Role of resource allocation and transport in emergence of cross-feeding in microbial consortia.

Microbial communities that implement mutual cross-feeding are commonly observed in nature and with synthetic constructs in laboratory experiments. A mathematical model of competition in a chemostat is developed to investigate the role that resource allocation and transport of metabolites play in cooperation. The model contains four cell types that differ by whether they produce two, one, or none of two essential metabolites. Producing cell types may export these resources into the environment, and those that do not produce both metabolites must import the missing resource. The contribution to the emergence of a collaborative consortium of single resource producers from the transport rate of these metabolites and the type of transport used by the cell (active vs. passive) is studied. Multiple instances of bi-stability and tri-stability are observed, and the effect of the initial concentration of a non-cooperative cheater cell type on the final outcome of the competition is examined. When the cost of producing metabolites is introduced into the model, significant changes to the outcome of the competition are observed, including coexistence of multiple cell types.

Potential role of Reynolds number in resolving Doppler- and catheter-based transvalvular gradient discrepancies in aortic stenosis.

BACKGROUND AND AIM OF THE STUDY: Discrepancies in mean transvalvular gradient have been observed between Doppler echocardiography and catheter-based techniques in the assessment of aortic stenosis (AS). The Reynolds number (RE) has been shown to influence Doppler-derived gradients, and may be useful in resolving Doppler- and catheter-based gradient discrepancies in AS. The study aim was to assess the influence of the RE on such discrepancies. METHODS: A pulsatile in-vitro heart model using a bioprosthetic aortic valve with leaflets sutured together was used to simulate AS. Simultaneous gradients were measured using Doppler echocardiography and high-fidelity catheters while the RE was varied, by testing solutions of different density and viscosity across a range of cardiac outputs. RESULTS: The echocardiographic and catheter-derived mean gradient (MG) values were correlated (r = 0.89; p < 0.0001); however, significant differences in the MG were observed across hemodynamic states. A direct linear relationship was identified between RE and the absolute difference in MG measured using the two techniques (r = 0.94, p < 0.0001). Relative to catheter-based measurements, the MG was underestimated by Doppler (range: 13-16 mmHg) at low RE (median 6,999) and overestimated (7-33 mmHg) at high RE (median 34,268). However, agreement between catheter- and Doppler-derived gradients was within 5 mmHg at intermediate RE (median 17,284) (p < 0.0001). CONCLUSION: The underestimation of Doppler-derived MGs at low RE relative to catheter-based measurements may be due to an exclusion of viscous friction from the simplified Bernoulli equation, while the overestimation of Doppler-derived MGs at high RE may be due to a pressure recovery effect. However, within an intermediate range of RE, where the effects of viscous and inertial forces are balanced, the agreement between catheter- and Doppler-derived gradients was excellent.