Question: Which are the main functions of G3BP1 and G3BP2 proteins?

Context:
Both G3BP1 and G3BP2 contribute to stress granule formation
G3BP1, G3BP2 and CAPRIN1 are required for translation of interferon stimulated mRNAs and are targeted by a dengue virus non-coding RNA
We examined three conserved host RNA-binding proteins (RBPs) G3BP1, G3BP2 and CAPRIN1 in dengue virus (DENV-2) infection and found them to be novel regulators of the interferon (IFN) response against DENV-2
Ras-GTPase-activating protein SH3 domain-binding protein 1 (G3BP1) is a component of SGs that initiates the assembly of SGs by forming a multimer
Although single knockdown of either G3BP1 or G3BP2 in 293T cells partially reduced the number of SG-positive cells induced by arsenite, the knockdowns of both genes significantly reduced the number
like G3BP1, the overexpression of G3BP2 induced SGs even without stress stimuli
Collectively, these results suggest that both G3BP1 and G3BP2 play a role in the formation of SGs in various human cells and thereby recovery from these cellular stresses
Regulation of PMP22 mRNA by G3BP1 affects cell proliferation in breast cancer cells
G3BP has been reported to both stabilize and induce degradation of specific mRNAs
Global gene expression analyses of G3BP1- and G3BP2-depleted cells indicate that primarily G3BP1, and much less G3BP2, influences mRNA expression levels. Peripheral myelin protein 22 (PMP22) was one gene that was significantly influenced by G3BP1 depletion which led to a 2-3 fold increased expression
Depletion of PMP22 resulted in increased proliferation and the G3BP1-mediated effect on proliferation was not seen upon PMP22-depletion
Ras-GTPase-activating protein SH3 domain-binding proteins (G3BP) are overexpressed in various human tumors and participate in several signaling pathways involved in growth, differentiation and apoptosis
Two related proteins found in association with nsP4 at both times of infection, GTPase-activating protein (SH3 domain) binding protein 1 (G3BP1) and G3BP2 were also previously identified as associated with SINV nsP2 and nsP3. We demonstrate a likely overlapping role for these host factors in limiting SINV replication events
Modulation of p53 and MDM2 activity by novel interaction with Ras-GAP binding proteins (G3BP)
we have found that members of the Ras network of proteins, Ras-GTPase activating protein-SH3-domain-binding proteins 1 and 2 (G3BP1 and 2), bind to p53 in vitro and in vivo. Our data show that expression of G3BPs leads to the redistribution of p53 from the nucleus to the cytoplasm. The G3BP2 isoform additionally associated with murine double minute 2 (MDM2), a negative regulator of p53. G3BP2 expression resulted in significant reduction in MDM2-mediated p53 ubiquitylation and degradation. Interestingly, MDM2 was also stabilized in G3BP2-expressing cells and its ability to ubiquitylate itself was compromised
We identified several proteins, including DDX6, G3BP1, G3BP2, Caprin1, and USP10, implicated in P body (PB) and stress granule (SG) function, and not previously known to bind DENV RNAs.
Additional experiments demonstrate that, in contrast to DDX6, the SG proteins G3BP1, G3BP2, Caprin1 and USP10 bind to the variable region (VR) in the 3' UTR.
G3BP1, G3BP2 and CAPRIN1 are required for translation of interferon stimulated mRNAs and are targeted by a dengue virus non-coding RNA.
Both G3BP1 and G3BP2 contribute to stress granule formation.
Although single knockdown of either G3BP1 or G3BP2 in 293T cells partially reduced the number of SG-positive cells induced by arsenite, the knockdowns of both genes significantly reduced the number. 
Collectively, these results suggest that both G3BP1 and G3BP2 play a role in the formation of SGs in various human cells and thereby recovery from these cellular stresses.
Furthermore, expression of shRNA targeting either G3BP1 or G3BP2 in human cancer cell lines resulted in marked upregulation of p53 levels and activity. 
Ras-GTPase-activating protein SH3 domain-binding protein 1 (G3BP1) is a component of SGs that initiates the assembly of SGs by forming a multimer.
Although single knockdown of either G3BP1 or G3BP2 in 293T cells partially reduced the number of SG-positive cells induced by arsenite, the knockdowns of both genes significantly reduced the number.
Moreover, like G3BP1, the overexpression of G3BP2 induced SGs even without stress stimuli.
We found that HDAC6 interacts with another SG protein, G3BP (Ras-GTPase-activating protein SH3 domain-binding protein 1), and localizes to SGs under all stress conditions tested.
Dengue virus (DENV) is a rapidly re-emerging flavivirus that causes dengue fever (DF), dengue hemorrhagic fever (DHF) and dengue shock syndrome (DSS), diseases for which there are no available therapies or vaccines.  The DENV-2 positive-strand RNA genome contains 5' and 3' untranslated regions (UTRs) that have been shown to form secondary structures required for virus replication and interaction with host cell proteins.  In order to comprehensively identify host cell factors that bind the DENV-2 UTRs, we performed RNA chromatography, using the DENV-2 5' and 3' UTRs as "bait", combined with quantitative mass spectrometry.  We identified several proteins, including DDX6, G3BP1, G3BP2, Caprin1, and USP10, implicated in P body (PB) and stress granule (SG) function, and not previously known to bind DENV RNAs.
 Additional experiments demonstrate that, in contrast to DDX6, the SG proteins G3BP1, G3BP2, Caprin1 and USP10 bind to the variable region (VR) in the 3' UTR.

Answer: The main functions of G3BP1 and/or G3BP2 include translation of interferon stimulated mRNAs during dengue virus infection, initiation of assembly of stress granules, regulation of PMP22 mRNA which was found to affect cell proliferation in breast cancer cells, participation in several signaling pathways involved in growth, differentiation and apoptosis in human tumor cells after overexpression, limit viral replication events during Sindbis virus (SINV) infection, and modulation of p53 and MDM2 activity.
Exact answer: Translation of interferon stimulated mRNAs during dengue virus infection
Initiation of assembly of stress granules
Regulation of PMP22 mRNA which was found to affect cell proliferation in breast cancer cells
Participation in several signaling pathways involved in growth, differentiation and apoptosis in human tumor cells after overexpression
Limit viral replication events during Sindbis virus (SINV) infection
Modulation of p53 and MDM2 activity