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The germinal center reaction is the process by which low-affinity B cells evolve into potent, immunoglobulin-secreting plasma and memory B cells. Since the recycling hypothesis was created, experimental studies have both tracked movement of a small population of B cells from the light zone into the dark zone, supporting the recycling model, and parallel to the light zone–dark zone interface, indicating a one-way trajectory. We present a novel, sequence-based ab initio model of protein stability and protein interactions. Our model contains a dark zone region of clonal expansion and somatic hypermutation and a light zone site of antigenic selection. We show not only that a one-shot model is sufficient to achieve biologically-realistic rates of affinity growth, population dynamics, and silent:non-silent mutation ratios in the complementary determining region and framework region of antibodies, but also that a stochastic recycling program with or without realistic constraints on the structural stabilities of GC antibodies cannot produce biologically-observed affinity growth, population dynamics or silent:non-silent mutation profiles. The effect of recycling erases affinity gains made by potent antibodies cycling back from the light zone and causes B cells to pool in the dark zone under high replication rates.

Using a dynamic model we study the adaptive immune response to a sequence of two infections. We incorporate lymphocyte diversity by modeling populations as continuous distributions in a multi-dimensional space. As expected, memory cells generated by the primary infection invoke a rapid response when the secondary infection is identical (homologous). When the secondary infection is different (heterologous), the memory cells have a positive effect or no effect at all depending on the similarity of the infections. This model displays 'original antigenic sin' where the average effector affinity for the heterologous infection is lower than it would be for a naive response, but in cases with original antigenic sin we see a reduction in pathogen density. We model pathology resulting from the immune system itself (immunopathology) but find that in cases of original antigenic sin, immunopathology is still reduced. Average effector affinity is not an accurate measure of the quality of an immune response. The effectivity, which is the total pathogen killing rate, provides a direct measure of quality. This quantity takes both affinity and magnitude into account.

Networks can be found everywhere—in technology, in nature and in our bodies. In this paper we present how antigen networks can be used as a model to study network interaction and architecture. Utilizing antigen microarray data of the reactivity of hundreds of antibodies of sera of ten mothers and their newborns, we reconstruct networks, either isotype specific (IgM or IgG) or person specific—mothers or newborns—and investigate the network properties. Such an approach makes it possible to decipher fundamental information regarding the personal immune network state and its unique characteristics. In the current paper we demonstrate how we are successful in studying the interaction between two dependent networks, the maternal IgG repertoire and the one of the offspring, using the concept of meta-network provides essential information regarding the biological phenomenon of cross placental transfer. Such an approach is useful in the study of coupled networks in variety of scientific fields.

Bacteria and archaea have evolved an adaptive, heritable immune system that recognizes and protects against viruses or plasmids. This system, known as the CRISPR-Cas system, allows the host to recognize and incorporate short foreign DNA or RNA sequences, called 'spacers' into its CRISPR system. Spacers in the CRISPR system provide a record of the history of bacteria and phage coevolution. We use a physical model to study the dynamics of this coevolution as it evolves stochastically over time. We focus on the impact of mutation and recombination on bacteria and phage evolution and evasion. We discuss the effect of different spacer deletion mechanisms on the coevolutionary dynamics. We make predictions about bacteria and phage population growth, spacer diversity within the CRISPR locus, and spacer protection against the phage population.

Oncolytic virotherapy—the use of viruses that specifically kill tumor cells—is an innovative and highly promising route for treating cancer. However, its therapeutic outcomes are mainly impaired by the host immune response to the viral infection. In this paper, we propose a multiscale mathematical model to study how the immune response interferes with the viral oncolytic activity. The model assumes that cytotoxic T cells can induce apoptosis in infected cancer cells and that free viruses can be inactivated by neutralizing antibodies or cleared at a constant rate by the innate immune response. Our simulations suggest that reprogramming the immune microenvironment in tumors could substantially enhance the oncolytic virotherapy in immune-competent hosts. Viable routes to such reprogramming are either in situ virus-mediated impairing of CD8⁺ T cells motility or blockade of B and T lymphocytes recruitment. Our theoretical results can shed light on the design of viral vectors or new protocols with neat potential impacts on the clinical practice.

The independence of genetic mutation rate from selection is central to neo-Darwinian evolutionary theory. However, it has been continuously challenged for more than 30 years by experimental evidence of genetic mutation rate transiently increasing in response to stress (stress-induced hypermutation, SIH). The prominent concept of evolved evolvability (EE) explains that natural selection for strategies more competitive at evolutionary adaptation itself gives rise to mechanisms dynamically adjusting mutation rates to environmental stress. Here, we theoretically investigate the alternative (not mutually exclusive) hypothesis that SIH is an inherent physical property of all genetically reproducing life. We define stress as any condition lowering the capability of utilizing metabolic resources for genome storage and replication. This thermodynamical analysis indicates stress-induced increases in the genetic mutation rate in genome storage and in genome replication as inherent physical properties of genetically reproducing life. Further integrating SIH into an overall organismic thermodynamic budget identifies SIH as a force of natural selection, alongside death rate, replication rate and constitutive mutation rate differences. We execute four thought experiments with a non-recombinant lesion mutant strain to predict experimental observations due to SIH in response to different stresses and stress combinations. We find (1) acceleration of adaptation over models without SIH, (2) possibility of adaptation at high stresses which are not explicable by mutation in genome replication alone and (3) different adaptive potential under high growth-inhibiting versus high lethal stresses. The predictions are directly comparable to culture experiments (colony size time courses, antibacterial resistance assay and occurrence of lesion-reversion mutant colonies) and genome sequence analysis. Considering suggestions of drug-mediated disruption of SIH and attempts to target mutation-associated sites with chemotherapeutic agents to prevent resistance, our findings seem to be relevant knowledge for resistance-averse drug development and administration.

Conditions and parameters affecting the range of bistability of the lac genetic switch in Escherichia coli are examined for a model which includes DNA looping interactions with the lac repressor and a lactose analogue. This stochastic gene–mRNA–protein model of the lac switch describes DNA looping using a third transcriptional state. We exploit the fast bursting dynamics of mRNA by combining a novel geometric burst extension with the finite state projection method. This limits the number of protein/mRNA states, allowing for an accelerated search of the model's parameter space. We evaluate how the addition of the third state changes the bistability properties of the model and find a critical region of parameter space where the phenotypic switching occurs in a range seen in single molecule fluorescence studies. Stochastic simulations show induction in the looping model is preceded by a rare complete dissociation of the loop followed by an immediate burst of mRNA rather than a slower build up of mRNA as in the two-state model. The overall effect of the looped state is to allow for faster switching times while at the same time further differentiating the uninduced and induced phenotypes. Furthermore, the kinetic parameters are consistent with free energies derived from thermodynamic studies suggesting that this minimal model of DNA looping could have a broader range of application.

The plasmodium of the slime mould Physarum polycephalum forms a transportation network of veins, in which protoplasm is transported due to peristaltic pumping. This network forms a planar, weighted, undirected graph that, for the first time, can be extracted automatically from photographs or movies. Thus, data from real transportation networks have now become available for the investigation of network properties. We determine the local drag of the vein segments and use these data to calculate the transport efficiency. We unravel which veins form the backbone of the transportation network by using a centrality measure from graph theory. The principal vein segments lie on relatively ample cycles of veins, and the most important segments are those that belong simultaneously to two of these principal cycles. Each principal cycle contains a series of smaller cycles of veins of lower transport efficiency, thus reflecting the hierarchical and self-similar structure of the transportation network. Finally, we calculate accessibility maps that show how easily different nodes of the network may be reached from a given reference node.

Traditional experimental biology has provided a mechanistic understanding of cancer in which the malignancy develops through the acquisition of mutations that disrupt cellular processes. Several drugs developed to target such mutations have now demonstrated clinical value. These advances are unequivocal testaments to the value of traditional cellular and molecular biology. However, several features of cancer may limit the pace of progress that can be made with established experimental approaches alone. The mutated genes (and resultant mutant proteins) function within large biochemical networks. Biochemical networks typically have a large number of component molecules and are characterized by a large number of quantitative properties. Responses to a stimulus or perturbation are typically nonlinear and can display qualitative changes that depend upon the specific values of variable system properties. Features such as these can complicate the interpretation of experimental data and the formulation of logical hypotheses that drive further research. Mathematical models based upon the molecular reactions that define these networks combined with computational studies have the potential to deal with these obstacles and to enable currently available information to be more completely utilized. Many of the pressing problems in cancer biology and cancer medicine may benefit from a mathematical treatment. As work in this area advances, one can envision a future where such models may meaningfully contribute to the clinical management of cancer patients.

Dynamic cell-to-cell interactions are a prerequisite to many biological processes, including development and biofilm formation. Flagellum induced motility has been shown to modulate the initial cell–cell or cell–surface interaction and to contribute to the emergence of macroscopic patterns. While the role of swimming motility in surface colonization has been analyzed in some detail, a quantitative physical analysis of transient interactions between motile cells is lacking. We examined the Brownian dynamics of swimming cells in a crowded environment using a model of motorized adhesive tandem particles. Focusing on the motility and geometry of an exemplary motile bacterium Azospirillum brasilense, which is capable of transient cell–cell association (clumping), we constructed a physical model with proper parameters for the computer simulation of the clumping dynamics. By modulating mechanical interaction ('stickiness') between cells and swimming speed, we investigated how equilibrium and active features affect the clumping dynamics. We found that the modulation of active motion is required for the initial aggregation of cells to occur at a realistic time scale. Slowing down the rotation of flagellar motors (and thus swimming speeds) is correlated to the degree of clumping, which is consistent with the experimental results obtained for A. brasilense.

Chromatin-related mechanisms, as e.g. histone modifications, are known to be involved in regulatory switches within the transcriptome. Only recently, mathematical models of these mechanisms have been established. So far they have not been applied to genome-wide data. We here introduce a mathematical model of transcriptional regulation by histone modifications and apply it to data of trimethylation of histone 3 at lysine 4 (H3K4me3) and 27 (H3K27me3) in mouse pluripotent and lineage-committed cells. The model describes binding of protein complexes to chromatin which are capable of reading and writing histone marks. Molecular interactions of the complexes with DNA and modified histones create a regulatory switch of transcriptional activity. The regulatory states of the switch depend on the activity of histone (de-) methylases, the strength of complex-DNA-binding and the number of nucleosomes capable of cooperatively contributing to complex-binding. Our model explains experimentally measured length distributions of modified chromatin regions. It suggests (i) that high CpG-density facilitates recruitment of the modifying complexes in embryonic stem cells and (ii) that re-organization of extended chromatin regions during lineage specification into neuronal progenitor cells requires targeted de-modification. Our approach represents a basic step towards multi-scale models of transcriptional control during development and lineage specification.

We report self-consistent Brownian dynamics simulations of a simple electrostatic model of the selectivity filters (SF) of calcium ion channels. They reveal regular structure in the conductance and selectivity as functions of the fixed negative charge Q_f at the SF. With increasing Q_f, there are distinct regions of high conductance (conduction bands) M0, M1, M2 separated by regions of almost zero-conductance (stop-bands). Two of these conduction bands, M1 and M2, are related to the saturated calcium occupancies of P = 1 and P = 2, respectively and demonstrate self-sustained conductivity. Despite the model's limitations, its M1 and M2 bands show high calcium selectivity and prominent anomalous mole fraction effects and can be identified with the L-type and RyR calcium channels. The non-selective band M0 can be identified with a non-selective cation channel, or with OmpF porin.

Cancer disease is inherent to, and widespread among, metazoans. Yet, some of the hallmarks of cancer such as uncontrolled cell proliferation, lack of apoptosis, hypoxia, fermentative metabolism and free cell motility (metastasis) are akin to a prokaryotic lifestyle, suggesting a link between cancer disease and evolution. In this hypothesis paper, we propose that cancer cells represent a phenotypic reversion to the earliest stage of eukaryotic evolution. This reversion is triggered by the dysregulation of the mitochondria due to cumulative oxidative damage to mitochondrial and nuclear DNA. As a result, the phenotype of normal, differentiated cells gradually reverts to the phenotype of a facultative anaerobic, heterotrophic cell optimized for survival and proliferation in hypoxic environments. This phenotype matches the phenotype of the last eukaryotic common ancestor (LECA) that resulted from the endosymbiosis between an α-proteobacteria (which later became the mitochondria) and an archaebacteria. As such, the evolution of cancer within one individual can be viewed as a recapitulation of the evolution of the eukaryotic cell from fully differentiated cells to LECA. This evolutionary model of cancer is compatible with the current understanding of the disease, and explains the evolutionary basis for most of the hallmarks of cancer, as well as the link between the disease and aging. It could also open new avenues for treatment directed at reestablishing the synergy between the mitochondria and the cancerous cell.