Fig 1.
PI3K → AKT1 signaling is regulated by multiple layers of negative feedback that fine-tune its control of growth, cell cycle commitment and survival.
(A) Feed-forward network of interactions from growth receptors to PI3K and AKT1 (detailed description of molecular mechanisms in Methods & Model). Box 1: AKT1 activates the mTORC1 pathway, driving volume growth; box 2: AKT1 blocks the GSK3β pathway responsible for dampening cell cycle entry and survival signaling; box 3: AKT1 blocks the FoxO transcription factors that drive expression of anti-proliferative and pro-apoptotic genes; box 4: AKT1 promotes cell survival by keeping the pro-apoptotic protein BAD in check. (B) The mTORC1 pathway feeds back to dampen PI3K → AKT1 signaling by mediating the degradation of insulin receptor substrates (red arrows), aiding the cytoplasmic translocation of PTEN (purple arrows) and dampening mTORC2 activation (orange arrows).
Fig 2.
Two hypothesized negative feedback loops control degradation and re-synthesis of PI3K and AKT1 signaling.
(A) Degradation of the PI3K subunit p110 may be driven by the PLCγ-dependent activation of the NEDDL4 ubiquitin ligase (red links); re-synthesis of p110 may be driven by FoxO3, which re-enters the nucleus following p110 degradation, as AKT1 activity falls (orange link). (B) Growth Signaling Module of our Boolean model, including the degradation/re-synthesis circuit in control of p110 expression (left, dark green), basal PI3K/AKT1 signaling (middle), downstream effectors of AKT1 (mTORC1 signaling, GSK3 & FoxO1, bottom), and the MAPK cascade (right). Black →: activation; red ⊣: inhibition; thick red links: p110 degradation; thick orange loop: p110 re-synthesis. (C) Periphery: sequence of network states along the synchronous limit cycle of the core PI3K circuit. Orange/blue borders: ON (expressed and/or active) / OFF (not expressed and/or inactive) node. Middle: state transition graph of the general asynchronous model (one random node updated per timestep; sampled for 10,000 steps), yielding a complex limit cycle that follows the synchronous cycle. Node size: visitation frequency; label: most similar synchronous cycle state; node color: overlap of similar synchronous cycle state (one minus normalized Hamming distance); layout: Kamada-Kawai algorithm (NetworkX [67], Python). (D) Overlap of states along a general asynchronous update trajectory (y axis) with each attractor state along the synchronous limit cycle (x axis). Time-step: update of a single random node.
Fig 3.
Modular Boolean model reproduces the expected quiescent, apoptotic, and cell cycle phenotypes in various extracellular environments.
(A) Stable attractor states of isolated regulatory switches. Blue / light brown / purple / dark red boxes: stable states of the Restriction / Origin of Replication Licensing / Phase / Apoptotic Switch. Orange / blue node border: ON / OFF state. (B) Network representation of the Boolean model partitioned into regulatory switches and processes. Gray: inputs representing environmental factors; green: Growth Signaling; dark red: Apoptotic Switch; light brown: Origin of Replication Licensing Switch; blue: Restriction Switch; purple: Phase Switch; orange: cell cycle processes and molecules that bridge between the multi-stable modules. Black →: activation; red ⊣: inhibition. (C) Cell phenotypes predicted for every combination of no/low/high growth-factor (x axis) and Trail exposure (y axis). The network-wide ON/OFF states of each attractor and the molecular signatures that define their phenotypes are detailed in S2 Table. Blue fragmented cell: apoptotic states (#1–6); gray elongated cell: quiescent/non-dividing states (#7–8); cell with mitotic spindle: cell undergoing repeated cycles (#9). Yellow circle around nucleus: 4N DNA content; double-/single-headed arrows between cells: reversible/ irreversible phenotypic transitions in response to changing environments; green arrow: change in growth factor levels; red: change in Trail exposure. Image credits: apoptotic cell [78]; quiescent cell: https://en.wikipedia.org/wiki/Cell_culture#/media/File:HeLa_cells_stained_with_Hoechst_33258.jpg; mitotic spindle: https://en.wikipedia.org/wiki/Cell_division#/media/File:Kinetochore.jpg.
Table 1.
Model attractors reproduce experimentally observed cell phenotypes.
Fig 4.
Module-level switches toggle each other to generate the cell cycle, locking PI3K oscillations to the rhythm of division.
Dynamics of regulatory molecule expression / activity during cell cycle entry from G0, showcasing the phase-locking of PI3K oscillations to the cell cycle. X-axis: time-steps; y-axis: nodes of the model organized in modules; orange/blue: ON/OFF; white boxes & arrows: first two peaks of AKT1 activation with respect to DNA replication; black dashed lines: cytokinesis; lime arrows: first AKT1-high pulse in each division cycle.
Fig 5.
The cycling regulatory cascades of cell division are robust under biased asynchronous update.
(A) Dynamics of regulatory molecule expression / activity during cell cycle entry from G0 using biased asynchronous update. X-axis: time-steps; y-axis: nodes organized in modules; orange/blue: ON/OFF. (B) Occurrence rate of normal cell cycle completion (mustard), G2 → G1 reset followed by genome duplication (purple), aberrant mitosis followed by genome duplication (turquoise), failed cytokinesis followed by genome duplication (blue) and apoptosis (dark red) per 100 timesteps, shown as stacked bar charts for increasing growth factor / Trail exposure (left/right) with random order asynchronous / biased asynchronous / synchronous update (top/middle/bottom).
Table 2.
Model reproduces experimentally documented dynamical behaviors.
Fig 6.
Plk1 inhibition at different points along the cell cycle can cause G2 arrest, mitotic catastrophe, aberrant mitosis, or failure of cytokinesis.
(A-D) Top: (A) Molecular mechanism leading to G2 arrest via Plk1 knockdown before the start of prometaphase due to a lack of Cdk1 activation; (B) mitotic catastrophe and apoptosis via Plk1 knockdown in prometaphase or early metaphase due to concurrent Casp2 activation and deactivation of the antiapoptotic BCL2 family; (C) aberrant (premature) anaphase and no cytokinesis via Plk1 knockdown later in metaphase due to premature APC/CCdh1 activation, and (D) normal anaphase but no cytokinesis via Plk1 knockdown post SAC passage due to loss of Plk1H in telophase. Orange/blue background: higher/lower than normal activity; gradient background: premature node transition; no background: other relevant node / process; →: activation; ⊣: inhibition. Bottom: Dynamics of expression / activity of Phase Switch, Cell cycle processes and Apoptotic Switch nodes in cells exposed to Plk1 inhibition at different stages of the cell cycle. X-axis: time-steps; y-axis: nodes of the model organized in modules; orange: ON (expressed and/or active); blue: OFF (not expressed and/or inactive); black: OFF, forcibly inhibited. Black dashed line: timing of Plk1 inhibition; white pathways: processes that initiate apoptosis (B), premature anaphase (C), or failed cytokinesis (D); red box & bar: telophase/G1 in the absence of cytokinesis, followed the next round of DNA synthesis; lime green line: point of normal APC/CCdh1 activation, marking the end of the Plk1 inhibition window that can compromise cytokinesis (D); only relevant module activity is shown (full dynamics available in S1 File).
Table 3.
Model reproduces the experimentally documented effects of Plk1 knockdown and p110/PI3K/AKT1 over-expression / hyperactivity.
Fig 7.
The strength of Plk1 inhibition sets the relative prominence of cell cycle failure modes.
Stacked bar charts showing the relative occurrence of normal cell cycle completion (mustard), G2 → G1 reset followed by genome duplication (purple), aberrant mitosis followed by genome duplication (turquoise), failed cytokinesis followed by genome duplication (blue) and apoptosis (dark red) relative to the rate of cell cycle in wild-type cells (black dashed line) at growth factor exposure of 40%, 60% and 80% in Plk1-deficient cells using synchronous (top) and biased asynchronous update (bottom).
Fig 8.
p110 degradation in G2 is required for cytokinesis.
(A) Top: Molecular mechanism leading to the failure of cytokinesis in the presence of non-degradable p110H. Blue background: lower than normal activity; no background: other relevant node / process; →: activation; ⊣: inhibition. Bottom: Dynamics of regulatory molecule activity during the transition from cell cycle to telophase, then genome duplication upon expression of non-degradable p110 (yellow). X-axis: time-steps; y-axis: nodes of the model organized in modules; orange/blue: ON/OFF; yellow: ON, forcibly expressed; white arrows & nodes: factors driving Plk1 expression and lack of Plk1H accumulation; red arrows & box: failure of cytokinesis followed by G1 in bi-nucleated cells; only relevant module activity is shown (full dynamics available in S1 File). (B-C) Relative occurrence of normal cell cycle completion (mustard) vs. genome duplication following failed cytokinesis (blue) relative to the rate of cell cycle in wild-type cells (stacked bar charts) at 80% growth factor exposure in cells with non-degradable p110H (top), non-degradable p110H + active PI3KH (middle) and hyperactive AKTH (bottom). Modeled using synchronous (B) and biased asynchronous update (C).
Fig 9.
Summary of the molecular mechanisms that link PI3K hyperactivity to attenuated Plk1 expression and failure of cytokinesis.
(A) Degradation and re-synthesis of the PI3K subunit p110 is driven by PLCγ-dependent activation of the NEDDL4 (red links) and FoxO3 (orange link), respectively. During G2, loss of strong PI3K / AKT1 signaling is required for nuclear translocation of FoxO3 and/or FoxO1, which aids Plk1 accumulation to levels that can outlast its degradation in anaphase (modeled via the Plk1H node). During telophase this remaining pool of Plk1 localizes to the central spindle and promotes the assembly of a contractile ring by recruiting the RhoA GEF Ect2. Red nodes: key pathway linking PI3K and AKT1 dynamics to Plk1 and cytokinesis. (B) Plk1 inhibition at different points along the cell cycle leads to four distinct failure modes. Image credits: https://commons.wikimedia.org/wiki/File:Mitosis_cells_ sequence.svg.