Model Predictions.

<p>A) Percentage of contact time between cell types in a mature crypt observed for 80 days. Colour code as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0037115#pone-0037115-g003" target="_blank">Figure 3</a>. B) The chance of successful propagation of mutations affecting stem cells is ∼50% when the mutated cell is on the floor of the crypt and <2% for locations above. C) The time for the propagation of a mutation to the stem cell compartment is shorter when the mutation decreases the duration of the division cycle. Black columns show time for the propagation of mutated cells with 10-fold shorter division cycle, grey columns for 2-fold shorter, and white columns when division cycle is not affected. D) Time to replenish the crypt with the initial number of cells (•) and to recover the cellular structure of mature crypts after random killing of cells in the crypt (○). E) The numerical recovery rate of the injured crypt is 0.78 cells/day. The maturation rate is 0.34 cells/day. The time required to reach the original number of cells for an injured crypt that has lost half of its cells is approximately 0.9 days while the time required to reach a structural steady state is approximately 2 days. F) Time to replenish the bottom of the crypt with 10 Lgr5^hi cells after random killing of stem cells.</p

Model for cellular differentiation and proliferation in the crypt of mouse small intestine.

<p>A) Fate of stem cells progeny. Stem cells at the crypt bottom and at position +4 replenish each other and give rise to different progeny according to the strength of Wnt signalling. Wnt signalling is quantified according to the local cell composition as described in Equation 1 with a maximum value of 1 in the crypt base. Under the highest levels of Wnt signalling at the crypt bottom (Wnt  = 1), stem cells progeny consists of secretory cells and stem cells. At lower levels of Wnt signalling (Wnt <0) stem cells give rise to secretory cells and proliferative absorptive progenitors. In both cases the decision between these two fates, secretory and stem/absorptive, depends on Notch signalling. Differentiation into the secretory cellular lineage is inhibited if Notch is activated (Notch^⊕) as a result of 50% or more of adjacent cells belonging to the secretory lineage. B) Secretory cell specification. Secretory cells differentiate into goblet Paneth cell common progenitors with a probability estimated as <i>q</i>  =  Wnt signalling (quantified from Equation 1), otherwise secretory cells become either Tuft or enteroendocrine cells with equal probability. Goblet-Paneth cell common progenitors differentiate into Paneth cells with probability <i>p</i>  =  Wnt signalling (Equation 1), otherwise they differentiate into goblet cells. C) A snapshot of the simulated crypt in steady state shows how all cell types locate on the three dimensional spiral.</p

Modelling Wnt and Notch signalling in Paneth cells intermingled with Lgr5^hi stem cells at the crypt base.

<p>A) Wnt signalling activity (grey circles) as simulated by our model and measured experimentally (solid line) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0037115#pone.0037115-Fevr1" target="_blank">[28]</a>. A Wnt activity level of 1 (Equation 1) is equivalent to 100%. The results shown were obtained from 30 simulated crypts. B) Number of Paneth or Paneth progenitor and stem cells at the bottom of the crypt under high Wnt signalling activity (100%) assuming that a newly generated cell differentiates into a common goblet Paneth cell progenitor if in contact with 1 or more stem cell; otherwise secretory fate is inhibited by Notch signalling (hypothesis I). Similarly, hypotheses II, III, IV, V and VI assume that newly generated cell differentiate into a Paneth cells if in contact with a number of stem cells equal or greater than 2, 3, 4, 5 and 6, respectively. The total number of cells in contact is 6. Hypothesis III, which states that secretory fate of a stem cell is inhibited by Notch signalling if it is in contact with more than 50% of cells that belong to the secretory lineage, which best fits empirical observations. The results shown are from 30 simulated crypts. Coefficient of variation for the number of cells (CV  =  standard deviation/mean) varied from 0.015 to 0.04 in all cases. C) Upper view of the distribution of Paneth and stem cells in the crypt base at day 20 according to the six hypotheses.</p

Modularity quantification in sub-networks extracted from the <i>Salmonella</i> genome scale network containing those genes differentially expressed during and after the heat treatment and comparison with random extracted sub-networks with the same number of genes.

1<p>Modularity coefficient from 0 to 1 (maximum modularity).</p>2<p>Mean value and standard deviation of the modularity coefficient of 10 random networks.</p>*<p>Significant: Smaller than the mean value minus 3 times the standard deviation of random networks.</p

Fold change of transcript levels of genes during heat stress and immediately and 30 minutes after temperature was set back at 25°C that exhibited hysteresis and encoded for heat shock proteins (A), for DNA repair (B) for products involved in protein stabilization (C) or were encoded in plasmids (D).

<p>Down-regulated genes throughout the experiment were associated with non stress specific response such as pathogenesis (E) and motility (F). Genes represented in each plot showed a similar tendency; they are listed by the side of each plot but not differentially represented.</p

Duration of the lag phase and maximum specific growth rate at 43°C and pH 4.5 of <i>S.</i> Typhimurium previously exposed to heat and acid shock.

*<p>mean±standard deviation of 3 independent replicated experiments.</p

Network representation of genes up- and down-regulated during and after the heat shock.

<p>Modularity of networks of down-regulated genes was significantly lower than that of up-regulated networks. The induction of genes belonging to a metabolic pathway or cellular function was more synchronized than their down-regulation because of the hysteretic transcriptional response or persistence of the induction of the majority of genes induced by the heat shock once the temperature is set back to 25°C. Different colours represent different modules in each network.</p

Number of genes up- (green) and down- (red) regulated in <i>S</i>. Typhimurium under acid and heat stressing conditions and immediately and 30 min after removing the stressing conditions.

<p>Few genes were affected by acid stress (A) while transcription of a large number of genes was altered under heat stress (B). Majority of up-regulated genes under heat stress remained up-regulated 30 minutes after stress condition ceased. Black numbers and solid lines show up- and down- regulated genes maintained throughout the experiment.</p

Comparison of the modified process model which includes higher-order spatial terms (blue) to the original model (grey, dashed), both at lowered proliferation rates (decreased 20%), which is required for a better fit to the data.

<p>The original model at the original fitted proliferation rates is also shown (grey, solid). Although the model with higher-order spatial terms gives a better qualitative fit to the data for the same proliferation rates, it is clear that the dominant cause of misfit is better attributed to (time) varying proliferation rates (in the context of the present set of models).</p

Simulated realisations from the prior (left) and posterior (right) distributions for proliferation profiles (top) and velocities (bottom).

<p>After data are obtained the posterior distributions are much more tightly-constrained, and are picking out biologically plausible results (see main text).</p