Pharmacodynamics of Antimicrobials


5
Pharmacodynamics of Antimicrobials


Andrew P. Woodward and Ted Whittem


Classically, in teaching, pharmacodynamics has been defined as “what the drug does to the body,” in contrast to pharmacokinetics which is “what the body does to the drug.” In modern scientific practice, these concepts overlap under the broader banner of quantitative pharmacology and are integrated in antimicrobial dosage design. The antimicrobials, along with the antiparasitic and antineoplastic agents, are unique among the therapeutics in that their pharmacodynamics do not express only those effects on the biochemistry or physiology of the patient but also that of a foreign invader. Therefore, considering the action of the drug on only the “body” is not quite correct, as the pharmacodynamics are complex actions of the drug on the interaction of the body and pathogen. Nonetheless, similar principles may be applied.


An important implication for veterinary clinical practice is that the pharmacodynamics ensuring the efficacy of antimicrobials are largely pathogen specific, rather than host specific, so similar principles are applicable for diverse patients.


In this chapter, we will explore the following key concepts in antimicrobial pharmacodynamics.



  • The mathematical foundations of pharmacodynamics, and how popular measures of antimicrobial effect are related to the fundamental theory.
  • Popular clinical models of pharmacodynamics, and how dosage regimen recommendations are derived from basic principles.
  • Scientific techniques that have been applied to study pharmacodynamics and the implications they have for clinical reasoning.

Measurements and Models in Pharmacodynamics


A Clinical Scenario


The treatment of disease in wildlife species is an emerging area of importance for veterinary therapeutics, with diseases such as chytridiomycosis, sarcoptic mange, chlamydiosis, and others important in Australia, for example (Smith et al., 2009). A challenging aspect of this undertaking is that clinical evidence in the form of randomized trials may not be available, and patient and pathogen diversity mean that direct extrapolation from clinical experience may be unreliable. Fortunately, as explored in this chapter, we can apply a bottom‐up style of reasoning to utilize our knowledge of antimicrobial drug action, even when we only have partial information.


Consider the following example: A colleague working in a zoological institution contacts you for help with a disease outbreak in a captive population of lizards, which are managed in a captive breeding program. This lizard species is critically endangered; no individuals are known to exist outside this managed population. The disease outbreak is potentially devastating for the future of this species; several individuals have died and at least a dozen more appear to have consistent clinical signs. Postmortem examination is consistent with bacterial pneumonia and secondary sepsis, so you send a series of samples to a reference microbiology lab for investigation.


The following afternoon, you receive a phone call from the microbiologist, who seems quite excited. Apparently, the laboratory team has isolated heavy pure growth of fast‐growing Gram‐negative bacteria, genus Pseudomonas, from all the postmortem samples. Previously, this organism has only been associated with disease in invertebrates. The laboratory team is keen to pursue a deep investigation to publish its findings about a novel pathogen; however, you have a more pressing problem. What action should you take to protect this population from disease? Isolation and biosecurity may help to prevent spread but will be of no benefit to those already infected. Vaccination might protect the whole population but inevitably requires substantial time and resources. Antimicrobial therapy seems necessary. But which drug? What dosage regimen? You’re just starting your literature search when you receive an email from the laboratory: “We just finished running some broth microdilution tests on that organism. I believe enrofloxacin is widely used in reptiles? Looks like the enrofloxacin minimum inhibitory concentration (MIC) is 1 μg/ml. The guideline doesn’t include any breakpoints for this organism but maybe you have some other information about the appropriate dose for this drug?”


This type of situation presents a substantial therapeutic challenge. There is a compelling need for antimicrobial therapy but past clinical experience provides little direct guidance. Evidence‐based medicine principles suggest that controlled trials are key support for therapeutic decisions but no relevant studies are available. How can more accessible pharmacological information be applied to make reasonable, bottom‐up decisions about antimicrobial therapy?



  • What does the MIC, among other laboratory measures, tell us about antimicrobial drug action?
  • Can the MIC, measured in vitro, provide useful predictions about drug activity in vivo?
  • What is required to translate our knowledge of antimicrobial drug effect to clinical action?

Similarly, after the identification of chytridiomycosis, a critically important fungal disease of amphibians, veterinarians attempted to treat the last known members of an Australian species, and wrote about their experience (Banks and McCracken, 2002). Though these examples seem extreme, every patient is ultimately unique and so every clinical decision requires consideration of a network of supporting evidence. These same questions are useful to consider in all our clinical applications of antimicrobials.


The Minimum Inhibitory Concentration: A Fundamental Quantity


In the clinical scenario, our colleagues from the microbiology laboratory reported the MIC to describe the effect of enrofloxacin. The MIC is the simplest quantitative summary of the effect of an antimicrobial drug in common use. As we will explore in this chapter, the MIC summarizes a functional relationship with just one value but the ease of generation, standardization, and interpretation has made the MIC the most widely reported and utilized measure of antimicrobial effect.


To determine the MIC, the microorganism of interest, typically bacteria, are inoculated into a suitable growth medium (Chapter 2). The experiment is usually conducted on a micro‐volume cell culture plate, such as a 96‐well plate. The growth medium contains antimicrobial drug in a dilution series, typically a two‐fold dilution. In clinical laboratories, for antimicrobial agents that are well characterized, the actual drug concentrations are standardized. In the development or research setting, the appropriate concentration range to test may be an open question, which may warrant use of a different dilution series (such as a five‐fold or ten‐fold series). The final assay therefore includes a growth assessment for each of a series of drug concentrations. The assessment is usually by a simple visual examination of each well, and is binary: either growth is observed (negative response) or it is not (positive response).

A histogram of probability density versus concentration in micrograms per milliliters. It depicts a bell-shaped trend.

Figure 5.1 Histogram capturing an observed MIC distribution for a sample of a hypothetical bacterial population. The underlying MICtrue was simulated from the normal distribution, on log2 scale, with mean 0.5 and standard deviation 2. The solid line captures the observed probability density of the MICtrue, while the histogram represents the MICobs under the usual case of interval censoring. Histogram break labels are centered, reflecting the MICobs.


Adapted from van de Kassteele, 2012.


An important characteristic of the MIC is that the observations actually represent a range rather than a point value. Presuming that there is a “true” underlying MIC value, MICtrue, that the assay is attempting to estimate, the observed MIC, MICobs, represents an interval in which MICtrue is estimated to occur. Because the assay response at the MIC was negative, the true MIC must be lower than that; conversely, because the response at the concentration below the MIC was positive, the true MIC must be higher than that. The observed MIC is therefore interval censored; the true minimum concentration could be the observed MIC but it must be smaller than the next concentration above the observed MIC. An MICobs value of 2 μg/ml, for example, represents any value greater than 1, and any value less than or equal to 2, and could be expressed as (1,2] μg/ml (Figure 5.1). This is an important consideration in the epidemiology of MICs for resistance monitoring, and experimental determination of MIC for new antimicrobials (van de Kassteele et al., 2012).


The MIC has substantial importance, as both the most common statistical summary of antimicrobial potency and as a parameter in pharmacodynamic models that express our understanding of drug effect in vivo. Potency in pharmacodynamics refers generically to the dose or drug concentration at which drug effect occurs. A widely discussed concept is that drug potency does not indicate efficacy, because it reflects only the dose at which effect occurs, not the size of the effect. A classic example of this principle is the use of the low‐potency opioids morphine and methadone in the dog and cat; analgesic efficacy is substantially better than the higher‐potency buprenorphine or butorphanol but a larger dose is required. The MIC can be considered as a hybrid measure, which reflects both a statement about the effect size and a statement about potency, and is closely related to other pharmacodynamic measures.


Quantitative Descriptions of Drug Action


Similarly to pharmacokinetics, pharmacodynamics has strong underlying mathematical theory, and much of our understanding and the way we communicate about pharmacodynamics are linked to that theory. Also like pharmacokinetics, the theory can be applied quite directly to clinical questions. Here is a simple conceptual model of drug effect:


Equation 1:  upper E left-parenthesis upper X right-parenthesis equals f left-parenthesis upper X right-parenthesis

where X is the concentration of drug at its site of action, E is the magnitude of the drug effect, and f (X) is the functional relationship between concentration and effect. This expression is read as a statement that the drug effect at some drug concentration depends upon the concentration.


Intuitively, when X is zero, E is also zero (though in the real biology, other processes might also influence the observed effect). Pharmacodynamics can be simply defined as the study of f(X) – the quantitative relationship between effect and drug concentration. In contrast, pharmacokinetics can be considered as the study of factors that control X. In living systems, drug action is inevitably occurring alongside drug disposition, meaning that X is not constant or controlled but is subject to diverse biological processes. By contrast, in the laboratory, pharmacodynamics is studied in isolated in vitro systems in which drug concentration can be closely controlled. Our understanding of f(X) as it occurs in vivo is closely linked to our understanding of the time course of X, and popular clinical models for antimicrobial effect actually pool information regarding X and f(X).


The receptor–ligand theory of drug action (Rang, 2006) poses that all pharmacological effects occur because of a direct chemical interaction between the drug and some biochemical process of a living system. Most drug action occurs via reversible chemical interaction between the drug molecule and one or more target molecules, which are usually proteins. These interactions typically involve hydrogen bonds, in which a weak electrostatic relationship forms between a hydrogen atom and an electronegative oxygen, nitrogen or fluorine atom. The biochemical target of drug action may be a membrane‐bound receptor, a cytoplasmic second messenger, a membrane‐spanning channel, or an enzyme, among other possibilities. Depending on the receptor type and the specific drug, the function of the receptor is suppressed, triggered or modified when drug binds to it. Formally, these interactions may be described as equilibrium processes:


Equation 2:  left-bracket upper D right-bracket plus left-bracket upper R right-bracket left right double arrow Underscript upper K d Endscripts left-bracket upper D upper R right-bracket

The interaction of free drug D with receptor R results in the formation of a drug–receptor complex DR, and the complex DR dissociates to return free drug D and receptor R; the concentration [DR] at equilibrium (the state at which there is no net change occurring over time) is dependent on the concentrations of drug [D] and receptor [R], and on the drug’s binding affinity. The binding affinity is determined by how energetically favorable the product is relative to the reactants. Binding affinity is expressed by an equilibrium disassociation constant Kd. Note that the bidirectional Equation 2 can be equivalently expressed as two linked unidirectional reactions, each with their own rate, and Kd is the ratio of those rates. Because the reaction is bidirectional, Equation 2 implies that after any individual drug–receptor interaction has occurred, both the drug and target molecules are recovered unchanged. The action of the majority of antimicrobials is of this reversible type, with some important exceptions. Drug action occurs via formation of the complex DR – either agonism, in which drug binding stimulates the activity of R, or antagonism, in which drug binding inhibits the activity of R.


Probably the most fundamental task in pharmacodynamics is to determine the shape of the relationship f(X); in other words, to learn the relationship between drug concentration and drug effect from experimental data. This is a statistical task; we obtain an understanding of the system by examining observations of its behavior. Similar to learning from experimental data in pharmacokinetics, a simple mathematical model is a useful way to ground our analysis in theory. Some important clues are given by Equation 2. For an equilibrium reaction, in a low‐concentration state for the drug, the concentration of the drug–receptor complex at equilibrium is also relatively low. If the effect of a drug is causally related to the concentration of the drug–receptor complex, the observed drug effect would be correspondingly low. At a high drug concentration, the concentration of the drug–receptor complex is also relatively high, because the equilibrium reaction energetically favors formation of the product (balance is shifted to the right), and a correspondingly high drug action would be observed.


An interesting implication of Equation 2 is that the shape of the relationship between drug concentration and effect is not linear. In the transition from a very low concentration state to a very high concentration state, drug effect will also increase but the amount of increase will not be constant. This is difficult to appreciate directly from Equation 2. A reformulation of Equation 2 called the Langmuir equation, a classic model from physical chemistry, can be specified in terms of drug concentration [D] and dissociation Kd:


Equation 3:  theta equals StartFraction left-bracket upper D right-bracket Over upper K d plus left-bracket upper D right-bracket EndFraction

where the proportion (between 0 and 1) of receptor binding θ at equilibrium is a function of both the drug concentration [D] and the disassociation rate constant Kd. This model presumes that the receptor concentration is constant, which is mostly reasonable in pharmacology. Figure 5.2 is a classic visualization of the general form of this relationship between a drug concentration [D] and the proportion of the receptor occupied, θ. The most important feature of Figure 5.2 is that for drugs with a single site of action, the transition from minimal drug effect to maximal drug effect occurs within a relatively narrow concentration range.


In practice, this underlying equilibrium reaction is difficult to work with, and is only indirectly related to our process of interest, the relationship between concentration and antimicrobial effect. Fortunately, a sigmoidal dose–response relationship can be conveniently defined using its own equation. The classic sigmoidal dose–response curve can be expressed as (note the similarity to Equation 3):


Equation 4:  StartFraction upper E left-parenthesis upper X right-parenthesis Over upper E Subscript upper M upper A upper X Baseline EndFraction normal equals normal StartFraction upper X Over left-parenthesis upper X plus upper E upper C 50 right-parenthesis EndFraction

An interesting feature is that the drug effect is expressed as a proportion of its maximum. Rearranging the equation by multiplication of both sides by EMAX allows this parameter to be determined:


Equation 5:  upper E left-parenthesis upper X right-parenthesis equals StartFraction left-parenthesis upper X dot upper E Subscript upper M upper A upper X Baseline right-parenthesis Over left-parenthesis upper X plus upper E upper C 50 right-parenthesis EndFraction
A graph of the proportion of receptor occupied versus drug concentration in arbitrary units depicts three S-shaped curves. All three curves start at 0 and end at 1 with variation in the dissociation constant values 1, 10, and 100.

Figure 5.2 A simple drug–receptor interaction model, Langmuir’s isotherm as in Equation 3, describing the proportion of receptor occupied θ as a function of drug concentration [D] (here in arbitrary units). The equilibrium dissociation constant Kd is set to one of three values (1, 10, or 100), which appear ordered from left to right. Note the logarithmic scale of the x‐axis.


This expression contains two parameters; a parameter is a quantity in our system that takes a constant but potentially unknown, value. EMAX defines the maximum possible effect, which is the effect E when the concentration X is infinitely large. This expression proposes that the effect E is zero where drug concentration is zero. In many cases, this is not reasonable. For example, the antifungal drug terbinafine (Chapter 19), a popular therapy for dermatophytosis, inhibits the enzyme squalene epoxidase which converts the metabolite squalene into precursors for ergosterol, a key cell membrane component. Squalene is present in the normal fungal cell but is toxic at high concentrations, so inhibiting this enzyme results in fungal cell damage. We could define the drug effect of terbinafine simply as the squalene concentration, which could be measured in an in vitro experiment. As terbinafine concentration increases, the squalene concentration will also increase. However, some squalene is present even if the terbinafine concentration is zero. In this case, Equation 6 would be more suitable:


Equation 6: upper E left-parenthesis upper X right-parenthesis equals upper E Subscript upper M upper I upper N Baseline plus StartFraction left-parenthesis upper X dot left-parenthesis upper E Subscript upper M upper A upper X Baseline minus upper E Subscript upper M upper I upper N Baseline right-parenthesis right-parenthesis Over left-parenthesis upper X plus upper E upper C 50 right-parenthesis EndFraction

Now we have parameters representing both the maximum effect (EMAX) and the minimum effect (EMIN). The value of E actually approaches these limits asymptotically (they are not reached at any real concentration), which is practically reasonable, as with real measurements we cannot distinguish zero from arbitrarily small values.


The remaining parameter EC50 is typically of most interest. This can be interpreted as the concentration at which the response is half of the maximum response. Strictly speaking, it is the concentration at which the effect is equidistant between the EMIN and EMAX, as specified in Equation 6. In some systems, depending on how response is defined, the EMIN may not be zero, in which case the effect at EC50 will not represent “half” but in practice the data are often scaled to set the minimum effect at zero. In that case the parameters then represent relative effects. This reflects the emphasis on the estimation of EC50 as a single summary of drug effect but it does not contain any information about the magnitude of the effect. Practical studies in drug development often focus on this parameter when reporting pharmacodynamics of novel drugs or systems.


A good way to understand the implications of these equations is to visualize them. Modifying the EMAX has the effect we would expect, which is that the y‐axis position of the upper asymptote changes directly with the value of EMAX (Figure 5.3).

A graph of response in arbitrary units versus drug concentration in arbitrary units depicts three increasing curves starting at the same point and ending at three different maximum possible effect values of 100, 125, and 150.

Figure 5.3 A typical sigmoid dose–response model, as in Equation 6, describing the system response E as a function of drug concentration X (both here in arbitrary units). The maximum possible effect EMAX is set to one of three values (150, 125, or 100), which appear ordered from top to bottom. EMIN is set to zero and EC50 to 10. Note the logarithmic scale of the x‐axis.


Similarly, modifying the EMIN simply changes the y‐axis position of the lower asymptote (Figure 5.4).


An important observation is that these adjustments to the EMAX and EMIN have no influence on the horizontal position of the relationship, that is, the drug concentration at which drug effects occur. The x‐axis position of the relationship is exclusively modified by the EC50 (Figure 5.5).


Increasing the EC50 shifts the x‐axis position of the relationship to the right, meaning that the same drug effect occurs at higher concentration. Decreasing the EC50 shifts the x‐axis position to the left, representing effects occurring at lower concentration. The EC50 is therefore often utilized as an expression of drug potency. Qualitatively, potency is simply the inverse of EC50, i.e., high‐potency drugs have a low EC50, meaning that their effect occurs at low concentration; conversely, low‐potency drugs have high EC50, i.e., their effect occurs at high concentrations. This highlights the common misuse of potency as a synonym for efficacy, which is in fact is related to the magnitude of the maximum drug effect (EMAX), not to the amount of drug required to generate that effect. High‐potency agents may have low clinical efficacy if their maximum effect is weak, and low‐potency agents may have high clinical efficacy if their maximum effect is large. Therefore, in pharmacodynamic studies we should be careful to assess the entire estimated relationship, rather than focus on individual parameters. In clinical practice, potency is one of the most important factors that dictates drug dose.

A graph of response in arbitrary units versus drug concentration in arbitrary units depicts three increasing curves starting at three different minimum possible effect values of 0, 25, and 50 and ending at the same point.

Figure 5.4 A typical sigmoid dose–response model, as in Equation 6, describing the system response E as a function of drug concentration X (both here in arbitrary units). The minimum possible effect EMIN is set to one of three values (50, 25, or 0), which appear ordered from top to bottom. EMAX is set to 150 and EC50 to 10. Note the logarithmic scale of the x‐axis.

A graph of the response in arbitrary units versus drug concentration in arbitrary units depicts three S-shaped curves. All three curves start at 0 and end at 1 with variation in concentration at which effect is 
half-maximal, 1, 10, and 100.

Figure 5.5 A typical sigmoid dose–response model, as in Equation 6, describing the system response E as a function of drug concentration X (both here in arbitrary units). The concentration at which effect is half‐maximal, EC50, is set to one of three values (1, 10, or 100), which appear ordered from left to right. EMAX is set to 100 and EMIN to 10. Note the logarithmic scale of the x‐axis.


Although the EC50 is often considered a default reporting standard for drug potency, which is convenient as it is a primary parameter in popular models like Equation 6, sometimes other potency measures are used. For example, if the concentration causing a mostly complete effect is of more interest, the EC90 or EC95 might be selected instead (note that the EC100 is always infinite, by definition). Often the highest drug concentration achievable in vivo is constrained by a solubility limit, toxicity, or pharmaceutical considerations; if a near‐maximal effect is desired, this information is poorly communicated by EC50.


Equation 6 implies that the relationship between a drug effect and concentration can be completely expressed by the magnitude of the effect, and the midpoint between the asymptotic minimum and maximum effects. This omits an important process, which is the slope of the relationship between effect and concentration. We can imagine a case in which the EC50, EMIN, and EMAX for two drugs under the same conditions are identical but the steepness of the change in effect with concentration is different between them. In equilibrium chemistry, a modification known as the Hill–Langmuir model (Hill, 1913) utilizes an exponent on X to modify the shape of the basic sigmoid function. This expression, initially applied to the study of hemoglobin oxygen binding, is foundational to quantitative pharmacology. This model has the form:


Equation 7:  upper E left-parenthesis upper X right-parenthesis equals upper E Subscript upper M upper I upper N Baseline plus StartFraction left-parenthesis upper X Superscript n Baseline dot left-parenthesis upper E Subscript upper M upper A upper X Baseline minus upper E Subscript upper M upper I upper N Baseline right-parenthesis right-parenthesis Over left-parenthesis upper X Superscript n Baseline plus upper E upper C 50 Superscript n Baseline right-parenthesis EndFraction

The simpler model in Equation 6 can be thought of as a special case of this model, where the exponent n is equal to 1. The value of this exponent must be positive. We can visualize how this value affects the shape of the concentration–effect relationship (Figure 5.6).


Applications of Pharmacodynamic Models


The model expressed in Equation 7, among other similar forms, is a common pharmacodynamic (dose–response) model in practical use, similarly to the compartmental model broadly applied in pharmacokinetics. Compared to Figure 5.4, note that in Figure 5.5 the horizontal position of the function is not exclusively contributed by the EC50 except at X equal to the EC50, which highlights the potential importance of secondary parameters such as EC90. In Hill (1913), the exponent n is proposed to have a physical interpretation in terms of nonindependent binding; that is, once some binding has already occurred, additional binding events are more or less likely than the first.


The original use for Equation 7 was the description of oxygen‐binding kinetics of hemoglobin, in which multiple oxygen molecules are bound to each hemoglobin molecule and n reflects the number of binding sites. The physical interpretability of these parameters is controversial (Weiss, 1997). In typical pharmacodynamic studies, the parameters, especially n, should not be taken as physically meaningful; they capture useful information about the behavior of the system but their value is not directly linked to any real quantity.

A graph of the response in arbitrary units versus drug concentration in arbitrary units depicts three S-shaped curves labeled 2, 1, and 0.5 intersecting at the center.

Figure 5.6 A typical sigmoid dose–response model including Hill coefficient, as in Equation 7, describing the system response E as a function of drug concentration X (both here in arbitrary units). The coefficient n which controls the steepness of the function is set to one of three values (0.5, 1, or 2) in order of increasing steepness. EMAX is set to 100, EMIN to 0, and EC50 to 10. Note the logarithmic scale of the x‐axis.


This issue highlights an important scientific principle, which has substantial implications for our understanding of pharmacology generally but especially pharmacokinetics and pharmacodynamics. Our sigmoid concentration–response model is a strongly empirical model. This model is a useful tool to formalize our understanding of experimental data but it has no clear relationship to real physical characteristics of the actual system being studied. Introducing the exponent parameter n increases the flexibility of our model, so that it is able to align more closely with our observations, but this does not mean that the value of the parameter n corresponds to any particular physical process or event. The popular pharmacokinetic parameters, such as clearance and volumes of distribution, have similar limitations. Though it is very clear that parameters of common statistical models, such as linear models, have no physical interpretability at all, pharmacokinetic and pharmacodynamic parameters are partially mechanistic, so the limits of their interpretation need to be carefully appreciated.


The same underlying model is often applied more generally, with indirect measures of concentration and response substituted. For example, a classic concept is a “dose–response” model, in which the predictor variable X is replaced with an administered dose, which is more direct. A further abstraction is to replace the drug effect with a population statistic representing the proportion of subjects that have positively responded. For example, in a dose‐finding study observing a large number of treated patients with a range of administered doses, the response may be defined as the cumulative proportion of subjects who have a successful outcome, which may be a useful approach to evaluate the benefit of antimicrobial therapy at different doses in clinical usage.


The final model expressed in Equation 7, and various reparameterizations, can be applied to data from diverse experimental designs. Like the compartmental models applied in pharmacokinetics, this model is statistically nonlinear, so requires iterative techniques for statistical analysis; multiple sets of parameter values are systematically searched to find those that provide the best fit to the data, given the proposed model structure. Similarly to statistical practice in pharmacokinetics (Chapter 4), two‐stage methods in which subject‐level data are individually assessed have predominated in the past and remain common, and are widely supported in many software environments. More cohesive and statistically rigorous estimation is provided by population methods, which use multilevel models to conduct analysis of all data together (Bon et al., 2018).


The Minimum Inhibitory Concentration is a Hybrid Parameter


The various pharmacodynamic parameters that we have explored are often described in drug development studies in the preclinical setting. The common quantitative parameters are more high level and easier to communicate in the context of clinical or epidemiology studies. We have already met one of the most popular, the MIC. As we have explored, the MIC is easy to conceptualize, based on the experimental design from which it is determined. But is it a good summary of drug action? Does it have meaning in terms of our more fundamental model?


If we’re willing to make some simplifying assumptions, we can express the MIC as fairly directly related to the sigmoidal model. It has a particularly close relationship with the classic measure of drug potency, the EC50 (Equation 3). Previously we expressed drug effect E as a real value, either directly or as a proportion of the maximum possible response. However, the experimental method of MIC determination proposes that the drug effect is binary; at any drug concentration, either growth occurred or it did not. But the actual effects of antimicrobials, as implied by the sigmoid models, are not binary. We can consider MIC as a dichotomised version of a truly smooth underlying relationship between concentration and effect. Instead of observing the effect directly, a threshold is applied, and the observed result for any concentration is whether or not the response threshold was exceeded.


The MIC therefore represents combined information regarding the antimicrobial effect. It is a potency measure, similar to the EC50, but also describes the size of the effect, which is an antimicrobial effect of sufficient magnitude that “no” pathogen replication occurs. Generally, in pharmacodynamics “potency”, as indicated by the EC50or similar parameter, represents nothing about the degree of effect. In contrast, the MIC implies a large effect, at least in vitro. We can visualize the MIC, with reference to the underlying “true” relationship, as Figure 5.7.


In contrast to the discrete MIC determined in the microdilution assay, the disk diffusion (Kirby–Bauer) method generates a smooth (continuous) measurement, which is proportional to antimicrobial drug concentration but does not indicate drug MIC concentration directly. In the disk diffusion method, an agar plate containing appropriate growth medium is inoculated with a suspended culture of the pathogen, to achieve uniform deposition across the plate surface area. Antimicrobial‐impregnated polymer disks are then placed on the agar surface. During the incubation period, antimicrobial drug diffuses from the disk into the agar medium. As the diffusion rate through the agar is slow, a concentration gradient develops during the incubation period, with drug concentration declining with increasing distance from the disk. Microorganism growth occurs across the agar plate surface, except in those regions where antimicrobial concentration is too high, corresponding to an estimate of the MIC. It is difficult to determine drug concentration at some position on the plate but the zone diameter is not usually reported directly but instead a judgment is made regarding its clinical interpretation using a breakpoint. which will be discussed later.


The disk diffusion assay essentially represents a rearrangement of the microdilution assay, in which the unknown continuous concentration gradient replaces the known discrete concentrations. In the laboratory, these may be run simultaneously, so that the zone diameter can be transformed to an estimate of the MIC. This is a more complete use of the information than the classic interpretation of discretising the zone diameter as “resistant” or “susceptible.” The continuous zone diameter is a surrogate variable for the MIC, and therefore antimicrobial potency.

A graph of growth inhibition in percentage versus drug concentration in arbitrary units depicts ta S shepd curve. A horizontal dashed line is drawn at 80 and a vertical dotted line is drawn at 0.5.

Figure 5.7 The relationship between the MICtrue, MICobs, and a proposed underlying sigmoid concentration response model for a hypothetical antimicrobial drug. In the practical determination of MIC, only a discrete set of concentrations are observed, corresponding to the x‐axis labels. In this example, observed growth occurs unless the degree of growth inhibition exceeds 90% (dashed line). For this set of observed concentrations, the nominated MICobs is 0.5 μg/ml, as the smallest observed drug concentration at which the effect was sufficient to preclude visible growth (dotted line). At the next smaller concentration 0.25 μg/ml, the degree of growth inhibition was not sufficient. The latent MICtrue is between 0.5 μg/ml and 0.25 μg/ml.


The Minimum Inhibitory Concentration in Context


We have explored the most common general quantitative description of drug action, and the use of simple mathematical models as a theoretical foundation for concentration–effect relationships. These models contain a high degree of abstraction, and present quantities that might be difficult to estimate in routine scientific practice. However, the pharmacodynamic measures that are frequently used in clinical and research practice are closely derived from the models we have explored, and considering them in this framework illuminates their implications and assumptions.


An interesting limitation of the MIC concept, which is common to all the simple in vitro assays for antimicrobial potency, is that the drug effect represented by the MIC is highly constrained. The “effect” expressed in Figure 5.7 has a very specific meaning: the degree of increase in density of a microorganism in culture, under specific environmental conditions (medium, temperature, oxygenation, etc.), that occurred after a specified period of growing time, with a controlled starting culture density. Substantial effort is invested by the clinical laboratory community to achieve uniformity in these conditions, so that MIC values obtained on different occasions, by different analysts, and at different laboratories share common meaning. These reflect internal validity; that is, the reliability of the measurement. The external validity of MIC, meaning the degree to which MIC information is clinically meaningful, is a more complex issue, because this depends on how closely the study design reflects the events occurring in the patient.


Small changes in experimental conditions may result in large changes in estimated MIC, and because those conditions have little relationship with the pathophysiology of infections, it is difficult to demonstrate how reasonable they are. Numerous effects may contribute to poor alignment of in vitro MIC to the magnitude of antimicrobial effects in vivo (Martinez et al., 2013). For example, the assay is usually conducted in a homogenous liquid culture, so the microorganism is exposed directly to the dissolved antimicrobial but in vivo the microorganisms may be sequestered within the three‐dimensional geometry of the infected tissue, adding additional diffusion distance and barriers. Some bacteria secrete biofilms, modifying their local environment and acting as a diffusion barrier; however, some biofilms enhance the activity of specific antimicrobials. In static culture, the drug concentration is constant and metabolic wastes accumulate over time, whereas in vivo, circulation and tissue fluid turnover imply that drug concentration is subject to continuous change, and nutrients and metabolic waste products undergo continuous turnover. In most infections, the effect of exogenous antimicrobials occurs together with an inflammatory and immune response, which contribute endogenous antimicrobial effects with an important role in the outcome of infections but are not represented by the MIC.


A key characteristic of the MIC is that it represents all antimicrobial effects equivalently as inhibition of growth. The specific effects of antimicrobials are in fact diverse although some do in fact inhibit metabolism, preventing cell activity and division, others inflict fatal cell damage over a shorter time. The MIC is a surrogate in vitro measure for relative efficacy, which is helpful for clinical planning because different antimicrobial–microorganism interactions have a common interpretation. However, the MIC is not informative about the actual mechanism of effects.


We have explored how the MIC is related to more fundamental, theoretical models of drug effect. The MIC combines a statement about the magnitude of effect, representing apparently complete inhibition of microbial growth, with a statement about potency, the drug concentration at which the effect occurs. Let’s reconsider our starting example in these terms.


The laboratory has reported that our novel bacterial pathogen infecting the lizards has an enrofloxacin MIC of 1 μg/ml. This demonstrates that in continuous exposure in an in vitro medium, the lowest concentration of enrofloxacin that will completely inhibit visible growth of our pathogen is somewhere between 0.5 μg/ml and 1 μg/ml. As described in Chapter 17, the fluoroquinolones, including enrofloxacin, are clinically most relevant for Gram‐negative infections. After reviewing the enrofloxacin MIC as reported from other Gram‐negative pathogens in reptiles, you find that most Pseudomonas isolates are classified as susceptible (Tang et al., 2020).



  • It seems like our evaluation has just led to further questions: Pseudomonas spp., a common Gram‐negative pathogen, is often found to be “susceptible”; can we apply that interpretation to our new pathogen? Why is this finding reported, and not the MIC?
  • “Susceptible” seems to imply that treatment would be effective. How can a prediction about clinical effectiveness be made from only in vitro data?
  • If this patient species has never been studied, are our predictions trustworthy?

We will now move forward to consider these new questions, which we will classify as clinical pharmacodynamics.


Clinical Pharmacodynamics


In many clinical situations, including our lizard example, we are forced to consider antimicrobial therapy from a bottom‐up perspective, based on theoretical knowledge, as we have no direct experience with our patient or pathogen. Despite obtaining some quantitative data about drug effect, it seems that we need to apply more information to evaluate our antimicrobial drug selection.


A key insight is to recognise that selecting an appropriate antimicrobial drug is not enough. The dose, frequency of administration, route of administration, and duration of therapy must all be specified. The objective of quantitative pharmacology, including pharmacodynamics, is to convert our understanding of drug–patient and drug–pathogen interactions into clinical decision making that maximizes the efficacy and safety of therapy. We have explored models that quantitatively describe antimicrobial effect; our next objective is to utilize those models to support rational clinical decision making with quantitative evidence.


A useful conceptualization is that the disease system has three parts: a host, a pathogen, and the antimicrobial drug. The outcome of the treatment of infectious disease results from interactions between these systems. The interaction between host and drug is known as pharmacokinetics, as we have explored in Chapter 4, which characterizes the time course of drug concentrations as functions of parameters which are estimated from experimental studies. The interactions between pathogen and drug are known as pharmacodynamics, and as we have described so far in this chapter, this represents the relationship between drug concentration and effect, including the drug susceptibility of the pathogen. The final component is the host–pathogen interaction; though typically considered outside the domain of pharmacology, this includes critical factors such as the pathophysiology, host immune response, and the clinical effects of disease.


In practice, the outcome of infection treatment depends on the simultaneous, combined effects of all these interactions. This is an overall scientific model by which the outcome of treatment for an infectious disease process can be understood, described, and predicted. This framework can be applied quantitatively, by defining formal mathematical and statistical models for the components, or qualitatively, as a tool to support clinical reasoning. These methods have been widely utilized in veterinary applications (Toutain et al., 2021).


After searching the scientific literature, you have located some pharmacokinetic reports that describe the pharmacokinetics of enrofloxacin in various lizards and snakes; nothing about the species of interest but a report in a species of similar body size (Agius et al., 2020), a good example of the style of information typically available. Our objective is to determine what strategy should be applied in clinical practice in order to achieve success with this drug. What are the pharmacodynamic principles that we need to consider?


A conceptually simple approach to this problem is to conduct a randomized controlled trial, or a series of trials, and observe the clinical outcome in an entirely empirical fashion. Where there is descriptive toxicology information available, which can be used to propose a maximal safe dosage or exposure, it is easy to select a small range of candidate dose regimens and apply them to either clinical patients or suitable experimental animals. The mode of reasoning being applied is simply that a treatment that was clinically effective in the past can reasonably be predicted to be effective in the future; no particular knowledge is required about the mechanism of its effectiveness. This is referred to as top‐down reasoning. This remains the predominant path of clinical development for many veterinary antimicrobial drugs; for example, intramammary drug development has emphasized clinical trials almost exclusively, as suitable pharmacokinetic modeling has only recently become available (Woodward et al., 2020).


The testing of candidate dosing strategies for antimicrobial therapies using randomized controlled trials is appealing; no knowledge about the mechanism of action is required, the study design is quite simple, communicating the findings is easy, and little specialized knowledge is required to understand the results. However, the practical drawbacks of this approach are substantial. As the dose and dosing frequency are approximately continuous variables, there is a practically infinite candidate set of dose regimens that could be tested, so the chance that the optimum strategy, or even close to an optimum strategy, will be selected is low. It is possible that efficacy might be reported as poor simply because a good strategy was not selected for study. Further, the design provides little evidence regarding the expected outcome if conditions change, because there is no theoretical framework to ground predictions.


Other problems with using randomized controlled trials are statistical; as the design does not propose any knowledge about the relationship between the dose strategy and outcome, the amount of information obtained from each subject is low, though these data are expensive to collect. Finally, practical challenges for adequate use of randomized controlled trials abound: the number of subjects required is generally large because of the low information obtained from each subject, it is ethically challenging to apply experimental therapies to large numbers of subjects, and external validity may be poor as no information is available about the impact of changing conditions. Though a simple and direct strategy is to extrapolate or adopt the dose regimen from another application, especially from human medicine, this takes little advantage of any species‐specific knowledge that is available, especially regarding pharmacokinetics. A clear issue in our scenario above, which is common in the discipline, is that there is simply no time or opportunity to conduct such a study anyway.


These limitations may be resolved by implementing a more bottom‐up approach: utilization of a theoretical model to justify what relationships are expected, and feed in background information to our design. We will now explore the basis of these models.


Time‐Dependent Antimicrobial Activity


Earlier, we explored how the MIC is a hybrid measure related to the potency of a particular antimicrobial drug for a particular pathogen of interest. Major advantages of the MIC are the ease of measurement for the majority of clinically relevant bacteria, and the ease of standardization. As the MIC is closely associated with the antimicrobial potency, the concentration of drug above which relevant antimicrobial effects occur, it is natural to utilize pharmacodynamic information contained by the MIC in dose regimen evaluation.


For simplicity, we will propose that the drug concentration to which the pathogen of interest is exposed is equal to the free drug concentration in plasma (CP). Remembering our sigmoidal model for the magnitude of drug effect (ignoring for now the coefficient n):


Equation 8:  upper E left-parenthesis upper X right-parenthesis equals upper E Subscript upper M upper I upper N Baseline plus StartFraction left-parenthesis upper X dot left-parenthesis upper E Subscript upper M upper A upper X Baseline minus upper E Subscript upper M upper I upper N Baseline right-parenthesis right-parenthesis Over left-parenthesis upper X plus upper E upper C 50 right-parenthesis EndFraction

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Mar 15, 2026 | Posted by in GENERAL | Comments Off on Pharmacodynamics of Antimicrobials

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