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Defective interfering particles (DIPs) are virus-like particles that occur naturally during virus infections. These particles are defective, lacking essential genetic materials for replication, but they can interact with the wild-type virus and potentially be used as therapeutic agents. However, the effect of DIPs on infection spread is still unclear due to complicated stochastic effects and nonlinear spatial dynamics. In this work, we develop a model with a new hybrid method to study the spatial-temporal dynamics of viruses and DIPs co-infections within hosts. We present two different scenarios of virus production and compare the results from deterministic and stochastic models to demonstrate how the stochastic effect is involved in the spatial dynamics of virus transmission. We compare the spread features of the virus in simulations and experiments, including the formation and the speed of virus spread and the emergence of stochastic patchy patterns of virus distribution. Our simulations simultaneously capture observed spatial spread features in the experimental data, including the spread rate of the virus and its patchiness. The results demonstrate that DIPs can slow down the growth of virus particles and make the spread of the virus more patchy. 

The Cdc42 guanosine triphosphatase (GTPase) plays a central role in polarity development in species ranging from yeast to humans. In budding yeast, a specific growth site is selected in the G1 phase. Rsr1, a Ras GTPase, interacts with Cdc42 and its associated proteins to promote polarized growth at the proper bud site. Yet how Rsr1 regulates cell polarization is not fully understood. Here, we show that Rsr1-GDP interacts with the scaffold protein Bem1 in early G1, likely hindering the role of Bem1 in Cdc42 polarization and polarized secretion. Consistent with these in vivo observations, mathematical modeling predicts that Bem1 is unable to promote Cdc42 polarization in early G1 in the presence of Rsr1-GDP. We find that a part of the Bem1 Phox homology domain, which overlaps with a region interacting with the exocyst component Exo70, is necessary for the association of Bem1 with Rsr1-GDP. Overexpression of the GDP-locked Rsr1 interferes with Bem1-dependent Exo70 polarization. We thus propose that Rsr1 functions in spatial and temporal regulation of polarity establishment by associating with distinct polarity factors in its GTP- and GDP-bound states.