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A Reaction-Diffusion Network model predicts a dual role of Cactus/IκB to regulate Dorsal/NFκB nuclear translocation in Drosophila

18 Jan 2020-bioRxiv (Cold Spring Harbor Laboratory)-
TL;DR: A predictive model based on a reaction-diffusion regulatory network considers non-uniform Toll activation as well as Toll-dependent Dl nuclear import and Cact degradation and indicates that the dual role of Cact depends on targeting distinct Dl complexes along the dorsal-ventral axis.
Abstract: Dorsal-ventral patterning of the Drosophila embryo depends on the NF{kappa}B superfamily transcription factor Dorsal (Dl). Toll receptor activation signals for degradation of the I{kappa}B inhibitor Cactus (Cact), leading to a ventral-to-dorsal nuclear Dl gradient. Cact is critical for Dl nuclear import, as it binds to and prevents Dl from entering the nuclei. Quantitative analysis of cact mutants revealed an additional Cact function to promote Dl nuclear translocation in ventral regions of the embryo. To investigate this dual Cact role, we developed a predictive model based on a reaction-diffusion regulatory network. This network considers non-uniform Toll activation as well as Toll-dependent Dl nuclear import and Cact degradation. In addition, it incorporates translational control of Cact levels by Dl, a Toll-independent pathway for Cact regulation and reversible nuclear-cytoplasmic Dl flow. Our model successfully reproduces wild-type data and emulates the Dl nuclear gradient in mutant dl and cact allelic combinations. Our results indicate that the dual role of Cact depends on targeting distinct Dl complexes along the dorsal-ventral axis: In the absence of Toll activation, free Dl-Cact trimers inhibit direct Dl nuclear entry; upon ventral-lateral Toll activation, Dl-Cact trimers are recruited into predominant signaling complexes and promote active Dl nuclear translocation. Simulations suggest that Toll-independent regulatory mechanisms that target Cact are fundamental to reproduce the full assortment of Cact effects. Considering the high evolutionary conservation of these pathways, our analysis should contribute to understand NF{kappa}B/c-Rel activation in other contexts such as in the vertebrate immune system and disease.

Summary (2 min read)

INTRODUCTION

  • In a developing organism, tissues are often patterned by long-range and spatially graded signaling factors called morphogens, which carry the positional information necessary to control gene expression.
  • Dl acts in a concentration-dependent manner to activate or repress target genes, defining three main territories of the embryo DV axis: the ventral mesoderm, lateral neuroectoderm, and dorsal ectoderm (Rushlow and Shvartsman, 2012).
  • In the absence of Toll signals, Cact binds to Dl and impairs its nuclear translocation (Bergmann et al., 1996).
  • Therefore, these analyses suggest that the establishment of the nDl gradient is a complex process yet to be fully understood.

A reaction-diffusion model that discriminates two routes for Dorsal nuclear localization

  • Highlights the distinctive contribution of Toll-activated versus free Dl flow to the nDl gradient Embryonically translated from maternal mRNAs deposited in the egg, Dl protein enters the nucleus through two different mechanisms: actively imported upon degradation of the Cact inhibitor by Toll signals, and by direct flow in and out of the nucleus (DeLotto et al., 2007).
  • This genotype shows two opposing effects reproduced by the model: a decrease in nDl in the ventral region and an increase in the lateral and dorsal regions of the embryo (Fig. 4A).
  • By analyzing direct and Toll dependent Dl nuclear entry modes separately the authors found that both are affected, albeit differently, by reducing Cact levels (Fig. 4C).
  • The model shows that lowering Cact levels in a dl[6]/+ background produces an additional impact in Dl nuclear translocation in the most ventral region and confirms that Cact has a positive role on Dl nuclear localization.
  • The dual effect of Cact reduction is no longer observed (compare Fig. 5A and Fig. 4B).

DISCUSSION

  • Cactus plays a positive role for Dl nuclear transport by controlling the levels of Tollresponsive Dorsal-Cactus complexes.
  • In this case less Cactus results in less DlC +.
  • DlCT complexes and consequently, contrary to the previous model, less Toll-induced Dorsal entry into the nuclei whenever the balance between Toll signals and availability of new DlC + DlCT signaling complexes is perturbed.
  • Therefore, alterations in DlC affect differently the two Dl nuclear translocation routes.
  • Thus, diffusive dynamics throughout the cytoplasm dominates the kinetics of cDl0, leading to uniform free Dorsal throughout the embryo, even though total nuclear Dl obeys a gradient.
  • The authors found an opposite behavior for the DorsalCact complex, which is not as diffusible as the free forms.

A conserved regulatory network for Cactus/IκB function

  • Toll was initially described in Drosophila embryos as a maternal effect allele regulating DV patterning (Anderson et al., 1985b).
  • It has been suggested that the function of Toll to pattern the DV axis is restricted to the insect lineage, while regulating the innate immune response is an ancient and widespread function (Benton et al., 2016; Lynch and Roth, 2011).
  • Furthermore, calcium-dependent Calpain proteases also target mammalian IκB independent of Toll receptors (Schaecher et al., 2004; Shen et al., 2001; Shumway et al., 1999), as reported for Cact in the embryo and immune system (Fontenele et al., 2009; Fontenele et al., 2013).
  • Unlike Drosophila, vertebrates rely on several IκB proteins, where the final effect on the immune response over time is a result of the compounded effect of three or more IκBs (Kearns et al., 2006).
  • Altogether, the results herein presented credit to IκB/Cact protein a key role in NFκB activity greater than previously reported.

METHODS

  • Mathematical modeling of Dl nuclear gradient formation.
  • The proposed reaction-diffusion model is a refinement of (Kanodia et al., 2009), in which the authors described Dl and Cact dynamics by a reaction-diffusion regulatory network along a 1D spatial domain that represents embryo’s outline in a dorsal-to-ventral cross section.
  • Here the authors expanded this model to take into account the translational control of Cact levels by Dl protein and the two different routes for Dorsal nuclear localization.
  • In addition to participating in the reactions, Fig. 1, some of the proteins can diffuse along the compartments.
  • Further details about the resulting differential equations are displayed in Supplementary Text.

Model calibration and simulation

  • The authors set up an optimization problem such that the objective function is the quadratic loss where the model total nuclear Dl (the sum of nDl0 and nDl*) was compared to experimental nuclear Dorsal data.
  • For each individual in the Genetic Algorithm population, which corresponds to a set of parameters to be evaluated and ranked by the objective function, the authors have solved the PDEs by doing a second-order central approximation to deal with spatial coordinates, giving rise to an ODE system for each compartment.
  • After running the program and finding out an optimized set of parameters, the mutant simulations have been done by changing specific parameters and comparing the newer simulations with determined set of experimental data (Cardoso et al., 2017).
  • Further details about the equations, GA’s parameters and other specifications can be found in Supplementary Text.

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Figures (8)

Content maybe subject to copyright    Report

1
A Reaction-Diffusion Network model predicts a dual role of Cactus/IκB to
regulate Dorsal/NFκB nuclear translocation in Drosophila
1
Barros, C.D.T.,
2,3
Cardoso, M.A.,
2
Bisch, P.M.,
3,*
Araujo, H.M.,
4,*
Lopes, F.J.P.
1
Laboratório Nacional de Computação Científica (LNCC), Petrópolis, Brasil.
2
Laboratório de Física Biológica, Instituto de Biofísica Carlos Chagas Filho (IBCCF),
Universidade Federal do Rio de Janeiro (UFRJ) - Rio de Janeiro, Brasil
3
Laboratório de Biologia Molecular do Desenvolvimento, Instituto de Ciências Biomédicas,
Universidade Federal do Rio de Janeiro (UFRJ), Centro de Ciências da Saúde - Rio de
Janeiro, Brasil
4
Grupo de Biologia do Desenvolvimento e Sistemas Dinâmicos, Campus Duque de Caxias
Professor Geraldo Cidade, Universidade Federal do Rio de Janeiro (UFRJ) – Duque de
Caxias, Brasil
* corresponding authors (haraujo@histo.ufrj.br; flopes@ufrj.br)
Keywords: NFkappaB, Dorsal gradient, morphogen, mathematical model, Toll
Running title: Cactus reaction-diffusion network
(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted January 18, 2020. ; https://doi.org/10.1101/2020.01.18.909416doi: bioRxiv preprint

2
ABSTRACT
Dorsal-ventral patterning of the Drosophila embryo depends on the NFκB superfamily
transcription factor Dorsal (Dl). Toll receptor activation signals for degradation of the IκB
inhibitor Cactus (Cact), leading to a ventral-to-dorsal nuclear Dl gradient. Cact is critical for Dl
nuclear import, as it binds to and prevents Dl from entering the nuclei. Quantitative analysis of
cact mutants revealed an additional Cact function to promote Dl nuclear translocation in
ventral regions of the embryo. To investigate this dual Cact role, we developed a predictive
model based on a reaction-diffusion regulatory network. This network considers non-uniform
Toll activation as well as Toll-dependent Dl nuclear import and Cact degradation. In addition,
it incorporates translational control of Cact levels by Dl, a Toll-independent pathway for Cact
regulation and reversible nuclear-cytoplasmic Dl flow. Our model successfully reproduces
wild-type data and emulates the Dl nuclear gradient in mutant dl and cact allelic combinations.
Our results indicate that the dual role of Cact depends on targeting distinct Dl complexes
along the dorsal-ventral axis: In the absence of Toll activation, free Dl-Cact trimers inhibit
direct Dl nuclear entry; upon ventral-lateral Toll activation, Dl-Cact trimers are recruited into
predominant signaling complexes and promote active Dl nuclear translocation. Simulations
suggest that Toll-independent regulatory mechanisms that target Cact are fundamental to
reproduce the full assortment of Cact effects. Considering the high evolutionary conservation
of these pathways, our analysis should contribute to understand NFκB/c-Rel activation in
other contexts such as in the vertebrate immune system and disease.
(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted January 18, 2020. ; https://doi.org/10.1101/2020.01.18.909416doi: bioRxiv preprint

3
INTRODUCTION
In a developing organism, tissues are often patterned by long-range and spatially
graded signaling factors called morphogens, which carry the positional information necessary
to control gene expression. Morphogens act in a concentration-dependent manner to activate
or repress target genes (Driever and Nusslein-Volhard, 1988; Lopes et al., 2008; Roth et al.,
1991; Struhl et al., 1989). Therefore, precisely defining the amount of activated morphogen is
crucial to determining their effects. In the Drosophila syncytial blastoderm, dorsal-ventral (DV)
patterning depends on the nuclear localization gradient of Dorsal (Dl), a NFκB superfamily
transcription factor homologous to mammalian c-Rel. Dl acts in a concentration-dependent
manner to activate or repress target genes, defining three main territories of the embryo DV
axis: the ventral mesoderm, lateral neuroectoderm, and dorsal ectoderm (Rushlow and
Shvartsman, 2012). A ventral-to-dorsal activity gradient of the Toll cell surface receptor
provides the activating signal for DV patterning. Dl nuclear translocation is controlled by
Cactus (Cact), a cytoplasmic protein related to mammalian IκB. In the absence of Toll signals,
Cact binds to Dl and impairs its nuclear translocation (Bergmann et al., 1996). Activated Toll
receptors on the ventral and lateral regions of the embryo lead to Cact phosphorylation
followed by ubiquitination and degradation, resulting in dissociation of the Dl-Cact complex
and Dl nuclear import. Different Dl levels subdivide the embryonic DV axis in target gene
expression domains, defined by distinct thresholds of sensitivity to control by Dl (Stein and
Stevens, 2014). Thus, the amount of Dl in the nuclei is key to defining ventral, lateral and
dorsal territories of the embryo.
In attempts to explain the complex Dl regulatory signaling network, mathematical
models were developed to simulate the Dl nuclear gradient. Early models simulated gradient
profiles throughout nuclear division cycles 10 to 14 in wild-type embryos, with parameters
(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted January 18, 2020. ; https://doi.org/10.1101/2020.01.18.909416doi: bioRxiv preprint

4
constrained by experimental data from endogenous nuclear Dl (nDl) levels in fixed embryos
or live imaging of Dl-GFP (Kanodia et al., 2009; Liberman et al., 2009). Their results showed
that the nuclear Dl gradient is dynamic, increasing in amplitude from cycle 10 to cycle 14,
without significantly changing its shape. Subsequently, it was shown that both the nDl
gradient amplitude and basal levels oscillate throughout early embryonic development
(Reeves et al., 2012). Recently, it was proposed that facilitated diffusion along the DV axis, or
“shuttling” via Dl-Cact complexes, plays a role in nDl gradient formation (Carrell et al., 2017).
Therefore, these analyses suggest that the establishment of the nDl gradient is a complex
process yet to be fully understood.
Former initiatives modeling the nDl gradient focused predominantly on processes
regulated by Toll. However, several proteins that impact Dl nuclear localization act
independent of Toll-receptor activation. For instance, adaptor proteins that are required to
transduce Toll signals, such as Tube, Pelle and Myd88, form pre-signaling complexes that
depend on the interaction with cytoskeletal elements (Edwards et al., 1997; Galindo et al.,
1995; Towb et al., 1998) and the membrane (Ji et al., 2014; Marek and Kagan, 2012). In
addition, alterations in Cact concentration and Calpain A protease activity perturb the nDl
gradient (Fontenele et al., 2013; Roth et al., 1991). Dl itself can flow into and out of the
nucleus in the absence of Toll (Carrell et al., 2017; DeLotto et al., 2007), with the potential to
contribute significantly to nDl concentration. Since Cact plays a critical role on the control of
Dl nuclear translocation, understanding how Cact is regulated is paramount.
Two pathways have been reported to regulate Cact levels: the Toll dependent
pathway, considered in all the models to date, that leads to Cact N-terminal phosphorylation
and degradation through the proteasome, and a Toll-independent pathway that targets Cact
C-terminal sequences for phosphorylation (Belvin et al., 1995). This originally termed "signal
independent pathway for Cact degradation" (Belvin et al., 1995; Bergmann et al., 1996; Liu et
(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted January 18, 2020. ; https://doi.org/10.1101/2020.01.18.909416doi: bioRxiv preprint

5
al., 1997; Reach et al., 1996) acts in parallel to Toll-induced signaling (Moussian and Roth,
2005). However, several reports indicate that the signal-independent pathway is regulated by
Casein kinase II (Liu et al., 1997; Packman et al., 1997), the BMP protein encoded by
decapentaplegic (Araujo and Bier, 2000; Carneiro et al., 2006) and by the calcium-dependent
modulatory protease Calpain A (Fontenele et al., 2009). Moreover, Calpain A generates a
Cact fragment that is more stable than full-length Cact (Araujo et al., 2018; Fontenele et al.,
2013), indicating that the Toll-independent pathway may perform unexplored roles in nDl
gradient formation.
Recently, by analyzing the effects of a series of cact and dorsal (dl) loss-of-function
alleles, we detected a novel function of Cact to promote Dl nuclear translocation. In addition
to inhibiting Dl nuclear import, Cact also acts to favor Dl nuclear translocation where Toll
signals are high (Cardoso et al., 2017). However, the mechanism behind this effect is unclear.
Since previous mathematical models for Dl gradient formation did not encompass the two
mechanisms that regulate Cact function, here we propose a new reaction-diffusion model to
describe this signaling network. We take into account non-uniform activation of Toll as in
current models, two Dl nuclear translocation mechanisms, translational regulation of Cact by
Dl (Govind et al., 1993; Kubota and Gay, 1995) and the two pathways leading to Cact
regulation: the Toll-regulated and Toll-independent pathways. Using a Genetic Algorithm and
experimental data from wild-type Drosophila embryos, we calibrate the model parameters,
such as kinetic constants, diffusion coefficients, Toll activation profile and total Dorsal
concentration in the embryo. The optimized parameters are then used to reproduce and
understand the nDl patterns of single and double mutants for cactus and dorsal genes. Our
model analysis indicates that, in the ventral region, Cact favors Dl nuclear translocation by the
formation of Toll-responsive Dl-Cact complexes that signal to Dl nuclear localization, while
throughout the entire embryo Cact binds to and prevents free Dl from entering the nuclei.
(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted January 18, 2020. ; https://doi.org/10.1101/2020.01.18.909416doi: bioRxiv preprint

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Frequently Asked Questions (1)
Q1. What are the contributions in "A reaction-diffusion network model predicts a dual role of cactus/iκb to regulate dorsal/nfκb nuclear translocation in drosophila" ?

Barros et al. this paper showed that the nuclear Dl gradient is dynamic, increasing in amplitude from cycle 10 to cycle 14, without significantly changing its shape.