$$C_\text{drug}$$ Drug concentration in blood serum
$$m_\text{drug}$$ Total mass of administered drug
$$k$$ Rate constant
$$t_{1/2}$$ Half-life (time required for $$C$$ to drop by factor of 2)
$$K_\text{clearance}$$ Clearance rate
$$V$$ Volume of distribution

# Drugs — how to define them, evaluate them, and consume them

Photo credit to Gras Grun

The topic of drugs is a minefield of emotional tripwires which prevent people from thinking about them coherently. For example, in 2016 this comment from a physician was published in a leading medical journal in response to a short article describing possible therapeutic uses of psilocybin mushrooms [1]. "All drugs are nightmarish and dangerous. They alter our perception of reality and diminish our ability to reason, both of which endanger us. Drugs create psychological and physical dependence, both of which enslave us." The bar for comments in medical journals is much higher than the bar for comments on a youtube video. Nonetheless, because this issue is emotionally charged, comments from the most esteemed fractions of society can be devoid of any nuance. Drugs, recreational or not, have tremendous potential both positive and negative. If that were not so, either no one would use them (if they had no positive effects) or everyone would use them (if they had no negative effects).

## What is a drug?

Because there is a lot of emotional baggage and social stigma around drug use, there are a lot of conflicting definitions. Most of these are drawn by people hoping to deny their drug use by invoking acrobatic definitions awkwardly bent around certain "acceptable" vices. In this blog, we will use the following definitions to avoid confusion.

drug: a substance introduced to the body for a specific physiological effect not related to nutrition or hydration and often marked by habituation or addiction

recreational drug: a drug that directly changes the conscious experience of the individual by directly acting on the central nervous system

These definitions are noteworthy for what they do not contain: there is deliberately no mention of the legal or cultural status of any substance. The legal status of any substance does not change how it interacts with biological systems.

The other interesting implication is in the phrase "changes the conscious experience". If the dose is low enough, it will not affect the conscious experience and is therefore not a recreational drug. For example, most people would require 10 mL of pure 100% (200 proof) alcohol to notice any effect. If I drink 1 µL of alcohol, I am not using alcohol as a drug; if I drink 100 mL, I absolutely am. Nutmeg is a similar example - at high doses (50-80 g), nutmeg is a powerful hallucinogen, at low doses (2 g divided by 20 cookies = 0.1 g) it is a common kitchen spice [2]. The psychoactive ingredient in nutmeg is myristicin; it comprises 0.2-1.3% of the dry weight of nutmeg putting the effective hallucinogenic dose in the 100s of mg range. Nutmeg overdose is rare but common enough that medical journals keep track of overdose rates [3]. Given than recreational myristicin use is significantly less common than other recreational drugs, it is likely more toxic given there are already several case reports of fatal poisonings [4] despite its relatively uncommon use as a drug.

## Arguments about what is and is not a drug

Of the five most commonly used drugs in the US - alcohol, tobacco, cannabis, caffeine, and sugar - one is illegal at all ages, two are legal for adults, and two are legal for children. There is a serious case to be made that two of those are not drugs - alcohol and sugar. Both are taken in doses two orders of magnitude greater than most drugs, both are metabolized out of the body primarily by cell metabolism, and sugar is not always a drug since it is necessary for our bodies to survive. Elimination of almost every drug follows first-order kinetics but sugar is never completely cleared from the bloodstream (a blood sugar concentration of 0 is lethal) and ethanol is cleared by zero-order kinetics meaning the rate of clearance from the blood is not proportional to concentration [5] (see section on pharmacokinetics). In these articles, we will rely heavily on "changes the conscious experience" in the definition and consider alcohol or sugar intake large enough to induce that change or intakes sufficient to induce "habituation or addiction" to be drugs. These doses correspond to intake levels most likely to lead to deceptively high spending.

Because of the difficulty in categorizing sugar and because it is inextricably linked to mouth pleasures, we will not dedicate a separate article to consuming sugar as a drug. If caffeine addicts are given intravenous caffeine, they are stimulated and satiated; if alcoholics are given intravenous alcohol, they are drunk and satiated; if cigarette smokers are given intravenous nicotine, they do not experience cravings except for forces of habit; but if we give a "sugar addict" intravenous glucose, they probably still want to eat a cake just as much. The desire for sugar is more complicated than blood serum levels can explain so it is not useful to spend a lot of time thinking about how to manipulate blood sugar levels as economically as possible. For health reasons, it is obviously in our interest to lower blood sugar levels (for most of us, and to some extent).

### Legal vs illegal

It is often argued that all illegal drugs are wretched and destructive. The distinction between legal and illegal drugs is only useful insofar as it helps one to avoid legal consequences by either hiding or avoiding certain substances. I am aware of no legal system where drugs are banned and punished in proportion to the hazards they present. Drugs are not banned in proportion to the hazards they present; drugs are banned in proportion to the pleasures they provide. US chemical supply companies can legally ship a plethora of compounds to any residence which have lower LD50s than anything in the controlled substances act (like hydrofluoric acid [6] and cyanide [7]).

There is an even more conclusive reason to agree that the discussion of which drugs are apt or inapt to cause harm requires more nuance than simply referencing a list of controlled substances. Most banned drugs are legal if prescribed by a physician and, regardless of their legal status, all of them have medical applications. Synthetic tetrahydrocannabinol (the active ingredient in cannabis) has been a prescription drug in the US since 1994 to increase appetite in HIV/Aids patients [8]. Cocaine (not a compound like cocaine but real cocaine) is a commonly used drug in the US in the ENT medical specialty as a local anesthetic [9]. Heroin (again, not something like heroin but pure, honest-to-God heroin) is a commonly-prescribed pain drug in the UK where it goes by the trade name "diamorphine" [10]. Methamphetamine is one of the most scare-mongered drugs in the western world at the time of this writing. In the US, it is also a second-line treatment for ADHD and obesity [11]. My goal is not to convince you drugs are hazard-free; there are many hazards associated with drug use. However, there is more nuance involved in deciding which drugs to take and when than can be found on a list titled "Bad chemicals: do not allow in the bloodstream for any reason."

## Trends in death by overdose

Whether supervised by a physician or not, drug consumption is associated with lots of hazards including death. The CDC and the National Center for Health Statistics are the US government bodies that keep track of the death rates associated with drug use. Most drug deaths in the US are caused by opioids or stimulants. Opioids, most famously heroin, shut down the respiratory center in the brain causing death by suffocation [12]. Stimulants, most famously cocaine and methamphetamine, cause death by interrupting the electrical signals in the heart causing cardiac arrest [13]. The frequency of deaths due to overdose, by both opioids and stimulants, has increased significantly in the last decade.

[Caption] The US loses about 20-25 per 100,000 people per year to drug overdose. Most drug deaths in the US are the result of opioid (15 per 100,000) or stimulant (8 per 100,000) overdoses. All data from the National Center for Health Statistics [14].

## How drugs affect you — pharmacodynamics

Drugs exert their effects by interacting with receptors on the surface of cells or interacting with neurotransmitters which normally interact with receptors. Cell receptors are proteins that sense the environment surrounding the cell via chemical interaction and cause chemical changes within the cell to occur which alter the cell's activity (cause it to make more of something, less of something, move, reproduce, etc). All drugs which directly affect our conscious experience interact with cells in the brain in ways we do not fully understand. This is true of all drugs with psychoactive effects including pharmaceuticals for mental and neurodegenerative conditions; we know more about some drugs than others but the brain is such a complex and poorly understood organ that any claim of the kind "we understand everything about the mechanism of this drug" is simply untrue.

We cannot deliver psychoactive drugs directly to their sites of action. There are only a few drugs we can deliver directly to their site of action: some ophthalmic drugs are administered directly to the eyes, topical anesthetics are administered directly to the site of pain, most dermatological drugs are administered to the skin at the location of disease, and some rectal/vaginal drugs are administered directly as well. Psychoactive drugs are not applied directly to the brain through a hole in our heads, they are administered to the bloodstream directly by IV or indirectly through the lungs, gastrointestinal tract, or absorption through the mucosal tissues within the mouth, vagina, or rectum. The blood carries the drug to the brain and from there it interacts with the receptors and creates a change in consciousness. Because all psychoactive (and the majority of non-psychoactive) drugs are administered to the bloodstream, we think of the strength of the dose as the concentration in the blood or concentration in the blood serum (the portion of the blood that is not red cells).

It is important to remember that drug serum concentration is not a complete description of how intoxicated a person is or how they feel. Consider this discussion of lithium treatment in bipolar patients [15]. The therapeutic serum concentrations and side-effect inducing concentrations have considerable overlap. This does not mean the drug is useless, it means that serum concentration alone cannot fully predict the effects of a drug. In addition to the variability of tolerance between people, how we feel is a function not only of the drug concentration but of the derivative of the drug concentration with respect to time, the sign of the derivative (is the concentration increasing or decreasing?), blood sugar levels, pain levels, and mental status (were you generally anxious, angry, sad, etc before taking the drug?). When measuring impairment, blood concentration and the derivative with respect to time are usually the most important factors. When attempting to quantify how a person feels, the other factors become significant as well.

## Effects of the route of administration

Recreational drugs have a site of action somewhere in the brain. Because we cannot administer drugs directly into the brain, we have to administer them into the bloodstream and let the blood take it to the brain. There are a few ways to do this [16]:

• injection (directly into the bloodstream)
• oral administration (we eat/drink it)
• inhalation (snort it for powders/solids, vaporize/nebulize it for liquids, or inhale directly for gases)
• smoke it (chemically alter via combustion immediately before inhalation)
• absorption (oral mucosa, "sublingual")
• absorption (through large intestine after rectal insertion, "suppository")
• absorption (through the skin, "patch")

For some of these methods, it is likely that most of the drug applied does not make it to the bloodstream. In terms of efficiency, injection is the gold standard - 100% of whatever is injected directly into the bloodstream arrives in the bloodstream (this is as tautologically true as it sounds). To evaluate the effectiveness of different routes of administration, pharmacologists use the definition of bio-availability - how much drug is in the bloodstream and for how long compared to the injection method [16,17].

$$\text{bioavailability}_\text{route} = \frac{\left(\int_0^\infty C_\text{drug} dt\right)_\text{route}} { \left(\int_0^\infty C_\text{drug} dt\right) _\text{injection}}$$

The concept of bioavailability is important because there are lots of reasons a molecule administered to the body may not ever see systemic circulation. Orally administered medication is the most susceptible because of "first-pass metabolism." All of the stomach contents that are absorbed into the bloodstream do not go back to the heart and then into the brain. Blood that passes the stomach and intestines travels directly to the liver where the majority of the CYP family of enzymes are expressed (more on them later). These liver enzymes have a chance to chemically modify anything entering the body via the GI tract before it can reach other organs like the brain.

[Caption] Blood from the gastrointestinal tract travels directly to the liver via the hepatic portal vein [18,19,20]. This allows the liver to make a first attempt processing any toxins before they enter the systemic circulation. Because all orally administered drugs enter the liver prior to systemic circulation, we refer to this process as "first-pass metabolism." First-pass metabolism significantly lowers the bioavailability of drugs which are processed in any significant way by the liver. Most capillary beds in the body are arranged in parallel. "Portal systems," circulation paths with two capillary beds in series, are rare. The hepatic portal system (described here) is the largest. Humans have two other portal systems: one in the brain (the hypophyseal portal system) and one in the kidneys (the renal portal system). The term "portal venous system" refers to the hepatic portal system unless otherwise indicated. Clipart lungs, heart, and body from free sources.

All methods of drug administration other than venous injection result in some loss of material that never arrives in systemic circulation. For any given drug, the concept of bioavailability is important for deciding on dosage and route and for comparing different routes of administration.

## How the body clears drugs — pharmacokinetics

Most drugs are removed from the body via first-order kinetics (meaning the differential equation describing their elimination is first-order). This is the simplest and most common equation describing drug concentrations in the body. It is most accurate in the context of an intravenous injection [21]. $$C_\text{drug}$$ is the concentration of the drug either in the blood or the serum.

$$\frac{dC_\text{drug}}{dt} = k C_\text{drug} = \frac{\log(2)}{t_{1/2}} C_\text{drug}$$

This equation is where the concept of a half-life comes from; it is inversely proportional to the rate constant. $$t_{1/2} = \frac{\log(2)}{k}$$

A small extension of this equation gives us the formula for clearance which describes the rate of elimination in terms relevant to the efficiency of the kidneys. Multiply both sides by $$V$$, the volume of distribution of the drug in the body. While the rate constant has units of min-1 or hr-1, the clearance rate is a volume per time, L min-1.

\begin{align} V \frac{dC_\text{drug}}{dt} =& Vk C_\text{drug} \\ \frac{dm_\text{drug}}{dt} =& K_\text{clearance} C_\text{drug} \end{align}

When we look at drugs in the body, we see that the vast majority exhibit decay curves like those shown below. Drugs which do not follow first-order kinetics are rare: ethanol (the alcohol you drink follows zero-order kinetics) [5], phenytoin (high therapeutic doses result in zero-order kinetics, low doses are first-order) [22], fluoxetine [23], and salicylates like aspirin [24].

[Caption] Decay curves for four drugs selected to show a range of decay constants and serum concentrations. [a.u.] = arbitrary units.

## Dosing and pharmacokinetics of common drugs

[Caption] Data on common recreational drugs from psychonautwiki.org (typical dosing) and wikipedia (half-life) retrieved 2019-07-04 except sugar which was decided by the author (1/2 bag to 10 bags of king size skittles). Upper limits are about a factor of 2 for the number given by pyschonautwiki.org "heavy" dose (for example ">500 mg" became 500-1000 mg on this chart). It is also worth noting that the majority of medical pharmaceuticals are dosed for adults in the same range (10s to 100s mg) as most of the drugs on this chart.

It is also worth noting that the half-life of drugs in the body varies over several orders of magnitude. LSD, cannabis, and methamphetamine can stay in the circulation with notable effects for over a day while heroin and DMT are typically cleared in a matter of minutes.

## How drugs are processed — the variation in half-lives

Metabolism of most drugs follows a two step process, "phase I" or modification, and "phase II" or conjugation [25]. Both reactions increase the water solubility of the target, allowing it to be more readily excreted in the urine. Phase I reactions add a hydroxyl or carboxyl group to a toxin/drug via an oxy/redox, hydroxylation, or hydrolysis reaction. Modification (phase I) relies on the cytochrome P450 enzyme superfamily and largely accounts for the variation between drug half-lives in different people. Phase II reactions add a sulfate [25], acetyl [26], methyl [25], glycine [27], or glucoronic acid (a glucose with an added carboxyl group) [25] to the drug/toxin. Usually this group is attached to the hydroxyl or carboxyl group applied in phase I. Conjugation (phase II) enzymes are more uniformly expressed. Because one of the most well-known conjugation reactions is acetylation, pharmacologists and doctors often describe people as either fast or slow "acetylizers" in reference to the half-lives of drugs in their bodies.

### The CYP450 enzyme system and the variability of drug metabolism rates

To be excreted efficiently by the kidney, and often to be inactivated before then, the body relies on a superfamily of enzymes - the cytochrome P450 system or CYP enzymes. Cytochromes are proteins bound to heme (an iron-containing molecule) which allow the heme to undergo redox reactions. This group of cytochromes was originally detected by their unusual absorption of 450 nm lightwaves, hence cytochrome p450 or CYP450. They are named CYP[family #][sub family letter][number designating the form] so CYP2D6 is CYP of family 2, subfamily D, and form 6 [28]. CYPs exist throughout the body but are most highly concentrated in the liver. Within this superfamily, over 50 varieties have been identified in humans. The most common CYP450s are CYP3A4 (most common, 30-40% of CYPs in the liver [25]), CYP3A5, CYP2C9, CYP2D6, and CYP2C19. Together, these five CYP450 enzymes do 80% of the work detoxifying drugs and preparing them for excretion [28].

The CYP450 system is highly adaptive and variable in its response to stimuli between people. A quick google for "cyp inhibitors and inducers table" can provide a whole list of compounds, mostly pharmaceuticals, which alter the expression of the CYP450 system (either inducing or inhibiting) or certain elements within it. This is one common mechanism of drug interaction [29]. For example, consider the following list of antidepressants: citalopram, norfluoxetine, sertraline, amitriptyline, clomipramine, imipramine, cyclobenzaprine, mirtazapine, nefazodone, reboxetine, venlafaxine, trazodone, and vilazodone. Every one of those antidepressants is metabolized by CYP3A4. St. Johns wort is an inducer of CYP3A4 so if a person on antidepressants starts taking St. John's wort (as the local hippie-mart often suggests), the serum concentration of their antidepressant will crater [30]. On the other hand, if they start chugging grapefruit juice as a part of a health kick, the grapefruit juice will inhibit CYP3A4, the serum concentration of their antidepressant will increase, and they may start experiencing nasty side effects [31,32]. Grapefruit is the most potent CYP inducer or inhibitor found in the grocery store. For example, a daily glass of grapefruit juice can increase the blood serum concentration of statins by 100-300% [33] and the effects of grapefruit juice on the CYP enzymes can persist through several days of abstinance [34]. CYP interactions are also the driver of Tylenol/alcohol toxicity [25].

This concept applies equally well to recreational drugs. Of the five most common drugs in the US, three of them are metabolized by the CYP system (ethanol and sugar are weird and not drug-like in their metabolism or dosing). Tetrahydrocannabinol (THC) from cannabis is metabolized by CYP2C9 and CYP3A4 [35]; nicotine is metabolized by CYP2A6 [36,37]; and caffeine is metabolized by CYP1A2 [38,39]. Additionally, chronic alcohol [40,41] and nicotine [42] are inducers of several CYP enzymes. There is some evidence THC is a CYP inducer while cannabidiol (CBD) is a CYP inhibitor [43] (THC and CBD are the primary compounds of interest in cannabis). Obviously, chronic consumption of a drug that induces the expression of CYP enzymes leads to higher tolerance and higher dosing to maintain efficacy. However, this is not the only mechanism of acquiring tolerance.

This system is further complicated by the variety of alleles each person may have of any one CYP enzyme and those alleles may vary in efficacy [44,45]. The study of allelic variation of CYP450 enzymes is a large enough effort to warrant a dedicated organization [46]. Data on the structure, sequence, and function of variant CYP450 enzymes are now cataloged at pharmvar.org. The only saving grace for any of us when taking drugs, recreationally or from a medical professional, is the wide range of serum concentrations we can tolerate for most drugs. Most drugs have a therapeutic window spanning at least one order of magnitude so if our dosing is off by a lot, maybe the effect is a little unexpectedly strong or weak, but we can tolerate a fair bit of error without dying from an overdose or missing the effective window completely.

Street drugs present a further problem. When you buy heroin off the street, you are buying a mystery powder of unknown concentration, which you are injecting into your bloodstream in the presence of CYP enzymes whose activity at the moment is but a guess, CYP enzymes whose activity is constantly changing in response to other things you may be taking, and you are aiming for a therapeutic window so narrow that if you were hoping for a small dose and missed by less than two orders of magnitude, you die. The only thing keeping junkies alive is the greed of street dealers diluting their products with other white powders and preventing the junkies from obtaining the quantities of drug they desire. An "honest, good" dealer selling much purer products than his/her competitors is likely to produce a host of deaths because of the sudden dramatic change in dosing required. For context, depending on the study, street heroin purity is between 20% and 99% with the rest comprised of baking soda, sugar, OTC pain pills (acetaminophen), or caffeine [47,48,49,50,51,52] (interestingly, caffeine increases the bioavailability of heroin so it functionally increases the potency [53]). If it has to be diluted with something, the best choice is probably sugar since OTC pain pills have liver toxicity issues (and do nothing for the goal of euphoria), and injecting baking soda is a uniquely unpleasant experience. Baking soda is basic so it changes the blood pH. The sensors the body uses to decide when to breathe and how much are pH sensors so changing the blood pH directly interferes with mechanisms that regulate breathing [54].

As a society, we could do a far better job getting junkies high. Consider Jessa Reed's meth binge when she decided the metabolism of meth was incomplete enough that drinking meth piss was the sensible economical choice. It probably was not as good an idea as it seemed at the time; 50% of the meth she injected was chemically modified before excretion into the urine [55] but that still represents a significant cost savings. She would have been even higher had she simply googled for CYP2D6 inhibitors [56] (amiodarone, buproprion, chloroquine, cinacalcet, diphenhydramine, fluoxetine, haloperidol, imatinib, paroxetine, propafenone, propoxyphene, quinidine, terbinafine, etc). If any meth addict is reading this, I am curious to know if the drowsiness of diphenhydramine (over-the-counter Benadryl) is countered by the increased meth concentrations from the CYP2D6 inhibition.

## Soapbox

This brings us to one of the great arguments in favor of legalization: quality control. If the junkies know what dose they are taking, you have to clean fewer bodies off the street, or so the argument goes. This argument has merits but it has been undermined by the opioid epidemic. For about 20 years, the US decided to treat drugs as dangerous as heroin with the nonchalance of drug store candy and the results have been catastrophic. For perspective, we kill 0.01% of the US population every year in auto accidents. We kill 0.023% of the population with opioid misuse and that number has doubled every decade, 3 decades running. Regardless of your stance on legalization, it is not a panacea.

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