A particle-based computational model to analyse remodelling of the red blood cell cytoskeleton during malaria infections.

Red blood cells can withstand the harsh mechanical conditions in the vasculature only because the bending rigidity of their plasma membrane is complemented by the shear elasticity of the underlying spectrin-actin network. During an infection by the malaria parasite Plasmodium falciparum, the parasite mines host actin from the junctional complexes and establishes a system of adhesive knobs, whose main structural component is the knob-associated histidine rich protein (KAHRP) secreted by the parasite. Here we aim at a mechanistic understanding of this dramatic transformation process. We have developed a particle-based computational model for the cytoskeleton of red blood cells and simulated it with Brownian dynamics to predict the mechanical changes resulting from actin mining and KAHRP-clustering. Our simulations include the three-dimensional conformations of the semi-flexible spectrin chains, the capping of the actin protofilaments and several established binding sites for KAHRP. For the healthy red blood cell, we find that incorporation of actin protofilaments leads to two regimes in the shear response. Actin mining decreases the shear modulus, but knob formation increases it. We show that dynamical changes in KAHRP binding affinities can explain the experimentally observed relocalization of KAHRP from ankyrin to actin complexes and demonstrate good qualitative agreement with experiments by measuring pair cross-correlations both in the computer simulations and in super-resolution imaging experiments.

KAHRP dynamically relocalizes to remodeled actin junctions and associates with knob spirals in Plasmodium falciparum-infected erythrocytes.

The knob-associated histidine-rich protein (KAHRP) plays a pivotal role in the pathophysiology of Plasmodium falciparum malaria by forming membrane protrusions in infected erythrocytes, which anchor parasite-encoded adhesins to the membrane skeleton. The resulting sequestration of parasitized erythrocytes in the microvasculature leads to severe disease. Despite KAHRP being an important virulence factor, its physical location within the membrane skeleton is still debated, as is its function in knob formation. Here, we show by super-resolution microscopy that KAHRP initially associates with various skeletal components, including ankyrin bridges, but eventually colocalizes with remnant actin junctions. We further present a 35 Å map of the spiral scaffold underlying knobs and show that a KAHRP-targeting nanoprobe binds close to the spiral scaffold. Single-molecule localization microscopy detected ~60 KAHRP molecules/knob. We propose a dynamic model of KAHRP organization and a function of KAHRP in attaching other factors to the spiral scaffold.

Role of bacterial persistence in spatial population expansion.

Bacterial persistence, tolerance to antibiotics via stochastic phenotype switching, provides a survival strategy and a fitness advantage in temporally fluctuating environments. Here we study its possible benefit in spatially varying environments using a Fisher wave approach. We study the spatial expansion of a population with stochastic switching between two phenotypes in spatially homogeneous conditions and in the presence of an antibiotic barrier. Our analytical results show that the expansion speed in growth-supporting conditions depends on the fraction of persister cells at the leading edge of the population wave. The leading edge contains a small fraction of persister cells, keeping the effect on the expansion speed minimal. The fraction of persisters increases gradually in the interior of the wave. This persister pool benefits the population when it is stalled by an antibiotic environment. In that case, the presence of persister enables the population to spread deeper into the antibiotic region and to cross an antibiotic region more rapidly. Further we observe that optimal switching rates maximize the expansion speed of the population in spatially varying environments with alternating regions of growth permitting conditions and antibiotics. Overall, our results show that stochastic switching can promote population expansion in the presence of antibiotic barriers or other stressful environments.

Microtubule number and length determine cellular shape and function in Plasmodium.

Microtubules are cytoskeletal filaments essential for many cellular processes, including establishment and maintenance of polarity, intracellular transport, division and migration. In most metazoan cells, the number and length of microtubules are highly variable, while they can be precisely defined in some protozoan organisms. However, in either case the significance of these two key parameters for cells is not known. Here, we quantitatively studied the impact of modulating microtubule number and length in Plasmodium, the protozoan parasite causing malaria. Using a gene deletion and replacement strategy targeting one out of two α-tubulin genes, we show that chromosome segregation proceeds in the oocysts even in the absence of microtubules. However, fewer and shorter microtubules severely impaired the formation, motility and infectivity of Plasmodium sporozoites, the forms transmitted by the mosquito, which usually contain 16 microtubules. We found that α-tubulin expression levels directly determined the number of microtubules, suggesting a high nucleation barrier as supported by a mathematical model. Infectious sporozoites were only formed in parasite lines featuring at least 10 microtubules, while parasites with 9 or fewer microtubules failed to transmit.

Systematic analysis of the Myxococcus xanthus developmental gene regulatory network supports posttranslational regulation of FruA by C-signaling.

Upon starvation Myxococcus xanthus undergoes multicellular development. Rod-shaped cells move into mounds in which some cells differentiate into spores. Cells begin committing to sporulation at 24-30 h poststarvation, but the mechanisms governing commitment are unknown. FruA and MrpC are transcription factors that are necessary for commitment. They bind cooperatively to promoter regions and activate developmental gene transcription, including that of the dev operon. Leading up to and during the commitment period, dev mRNA increased in wild type, but not in a mutant defective in C-signaling, a short-range signaling interaction between cells that is also necessary for commitment. The C-signaling mutant exhibited ~20-fold less dev mRNA than wild type at 30 h poststarvation, despite a similar level of MrpC and only 2-fold less FruA. Boosting the FruA level twofold in the C-signaling mutant had little effect on the dev mRNA level, and dev mRNA was not less stable in the C-signaling mutant. Neither did high cooperativity of MrpC and FruA binding upstream of the dev promoter explain the data. Rather, our systematic experimental and computational analyses support a model in which C-signaling activates FruA at least ninefold posttranslationally in order to commit a cell to spore formation.

Mechanism of Kin-Discriminatory Demarcation Line Formation between Colonies of Swarming Bacteria.

Swarming bacteria use kin discrimination to preferentially associate with their clonemates for certain cooperative behaviors. Kin discrimination can manifest as an apparent demarcation line (a region lacking cells or with much lower cell density) between antagonist strains swarming toward each other. In contrast, two identical strains merge with no demarcation. Experimental studies suggest contact-dependent killing between different strains as a mechanism of kin discrimination, but it is not clear whether this killing is sufficient to explain the observed patterns. Here, we investigate the formation of demarcation line with a mathematical model. First, using data from competition experiments between kin discriminating strains of Myxococcus xanthus and Proteus mirabilis, we found the rates of killing between the strains to be highly asymmetric, i.e., one strain kills another at a much higher rate. Then, to investigate how such asymmetric interactions can lead to a stable demarcation line, we construct reaction-diffusion models for colony expansion of kin-discriminatory strains. Our results demonstrate that a stable demarcation line can form when both cell movement and cell growth cease at low nutrient levels. Further, our study suggests that, depending on the initial separation between the inoculated colonies, the demarcation line may move transiently before stabilizing. We validated these model predictions by observing dynamics of merger between two M. xanthus strains, where one strain expresses a toxin protein that kills a second strain lacking the corresponding antitoxin. Our study therefore provides a theoretical understanding of demarcation line formation between kin-discriminatory populations, and can be used for analyzing and designing future experiments.

Colony Expansion of Socially Motile Myxococcus xanthus Cells Is Driven by Growth, Motility, and Exopolysaccharide Production.

Myxococcus xanthus, a model organism for studies of multicellular behavior in bacteria, moves exclusively on solid surfaces using two distinct but coordinated motility mechanisms. One of these, social (S) motility is powered by the extension and retraction of type IV pili and requires the presence of exopolysaccharides (EPS) produced by neighboring cells. As a result, S motility requires close cell-to-cell proximity and isolated cells do not translocate. Previous studies measuring S motility by observing the colony expansion of cells deposited on agar have shown that the expansion rate increases with initial cell density, but the biophysical mechanisms involved remain largely unknown. To understand the dynamics of S motility-driven colony expansion, we developed a reaction-diffusion model describing the effects of cell density, EPS deposition and nutrient exposure on the expansion rate. Our results show that at steady state the population expands as a traveling wave with a speed determined by the interplay of cell motility and growth, a well-known characteristic of Fisher's equation. The model explains the density-dependence of the colony expansion by demonstrating the presence of a lag phase-a transient period of very slow expansion with a duration dependent on the initial cell density. We propose that at a low initial density, more time is required for the cells to accumulate enough EPS to activate S-motility resulting in a longer lag period. Furthermore, our model makes the novel prediction that following the lag phase the population expands at a constant rate independent of the cell density. These predictions were confirmed by S motility experiments capturing long-term expansion dynamics.

Emergence of phenotype switching through continuous and discontinuous evolutionary transitions.

Bacterial persistence (phenotypic tolerance to antibiotics) provides a prime example of bet-hedging, where normally growing cells generate slow-growing but antibiotic-tolerant persister cells to survive through periods of exposure to antibiotics. The population dynamics of persistence is explained by a phenotype switching mechanism that allows individual cells to switch between these different cellular states with different environmental sensitivities. Here, we perform a theoretical study based on an exact solution for the case of a periodic variation of the environment to address how phenotype switching emerges and under what conditions switching is or is not beneficial for long-time growth. Specifically we report a bifurcation through which a fitness maximum and minimum emerge above a threshold in the duration of exposure to the antibiotic. Only above this threshold, the optimal phenotype switching rates are adjusted to the time scales of the environment, as emphasized by previous theoretical studies, while below the threshold a non-switching population is fitter than a switching one. The bifurcation can be of different type, depending on how the phenotype switching rates are allowed to vary. If the switching rates for both directions of the switch are coupled, the transition is discontinuous and results in evolutionary hysteresis, which we confirm with a stochastic simulation. If the switching rates vary individually, a continuous transition is obtained and no hysteresis is found. We discuss how both scenarios can be linked to changes in the underlying molecular networks.

Phenotypically heterogeneous populations in spatially heterogeneous environments.

The spatial expansion of a population in a nonuniform environment may benefit from phenotypic heterogeneity with interconverting subpopulations using different survival strategies. We analyze the crossing of an antibiotic-containing environment by a bacterial population consisting of rapidly growing normal cells and slow-growing, but antibiotic-tolerant persister cells. The dynamics of crossing is characterized by mean first arrival times and is found to be surprisingly complex. It displays three distinct regimes with different scaling behavior that can be understood based on an analytical approximation. Our results suggest that a phenotypically heterogeneous population has a fitness advantage in nonuniform environments and can spread more rapidly than a homogeneous population.

Population dynamics of bacterial persistence.

Persistence is a prime example of phenotypic heterogeneity, where a microbial population splits into two distinct subpopulations with different growth and survival properties as a result of reversible phenotype switching. Specifically, persister cells grow more slowly than normal cells under unstressed growth conditions, but survive longer under stress conditions such as the treatment with bactericidal antibiotics. We analyze the population dynamics of such a population for several typical experimental scenarios, namely a constant environment, shifts between growth and stress conditions, and periodically switching environments. We use an approximation scheme that allows us to map the dynamics to a logistic equation for the subpopulation ratio and derive explicit analytical expressions for observable quantities that can be used to extract underlying dynamic parameters from experimental data. Our results provide a theoretical underpinning for the study of phenotypic switching, in particular for organisms where detailed mechanistic knowledge is scarce.

Interplay between population dynamics and drug tolerance of Staphylococcus aureus persister cells.

Population dynamics parameters of Staphylococcus aureus strain SA113 were quantified based on growth and killing experiments with batch culture cells in rich medium. Eradication kinetics and the concomitant isolation of a subpopulation of drug-tolerant SA113 persisters upon treatment with super-minimal inhibitory concentrations of antibiotics such as ciprofloxacin, daptomycin, and tobramycin served as a basis for mathematical analyses. According to a two-state model for stochastic phenotype switching, levels of persister cells and their eradication rates were influenced by the antibiotics used for isolation, clearly indicating a heterogeneous pool of S. aureus persisters. Judging from time-dependent experiments, the persisters' degree of drug tolerance correlated with the duration of antibiotic challenge. Moreover, cross-tolerance experiments with cells consecutively treated with two different antibiotics revealed that multi-drug tolerance is not a necessary trait of S. aureus persisters isolated by antibiotic challenge. In some cases, the results depended on the order of the two antibiotic treatments, suggesting that antibiotic tolerance may be achieved by a combination of preexisting persisters and an adaptive response to drug exposure. Counts of live cells which had endured drug treatment increased only after lag phases of at least 3 h after the shift to non-selective conditions. Thus, this study provides quantitative insights into population dynamics of S. aureus persisters with regard to antibiotic challenge.