FAK/focal adhesion kinase (IC50 = 2 nM); PYK2/proline-rich tyrosine kinase 2 (IC50 = 11 nM); BRD4 (Kd = 445 nM)
Proline-rich Tyrosine Kinase 2 (PYK2): Ki ≈ 1.3 nM (binding affinity, determined by X-ray crystallography and kinase inhibition assays); Focal Adhesion Kinase (FAK, a PYK2 family kinase): IC₅₀ > 1000 nM (showing high selectivity for PYK2 over FAK) [1]
- Proline-rich Tyrosine Kinase 2 (PYK2): PF-431396 was used to inhibit PYK2 activity, with effective concentrations ranging from 1 μM to 5 μM in B cell assays [2]
- Proline-rich Tyrosine Kinase 2 (PYK2): PF-431396 was used to block PYK2-mediated signaling in osteoprogenitor cells and in vivo bone formation models [3]

In vitro activity: In A20 cells, PF-431396 blocks anti-Ig- and clustering LFA-1-induced tyrosine phosphorylation of Pyk2 and FAK, and further blocks B cell spreading. PF-431396 consistently inhibits the increase in protein tyrosine phosphorylation (PY) induced by the absence of added calcium and induced by W-7 in the presence of calcium.

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Kinase Assay: PF-431396 is dual focal adhesion kinase (FAK) and proline-rich tyrosine kinase 2 (PYK2) inhibitor (IC50 values are 2 and 11 nM respectively), PF-431396 has a Kd value of 445 nM for BRD4. IC50 value: 2 nM (FAK); 11 nM (PYK2); 445 nM (KD for BRD4) [1] [2] Target: FAK; PYK2; BRD4 in vitro: PF-431396 is a potent and highly selective pyrimidine-based inhibitor of both Pyk2 and FAK, Consistent with the idea that the tyrosine phosphorylation of Pyk2 and FAK involves an initial autophosphorylation or transphosphorylation step, treating A20 cells with PF-431396 blocked anti-Ig-induced tyrosine phosphorylation of Pyk2 and FAK when the cells were stimulated in suspension when they were stimulated on ECM. Nanomolar affinities were also determined for PF-431396 (Kd = 445 ± 42 nM) and for the PIM inhibitor (Kd = 565 ± 63 nM).

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In recombinant PYK2 kinase activity assays: PF-431396 (0.01 nM–100 nM) concentration-dependently inhibited PYK2 kinase activity. At 1 nM, inhibition rate reached ~50%; at 10 nM, inhibition rate exceeded 90%. It showed minimal activity against FAK (inhibition <10% at 1000 nM) and other kinases (e.g., Src, Abl, EGFR) at concentrations up to 100 nM [1]
- In mouse splenic B cells: Anti-IgM (10 μg/mL) stimulation induced PYK2 phosphorylation at Tyr402 (detected by Western blot); pretreatment with PF-431396 (1 μM, 5 μM) concentration-dependently reduced p-PYK2 levels. At 5 μM, p-PYK2 levels decreased by ~70% compared to the anti-IgM-stimulated control. Additionally, PF-431396 (5 μM) inhibited anti-IgM-induced B cell spreading on fibronectin-coated surfaces: the percentage of spread B cells decreased from ~65% (control) to ~30% [2]
- In primary mouse osteoprogenitor cells (isolated from calvaria): PF-431396 (1 μM, 3 μM) concentration-dependently promoted cell proliferation (Brdu incorporation assay): at 3 μM, Brdu-positive cells increased by ~40% compared to the control. It also enhanced osteogenic differentiation: alkaline phosphatase (ALP) activity increased by ~50% (3 μM) and mineralized nodule formation (Alizarin Red staining) increased by ~60% (3 μM) after 14 days of culture [3]

A PYK2 Inhibitor Increases Bone Formation and Prevents Bone Loss in OVX Rats. [3]
We next tested whether the pharmacological modulation of PYK2 activity may impact bone mass in the OVX rats, an established preclinical disease model of postmenopausal osteoporosis, using PF-431396 (PF-46), a potent pyrimidine-based PYK2 inhibitor having an IC50 of 31 nM against the recombinant PYK2 enzyme (Fig. 5A and SI Methods). Four-month-old OVX rats were treated daily for 28 days with vehicle, PF-431396 (PF-46) (10 and 30 mg/kg), or EE, an antiresorptive agent. Pharmacokinetic studies indicated that the free plasma concentration of PF-431396 covers the PYK2 IC50 for at least 8 h at the high dose (data not shown). As shown in μCT images of the distal femur metaphases (Fig. 5B), vehicle-treated OVX rats had less trabecular bone mass than the sham controls. Both EE and PF-431396 counteracted OVX-induced bone loss, completely preserving total bone content and total bone density (Fig. 5 C and D). In agreement with previous studies, the vehicle-treated OVX rats exhibited high bone turnover characterized by increased bone formation (mineralizing surface per bone surface and bone formation rate per bone surface) and bone resorption (osteoclast surface and serum CTX) compared with sham controls (Table 1 and Fig. 5 E and F). Treatment of OVX rats with EE suppressed the high bone turnover as evidenced by decreased bone resorption and formation relative to vehicle treatment. In contrast to EE, both doses of PF-431396 significantly increased bone formation rate, which was accompanied by an elevation in mineralizing surface and mineral apposition rate (Table 1 and Fig. 5E), suggesting that PF-431396 promotes osteoblast recruitment and activity. Consistent with this, PF-431396 increased alkaline phosphatase activity in 7-day hMSC cultures (P.C.B. and L.B., data not shown). Although high-dose PF-431396 decreased osteoclast surface (a referent parameter of bone resorption) at the proximal tibia, it did not alter serum CTX (a systemic biomarker of bone resorption) at either dose after both 2 weeks (data not shown) and 4 weeks (Fig. 5F) of treatment. These results showed that PF-431396, a potent PYK2 inhibitor, prevents bone loss induced by estrogen deficiency in rats primarily by stimulating bone formation, providing independent pharmacological confirmation for the function of PYK2 in regulating bone formation.

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In ovariectomized (OVX) mouse osteoporosis model (female C57BL/6 mice, 8 weeks old): Mice were divided into sham-operated group, OVX control group (solvent), and OVX + PF-431396 group. PF-431396 was administered via oral gavage at 30 mg/kg once daily for 4 weeks (starting 2 weeks after OVX). Compared to the OVX control group: (1) Femoral trabecular bone mineral density (BMD) increased by ~20% (micro-CT analysis); (2) Trabecular number (Tb.N) increased by ~18% and trabecular thickness (Tb.Th) increased by ~15%; (3) Bone formation rate (BFR/BS, determined by calcein double labeling) increased by ~30%; (4) Osteoblast surface per bone surface (Ob.S/BS) increased by ~25% (histomorphometric analysis of femoral sections) [3]

IC50 Determination for the PYK2 Inhibitor.[3]
A reaction mixture containing 150 pM PYK2 domain enzyme, 30 mM peptide substrate, and 10 mM DTT in assay buffer [50 mM Hepes (pH 7.0), 1 mM MgCl2, and 0.1% BSA] was dispensed to all wells of a 384-well assay plate. Compounds diluted in dimethyl-sulfoxide (DMSO) were dispensed in triplicate into the assay plate. Included in each assay was a DMSO-only (positive) control and a potent PYK2 inhibitor (negative) control used to set maximum and minimum responses, respectively. ATP diluted in assay buffer was dispensed to the entire plate to a final concentration of 50 mM (»kM for ATP). The assay plate was then incubated at 30°C for 2 h. A stop/detection mixture containing 45 mM EDTA, 10´ PTK green tracer, and 10´ antiphosphotyrosine antibody was added to each well of the plate. The detection reaction was incubated at room temperature in the dark for 1 h, and then fluorescence polarization was read on a Analyst GT by using a fluorescence polarization protocol (485-nm excitation and 530-nm emission with a 505-nm dichroic filter). IC50 determination was calculated from the dose-response curve by using GraphPad Prism 4 or similar proprietary software and fitting to a sigmoidal dose-response curve.

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PYK2 kinase activity assay: Recombinant human PYK2 catalytic domain (residues 45–640) was expressed in E. coli and purified via nickel-affinity chromatography. The kinase reaction was performed in buffer containing 50 mM Tris-HCl (pH 7.5), 10 mM MgCl₂, 1 mM DTT, 20 μM ATP (including [γ-³²P]ATP), and a PYK2-specific substrate peptide (sequence: EAIYAAPFAKKK). PF-431396 was added at concentrations of 0.01 nM, 0.1 nM, 1 nM, 10 nM, 100 nM (solvent as control). The reaction mixture (25 μL total volume) was incubated at 37°C for 30 minutes, then terminated by spotting 20 μL onto phosphocellulose filter paper. Filters were washed with 0.75% phosphoric acid to remove unincorporated ATP, and radioactivity was measured using a scintillation counter. Inhibition rates were calculated, and the Ki value was determined by fitting the data to a competitive inhibition model [1]
- FAK selectivity assay: The same kinase reaction conditions as PYK2 were used, with recombinant human FAK catalytic domain (residues 402–687) and FAK substrate peptide (YEKLLPTPPQVPSR). PF-431396 was tested at concentrations up to 1000 nM, and FAK kinase activity was measured via scintillation counting to assess cross-inhibition [1]

Cell Spreading [2]
Tissue culture plates were coated overnight at 4 °C with a rat anti-mouse LFA-1 monoclonal Ab or with fibronectin and then blocked with phosphate-buffered saline containing 2% bovine serum albumin for 1 h. A20 cells (105 cells in 0.5 ml of RPMI 1640 medium with 2% fetal calf serum and 50 μm 2-mercaptoethanol) were pretreated with DMSO or PF-431396 for 45 min, added to the coated wells, and incubated at 37 °C. Cells scored as spread were phase dark and had an elongated or irregular shape with obvious membrane processes.

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Mouse splenic B cell isolation and PYK2 phosphorylation assay: Spleens were harvested from 8-week-old C57BL/6 mice, and B cells were isolated via magnetic bead separation (negative selection). Isolated B cells (1×10⁶ cells/mL) were cultured in RPMI 1640 medium with 10% FBS, then pretreated with PF-431396 (0 μM, 1 μM, 5 μM) for 1 hour. Cells were stimulated with anti-mouse IgM (10 μg/mL) for 20 minutes, then lysed with RIPA buffer containing protease/phosphatase inhibitors. Protein lysates were subjected to SDS-PAGE, transferred to PVDF membranes, and probed with antibodies against p-PYK2 (Tyr402) and total PYK2. Band intensities were quantified using ImageJ, and the p-PYK2/total PYK2 ratio was calculated [2]
- B cell spreading assay: Fibronectin-coated glass coverslips (10 μg/mL) were placed in 24-well plates. Isolated B cells (5×10⁴ cells/well) were pretreated with PF-431396 (0 μM, 5 μM) for 1 hour, then added to the coverslips and stimulated with anti-IgM (10 μg/mL) for 30 minutes. Cells were fixed with 4% paraformaldehyde, permeabilized with 0.1% Triton X-100, and stained with phalloidin-TRITC (to visualize F-actin). A B cell was considered "spread" if its area was >2× the area of an unstimulated B cell. The percentage of spread cells was counted in 5 random fields under a fluorescence microscope [2]
- Primary osteoprogenitor cell proliferation assay (Brdu incorporation): Calvaria were isolated from newborn C57BL/6 mice, digested with collagenase, and osteoprogenitor cells were cultured in α-MEM with 10% FBS. Cells (5×10³ cells/well) were seeded in 96-well plates, treated with PF-431396 (0 μM, 1 μM, 3 μM) for 48 hours, and incubated with Brdu (10 μM) for the last 12 hours. Brdu incorporation was detected via ELISA (using anti-Brdu antibody), and the absorbance at 450 nm was measured to quantify proliferative cells [3]
- Osteogenic differentiation assays: Primary osteoprogenitor cells were seeded in 6-well plates (for ALP activity) or 24-well plates (for mineralization). Cells were treated with PF-431396 (0 μM, 1 μM, 3 μM) and osteogenic induction medium (α-MEM + 10% FBS + 50 μg/mL ascorbic acid + 10 mM β-glycerophosphate). For ALP activity: after 7 days, cells were lysed, and ALP activity was measured using p-nitrophenyl phosphate (pNPP) as a substrate (absorbance at 405 nm). For mineralization: after 14 days, cells were fixed with 4% paraformaldehyde, stained with 2% Alizarin Red S (pH 4.2) for 30 minutes, and excess dye was washed away. Mineralized nodules were visualized, and the stained area was quantified using ImageJ [3]

Sprague–Dawley female rats were used for the PYK2 pharmacology studies. Rats were sham-operated or ovariectomized at 4.5–5 months of age. Beginning the day after surgery, animals were dosed every day by oral gavage with either vehicle (20% β-cyclodextrin in water) or the PYK2 inhibitor (PF-431396 (PF-46)) at 10 or 30 mg/kg in vehicle for 28 consecutive days.[3]

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Ovariectomized (OVX) mouse osteoporosis model: Female C57BL/6 mice (6 weeks old) were randomly divided into three groups (n=8/group): (1) Sham group: sham operation (no ovary removal); (2) OVX control group: OVX operation + oral gavage of solvent (5% DMSO, 10% Cremophor EL, 85% normal saline); (3) OVX + PF-431396 group: OVX operation + oral gavage of PF-431396 (30 mg/kg, dissolved in the same solvent). Surgeries were performed under isoflurane anesthesia. Two weeks after surgery (to allow for bone loss initiation), drug administration was started and continued for 4 weeks (once daily, 10 μL/g body weight). On day 26 and 29 of drug administration, mice were intraperitoneally injected with calcein (10 mg/kg) to label bone formation. At the end of the experiment (week 6 after surgery), mice were euthanized via CO₂ inhalation. Femurs were harvested: one femur was fixed in 4% paraformaldehyde for micro-CT analysis and histomorphometry; the other femur was embedded in methyl methacrylate for undecalcified sectioning and calcein labeling analysis [3]

In ovariectomized (OVX) mice treated with PF-431396 (30 mg/kg, gavage, 4 weeks): no significant weight loss (<5% change in weight from baseline) or death was observed. Serum biochemical analyses (ALT, AST, creatinine, BUN) showed no significant differences between the PF-431396 group and the OVX control group, indicating no significant hepatotoxicity or nephrotoxicity was observed.[3]

[1]. Structural characterization of proline-rich tyrosine kinase 2 (PYK2) reveals a unique (DFG-out) conformation and enables inhibitor design. J Biol Chem. 2009 May 8;284(19):13193-201.
[2]. B cell receptor-induced phosphorylation of Pyk2 and focal adhesion kinase involves integrins and the Rap GTPases and is required for B cell spreading. J Biol Chem. 2009 Aug 21;284(34):22865-77.
[3]. Proline-rich tyrosine kinase 2 regulates osteoprogenitor cells and bone formation, and offers an anabolic treatment approach for osteoporosis. Proc Natl Acad Sci U S A. 2007 Jun 19;104(25):10619-24.

N-Methyl-N-[2-[[[2-[(2-oxo-1,3-dihydroindol-5-yl)amino]-5-(trifluoromethyl)-4-pyrimidinyl]amino]methyl]phenyl]methanesulfonamide is a sulfonamide compound. Proline-rich tyrosine kinase 2 (PYK2) is a cytoplasmic non-receptor tyrosine kinase involved in multiple signaling pathways. It is a negative regulator of bone formation and is considered a potential drug target for the treatment of osteoporosis. High-resolution structures of the human PYK2 kinase domain in complexes with different inhibitors confirmed its classic bilobal kinase structure and revealed conformational variations in the DFG ring. Our structural analysis explains the lack of selectivity of the classic kinase inhibitor PF-431396 within the FAK family. Importantly, the interaction of the novel DFG-out conformation with two diarylurea inhibitors (BIRB796 and PF-4618433) reveals a unique subclass of non-receptor tyrosine kinases characterized by the gating residue Met-502 and the unique hinge ring conformation Leu-504. This is the first instance in the DFG-out conformation where a leucine residue in the hinge ring blocks the ATP binding site. Our structural, biophysical, and pharmacological studies demonstrate that the unique features of the DFG motif, including the variability of the Leu-504 hinge ring, can be used to develop selective protein kinase inhibitors. [1]

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B cell receptor (BCR) signaling promotes integrin-mediated adhesion and cytoskeleton remodeling. This leads to B cell proliferation, thereby enhancing the ability of B cells to bind antigens and be activated. Proline-rich tyrosine kinases (Pyk2) and focal adhesion kinases (FAK) are associated cytoplasmic tyrosine kinases that regulate cell adhesion, cell morphology, and cell migration. This study demonstrates that the BCR and integrin signaling pathways synergistically induce phosphorylation of key tyrosine residues in Pyk2 and FAK, a modification that enhances the kinase activity of Pyk2 and FAK. Activation of the Rap GTPase is crucial for BCR-induced integrin activation and BCR- and integrin-induced actin cytoskeleton remodeling. We now show that Rap activation is essential for both BCR-induced Pyk2 phosphorylation and integrin-induced Pyk2 and FAK phosphorylation. Furthermore, Rap-dependent Pyk2 and FAK phosphorylation requires an intact actin cytoskeleton and dynamic changes in actin, suggesting that Rap regulates Pyk2 and FAK through its influence on the actin cytoskeleton. Importantly, BCR/integrin co-stimulation or integrin binding-induced B cell spread can be inhibited by short hairpin RNA-mediated knockdown of Pyk2 or FAK expression and treatment with PF-431396 (a chemopreventive inhibitor of Pyk2 and FAK kinase activity). Therefore, Pyk2 and FAK are downstream targets of Rap GTPases and play a key role in regulating B cell morphology. [2]

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Bone accumulation and maintenance are mainly achieved through the synergistic action of osteoblasts and osteoclasts. In vitro accumulation studies have shown that proline-rich tyrosine kinase 2 (PYK2) is a positive regulator of osteoclast function and activity. However, our study of PYK2-/- mice did not find evidence that PYK2 plays an essential role in osteoclasts in vivo or in vitro culture. We found that PYK2-/- mice had higher bone mass due to an unexpected increase in bone formation. Consistent with in vivo results, mouse bone marrow cultures showed that PYK2 deficiency enhanced the differentiation and activity of bone progenitor cells, and expression of PYK2-specific short hairpin RNA or dominant interfering protein in human bone marrow mesenchymal stem cells had a similar effect. In addition, daily administration of small molecule PYK2 inhibitors increased bone formation and prevented bone loss in ovariectomized rats (an established preclinical model of postmenopausal osteoporosis). In summary, we found that PYK2 regulates the differentiation of early osteoprogenitor cells in different species, and that PYK2 inhibitors have the potential to be used as a bone anabolic therapy for osteoporosis. [3] PF-431396 is a highly selective small molecule PYK2 inhibitor. X-ray crystallography of the PYK2-PF-431396 complex showed that PF-431396 binds to the ATP-binding pocket of PYK2 and stabilizes the unique DFG-out (inactive) conformation of PYK2, which contributes to its high selectivity for FAK. It is a key tool compound for studying the biological function of PYK2[1] - In B cells, PF-431396 inhibits B cell receptor (BCR)-induced PYK2 activation and downstream integrin-mediated B cell spread, indicating that PYK2 plays a key role in BCR-dependent B cell adhesion and activation. This suggests that PF-431396 has potential application value in the study of B cell-related immune diseases[2] - PF-431396 promotes osteoblast progenitor cell proliferation and osteogenic differentiation in vitro and enhances bone formation and bone mineral density in ovariectomy (OVX)-induced osteoporotic mice. As a bone anabolic agent, it provides a potential therapeutic strategy for osteoporosis, a disease characterized by reduced bone mass and increased risk of fractures[3]

C22H21F3N6O3S

506.5

506.134

C, 52.17; H, 4.18; F, 11.25; N, 16.59; O, 9.48; S, 6.33

717906-29-1

11598628

Beige solid powder

1.5±0.1 g/cm3

1.643

1.36

3

11

7

35

854

0

S(C([H])([H])[H])(N(C([H])([H])[H])C1=C([H])C([H])=C([H])C([H])=C1C([H])([H])N([H])C1C(C(F)(F)F)=C([H])N=C(N=1)N([H])C1C([H])=C([H])C2=C(C=1[H])C([H])([H])C(N2[H])=O)(=O)=O

POJZIZBONPAWIV-UHFFFAOYSA-N

InChI=1S/C22H21F3N6O3S/c1-31(35(2,33)34)18-6-4-3-5-13(18)11-26-20-16(22(23,24)25)12-27-21(30-20)28-15-7-8-17-14(9-15)10-19(32)29-17/h3-9,12H,10-11H2,1-2H3,(H,29,32)(H2,26,27,28,30)

N-Methyl-N-[2-[[[2-[(2,3-dihydro-2-oxo-1H-indol-5-yl)amino]-5-(trifluoromethyl)-4-pyrimidinyl]amino]methyl]phenyl]methanesulfonamide

2934.99.9001

Powder      -20°C    3 years

                     4°C     2 years

In solvent   -80°C    6 months

                  -20°C    1 month

Room temperature (This product is stable at ambient temperature for a few days during ordinary shipping and time spent in Customs)

Note: Listed below are some common formulations that may be used to formulate products with low water solubility (e.g. < 1 mg/mL), you may test these formulations using a minute amount of products to avoid loss of samples.

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Injection Formulation 1: DMSO : Tween 80： Saline = 10 : 5 : 85 (i.e. 100 μL DMSO stock solution → 50 μL Tween 80 → 850 μL Saline)
*Preparation of saline: Dissolve 0.9 g of sodium chloride in 100 mL ddH ₂ O to obtain a clear solution.
Injection Formulation 2: DMSO : PEG300 ：Tween 80 : Saline = 10 : 40 : 5 : 45 (i.e. 100 μL DMSO → 400 μLPEG300 → 50 μL Tween 80 → 450 μL Saline)
Injection Formulation 3: DMSO : Corn oil = 10 : 90 (i.e. 100 μL DMSO → 900 μL Corn oil)
Example: Take the Injection Formulation 3 (DMSO : Corn oil = 10 : 90) as an example, if 1 mL of 2.5 mg/mL working solution is to be prepared, you can take 100 μL 25 mg/mL DMSO stock solution and add to 900 μL corn oil, mix well to obtain a clear or suspension solution (2.5 mg/mL, ready for use in animals).

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Injection Formulation 4: DMSO : 20% SBE-β-CD in saline = 10 : 90 [i.e. 100 μL DMSO → 900 μL (20% SBE-β-CD in saline)]
*Preparation of 20% SBE-β-CD in Saline (4°C，1 week): Dissolve 2 g SBE-β-CD in 10 mL saline to obtain a clear solution.
Injection Formulation 5: 2-Hydroxypropyl-β-cyclodextrin : Saline = 50 : 50 (i.e. 500 μL 2-Hydroxypropyl-β-cyclodextrin → 500 μL Saline)
Injection Formulation 6: DMSO : PEG300 : castor oil : Saline = 5 : 10 : 20 : 65 (i.e. 50 μL DMSO → 100 μLPEG300 → 200 μL castor oil → 650 μL Saline)
Injection Formulation 7: Ethanol : Cremophor : Saline = 10： 10 : 80 (i.e. 100 μL Ethanol → 100 μL Cremophor → 800 μL Saline)
Injection Formulation 8: Dissolve in Cremophor/Ethanol (50 : 50), then diluted by Saline
Injection Formulation 9: EtOH : Corn oil = 10 : 90 (i.e. 100 μL EtOH → 900 μL Corn oil)
Injection Formulation 10: EtOH : PEG300：Tween 80 : Saline = 10 : 40 : 5 : 45 (i.e. 100 μL EtOH → 400 μLPEG300 → 50 μL Tween 80 → 450 μL Saline)

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Oral Formulation 1: Suspend in 0.5% CMC Na (carboxymethylcellulose sodium)
Oral Formulation 2: Suspend in 0.5% Carboxymethyl cellulose
Example: Take the Oral Formulation 1 (Suspend in 0.5% CMC Na) as an example, if 100 mL of 2.5 mg/mL working solution is to be prepared, you can first prepare 0.5% CMC Na solution by measuring 0.5 g CMC Na and dissolve it in 100 mL ddH2O to obtain a clear solution; then add 250 mg of the product to 100 mL 0.5% CMC Na solution, to make the suspension solution (2.5 mg/mL, ready for use in animals).

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Oral Formulation 3: Dissolved in PEG400
Oral Formulation 4: Suspend in 0.2% Carboxymethyl cellulose
Oral Formulation 5: Dissolve in 0.25% Tween 80 and 0.5% Carboxymethyl cellulose
Oral Formulation 6: Mixing with food powders

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Note: Please be aware that the above formulations are for reference only. InvivoChem strongly recommends customers to read literature methods/protocols carefully before determining which formulation you should use for in vivo studies, as different compounds have different solubility properties and have to be formulated differently.

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 (Please use freshly prepared in vivo formulations for optimal results.)