibitors and P-TEFb agonists. However, uDNA responses displayed a wider dynamic range, indicating differential regulation of expression relative to integrated proviruses. Similar to what has recently been demonstrated for latent integrated proviruses, one or two applications of latency reversing agents failed to activate all latent unintegrated genomes. Unlike integrated proviruses, uDNA gene expression did not down modulate expression of HLA Class I on resting CD4 T cells. uDNA did, however, efficiently prime infected cells for killing by HIV-1-specific cytotoxic T cells.
Conclusions
These studies demonstrate that contributions by unintegrated genomes to HIV-1 gene expression, virus production, latency and immune responses are inherent properties of the direct infection of resting CD4 T cells. Experimental models of HIV-1 latency employing directly infected resting CD4 T cells should calibrate the contribution of unintegrated HIV-1.
Electronic supplementary material
The online version of this article (doi:10.1186/s12977-015-0234-9) contains supplementary material, which is available to authorized users.
doi:10.1186/s12977-015-0234-9
PMCID: PMC4700562  PMID: 26728316
HIV-1; Latency; Unintegrated DNA; Raltegravir; Integration; Cytotoxic T cells
7.  Quantifying replicative senescence as a tumor suppressor pathway and a target for cancer therapy 
Scientific Reports  2015;5:17660.
To study quantitatively replicative senescence as a tumor suppressor mechanism, we investigate the distribution of a growing clonal cell population restricted by Hayflick’s limit. We find that in the biologically relevant range of parameters, if the imbalance between cell division and death is moderate or low (high death-to-birth ratio), senescence offers significant protection against cancer by halting abnormal cell proliferation at early pre-diagnostic stages of tumor development. We also find that by the time tumors are typically detected, there is a high probability that telomerase is activated, even if the cell of origin was telomerase negative. Hence, the fact that most cancers are positive for telomerase is not necessarily an indication that cancer originated in a telomerase positive cell. Finally, we discuss how the population dynamics of cells can determine the outcomes of anti-telomerase cancer therapies, and provide guidelines on how the model could potentially be applied to develop clinically useful tools to predict the response to treatment by telomerase inhibitors in individual patients.
doi:10.1038/srep17660
PMCID: PMC4673423  PMID: 26647820
8.  Modeling T cell responses to antigenic challenge 
T cell responses are a crucial part of the adaptive immune system in the fight against infections. This article discusses the use of mathematical models for understanding the dynamics of cytotoxic T lymphocyte (CTL) responses against viral infections. Complementing experimental research, mathematical models have been very useful for exploring new hypotheses, interpreting experimental data, and for defining what needs to be measured to improve understanding. This review will start with minimally parameterized models of CTL responses, which have generated some valuable insights into basic dynamics and correlates of control. Subsequently, more biological complexity is incorporated into this modeling framework, examining different mechanisms of CTL expansion, different effector activities, and the influence of T cell help. Models and results are discussed in the context of data from specific infections.
doi:10.1007/s10928-014-9387-8
PMCID: PMC4210371  PMID: 25269610
10.  Complex role of space in the crossing of fitness valleys by asexual populations 
The evolution of complex traits requires the accumulation of multiple mutations, which can be disadvantageous, neutral or advantageous relative to the wild-type. We study two spatial (two-dimensional) models of fitness valley crossing (the constant-population Moran process and the non-constant-population contact process), varying the number of loci involved and the degree of mixing. We find that spatial interactions accelerate the crossing of fitness valleys in the Moran process in the context of neutral and disadvantageous intermediate mutants because of the formation of mutant islands that increase the lifespan of mutant lineages. By contrast, in the contact process, spatial structure can accelerate or delay the emergence of the complex trait, and there can even be an optimal degree of mixing that maximizes the rate of evolution. For advantageous intermediate mutants, spatial interactions always delay the evolution of complex traits, in both the Moran and contact processes. The role of the mutant islands here is the opposite: instead of protecting, they constrict the growth of mutants. We conclude that the laws of population growth can be crucial for the effect of spatial interactions on the rate of evolution, and we relate the two processes explored here to different biological situations.
doi:10.1098/rsif.2014.0014
PMCID: PMC4006240  PMID: 24671934
sequential evolution; stochastic tunnelling; complex phenotype; mutations
11.  On the Laws of Virus Spread through Cell Populations 
Journal of Virology  2014;88(22):13240-13248.
ABSTRACT
The dynamics of viral infections have been investigated extensively, often with a combination of experimental and mathematical approaches. Mathematical descriptions of virus spread through cell populations are well established in the literature and have yielded important insights, yet the formulation of certain fundamental aspects of virus dynamics models remains uncertain and untested. Here, we investigate the process of infection and, in particular, the effect of varying the target cell population size on the number of productively infected cells generated. Using an in vitro single-round HIV-1 infection system, we find that the established modeling framework cannot accurately fit the data. If the model is fit to data with the lowest number of cells and is used to predict data generated with larger cell populations, the model significantly overestimates the number of productively infected cells generated. Interestingly, this deviation becomes stronger under experimental conditions that promote mixing of cells and viruses. The reason for the deviation is that the standard model makes certain oversimplifying assumptions about the fate of viruses that fail to find a cell in their immediate proximity. We derive from stochastic processes a different model that assumes simultaneous access of the virus to multiple target cells. In this scenario, if no cell is available to the virus at its location, it has a chance to interact with other cells, a process that can be promoted by mixing of the populations. This model can accurately fit the experimental data and suggests a new interpretation of mass action in virus dynamics models.
IMPORTANCE Understanding the principles of virus growth through cell populations is of fundamental importance to virology. It helps us make informed decisions about intervention strategies aimed at preventing virus growth, such as drug treatment or vaccination approaches, e.g., in HIV infection, yet considerable uncertainty remains in this respect. An important variable in this context is the number of susceptible cells available for virus replication. How does the number of susceptible cells influence the growth potential of the virus? Besides the importance of such information for clinical responses, a thorough understanding of this is also important for the prediction of virus levels in patients and the estimation of crucial patient parameters through the use of mathematical models. This paper investigates the relationship between target cell availability and the virus growth potential with a combination of experimental and mathematical approaches and provides significant new insights.
doi:10.1128/JVI.02096-14
PMCID: PMC4249084  PMID: 25187551
12.  Tissue architecture, feedback regulation, and resilience to viral infection 
Journal of theoretical biology  2013;340:131-138.
Tissue homeostasis is one of the central requirements for the existence of multicellular organisms, and is maintained by complex feedback regulatory processes. Homeostasis can be disturbed by diseases such as viruses and tumors. Here, we use mathematical models to investigate how tissue architecture influences the ability to maintain tissue homeostasis during viral infections. In particular, two different tissue designs are considered. In the first scenario, stem cells secrete negative feedback factors that influence the balance between stem cell self-renewal and differentiation. In the second scenario, those feedback factors are not produced by stem cells but by differentiated cells. The model shows a tradeoff. If feedback factors are produced by stem cells, then a viral infection will lead to a significant reduction in the number of differentiated cells leading to tissue pathology, but the number of stem cells is not affected at equilibrium. In contrast, if the feedback factors are produced by differentiated cells, a viral infection never reduces the number of tissue cells at equilibrium because the feedback mechanism compensates for virus-induced cells death. The number of stem cells, however, becomes elevated, which could increase the chance of these stem cells to accumulate mutations that can drive cancer. Interestingly, if the virus interferes with feedback factor production by cells, uncontrolled growth can occur in the presence of the virus even in the absence of genetic lesions in cells. Hence, the optimal design would be to produce feedback factors by both stem and differentiated cells in quantities that strike a balance between protecting against tissue destruction and stem cell elevation during infection.
doi:10.1016/j.jtbi.2013.09.011
PMCID: PMC4102259  PMID: 24056215
virus dynamics; mathematical models; tissue architecture; tissue design; stem cells
13.  Minimizing the risk of cancer: tissue architecture and cellular replication limits 
Normal somatic cells are capable of only a limited number of divisions, which prevents unlimited cell proliferation and the onset of tumours. Cancer cells find ways to circumvent this obstacle, typically by expressing the enzyme telomerase and less often by alternative recombination strategies. Given this fundamental link between cellular replication limits and cancer, it is important to understand how a tissue's architecture affects the replicative capacity of a cell population. We define this as the average number of remaining divisions at equilibrium. The lower the replication capacity, the lower the chances to escape the replication limit during abnormal growth when a tumour develops. In this paper, we examine how the replication capacity is influenced by defining characteristics of cell lineages, such as the number of intermediate cell compartments, self-renewal capability of cells and division rates. We describe an optimal tissue architecture that minimizes the replication capacity of dividing cells and thus the risk of cancer. Interestingly, some of the features that define an optimal tissue architecture have been documented in a variety of tissues, suggesting that they may have evolved as a cancer-protecting strategy in multicellular organisms.
doi:10.1098/rsif.2013.0410
PMCID: PMC3730689  PMID: 23825115
cancer; telomeres; cell lineages
14.  Virus dynamics in the presence of synaptic transmission 
Mathematical biosciences  2013;242(2):161-171.
Traditionally, virus dynamics models consider populations of infected and target cells, and a population of free virus that can infect susceptible cells. In recent years, however, it has become clear that direct cell-to-cell transmission can also play an important role for the in vivo spread of viruses, especially retroviruses such as human T lymphotropic virus-1 (HTLV-1) and Human immundeficeincy virus (HIV). Such cell-to-cell transmission is thought to occur through the formation of virological synapses that are formed between an infected source cell and a susceptible target cell. Here we formulate and analyze a class of virus dynamics models that include such cell-cell synaptic transmission. We explore different ”strategies” of the virus defined by the number of viruses passed per synapse, and determine how the choice of strategy influences the basic reproductive ratio, R0, of the virus and thus its ability to establish a persistent infection. We show that depending on specific assumptions about the viral kinetics, strategies with low or intermediate numbers of viruses transferred may correspond to the highest values of R0. We also explore the evolutionary competition of viruses of different strains, which differ by their synaptic strategy, and show that viruses characterized by synaptic strategies with the highest R0 win the evolutionary competition and exclude other, inferior, strains.
doi:10.1016/j.mbs.2013.01.003
PMCID: PMC4122664  PMID: 23357287
15.  Infection of HIV-specific CD4 T helper cells and the clonal composition of the response 
Journal of theoretical biology  2012;304:143-151.
A hallmark of human immunodeficiency virus is its ability to infect CD4+ T helper cells, thus impairing helper cell responses and consequently effector responses whose maintenance depends on help (such as killer T cells and B cells). In particular, the virus has been shown to infect HIV specific helper cells preferentially. Using mathematical models, we investigate the consequence of this assumption for the basic dynamics between HIV and its target cells, assuming the existence of two independently regulated helper cell clones, directed against different epitopes of the virus. In contrast to previous studies, we examine a relatively simple scenario, only concentrating on the interactions between the virus and its target cells, not taking into account any helper-dependent effector responses. Further, there is no direct competition for space or antigenic stimulation in the model. Yet, a set of interesting outcomes is observed that provide further insights into factors that shape helper cell responses. Despite the absence of competition, a stronger helper cell clone can still exclude a weaker one because the two clones are infected by the same pathogen, an ecological concept called “apparent competition”. Moreover, we also observe “facilitation”: if one of the helper cell clones is too weak to become established in isolation, the presence of a stronger clone can provide enhanced antigenic stimulation, thus allowing the weaker clone to persist. The dependencies of these outcomes on parameters is explored. Factors that reduce viral infectivity and increase the death rate of infected cells promote coexistence, which is in agreement with the observation that stronger immunity correlates with broader helper cell responses. The basic model is extended to explicitly take into account helper-dependent CTL responses and direct competition. This study sheds further light onto the factors that can influence the clonal composition of HIV-specific helper cell responses, which has implications for the overall pattern of disease progression.
doi:10.1016/j.jtbi.2012.03.015
PMCID: PMC4082790  PMID: 22480435
16.  On the relative fitness of early and late stage Simian Immunodeficiency Virus isolates 
Theoretical population biology  2007;72(3):426-435.
Simian immunodeficiency virus (SIV) has been shown to evolve from a relatively slowly replicating and mildly cytopathic virus early in the infection (SIVMneCL8) to a faster replicating and more cytopathic virus at later stages of the infection (SIVMne170). It has recently been demonstrated that the early and mildly cytopathic variant SIVMneCL8 out-competed the late and highly cytopathic strain SIVMne170 in cell culture experiments, because the fitness disadvantage derived from the higher cytopathicity was not matched by a sufficient increase in the viral replication rate. However, in another set of experiments where the life span of cells in culture was artificially limited, the late and more cytopathic virus won the competition, because under this condition cytopahticity was not an important determinant of viral fitness. It was hypothesized that the limited life span experiment reflected the immune-mediated high turnover environment in vivo more accurately, and that the presence of immune responses accounts for the selection of the cytopathic strain SIVmne170 during later stages of the infection. This paper investigates the effect of immune responses, in particular cytotoxic T lymphocyte (CTL) responses, on the competition dynamics between these two SIV strains with the help of mathematical models. Model analysis and parameter estimates derived from previously published data on SIV growth kinetics suggest that the SIV-specific CTL response might not be the driving force that leads to the selection of the cytopathic strain SIVMne170 during later stages of the infection. This implies that more complex evolutionary mechanisms might have to be invoked in order to explain the emergence of these strains in vivo. One possibility is that the ability of multiple virus particles to infect the same cell (coinfection) might be a prerequisite for the emergence of the cytopathic strain SIVMne170 as the disease progresses.
doi:10.1016/j.tpb.2007.03.005
PMCID: PMC4058051  PMID: 17499829
17.  Infection dynamics in HIV-specific CD4 T cells: does a CD4 T cell boost benefit the host or the virus? 
Mathematical biosciences  2007;209(1):14-29.
Recent experimental data have shown that HIV specific CD4 T cells provide a very important target for HIV replication. We use mathematical models to explore the effect of specific CD4 T cell infection on the dynamics of virus spread and immune responses. Infected CD4 T cells can provide antigen for their own stimulation. We show that such auto-catalytic cell division can significantly enhance virus spread, and can also provide an additional reservoir for virus persistence during anti-viral drug therapy. In addition, the initial number of HIV-specific CD4 T cells is an important determinant of acute infection dynamics. A high initial number of HIV-specific CD4 T cells can lead to a sudden and fast drop of the population of HIV-specific CD4 T cells which results quickly in their extinction. On the other hand, a low initial number of HIV-specific CD4 T cells can lead to a prolonged persistence of HIV specific CD4 T cell help at higher levels. The model suggests that boosting the population of HIV-specific CD4 T cells can increase the amount of virus-induced immune impairment, lead to less efficient anti-viral effector responses, and thus speed up disease progression, especially if effector responses such as CTL have not been sufficiently boosted at the same time.
doi:10.1016/j.mbs.2007.01.007
PMCID: PMC4058052  PMID: 17379260
18.  An HIV-1 Replication Pathway Utilizing Reverse Transcription Products That Fail To Integrate 
Journal of Virology  2013;87(23):12701-12720.
Integration is a central event in the replication of retroviruses, yet ≥90% of HIV-1 reverse transcripts fail to integrate, resulting in accumulation of unintegrated viral DNA in cells. However, understanding what role, if any, unintegrated viral DNA plays in the natural history of HIV-1 has remained elusive. Unintegrated HIV-1 DNA is reported to possess a limited capacity for gene expression restricted to early gene products and is considered a replicative dead end. Although the majority of peripheral blood CD4+ T cells are refractory to infection, nonactivated CD4 T cells present in lymphoid and mucosal tissues are major targets for infection. Treatment with cytokine interleukin-2 (IL-2), IL-4, IL-7, or IL-15 renders CD4+ T cells permissive to HIV-1 infection in the absence of cell activation and proliferation and provides a useful model for infection of resting CD4+ T cells. We found that infection of cytokine-treated resting CD4+ T cells in the presence of raltegravir or with integrase active-site mutant HIV-1 yielded de novo virus production following subsequent T cell activation. Infection with integration-competent HIV-1 naturally generated a population of cells generating virus from unintegrated DNA. Latent infection persisted for several weeks and could be activated to virus production by a combination of a histone deacetylase inhibitor and a protein kinase C activator or by T cell activation. HIV-1 Vpr was essential for unintegrated HIV-1 gene expression and de novo virus production in this system. Bypassing integration by this mechanism may allow the preservation of genetic information that otherwise would be lost.
doi:10.1128/JVI.01939-13
PMCID: PMC3838139  PMID: 24049167
19.  Dynamics of Cellular Responses to Radiation 
PLoS Computational Biology  2014;10(4):e1003513.
Understanding the consequences of exposure to low dose ionizing radiation is an important public health concern. While the risk of low dose radiation has been estimated by extrapolation from data at higher doses according to the linear non-threshold model, it has become clear that cellular responses can be very different at low compared to high radiation doses. Important phenomena in this respect include radioadaptive responses as well as low-dose hyper-radiosensitivity (HRS) and increased radioresistance (IRR). With radioadaptive responses, low dose exposure can protect against subsequent challenges, and two mechanisms have been suggested: an intracellular mechanism, inducing cellular changes as a result of the priming radiation, and induction of a protected state by inter-cellular communication. We use mathematical models to examine the effect of these mechanisms on cellular responses to low dose radiation. We find that the intracellular mechanism can account for the occurrence of radioadaptive responses. Interestingly, the same mechanism can also explain the existence of the HRS and IRR phenomena, and successfully describe experimentally observed dose-response relationships for a variety of cell types. This indicates that different, seemingly unrelated, low dose phenomena might be connected and driven by common core processes. With respect to the inter-cellular communication mechanism, we find that it can also account for the occurrence of radioadaptive responses, indicating redundancy in this respect. The model, however, also suggests that the communication mechanism can be vital for the long term survival of cell populations that are continuously exposed to relatively low levels of radiation, which cannot be achieved with the intracellular mechanism in our model. Experimental tests to address our model predictions are proposed.
Author Summary
The effect of low-dose radiation on cells and tissues is a public health concern, because the human population is exposed to low-dose ionizing radiation coming from a variety of sources, such as cosmic rays, soil radioactivity, environmental contaminations, and various medical procedures. At low doses of radiation, phenomena are observed that do not occur at higher doses, such as radioadaptive responses as well as low-dose hyper-radiosensitivity (HRS) and increased radioresistance (IRR), which are so far not fully understood. Each of these phenomena have been investigated separately, and specific mechanisms have been suggested to explain them. Using mathematical models that are successfully fitted to experimental data under a variety of conditions, we show that a set of basic and documented assumptions about cellular responses to low-dose radiation can explain all three low-dose phenomena, indicating that they are inter-related. According to the model, these phenomena are brought about by the multi-factorial interactions that underlie the population dynamics of the cells involved, and this provides a new framework to understand these responses, and to evaluate the risk to human health posed by exposure to low-dose radiation.
doi:10.1371/journal.pcbi.1003513
PMCID: PMC3983039  PMID: 24722167
20.  Relative contribution of free-virus and synaptic transmission to the spread of HIV-1 through target cell populations 
Biology Letters  2013;9(1):20121049.
Human immunodeficiency virus can spread through target cells by transmission of cell-free virus or directly from cell-to-cell via formation of virological synapses. Although cell-to-cell transmission has been described as much more efficient than cell-free infection, the relative contribution of the two transmission pathways to virus growth during multiple rounds of replication remains poorly defined. Here, we fit a mathematical model to previously published and newly generated in vitro data, and determine that free-virus and synaptic transmission contribute approximately equally to the growth of the virus population.
doi:10.1098/rsbl.2012.1049
PMCID: PMC3565528  PMID: 23269844
human immunodeficiency virus; mathematical model; virological synapse
21.  Dependence of the Firearm-Related Homicide Rate on Gun Availability: A Mathematical Analysis 
PLoS ONE  2013;8(7):e71606.
In the USA, the relationship between the legal availability of guns and the firearm-related homicide rate has been debated. It has been argued that unrestricted gun availability promotes the occurrence of firearm-induced homicides. It has also been pointed out that gun possession can protect potential victims when attacked. This paper provides a first mathematical analysis of this tradeoff, with the goal to steer the debate towards arguing about assumptions, statistics, and scientific methods. The model is based on a set of clearly defined assumptions, which are supported by available statistical data, and is formulated axiomatically such that results do not depend on arbitrary mathematical expressions. According to this framework, two alternative scenarios can minimize the gun-related homicide rate: a ban of private firearms possession, or a policy allowing the general population to carry guns. Importantly, the model identifies the crucial parameters that determine which policy minimizes the death rate, and thus serves as a guide for the design of future epidemiological studies. The parameters that need to be measured include the fraction of offenders that illegally possess a gun, the degree of protection provided by gun ownership, and the fraction of the population who take up their right to own a gun and carry it when attacked. Limited data available in the literature were used to demonstrate how the model can be parameterized, and this preliminary analysis suggests that a ban of private firearm possession, or possibly a partial reduction in gun availability, might lower the rate of firearm-induced homicides. This, however, should not be seen as a policy recommendation, due to the limited data available to inform and parameterize the model. However, the model clearly defines what needs to be measured, and provides a basis for a scientific discussion about assumptions and data.
doi:10.1371/journal.pone.0071606
PMCID: PMC3724776  PMID: 23923062
22.  Synaptic transmission and the susceptibility of HIV infection to anti-viral drugs 
Scientific Reports  2013;3:2103.
Cell-to-cell viral transmission via virological synapses has been argued to reduce susceptibility of the virus population to anti-viral drugs through multiple infection of cells, contributing to low-level viral persistence during therapy. Using a mathematical framework, we examine the role of synaptic transmission in treatment susceptibility. A key factor is the relative probability of individual virions to infect a cell during free-virus and synaptic transmission, a currently unknown quantity. If this infection probability is higher for free-virus transmission, then treatment susceptibility is lowest if one virus is transferred per synapse, and multiple infection of cells increases susceptibility. In the opposite case, treatment susceptibility is minimized for an intermediate number of virions transferred per synapse. Hence, multiple infection via synapses does not simply lower treatment susceptibility. Without further experimental investigations, one cannot conclude that synaptic transmission provides an additional mechanism for the virus to persist at low levels during anti-viral therapy.
doi:10.1038/srep02103
PMCID: PMC3696900  PMID: 23811684
23.  Evolutionary dynamics of giant viruses and their virophages 
Ecology and Evolution  2013;3(7):2103-2115.
Giant viruses contain large genomes, encode many proteins atypical for viruses, replicate in large viral factories, and tend to infect protists. The giant virus replication factories can in turn be infected by so called virophages, which are smaller viruses that negatively impact giant virus replication. An example is Mimiviruses that infect the protist Acanthamoeba and that are themselves infected by the virophage Sputnik. This study examines the evolutionary dynamics of this system, using mathematical models. While the models suggest that the virophage population will evolve to increasing degrees of giant virus inhibition, it further suggests that this renders the virophage population prone to extinction due to dynamic instabilities over wide parameter ranges. Implications and conditions required to avoid extinction are discussed. Another interesting result is that virophage presence can fundamentally alter the evolutionary course of the giant virus. While the giant virus is predicted to evolve toward increasing its basic reproductive ratio in the absence of the virophage, the opposite is true in its presence. Therefore, virophages can not only benefit the host population directly by inhibiting the giant viruses but also indirectly by causing giant viruses to evolve toward weaker phenotypes. Experimental tests for this model are suggested.
doi:10.1002/ece3.600
PMCID: PMC3728950  PMID: 23919155
Evolutionary dynamics; giant viruses; mathematical models; virophages
24.  Methylation kinetics and CpG-island methylator phenotyope status in colorectal cancer cell lines 
Biology Direct  2013;8:14.
Background
Hypermethylation of CpG islands is thought to contribute to carcinogenesis through the inactivation of tumor suppressor genes. Tumor cells with relatively high levels of CpG island methylation are considered CpG island methylator phenotypes (CIMP). The mechanisms that are responsible for regulating the activity of de novo methylation are not well understood.
Results
We quantify and compare de novo methylation kinetics in CIMP and non-CIMP colon cancer cell lines in the context of different loci, following 5-aza-2’deoxycytidine (5-AZA)-mediated de-methylation of cells. In non-CIMP cells, a relatively fast rate of re-methylation is observed that starts with a certain time delay after cessation of 5-AZA treatment. CIMP cells, on the other hand, start re-methylation without a time delay but at a significantly slower rate. A mathematical model can account for these counter-intuitive results by assuming negative feedback regulation of de novo methylation activity and by further assuming that this regulation is corrupted in CIMP cells. This model further suggests that when methylation levels have grown back to physiological levels, de novo methylation activity ceases in non-CIMP cells, while it continues at a constant low level in CIMP cells.
Conclusions
We propose that the faster rate of re-methylation observed in non-CIMP compared to CIMP cells in our study could be a consequence of feedback-mediated regulation of DNA methyl transferase activity. Testing this hypothesis will involve the search for specific feedback regulatory mechanisms involved in the activation of de novo methylation.
Reviewers’ report
This article was reviewed by Georg Luebeck, Tomasz Lipniacki, and Anna Marciniak-Czochra
doi:10.1186/1745-6150-8-14
PMCID: PMC3691599  PMID: 23758948
Methylation kinetics; Methylator phenotype; Methylation rates; Mathematical modeling
25.  Stem Cell Control, Oscillations, and Tissue Regeneration in Spatial and Non-Spatial Models 
Normal human tissue is organized into cell lineages, in which the highly differentiated mature cells that perform tissue functions are the end product of an orderly tissue-specific sequence of divisions that start with stem cells or progenitor cells. Tissue homeostasis and effective regeneration after injuries requires tight regulation of these cell lineages and feedback loops play a fundamental role in this regard. In particular, signals secreted from differentiated cells that inhibit stem cell division and stem cell self-renewal are important in establishing control. In this article we study in detail the cell dynamics that arise from this control mechanism. These dynamics are fundamental to our understanding of cancer, given that tumor initiation requires an escape from tissue regulation. Knowledge on the processes of cellular control can provide insights into the pathways that lead to deregulation and consequently cancer development.
doi:10.3389/fonc.2013.00082
PMCID: PMC3625858  PMID: 23596567
tissue regeneration; cell linage control; tissue stability; mathematical models; cancer

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