MURPHY, Circuit Judge.

Defendants James Carlson, Lava Haugen, and Joseph Gellerman were charged with violating provisions of the Food Drug and Cosmetic Act (FDCA), the Controlled Substances Act (CSA), and the Controlled Substance Analogue Enforcement Act of 1986 (Analogue Act) for selling misbranded synthetic drugs at a head shop in Duluth, Minnesota. The jury found the defendants guilty on several counts. The district court1 rejected defense challenges to the constitutionality of the Analogue Act, to the sufficiency of evidence, and to jury instructions. The defendants now appeal from their convictions and their sentences. We affirm.

I.

Carlson was the owner and operator of the Last Place on Earth (Last Place), a head shop in Duluth, Minnesota which sold synthetic drugs from 2010 until 2012. Both Haugen, Carlson's domestic partner, and Carlson's son Gellerman worked at the shop. As store clerks, Gellerman and Haugen received shipments of misbranded synthetic drugs from Last Place suppliers and sold such products to customers. Haugen also weighed and bagged synthetic drugs, helped order them from suppliers, and took inventory. Although the drugs were labeled "not for human consumption," store employees knew that customers purchased them to consume as drugs.

From August 10, 2011 through September 21, 2012, law enforcement obtained 75 synthetic drug products from Last Place through controlled purchases and search warrants. One purchase included a product containing a trace amount of the controlled substance JWH-018, a synthetic cannabinoid. The government charged the defendants with violating the FDCA, the CSA, and the Analogue Act. Among the charges were allegations that the defendants sold products containing six analogues: (1) AM-2201, (2) UR-144, (3) XLR-11, (4) 5-MeO-DALT, (5) MPPP, and (6) 4-FA. Carlson was also charged with money laundering.

The witnesses at trial included law enforcement officers, former Last Place employees, and individuals who had supplied, manufactured, and used its synthetic drugs. Former employee Sherry Anderson testified that she and Haugen prepared order forms for Carlson who ordered drugs by telephoning suppliers in the presence of her or Haugen. Anderson also testified that once the government scheduled a substance, Carlson would move drugs containing that substance into the basement of the store and later sell those products "under the counter" to trustworthy customers.

The parties also presented testimony from dueling experts about the chemistry of the substances. The defense experts testified that the substances sold by the defendants were not structurally similar to controlled substances even though they had similar pharmacological effects. Government expert Dr. Terrance Boos, acting section chief of the Drug and Chemical Evaluation Section of the DEA, testified that the chemical structures of analogues sold at Last Place were substantially similar to those of controlled substances. This conclusion was based on visual inspections, scientific literature, and discussions with colleagues about the chemical structures of the products. Dr. Boos reported that no objective scientific consensus exists for determining "substantial similarity" between two different chemical structures. He also conceded that his opinion was not subject to peer review outside the DEA and did not have a known rate of error.

The jury was instructed that in order to find a defendant guilty of violating the Analogue Act the prosecution must have proven that the defendant knew that the substance at issue was a controlled substance analogue. That required proof beyond a reasonable doubt that (1) the defendant knew that the substance had a chemical structure that was substantially similar to a controlled substance in Schedule I or II of the CSA, and (2) the defendant knew that the substance either actually had, or the defendant represented or intended it to have, an effect on the central nervous system that is substantially similar to or greater than a controlled substance in Schedule I or II of the CSA. The district court also instructed the jury, "if you find the government has proved beyond a reasonable doubt that the defendant knew facts that satisfy part 2 of the test above, that is evidence from which you may, but are not required to, find or infer that the defendant knew facts that satisfy part 1 of the test above."

The jury found Carlson guilty of conspiracy to violate the FDCA, nine felony violations of the FDCA, eight misdemeanor violations of the FDCA, one violation of the CSA, conspiracy to violate the Analogue Act, nine violations of the Analogue Act, and twenty three money laundering violations under 18 U.S.C. § 1957. In calculating Carlson's guideline sentence, the district court used a 1:167 tetrahydrocannabinol ("THC") to marijuana conversion ratio and a two level firearm enhancement, resulting in a sentence of 210 months. Haugen was found guilty of conspiracy to violate the FDCA, two felony violations of the FDCA, and conspiracy to violate the Analogue Act. She received a 60 month sentence. Gellerman was convicted of two misdemeanor violations of the FDCA and was sentenced to three years probation.

II.

A.

Carlson and Haugen both appeal their Analogue Act convictions. Under that statute it is unlawful knowingly or intentionally to manufacture, distribute, or dispense a controlled substance analogue. See 21 U.S.C. §§ 813, 841. A controlled substance analogue is defined as a substance:

21 U.S.C. § 802(32)(A).

The Supreme Court has explained that the government may prove a defendant knowingly distributed a controlled substance analogue in violation of the Analogue Act in two ways. See McFadden v. U.S., ___ U.S. ___, 135 S.Ct. 2298, 2305, 192 L.Ed.2d 260 (2015). First, the government may demonstrate that the "defendant knew that the substance with which he was dealing [was] some controlled substance—that is, one actually listed on the federal drug schedules or treated as such by operation of the Analogue Act—regardless of whether he knew the particular identity of the substance." Id. Alternatively, the government may satisfy a two part test to prove that the defendant knew that the analogue he was dealing with (1) had a chemical structure that was substantially similar to a controlled substance, and (2) had similar effects to a controlled substance or the defendant represented or intended it to have those effects. See id.

Carlson contends that the Analogue Act is unconstitutional because it does not provide notice of which acts are criminal and permits arbitrary enforcement contrary to the Due Process Clause. "We review a challenge to the constitutionality of a federal statute de novo." United States v. Stephens, 594 F.3d 1033, 1036-37 (8th Cir.2010) (internal quotation marks omitted). The Supreme Court recently determined in McFadden v. United States that the Analogue Act is not unconstitutionally vague because the statute's "knowingly or intentionally" scienter requirement alleviates vagueness concerns by "narrow[ing] the scope of its prohibition, and limit[ing] prosecutorial discretion." ___ U.S. ___, 135 S.Ct. 2298, 2307, 192 L.Ed.2d 260 (2015). Carlson's constitutional challenge thus fails.

B.

Carlson and Haugen additionally argue that the district court failed to instruct the jury properly about the necessary elements for an Analogue Act conviction. Although jury instructions are regularly reviewed for abuse of discretion, if as here statutory interpretation is required, "it is an issue of law that we consider de novo." United States v. Petrovic, 701 F.3d 849, 858 (8th Cir.2012). "If we conclude that the district court's interpretation of the statute resulted in the omission of a required element of the offense, we then apply harmless error review." Preston v. United States, 312 F.3d 959, 960 (8th Cir.2002).

Carlson and Haugen argue that the district court erred by improperly instructing the jury about the two part test to prove a knowing violation of the Analogue Act. The court instructed the jury that if "the government has proved beyond a reasonable doubt that the defendant knew facts that satisfy part 2 of the test above [similar nervous system effects], that is evidence from which you may, but are not required to, find or infer that the defendant knew facts that satisfy part 1 of the test above [similar chemical structure]." The parties refer to this permissive inference as a "Turcotte inference" because it was discussed in the Seventh Circuit decision United States v. Turcotte. In Turcotte, the circuit court determined that if the "scienter requirement is met with regard to the second part of the analogue definition (knowledge or representation of similar physiological effects), the jury is permitted— but not required—to infer that the defendant also had knowledge of the relevant chemical similarities." See 405 F.3d 515, 527 (7th Cir.2005). Without such a permissive inference, it may be "extremely difficult" and "a significant prosecutorial burden" to prove to a jury that a defendant knew about the chemical structure of a substance. Id.

Under the Supreme Court's approach in County Court of Ulster County, New York, et al. v. Allen, we analyze whether a permissive inference is valid "as applied to the record before [us]." See 442 U.S. 140, 163, 99 S.Ct. 2213, 60 L.Ed.2d 777 (1979). The court's instruction did not violate due process if, in light of the record as a whole, there is a "rational connection" between the existence of one or more "evidentiary" or "basic facts" that the prosecution proved, and the "ultimate fact" or the element of the crime the prosecution must prove. Id. at 156, 165, 99 S.Ct. 2213 (internal quotation marks omitted). As applied to this case, we must determine whether all of the evidence in the record is sufficient to prove the ultimate fact at issue—defendants' knowledge of the chemical structure of the substances they sold—beyond a reasonable doubt. See id. at 167, 99 S.Ct. 2213.

The evidence in the record showed that Carlson knew that the chemical structures of the analogues he sold were substantially similar to those of scheduled controlled substances. One of Carlson's suppliers sent him a chart by email demonstrating that the molecular formula of AM-2201 and JWH-018 differed by only one atom. A reasonable juror could find that because Carlson knew about the similar molecular formulas, he also knew about the substantial similarity between the chemical structures of the substances. Although direct evidence for the other analogues that Carlson distributed was not presented, circumstantial evidence was offered. Carlson stated to the media that the government could not keep up with policing synthetic drug distribution because he believed that his conduct was legal as long as the substances he sold were "one little molecule" different from banned controlled substances. Reasonable jurors could interpret this statement as circumstantial evidence that Carlson knew that the other five analogues he sold were substantially similar in chemical structure to controlled substances. The district court also instructed the jury that it should consider all of the evidence, that the prosecution had the burden of proof and the defense had no burden to present evidence, and that it was not required to accept the permissive inference. See Allen, 442 U.S. at 160-62 & nn. 19-22, 99 S.Ct. 2213. In light of the full record here, we conclude that the district court did not err by using the permissive inference.

Similarly, we conclude that the record evidence was sufficient to prove beyond a reasonable doubt that Lava Haugen knew that the analogues she distributed were substantially similar in chemical structure to scheduled controlled substances. Since she had used Carlson's email account to communicate with synthetic drug suppliers, she had opportunity to see the chart comparing the molecular formula of AM-2201 and JWH-018. According to a former employee's testimony, Haugen also prepared order forms for Carlson and sometimes stood next to him while he called his suppliers to order additional products. On one of the forms prepared by Haugen, Carlson had written "Amphed + MD" to describe the composition of the chemicals ordered. The jury could therefore infer that Haugen was familiar with the chemical structures of the products she sold. Finally, the jury could also find that Haugen knew their structural similarities because she could have either heard or been willfully blind to Carlson's public statements about the substantial structural similarities between the drugs sold at his store and scheduled controlled substances.

We conclude that the district court properly applied a Turcotte inference to the record in this case. We recognize that the Tenth Circuit reached a different conclusion on the record in United States v. Makkar, ___ F.3d ___, 2015 WL 7422599 (10th Cir. Nov. 23, 2015). There, the Tenth Circuit concluded that the trial court had erred by applying the Turcotte inference, for in that case "the government [had] introduced no evidence suggesting that the defendants knew anything about the chemical structure of the incense they sold." Makkar, ___ F.3d at ___, 2015 WL 7422599, *2. But that record was different than the one in our case. Here, there was a "rational connection" between all the evidence in the record and the defendants' apparent knowledge about the chemical structures of the substances they sold in Duluth. See Allen, 442 U.S. at 165, 99 S.Ct. 2213. There are reasons, however, why a district court may deliberately avoid using the Turcotte instruction, even where the instruction is permissible. Cf. Allen, 442 U.S. at 175-77 & n. 8, 99 S.Ct. 2213 (Powell, J., dissenting). A Turcotte instruction could potentially mislead a jury to think that knowledge that a substance had a similar pharmacological effect as a controlled substance would alone be sufficient to prove knowledge that the substance had a similar chemical structure to a controlled substance, collapsing the two knowledge elements of the Analogue Act into one. See 21 U.S.C. §§ 802(32)(A), 841; Makkar, ___ F.3d at ___, 2015 WL 7422599, at *2. Although evidence of a defendant's knowledge that a particular substance has a pharmacological effect similar to that produced by a controlled substance is ambiguous proof of scienter by itself, it may be probative of the defendant's knowledge of chemical structure when considered in the context provided by other evidence. See United States v. Ali, 735 F.3d 176, 189-90 (4th Cir.2013), cited in McFadden, 135 S.Ct. at 2304, n. 1. In order, therefore, to instruct a jury properly and consistently with the footnotes in McFadden, the trial court may instruct that knowledge of similar pharmacological effect may be considered as circumstantial evidence, along with the other evidence, in deciding whether the evidence as a whole proved knowledge of similar chemical structure beyond a reasonable doubt. See McFadden, 135 S.Ct. at 2305 & nn. 1-3.

The defendants take issue with another jury instruction pertaining to the Analogue Act charges. The district court instructed the jury that to find the defendants guilty, the government was not required to prove that the analogue was similar in chemical structure to the same controlled substance that it was similar to in pharmacological effects. This instruction is consistent with the text of the statute. Each subparagraph in 21 U.S.C. § 802(32)(A) refers only to "a" controlled substance in Schedule I or II. While an analogue substance must have a similar chemical structure as a controlled substance, its physiological effects may be similar to a different controlled substance. As the government notes, this is part of the practical realities of illicit drug dealing. While a dealer may claim that a substance will give a user a cocaine like high, the substance may be structurally similar to a less well known controlled substance. The statute does not require that a jury find that the analogue at issue has a similar effect and structure to a particular controlled substance. We conclude that the district court did not abuse its discretion by permitting the jury to find that the analogue was similar in chemical structure to a controlled substance, but similar in pharmacological effects to a different controlled substance.

C.

Carlson and Haugen also contend that the district court abused its discretion by permitting Dr. Boos to testify as an expert about the substantial similarity in chemical structure between scheduled controlled substances and the products sold at Last Place. The defendants contend that Dr. Boos's methodology did not satisfy any of the Daubert factors for admissibility. See Daubert v. Merrell Dow Pharms., Inc., 509 U.S. 579, 593-94, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993). We review the district court's decision to admit expert testimony for abuse of discretion. See Peitzmeier v. Hennessy Indus., Inc., 97 F.3d 293, 296 (8th Cir.1996).

The district court did not abuse its discretion by permitting Dr. Boos to testify. He testified that his conclusion was based on relevant evidence he had observed, his specialized knowledge in the field, his review of the scientific literature, and discussions with other scientists at the DEA. See Russell v. Whirlpool Corp., 702 F.3d 450, 457 (8th Cir.2012). Although the defendants contend that Dr. Boos's testimony did not flow naturally from disinterested research, that his methodology was not subject to peer review or publication, and that his theory had no known rate of error, these objections go to the weight of Dr. Boos's testimony, not to its admissibility. See id. at 458. The district court properly exercised its discretion under Rule 702 in allowing Dr. Boos to testify as an expert.

D.

Carlson also claims that the district court erred by denying him the right to present an entrapment by estoppel defense to the Analogue Act charges. We review this denial de novo "because it is a question of law." United States v. Benning, 248 F.3d 772, 775 (8th Cir.2001). The defense of entrapment by estoppel only applies when an official has affirmatively assured "a defendant that certain conduct is legal, and the defendant reasonably relie[d] on that advice and continue[d] or initiate[d] the conduct." Id. (internal quotation marks omitted). Carlson relies exclusively on one news article to support his entrapment by estoppel defense. According to the article, Carlson told the Duluth News Tribune that although the government had scheduled five new substances, he intended to "pull in the ones with different compounds—and they are readily available." Carlson also predicted that with about 210 similar chemicals available, manufacturers would try to keep one step ahead of the government.

DEA spokeswoman Barbara Carreno is quoted in the article as responding that "[u]nfortunately he is correct." Carlson could not have reasonably relied on the quotation attributed to Carreno as a statement that his conduct was legal because it did not say that. Carreno may have simply intended to agree with him that manufacturers are trying to avoid apprehension or that many unscheduled substances continue to be sold. Carlson has not shown that Carreno was affirmatively misleading. See Benning, 248 F.3d at 776. Moreover, Carlson does not allege that Carreno knew any of the relevant facts about his drug business at Last Place. See United States v. Batterjee, 361 F.3d 1210, 1216 (9th Cir.2004). The district court therefore did not err in prohibiting Carlson from presenting an entrapment by estoppel defense.

III.

A.

Carlson and Haugen also appeal their felony FDCA convictions. Under the FDCA, "[t]he introduction or delivery for introduction into interstate commerce of any food, drug, device, tobacco product, or cosmetic that is adulterated or misbranded" is prohibited. 21 U.S.C. § 331(a). Carlson and Haugen argue that the district court erred by not requiring the jury to find that "the defendants knew of this regulatory `misbranding' law," knew the definition of "misbranding" as defined under the FDCA, and acted with the intent to violate the FDCA.

We review defense challenges to the district court's jury instructions for abuse of discretion. United States v. Beckman, 222 F.3d 512, 520 (8th Cir.2000). The test is "whether the instructions, taken as a whole and viewed in light of the evidence and applicable law, fairly and adequately submitted the issues in the case to the jury." Id. We concluded in United States v. Hiland that for felony FDCA convictions, defendants need only have "knowledge of the essential nature of the alleged fraud" and are not required to be familiar with the misbranding law or with the statutory definition of "misbranding." See 909 F.2d 1114, 1128-29 & n. 21 (8th Cir.1990) (citing 21 U.S.C. § 333(a)(2)). They must nevertheless have known that the products they sold were misbranded drugs. See id. at 1129.

After viewing the district court's instructions as a whole, we conclude that the court did not abuse its discretion. The court satisfied Hiland's requirements by instructing the jury that in order to be found guilty of felony FDCA violations, Carlson and Haugen had to have been shown to know that the products they sold were misbranded drugs, and to have acted with the intent to defraud or mislead a government agency. See id. The court defined "to act with the intent to defraud" to mean "to act with the specific intent to deceive or cheat," and it instructed the jury that "`[g]ood faith' is a complete defense to the FDCA misbranding claims if the defendant[s] did not act with the `intent to defraud' or `intent to mislead.'" The court instructed the jury that a substance is a drug if it is "intended to affect the structure or any function of the body of human beings," and a drug is "misbranded" if its labeling was false or misleading. The court thus appropriately required the jury to consider whether Carlson and Haugen knew "material facts they failed to reveal" while knowingly selling mislabeled drugs. See id.

B.

Gellerman similarly appeals his misdemeanor convictions under the FDCA. He claims that the district court improperly instructed the jury and that his actions did not violate the statute. To the extent that his appeal is a challenge to the district court's jury instructions, we review the question for "plain error" because he failed timely to object to this instruction at trial. United States v. Poitra, 648 F.3d 884, 887 (8th Cir.2011). As we explained in Hiland, "neither knowledge nor intent is required" for a misdemeanor violation of § 331. Id. at 1127-28. In this case, the district court instructed the jury that if a defendant did not have the intent to defraud the government, but all the other elements of a FDCA violation were proved beyond a reasonable doubt, then the jury could find the defendant guilty of a misdemeanor misbranding offense. The district court did not err when instructing the jury about the requisite elements for a misdemeanor FDCA violation.

If Gellerman is seeking to challenge the sufficiency of the evidence, the issue is reviewed de novo. United States v. Clark, 668 F.3d 568, 573 (8th Cir.2012). "We must affirm if, taking all the facts in the light most favorable to the verdict, a reasonable juror could have found the defendant guilty of the charged conduct beyond a reasonable doubt." United States v. Balanga, 109 F.3d 1299, 1301 (8th Cir.1997). Because misbranding drugs is a strict liability misdemeanor offense, the government only had to prove beyond a reasonable doubt that Gellerman was responsible for, or aided and abetted in the commission of, delivering misbranded drugs after they had been received in interstate commerce. See United States v. Dotterweich, 320 U.S. 277, 281, 284, 64 S.Ct. 134, 88 L.Ed. 48 (1943). Misdemeanor liability stems not from "corporate hierarchy," but from an individual's role in the sale of misbranded drugs. United States v. Park, 421 U.S. 658, 675, 95 S.Ct. 1903, 44 L.Ed.2d 489 (1975). Although Gellerman had limited responsibilities as a store clerk, the government presented evidence that on September 16, 2011 and September 21, 2012 field agents purchased six misbranded drugs from him, all of which had been received in interstate commerce. Viewing the evidence in the light most favorable to the verdicts, a reasonable juror could have found Gellerman guilty beyond a reasonable doubt of two strict liability FDCA violations for distributing misbranded drugs.

IV.

A.

Carlson also appeals his CSA conviction for knowingly distributing JWH-018, a scheduled controlled substance. Under the CSA it is unlawful to "manufacture, distribute, or dispense" a controlled substance knowingly or intentionally. 21 U.S.C. § 841(a)(1). Carlson argues that there was insufficient evidence to convict him of this because he did not knowingly distribute JWH-018, and the district court improperly denied his motion for judgment of acquittal on this count. We review the issue de novo, "view[ing] the evidence in the light most favorable to the guilty verdict, granting all reasonable inferences that are supported by that evidence." United States v. Milk, 447 F.3d 593, 598 (8th Cir.2006).

Under this standard, a reasonable juror could have found Carlson guilty of knowingly distributing JWH-018. In a controlled buy on August 10, 2011 a government agent purchased a substance from Gellerman at Last Place which contained a detectable amount of JWH-018. A former employee testified that Carlson kept products containing banned substances in the basement and later used them to make "under the counter" sales to trustworthy customers. Although Carlson contends that he deliberately avoided selling banned substances by removing such items from the floor and regularly testing his products, a reasonable juror could have found the employee's testimony credible and inferred that Carlson knowingly distributed JWH-018.

B.

Carlson also claims that the district court miscalculated his sentencing guideline range by using an improper conversion ratio for THC and marijuana and by erroneously applying a sentencing enhancement. "We review the sentencing court's construction and application of the sentencing guidelines de novo and its factual findings for clear error." United States v. Muckle, 755 F.3d 1024, 1025 (8th Cir.2014). We see no error in the 1:167 THC conversion ratio applied by the district court in respect to Carlson, and we conclude the court did not err. Based on expert testimony the court determined that the synthetic cannabinoids that Carlson had distributed were "most closely related" to THC. The court then applied the 1:167 conversion ratio from the drug equivalency tables in the guidelines. See U.S.S.G. § 2D1.1, Notes 6 & 8(D). Although Carlson argues that the 1:167 ratio lacks scientific support because recreational marijuana contains a higher level of THC than the guideline ratio assumes, a sentencing court may use guideline commentary "as a tool for calculating the base offense level" for a convicted defendant. Muckle, 755 F.3d at 1026. We conclude that in this instance the district court did not err by relying on the guideline commentary from § 2D1.1 to apply a 1:167 THC to marijuana conversion ratio.

We review Carlson's objection to the district court's application of the firearm sentencing enhancement under § 2D1.1(b)(1) for clear error because he appears to challenge the factual findings supporting a nexus between the firearms and his drug activity. See U.S.S.G. § 2D1.1(b)(1). For § 2D1.1(b)(1) to apply, "the government must prove by a preponderance of the evidence that a weapon was present, and that it was not clearly improbable that the weapon had a nexus with this conspiracy." United States v. Perez-Guerrero, 334 F.3d 778, 783 (8th Cir.2003). "A nexus exists where there is a temporal and spatial relation between the weapon, the drug trafficking activity, and the defendant." United States v. Thompson, 210 F.3d 855, 862 (8th Cir.2000). In this case, the nexus between Carlson, weapons, and drug activity was strong because the record showed that Carlson kept guns at Last Place and also carried a loaded gun while selling regulated substances there. See United States v. Hiveley, 61 F.3d 1358, 1362-63 (8th Cir.1995) (per curiam). Although Carlson claims that he had a permit to carry a loaded handgun, § 2D1.1(b)(1) does not require the district court to take account of such a permit. He also contends that the other 28 firearms recovered at Last Place were mostly unloaded and stored in a safe on the floor below the retail level as part of his gun collection. This however does not show that the district court clearly erred by finding a nexus between the firearms and his drug activity. The district court did not err by applying the firearm sentencing enhancement in this case.

C.

Finally, Carlson and Haugen both argue that if their drug convictions are reversed, then the final forfeiture order and judgment and Carlson's money laundering convictions must also be vacated because they are predicated on the drug convictions. We need not address these claims since the record demonstrates that all the drug convictions here should be affirmed.

V.

For these reasons the judgments of the district court are affirmed.