Plants perceive information from the surroundings and elicit appropriate molecular responses. How plants dynamically respond to combinations of external inputs is yet to be revealed, despite the detailed current knowledge of intracellular signaling pathways. We measured dynamics of Response-to-Dehydration 29A (RD29A) expression induced by single or combined NaCl and ABA treatments in Arabidopsis thaliana. RD29A expression in response to a combination of NaCl and ABA leads to unique dynamic behavior that cannot be explained by the sum of responses to individual NaCl and ABA. To explore the potential mechanisms responsible for the observed synergistic response, we developed a mathematical model of the DREB2 and AREB pathways based on existing knowledge, where NaCl and ABA act as the cognate inputs, respectively, and examined various system structures with cross-input modulation, where non-cognate input affects expression of the genes involved in adjacent signaling pathways. The results from the analysis of system structures, combined with the insights from microarray expression profiles and model-guided experiments, predicted that synergistic activation of RD29A originates from enhancement of DREB2 activity by ABA. Our analysis of RD29A expression profiles demonstrates that a simple mathematical model can be used to extract information from temporal dynamics induced by combinatorial stimuli and produce experimentally testable hypotheses.

Streptococcus pneumoniae (Sp) is a commensal bacterium that normally resides on the upper airway epithelium without causing infection. However, factors such as co-infection with influenza virus can impair the complex Sp-host interactions and the subsequent development of many life-threatening infectious and inflammatory diseases, including pneumonia, meningitis or even sepsis. With the increased threat of Sp infection due to the emergence of new antibiotic resistant Sp strains, there is an urgent need for better treatment strategies that effectively prevent progression of disease triggered by Sp infection, minimizing the use of antibiotics. The complexity of the host-pathogen interactions has left the full understanding of underlying mechanisms of Sp-triggered pathogenesis as a challenge, despite its critical importance in the identification of effective treatments. To achieve a systems-level and quantitative understanding of the complex and dynamically-changing host-Sp interactions, here we developed a mechanistic mathematical model describing dynamic interplays between Sp, immune cells, and epithelial tissues, where the host-pathogen interactions initiate. The model serves as a mathematical framework that coherently explains various in vitro and in vitro studies, to which the model parameters were fitted. Our model simulations reproduced the robust homeostatic Sp-host interaction, as well as three qualitatively different pathogenic behaviors: immunological scarring, invasive infection and their combination. Parameter sensitivity and bifurcation analyses of the model identified the processes that are responsible for qualitative transitions from healthy to such pathological behaviors. Our model also predicted that the onset of invasive infection occurs within less than 2 days from transient Sp challenges. This prediction provides arguments in favor of the use of vaccinations, since adaptive immune responses cannot be developed de novo in such a short time. We further designed optimal treatment strategies, with minimal strengths and minimal durations of antibiotics, for each of the three pathogenic behaviors distinguished by our model. The proposed mathematical framework will help to design better disease management strategies and new diagnostic markers that can be used to inform the most appropriate patient-specific treatment options.

The human lung is constantly exposed to spores of the environmental mould Aspergillus fumigatus, a major opportunistic pathogen. The spectrum of resultant disease is the outcome of complex host-pathogen interactions, an integrated, quantitative understanding of which lies beyond the ethical and technical reach permitted by animal studies. Here we construct a mathematical model of spore inhalation and clearance by concerted actions of macrophages and neutrophils, and use it to derive a mechanistic understanding of pathogen clearance by the healthy, immunocompetent host. In particular, we investigated the impact of inoculum size upon outcomes of single-dose fungal exposure by simulated titrations of inoculation dose, from 106 to 102 spores. Simulated low-dose (102) spore exposure, an everyday occurrence for humans, revealed a counter-intuitive prediction of fungal persistence (>3 days). The model predictions were reflected in the short-term dynamics of experimental murine exposure to fungal spores, thereby highlighting the potential of mathematical modelling for studying relevant behaviours in experimental models of fungal disease. Our model suggests that infectious outcomes can be highly dependent upon short-term dynamics of fungal exposure, which may govern occurrence of cyclic or persistent subclinical fungal colonisation of the lung following low dose spore inhalation in non-neutropenic hosts.

Molecular motors play important roles within a biological cell, performing functions such as intracellular transport and gene transcription. Recent experimental work suggests that there are many plausible biochemical mechanisms that molecules such as myosin-V could use to achieve motion. To account for the abundance of possible discrete-stochastic frameworks that can arise when modeling molecular motor walks, a generalized and straightforward graphical method for calculating their dynamic properties is presented. It allows the calculation of the velocity, dispersion, and randomness ratio for any proposed system through analysis of its structure. This article extends work of King and Altman ["A schematic method of deriving the rate laws of enzyme-catalyzed reactions," J. Phys. Chem. 60, 1375-1378 (1956)] on networks of enzymatic reactions by calculating additional dynamic properties for spatially hopping systems. Results for n-state systems are presented: single chain, parallel pathway, divided pathway, and divided pathway with a chain. A novel technique for combining multiple system architectures coupled at a reference state is also demonstrated. Four-state examples illustrate the effectiveness and simplicity of these methods.

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