Cassava storage : post-harvest deterioration and storage of fresh cassava roots

<p>Sum of squares of the errors (SSE) between data from patients <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014531#pone.0014531-Shankarappa1" target="_blank">[36]</a> and our predictions of viral diversity, <i>d_G</i>, and divergence, <i>d_S</i>, for different values of the population size, <i>C</i>, (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014531#pone-0014531-g005" target="_blank">Fig. 5</a>) and the viral generation time, τ, shown for each of the nine patients. <i>C</i> and τ that yield the lowest SSE provide the best fit to the data. The best-fit value of <i>C</i> yields <i>N_e</i> (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014531#pone-0014531-t001" target="_blank">Table 1</a>).</p

Clustering behavior of periodically reversing agents in simulations.

<p>(A) Snapshot of the simulation with periodically reversing agents (<i>η</i> = 0.24) at 180 min of simulation time. Reversing agents did not show significant clustering. (B) Mean cluster sizes, 〈<i>m</i>〉, in simulation as a function of cell density, <i>η</i>, for agents following slime trails (green line) and agents without slime trails (black line). Agents following slime trails showed a significant increase in mean cluster size compared to agents without slime-trail-following. (C) Snapshot of the simulation for periodically reversing cells with the slime-trail-following mechanism (<i>η</i> = 0.24, <i>L</i>_<i>s</i> = 11 <i>μm</i>, <i>ε</i>_<i>s</i> = 1.0, refer to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004474#sec009" target="_blank">Methods</a> for details) at 180 min of simulation time. Agents show improved clustering compared to those without the slime-trail-following mechanism. (D) Orientation correlation 〈cos 2Δ<i>θ</i>_<i>r</i>〉 among agents for reversing cells (black) and reversing cells with the slime-trail-following mechanism (green). Dashed and solid lines are orientation correlation values at 1 min and 180 min of simulation time, respectively. Orientation correlation with neighbors improved for larger neighbor distances with the slime-trail-following mechanism.</p

Clustering behavior of non-reversing flexible agents in simulations.

<p>(A-D) Snapshots of the simulation region at 180 min of simulation time for different cell densities, <i>η</i>. (A) <i>η</i> = 0.08, (B) <i>η</i> = 0.16, (C) <i>η</i> = 0.24, (D) <i>η</i> = 0.32. Flexible agents formed aligned clusters at moderate to high cell densities (<i>η</i> ≥ 0.16). (E) Mean cluster sizes, 〈<i>m</i>〉, from simulation as a function of cell density, <i>η</i>. The error bars indicate the standard deviation in the data. The results are averaged over 5 independent simulation runs. The mean cluster sizes increased with increases in cell density. (F) Orientation correlation 〈cos 2Δ<i>θ</i>_<i>r</i>〉 among cells as a function of neighbor cell distance, <i>r</i>. Δ<i>θ</i>_<i>r</i> is the angle deviation between orientations (<i>θ</i>) of a pair of neighbor cells separated by a distance <i>r</i>. Orientation correlation (cos 2Δ<i>θ</i>_<i>r</i>) values from all cell pairs are binned based on <i>r</i> (bin width = 1 <i>μm</i>) and averaged. Dashed and solid lines represent orientation correlation values at 1 min and 180 min of simulation time, respectively. Agents in clusters showed higher neighbor alignment at larger distances compared to the initial randomly oriented cells. Furthermore, the alignment increases with increases in cell density.</p

Comparison of cell clustering behavior in simulations with experiments.

<p>(A-B) Comparison of cluster size distributions (CSD) from simulations (lines) with experimental data (symbols, digitized from Starruẞ et al. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004474#pcbi.1004474.ref016" target="_blank">16</a>]) for non-reversing (A) and reversing (B) cells. Probability, <i>p</i>(<i>m</i>), of finding a cell in a cluster is plotted as a function of the cluster size <i>m</i>. We use different sets of slime-trail-following mechanism parameters for non-reversing (<i>L</i>_<i>s</i> = 0.6 <i>μm</i>, <i>ε</i>_<i>s</i> = 0.5) and reversing (<i>L</i>_<i>s</i> = 11 μ<i>m</i>, <i>ε</i>_<i>s</i> = 0.2) agents. CSD results from simulations show a similar trend to that of the experimental data. (A) Non-reversing cells show a power-law-like CSD, whereas reversing cells show a monotonically decreasing CSD (B). (C-D) Heat maps of cell visit frequencies over the simulation region for 2 consecutive hours (<i>η</i> = 0.24). The color bar represents the number of cell visits per hour at a particular location. Non-reversing cells show a dynamic cluster pattern with changes in cell traces (C), whereas reversing cells show a static cluster pattern with the pattern of cell traces remaining approximately the same over time (D). (E) Probability of cell visits, <i>p</i>(<i>N</i>), as a function of visit frequency, <i>N</i>, for non-reversing (red) and reversing cells (green) over a 1-hr simulation time (120–180 min). Reversing cells show a large fraction of sites with high visit frequencies compared to non-reversing cells.</p

(A) Hypothetical mechanism of cell clustering through slime-trail-following in reversing <i>M</i>. <i>xanthus</i> cells. (B) Circular cell aggregates observed in simulation for non-reversing agents with the slime-trail-following mechanism (<i>η</i> = 0.24, <i>L</i>_<i>s</i> = 11 <i>μm</i>, <i>ε</i>_<i>s</i> = 1.0).

<p>(A) Hypothetical mechanism of cell clustering through slime-trail-following in reversing <i>M</i>. <i>xanthus</i> cells. (B) Circular cell aggregates observed in simulation for non-reversing agents with the slime-trail-following mechanism (<i>η</i> = 0.24, <i>L</i>_<i>s</i> = 11 <i>μm</i>, <i>ε</i>_<i>s</i> = 1.0).</p

Simulations of viral genomic diversification with a low frequency of multiple infections.

<p>The evolution of (A) viral diversity, <i>d_G</i>, (B) divergence, <i>d_S</i>, and (C) average fitness, <i>f</i>, with generations predicted by our simulations for different population sizes, <i>C</i>. Each cell is assumed to be infected with <i>M</i> virions drawn from a distribution based on a viral dynamics model (see text). Error bars represent standard deviations.</p

Stochastic Simulations Suggest that HIV-1 Survives Close to Its Error Threshold

<div><p>The use of mutagenic drugs to drive HIV-1 past its error threshold presents a novel intervention strategy, as suggested by the quasispecies theory, that may be less susceptible to failure via viral mutation-induced emergence of drug resistance than current strategies. The error threshold of HIV-1, , however, is not known. Application of the quasispecies theory to determine poses significant challenges: Whereas the quasispecies theory considers the asexual reproduction of an infinitely large population of haploid individuals, HIV-1 is diploid, undergoes recombination, and is estimated to have a small effective population size in vivo. We performed population genetics-based stochastic simulations of the within-host evolution of HIV-1 and estimated the structure of the HIV-1 quasispecies and . We found that with small mutation rates, the quasispecies was dominated by genomes with few mutations. Upon increasing the mutation rate, a sharp error catastrophe occurred where the quasispecies became delocalized in sequence space. Using parameter values that quantitatively captured data of viral diversification in HIV-1 patients, we estimated to be substitutions/site/replication, ∼2–6 fold higher than the natural mutation rate of HIV-1, suggesting that HIV-1 survives close to its error threshold and may be readily susceptible to mutagenic drugs. The latter estimate was weakly dependent on the within-host effective population size of HIV-1. With large population sizes and in the absence of recombination, our simulations converged to the quasispecies theory, bridging the gap between quasispecies theory and population genetics-based approaches to describing HIV-1 evolution. Further, increased with the recombination rate, rendering HIV-1 less susceptible to error catastrophe, thus elucidating an added benefit of recombination to HIV-1. Our estimate of may serve as a quantitative guideline for the use of mutagenic drugs against HIV-1.</p> </div

Estimates of synonymous and non-synonymous substitution rates.

<p>The rates of synonymous and non-synonymous substitutions estimated by Lemey et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014531#pone.0014531-Lemey1" target="_blank">[14]</a> in the patients we consider (except Patient 11) from seroconversion until the CD4⁺ T cell count dropped to 200 cells/µL (mean 7 years). The ratio of the mean non-synonymous and synonymous substitution rates is 2.16.</p

Fits of our simulations to data from patients.

<p>Best-fit predictions of our simulations (solid lines) presented with experimental data (symbols) of the evolution of viral diversity, <i>d_G</i>, (cyan) and divergence, <i>d_S</i>, (purple) for each patient. Each cell is assumed to be infected with <i>M</i> = 3 virions in our simulations. The values of <i>N_e</i> (cells) and τ (days) employed for the predictions are indicated.</p

Comparisons of our simulations with the quasispecies theory.

<p>Structure of the quasispecies for different values of (substitutions/site/replication) indicated determined by our simulations (circles connected by lines) and by the quasispecies theory (pluses) for (A) isolated peak fitness landscape, (B) exponential landscape with <i>s</i> = 0.01, and (C) the experimental landscape with <i>d₅₀</i> = 3.</p