Cell Lineages and Growth Control by Feedback

The molecular mechanisms that regulate tissue growth are diverse, but the objectives of growth control are generic in many tissues: to reach and stably maintain an appropriate size, to regenerate rapidly following injury, to possess appropriate proportions of different cell types, and to form specific tissue structures during development. It is known that feedback mechanisms play a role in growth control, and that cells the give rise to a tissue are organized into lineages—successive stages in which cells at each stage have the option either to self-renew or differentiate to the next stage. Negative feedback on progenitor cell self-renewal has been previously shown to confer “perfect adaptation” for steady-state size control (maintenance of an exact tissue size independent of numbers of starting cells, rates of cell division, or rates of cell death), stability, and a low steady-state load of progenitor cells (Lander, Gokoffski et al. 2009). Negative feedback is also useful for fast regeneration, and it will be shown that negative feedback can be used to approximate a bang-bang controller and therefore be used to build a tissue in the shortest time possible. This control strategy, however, suffers from inherent performance tradeoffs. Namely, rapid regeneration and robustness to parameters/initial conditions tend to be competing objectives, and certain perturbations can result in undesirable oscillations. Stem cells in lineages, such as in the olfactory epithelium (OE), are also known to undergo branching decisions (i.e. to be bipotent) (Gokoffski, Wu et al. 2011) and to receive feedback that promotes self-renewal divisions, such as by FGFs (DeHamer, Guevara et al. 1994). This study seeks to understand the role of the latter phenomenon, which amounts to a type of positive feedback. We find that mixing negative and positive feedback on progenitor self-renewal enables two distinct types of stable growth: either high or low, which we refer to as bi-modality. A critical feedback ratio sets the threshold between the two states, and spatial simulations reveal that this threshold can be used by tissues to self-organize into distinct shapes. A transient, local exogenous positive signal can boost progenitor self-renewal within a discrete zone of planar tissue, which induces bud formation and self-sustaining growth. Furthermore, these zones can self-organize in ways that control tissue shape with spatial precision – i.e. a bud elongates and maintains a constant width as growth self-sustains at its tip, neighboring elongating branches maintain even spacing, and branch numbers change according to changes in the feedback ratio. Disturbances to growth factors that regulate progenitor self-renewal have been previously shown to have morphological consequences during early branching of the olfactory epithelium (OE) (Kawauchi, Kim et al. 2009). Finally, results will be presented from counting progenitor cells in BrdU/EdU pulse-chase/fix experiments in the embryonic OE to measure regional differences in progenitor self-renewal. Preliminary data reveals high progenitor self-renewal in regions undergoing branching morphogenesis, while low self-renewal maintains cell populations in equilibrium at the anterior end of the OE

Self-organizing pattern.

<p><b>A-U.</b> Simulations were carried out as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004814#pcbi.1004814.g007" target="_blank">Fig 7</a>, except that no exogenous source of <i>F</i> was provided, higher values of the <i>ϕ</i>/<i>γ</i> ratio were used, and the initial shape of the BM was perturbed by the addition of a small amount of “noise”, creating a slightly rough contour (see section 7 of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004814#pcbi.1004814.s002" target="_blank">S1 Text</a> for details). Under such conditions, small inhomogeneities in levels of endogenous <i>F</i> and <i>G</i> near the BM lead to spontaneous and sustained finger growth. In the first two rows (panels A-G and H-N), <i>ϕ</i> = 3.0 and <i>γ</i> = 5.0 (thus <i>ϕ</i>/<i>γ</i> = 0.6), but different noisy initial conditions were used. The third row (O-U) starts from the same initial conditions as H-N, but with <i>ϕ</i> = 3.5 and <i>γ</i> = 5.0 (thus <i>ϕ</i>/<i>γ</i> = 0.7). Panels A-C, H-K and O-Q show the progress of finger growth, shaded as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004814#pcbi.1004814.g007" target="_blank">Fig 7</a>, at the indicated times (numbers of CP cell cycles). The scale bar shows five times the characteristic decay lengths of <i>F</i> and <i>G</i>. To facilitate quantitative analysis of these simulations, BM heights were measured as a function of relative position along the BM contour arc length. In panels D, K and R, these measurements are plotted for every other cell cycle from the start to the end of the simulation. Fourier transforms were used to identify the power spectra (power as a function of spatial frequency) of these graphs, and the evolution of such spectra over time was summarized in the form of kymographs, shown in E, L and S, in which intensity at different frequencies is displayed via a heat map, and time is on the ordinate axis. Panels F,G,M,N,T, and U are periodograms—essentially excerpts from these kymographs at single time points—at the end (F, M, T) or beginning (G, N, U) of the simulations, with power displayed on the ordinate axis (units of dB). In all cases, the results show that dominant frequencies present in the noisy initial conditions (arrowheads at the bottoms of kymographs E, L and S) quickly become replaced by lower frequency components (arrowheads at the top of kymographs E, L and S; dominant frequencies are also shown as dashed red lines in F-G, M-N and T-U). <b>V-W</b>. Results from the three cases presented in A-U and 21 additional independent simulations, initiated from a variety of noisy initial conditions with a range of initial frequency components and <i>ϕ</i>/<i>γ</i> values (see section 7 of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004814#pcbi.1004814.s002" target="_blank">S1 Text</a>), were analyzed by plotting spectral moment (V) and average power across all frequencies (W), as a function of time (spectral moment is an aggregate measurement that captures the frequency at which power is “centered”). All simulations show a similar pattern: during the first two CP cell cycles, average power declines as most of the noise in the initial conditions is averaged away (in the inset in V, a logarithmic axis is used to show the pruning of both low and high frequencies; <i>ϕ</i>/<i>γ</i> = 0.6 for these cases). Afterwards, power centered on a low frequency band increases continually, reflecting the elongation of fingers of relatively constant width. The subset of cases in panel W in which power grows more rapidly are those for which <i>ϕ</i>/<i>γ</i> = 0.7, as opposed to 0.6. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004814#pcbi.1004814.s001" target="_blank">S1 Table</a> for a complete list of parameter values.</p

Summary of possible behaviors with feedback when <i>p</i> > 0.5.

<p>This table summarizes possible steady state and final state behaviors when maximal progenitor self-renewal is greater than 0.5. Without feedback, the open loop system’s output is largely dependent on <i>p</i>, the probability that a progenitor cell will divide into an identical cell type instead of a differentiated cell type. Negative feedback eliminates this dependence on <i>p</i>, but such systems can only reach a single fixed point in both the steady and final state scenarios. Positive feedback, on the other hand, permits unbounded growth, which would be detrimental to achieving precision in tissue and organ growth. Together, however, lineages can growth to one of two distinct fixed points, which are either bistable (in homeostatic equilibrium) or bi-modal (i.e. stationary and non-dynamic).</p

Final-state analysis of the two-stage lineage.

<p>When cell death is negligible, lineages with negative feedback on progenitor self-renewal <b>(A)</b> eventually reach a final state for <i>χ</i>₁ <b>(B)</b> that must lie either below or above a “growth leap” region. The bounds on this region (denoted <i>χ</i>₁^{<i>critlow</i>} and <i>χ</i>₁^{<i>crithigh</i>}), are the values of <i>χ</i>₁ at which <i>χ</i>₀' changes sign. As shown in <b>(C),</b> for initial values <i>χ</i>₁(0) below <i>χ</i>₁^{<i>critlow</i>} (blue) or above <i>χ</i>₁^{<i>crithigh</i>} (red), SC numbers (<i>χ</i>₀) necessarily shrink monotonically; otherwise <i>χ</i>₀ grows transiently (green line) and then shrinks to zero. <b>(D)</b> Whether a growth leap occurs is determined by the initial values of both <i>χ</i>₀ and <i>χ</i>₁. Here the presence of a growth leap is manifested as a large net increase in total cell number of cells. For small enough initial values of <i>χ</i>₀, such a leap occurs as in panel B, when initial <i>χ</i>₁ values lie between <i>χ</i>₁^{<i>critlow</i>} and <i>χ</i>₁^{<i>crithigh</i>} (denoted by red planes). For larger initial values of <i>χ</i>₀ however, the growth leap regime can be accessed at initial values of <i>χ</i>₁ below <i>χ</i>₁^{<i>critlow</i>}. Parameter values for panels B—D are <i>p</i> = 0.8, <i>ϕ</i> = 0.05, and <i>γ</i> = 0.002. The initial conditions in B were <i>χ</i>₁(0) = 20, 120, and 260, with <i>χ</i>₀(0) = 1, as shown in C.</p

Feedback, Lineages and Self-Organizing Morphogenesis

<div><p>Feedback regulation of cell lineage progression plays an important role in tissue size homeostasis, but whether such feedback also plays an important role in tissue morphogenesis has yet to be explored. Here we use mathematical modeling to show that a particular feedback architecture in which both positive and negative diffusible signals act on stem and/or progenitor cells leads to the appearance of bistable or bi-modal growth behaviors, ultrasensitivity to external growth cues, local growth-driven budding, self-sustaining elongation, and the triggering of self-organization in the form of lamellar fingers. Such behaviors arise not through regulation of cell cycle speeds, but through the control of stem or progenitor self-renewal. Even though the spatial patterns that arise in this setting are the result of interactions between diffusible factors with antagonistic effects, morphogenesis is not the consequence of Turing-type instabilities.</p></div

Shear-stress-mediated refolding of proteins from aggregates and inclusion bodies.

Recombinant protein overexpression of large proteins in bacteria often results in insoluble and misfolded proteins directed to inclusion bodies. We report the application of shear stress in micrometer-wide, thin fluid films to refold boiled hen egg white lysozyme, recombinant hen egg white lysozyme, and recombinant caveolin-1. Furthermore, the approach allowed refolding of a much larger protein, cAMP-dependent protein kinase A (PKA). The reported methods require only minutes, which is more than 100 times faster than conventional overnight dialysis. This rapid refolding technique could significantly shorten times, lower costs, and reduce waste streams associated with protein expression for a wide range of industrial and research applications