Fig 1.
A conceptual summary of our model of anterior-posterior axis control in planaria regeneration.
We hypothesize morphogens to be transported on a vector field coincident with neuronal axons (A), with hypothesized transport polarity as shown in (B). We further hypothesize that vector transport of morphogens occurs on aligned microtubule arrays in nerve axons (C, D). A regulatory network (E) integrates molecular-genetic interactions with vector transport in nerves to produce stable, self-assembling morphogen gradients consistent with planarian body-plan in homeostasis (F), and capable of responding to cutting event perturbations to establish new gradients (G). Head and tail regeneration are assumed to be related to concentrations of ERK and β-Cat, respectively (F, G, H). The percentage of regenerated heteromorphoses in a population was estimated from steady-state ERK and β-Cat gradients after cutting (G), where average morphogen concentration at wound edges (G ii, and iii) were used to define the probability of the blastema developing into a head or tail (G, H) using a Markov Chain Model for Regeneration (see text and Fig 3 for details). Head (G, transition ‘i’) and tail (G, transition ‘iv’) regions existing on a fragment prior to cutting were assumed to be terminally differentiated, and to therefore remain as head or tail in the regenerated fragment. In the regulatory network of E, blue lines with circular endpoints represent activating interaction, whereas red lines with flat-line ends represent an inhibitory relationship. Kinesin symbol on Hedgehog node, and dynein symbol on NRF, signify proposed transport of the respective factors. Hh—Hedgehog, Ptc—Patched, Wnt—Wingless/integrated (Wnt1 and Wnt11 combined), β-Cat—β-Catenin, ERK—extracellular-signal regulated kinase, cAMP—cyclic adenosine monophophate, NRF—Notum Regulating Factor.
Fig 2.
Planarian body-plan can be altered by a variety of treatments, which are also consistent with various steady-state outcomes of our computational model.
Heteromorphoses resulting from 10 different RNAi/pharmacological manipulations (A ‘i’ through ‘x’) are predicted by experimentally-consistent perturbations to our regulatory network model (A ‘i’ through ‘x’ and B). Experimentally-consistent model-predicted morphogen gradients are found for homeostasis (A, leftmost panel), normal wild-type regeneration (A, transition ‘o’), and interventions associated with abnormal posterior regeneration (head on the posterior to regenerate 2H, A, transition ‘i’ through ‘iii’), abnormal posterior regeneration (e.g. loss of tail, A ‘iv’), abnormal anterior regeneration (loss of head, A transitions ‘v’ to ‘viii’), or duplication of tail on the anterior (A, transition ‘ix’ and ‘x’). Specific sites of the regulatory network model where treatments ‘i’ through ‘x’ act as perturbations, are shown as yellow ellipses in (B). References to intervention outcomes are summarized in Table 1. In the regulatory network of B, blue lines with circular endpoints represent activating interaction, whereas red lines with flat-line ends represent an inhibitory relationship. Dark blue lines represent a proposed activation interaction induced by a pharmacological agent, whereas dark red arrows represent a proposed inhibition interaction induced by a pharmacological agent or RNAi. Dopamine 2 receptor—D2R, Serotonin 7 receptor—5HT7R.
Table 1.
A summary of gene products and chemical messengers that are known to alter regenerated planarian body-plan when inhibited by RNAi or pharmacological agents.
Table 2.
Summary of model predictions and their state of experimental validation.
Fig 3.
Key concepts underlying the Markov Chain Model of Regeneration used to predict regeneration outcomes from modeled steady-state morphogen concentrations averaged at the wound sites of the model.
Concentrations of key instructive morphogens (ERK and β-Cat) were sampled and averaged at each model cut line (A). The base Markov Chain assumed possible transitions of the blastema at the cutting site into a potential head or tail, with the additional case that failure to transition to head or tail represents a failed regeneration (B). Head, tail, or blastema (failed) probabilities were represented by pH, pT, and pB, respectively (B, C). Transition rates from blastema to head (αBH) were assumed to be increased by ERK concentrations at the wound (B, Eq 3), while transitions from blastema to tail (αBT) were assumed to be increased by β-Cat concentrations at the wound (B, Eq 4). Regeneration outcomes at cut-lines were calculated probabilistically, where existing head and tail remained unchanged on top and bottommost fragments (C). To determine the frequencies of heteromorphoses in a particular fragment appearing in a population of regenerates, the probabilities of each possible outcome at each cut line of the fragment were multiplied (D). The respective predicted fraction of heteromorphoses appearing in the population were inferred from the combinations shown in (D), where the possible heteromorphoses and their net probabilities are shown in (E).
Table 3.
Pharmacological agents explored in this work, including their dose, targets, replicates, relevant references, and effects on regenerated planarian morphology.
Fig 4.
Model predictions and experimental regenerative outcomes show matching trends for different fragments along the anterior-posterior axis under different cases.
For normal wild-type regeneration, the model predicts polarized gradients of ERK, β-Cat and Notum for each of the 5 cut fragments (A), which are predicted and found to regenerate as 100% 1H in each of the 5 cut fragments (0% 2H heteromorphoses). Partial (i.e. incompletely blocked) RNAi of β-Cat is predicted to show more morphogen gradient polarity disruption, and therefore more 2H regenerates, in fragments progressively closer to the head (B), a prediction that parallels experimental observations (D). In contrast, model perturbations inhibiting β-Cat stability (e.g. via decreased cAMP with bromocriptine treatment) are predicted to show more morphogen polarity disruption (C), and therefore, a higher frequency of 2H regenerates, in fragments cut closer to the tail (E). These modeling prediction trends are corroborated by experiment (D, E). Note that experimentally, the tail piece was only cut on one side and can consequently only regenerate as a 1H, as it only has one blastema.
Fig 5.
Unique cutting arrangements of 1H worms highlight the key role ventral nerve cords (VNC) play in directing regeneration outcomes.
Excised trunk fragments of planaria were cut with an additional incision to generate a long segment containing a VNC with backwards polarity (cuts shown as red dotted line on traced nerve map in A, and on synapsin stain in B), or with an inverted incision of the same pattern to generate a long, free segment containing a VNC with forwards polarity (red dotted line on traced nerve map in I, and on synapsin stain in J). Modeling-predicted morphogen gradients were consistent with the formation of a tail on the long, free segment for the backward-polarity VNC incision pattern (G, H), and head formation on the long, free segment for the forwards-polarity VNC cutting pattern (O, P). These predictions were a direct match to actual regeneration outcomes (N = 80/80). The backwards-polarity VNC (synapsin stains in C, D, E, and final body-plan in F) showed regeneration of a tail on the long, free segment, as predicted. The forwards-polarity VNC (synapsin stains in K, L, M, and final body-plan in N), showed regeneration of a head on the long, free segment, as predicted.
Fig 6.
The net nerve alignment in a fragment determines regenerated anterior-posterior axis, where fragments with initial axon orientation perpendicular to the original axis show 90° rotation of the regenerated anterior-posterior axis.
Synapsin stains of whole 1H worms (A) and hypothesized nerve polarity map traces with location of rectangular fragment cut regions are shown (B, G). The aspect ratio of all fragments was cut such that the longest side of the rectangular fragment corresponded with the original anterior-posterior axis. Rectangular fragments cut from the side margin of worms (B, with time-course of synapsin stains of fragments shown in C, D, and E) regenerated with anterior-posterior axis oriented perpendicular to the original axis (F), consistent with the fragment’s proposed net nerve polarity (B and C), an outcome which was observed in N = 94/94 replicates. In contrast, fragments of the same size and shape cut to include a portion of the ventral nerve cord (G, with time-course shown in H, I and J) regenerated as 1H worms with new axis corresponding to that of the original worm (K), an outcome observed in N = 103/103 replicates.
Fig 7.
Model-predicted morphogen gradients are consistent with experimentally-observed regeneration outcomes for a variety of cutting scenarios of 2H worms, supporting the vector transport hypothesis.
Planaria heteromophoses show organism-level polarities consistent with head number. In 1H worms (A), cilia flow vector fields (B) occur as monopolar gradients with flow directed away from the single head (B, C). In 2H worms (D) bipolar cilia flow fields were observed (E), which exhibit coordinated beat movement away from each of the two heads (F). From the bipolar cilia beat in 2H worms, we hypothesize a bipolar nervous system, where example synapsin stains of a whole 2H worm (F, G) and nerve polarity map trace (H) are shown. The white dotted line shows location of proposed line of symmetry at the midpoint between the two pharnyx for the bipolar 2H transport gradient (H), which is consistent with the observed location of cilia beat flow pattern symmetry in 2H worms. Panels I, J, K, L, M, and N show model-predicted steady-state ERK concentrations, where higher ERK levels are probabilistically associated with head outcomes (as shown in O). Cutting 2H worms showed experimental regeneration outcomes consistent with model predictions for a variety of cutting scenarios (I, J, K, L, M, N). A Chi2 test was used to compare model and experimental frequencies which showed corroboration between experiment and the model with p < 0.05.