Tom kelly genetics journal club 2016

Viva la Resistance
Does High-Dose Antimicrobial Chemotherapy
Prevent the Evolution of Resistance?
Tom Kelly – PhD candidate approx. 2 years
Supervised by Mik Black & Parry Guilford (Biochemistry Dept)
Genetics Journal Club 2016

Antibiotic Resistance
Source: GuardianLV

Antibiotic ResistanceSource: beatricebiologist.com

A Rapid Evolutionary Arm’s Race
Source: xkcd.com

A serious health issue
Source: Nature Chem Bio 3:541-548 (2007)
Source: emed.com.au

A serious health issue
Source: Nature 431:892-893 (2004)
Source: dfwhc Foundation
Source: The Atlanic

A serious (global) health issue
Source: BBC Health

A serious (global) health issue

Why biologists are investigating
 Novel antibiotic classes have not been discovered in some time
 Multi-resistance bacteria are becoming a serious problem
 We need to understand how antibiotics work and how resistance develops
 Understanding non-pathogenic bacteria is also important to our health
 Bacteria are an ideal system to study genes and evolution

Why it interests me
 Mathematics + Genetics =
 Bioinformatics / Computational Biology / Genomics
 Rethinking conventional wisdom
 Immediate clinical implications
 Some neat mathematics that really matters
 Similar rationale could apply to other systems, e.g., cancer

Day T, Read AF (2016) Does High-Dose Antimicrobial Chemotherapy Prevent the Evolution of Resistance?
PLoS Comput Biol 12(1): e1004689. doi:10.1371/journal.pcbi.1004689
Published 28 January 2016

The “Hit Hard” Hypothesis
 Ehrlich: “Hit Hard”
 Fleming: “if you use penicillin, use enough”
 Modern clinical advice: to administer ‘the highest tolerated antibiotic dose’
 a high concentration of drug will eliminate drug-sensitive microbes quickly and thereby
limit the appearance of resistant strains.
 a high concentration of drug will also eliminate strains that have some partial resistance,
provided the concentration is above the so-called mutant prevention concentration (MPC)

 Resistant bacteria can grow above the Minimum Inhibitory Concentration (MIC)
 The MPC is designed to kill all resistant single-step mutants
 If the MPC is unknown clinicians are advised to give the highest possible dose

 Resistant bacteria can grow above the Minimum Inhibitory Concentration (MIC)
 The MPC is designed to kill all resistant single-step mutants
 If the MPC is unknown clinicians are advised to give the highest possible dose
 High level resistance (HLR) strains have resistance so high the drug is ineffective
 Resistant to drug concentrations above those tolerable / feasible in the clinic

Source: sciencedaily.com (press release from Penn State University, Jan 28 2016)

Considering Lower Doses
 Does this hold up in light of evolutionary biology?
 Are we not selecting for the very microbes we fear most?
 Those with resistance to higher doses than safe to use in patients
 Can we design drugs / dosage to reduce the risk of developing resistance in
the future
 May also lead to better patient outcomes
 Hitting hard may work sometimes but it isn’t a good ‘rule of thumb’
 Need to consider drugs on case-by-case basis based on therapeutic window
 Could lead to immediate changes in existing clinical practice and new clinical trials
 Could reduce the risk of adverse drug effects and allergic reactions

Evolutionary Processes
 Competitive Suppression
 Occurs at low doses of antibiotics
 Wild-type has a selective advantage
(due to cost of resistance)
 Competitive Release / Escape
 Occurs at high doses of antibiotics
 Drug susceptible population removed
(freeing resistant strains from
competition)

H
(Infected)

H
(Infected)
H
(Cured)
Killed by
Treatment

H
(Infected)
H
(Cured)
Wild-type
Killed by
Treatment
H
(Hidden)
Mutation
H
(Hidden)
H
(Hidden)

H
(Infected)
H
(Cured)
H
(Hidden)
H
(Emerge)
Mutation
Escape /
Release
At high doses
H
(Hidden)
H
(Emerge)
Wild-type
Killed by
Treatment

H
(Infected)
H
(Cured)
H
(Hidden)
Mutation
Suppression /
Outcompeted
At low doses
H
(Hidden)
H
(Hidden)
Wild-type
Killed by
Treatment

H
(Infected)
H
(Cured)
H
(Hidden)
H
(Emerge)
Mutation
Escape /
Release
Suppression /
Outcompeted
At low doses
At high doses
Wild-type
Killed by
Treatment

Understanding Drug treatment
 Patient treatment regimen depends on:
 choice of antimicrobial drug (or drugs)
 determining the frequency, timing, and duration of administration
 dosage / concentration (most controversial)
 Aim: to determine how the probability of resistance emergence depends on
drug concentration

drug concentration
 Emergence of resistances requires occurrence of a rare mutant strain (pre-existing
or de novo mutation) and it’s proliferation to clinically significant levels (in
competition with the wild-type strain).

drug concentration
 Emergence of resistances requires occurrence of a rare mutant strain (pre-existing
or de novo mutation) and it’s proliferation to clinically significant levels (in
competition with the wild-type strain).
 Concentrations limited to a within “therapeutic window” between:
 Lowest dose effective against wildtype strains
 Highest dose safe to use without host toxicity

Assumptions
 Assume drug concentration is a constant ‘dose’ during treatment
 Tool to understand evolution of resistance
 Host factors (e.g., immune density) proliferate and act against a pathogen
 Model across all theoretically possible doses, consider feasible doses within
therapeutic window (lowest effective dose, highest safe dose)
 Highly resistant HLR is one mutational step from wild-type
 Focus on extreme resistance that cannot be treated, makes drug useless
 MIC, MPC, and intermediate resistance levels ignored
 HLR strain has a metabolic or replicative cost
 Unable to replicate if vastly outnumbered by wildtype
 Most assumptions are relaxed in supplementary (with no impact on findings)

Assumptions and parameters
 Assume drug concentration is a constant ‘dose’ during treatment
 Constant dose c
 Host factors (e.g., immune density) proliferate and act against a pathogen
 Pathogen (wildtype) density P(t) and Host factors X(t) over time
 X defined as the inverse of immune density = How good environment for wildtype
 Depend on duration of treatment and dose: p(t,c) and x(t, c)
 Model across all theoretically possible doses c, consider feasible doses within
therapeutic window: cϵ[cL, cU]
 Mutation to HLR occurs from wildtype population as it goes extinct at rate λ(p(t,c),c)
 Probability of escape from competitive suppression π(x(t,c),c)

Assumptions and parameters
 Mutation to HLR occurs from wildtype population as it goes extinct at rate λ(p(t,c),c)
 limc→ ∞ λ(p,c) = 0 (enough drug kills all wildtype, no mutation possible)
 Probability of escape from competitive suppression π(x(t,c),c)
 limc→ ∞ π(x,c) = 0 (high enough drug kills even resistant strains, even if above safe doses)
 Formal definition of HLR, either:
 π(x,c) ≈ π(x,0) ∀ c > cU (HLR - clinically accepted doses give more selective advantage than
inhibiting growth to resistant strains)
 Otherwise there is no resistance problem - strains are treatable within therapeutic window

Modelling Risk of Resistance Evolving

Rate of Risk of Resistance Evolving

Derivatives
(initial rate of change)
Derivative

Emergence of rare resist strains (to clinically significant levels)
Depends on drug concentration

Change in de novo mutation
(towards highly resistant)

Higher mutation in larger
wildtype population (+ve)
Lower mutation with higher
dose against replication (-ve)
Wildtype density decreases
during treatment (usually -ve)

 Therefore high-dose decreases rate mutations arise during treatment
 As assumed by clinicians are proponents of the “Hit Hard” Model
 Unless treatment is mutagenic, or resistance conc. dependent (efflux, metabolised)

Replication of newly emerged
highly resistant strains

More favourable host
environment for escape (+ve)
dx/dc higher dose removes
wildtype aiding host (often +ve)
Drug directly supresses
proliferation (-ve) small in HLR

 Therefore high-dose indirectly increases replication of HLR that arise during treatment
 Evolutionary processes during emergence (to clinically significant levels) need to be considered

Replication of pre-existing

dx/dc higher dose removes
wildtype aiding host (often +ve)
Drug directly supresses
proliferation (-ve) small in HLR
More favourable host
environment for escape (+ve)

 Therefore high-dose indirectly increases replication of HLR that existed before treatment
 Evolutionary processes during emergence oppose (resistance is unfavourable at either extreme)

Solving An Integral – Numerical Integration
 There are several ways to solve or approximate an integral (as a sum)
 Risk is the area under a curve

Rectangle Rule
Simpson’s
Method
Trapezium Rule

 Straightforward to compute, scale, and simulate on a computer
Rectangle Rule
Source: Khurram Wadee (CC) Wikipedia

Rectangle Rule Trapezium Rule

Rectangle Rule Simpson’s MethodTrapezium Rule

General Findings
 Intermediate doses have the highest risk of highly resistant strains
 Optimal dose is either:
 the largest tolerable dose
 or the smallest clinically effective dose

General Findings
 Intermediate doses have the highest risk of highly resistant strains
 Optimal dose is
 the largest tolerable dose
Never anything between

Specific Examples
 Model of within-host dynamics of infection and resistance
 Acute infection
 Elicits immune response
 Can clear infection
 Treatment to reduce mortality and patient harm
 Consider cases where:
 1) max safe dose sufficient to cause suppression of resistant strains
 2) max safe dose is not sufficient to cause suppression of resistant strains
 Notice how a small difference in conditions (parameter values)

Specific Examples – High Dose Effective
High dose more effective
“Hit Hard” works (as expected)

Specific Examples – Low Dose Effective
Lowest dose more effective at
controlling resistance emergence
High dose leads to rampant resistance
“Hit Hard” backfires
Resistant strain appears
Resistant strain emerges

Specific Examples – Strain Outbreak

Implications – balance of opposing forces
Derivatives
(initial rate of change)

Evolutionary Theory for Drug Treatment
 General theoretical treatment of drug treatment strategies
 Opposing Evolutionary processes
 Higher Energy cost – outcompeted by drug susceptible bacteria at low doses
 Drug Resistance benefit – selective advantage at higher doses
 Leads to a unimodal relationship between drug concentration and resistance emergence
 Optimal Strategies
 either the largest tolerable dose
 Combination therapy may be more effective than high dose monotherapy

Comparison to earlier studies
 Ankomah & Levin (2014)
 Used a more complex model
 These considerations did not change the overall findings (supplementary)
 Defined resistance evolution in terms of
 1) probability of appearance (comparable to Day & Read without emergence / escape)
 2) time to clear infection
 Consistent with mutation appearing de novo reduced by high dose
 Did not account for selective suppression while reaching clinically significant levels once a
mutant strain had appeared
 Predicted the case where higher doses are more effective, not where lower doses are a more
suitable alternative
 Higher dose reduces probability that mutations occur
 However, resistant strains are also more likely to replicate to clinically significant
levels at higher doses (higher competitive advantage)

Does the MPC Rationale work?
 MPC inhibits replication of every ‘single step’ mutant
 Assumes: MPC within window, no variation in dosage below MPC, no horizontal gene transfer
 Finding the MPC is a waste of time, worst strategy in some cases (controversial conclusion)
 Better treatment at either extreme of therapeutic window, good source of empirical evidence
Good idea
Better idea

Does the “Hit Hard” Rationale work?
 Often recommended if MPC is unknown
 Works in some cases but has potential to backfire (one of two possible optimal strategies)
 Inherent focus on high-dose treatment in research / clinic – need to consider low doses too
Better idea
Counterproductive

Empirical Evidence for Unimodal Distribution
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for penicillin-resistant Streptococcus-pneumoniae populations. Antimicrobial Agents and Chemotherapy.
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24.Firsov AA, Vostrov SN, Lubenko IY, Drlica K, Portnoy YA, Zinner SH. In vitro pharmacodynamic
evaluation of the mutant selection window hypothesis using four fluoroquinolones against Staphylococcus
aureus. Antimicrobial Agents and Chemotherapy. 2003;47:1604–1613. doi: 10.1128/AAC.47.5.1604-
1613.2003. pmid:12709329
25.Zinner SH, Lubenko IY, Gilbert D, Simmons K, Zhao X, Drlica K, et al. Emergence of
resistant Streptococcus pneumoniae in an in vitro dynamic model the simulates moxifloxacin
concentrations inside and outside the mutant selection window: related changes in susceptibility,
resistance frequency and bacterial killing. Journal of Antimicrobial Chemotherapy. 2003;52:616–622. doi:
10.1093/jac/dkg401. pmid:12951352
26.Jumbe N, Louie A, Leary R, Liu WG, Deziel MR, Tam VH, et al. Application of a mathematical model to
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that suppresses drug resistance in Mycobacterium tuberculosis, by use of an in vitro pharmacodynamic
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10.1086/424849. pmid:15478070
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comparison of their pharmacodynamics and their abilities to prevent the selection of
resistant Staphylococcus aureus in an in vitro model. Journal of Antimicrobial Chemotherapy.
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29.Croisier DE, M Etienne M, Bergoin E, Charles PE, Lequeu C, Piroth L, et al. Mutant selection window in
levofloxacin and moxifloxacin treatments of experimental pneumococcal pneumonia in a rabbit model of
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pmid:17028094
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pmid:17083047
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doi: 10.1128/AAC.00334-06. pmid:17116679
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dependent Mycobacterium tuberculosis killing and prevention of resistance by rifampin. Antimicrobial
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10.1093/jac/dkl529. pmid:17289765
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efficacy of ceftizoxime and the emergence of ceftizoxime resistance during the early development of
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pmid:22751536

Recommendations for Clinical Practice
 If relative positions of hazard curve and therapeutic window are known
 Rational choice of dose (to minimise risk of resistance) is possible
 Choose the end of therapeutic window with lowest hazard (zero if possible)
 This is well known for a range of strains and drugs (MPC/MIC experiments)
 If HLR hazard curve is unknown
 No need to estimate whole curve – test extreme values
 Possible to compare extremes in vitro (culture) or in vivo (animal) experiments
 Ethical and Practical to test in patients (clinical trials) as we’re comparing known clinically safe doses,
particularly for altering use of existing / approved drugs
 Could be possible to switch dosage in response to changing optimal treatment if conditions change
 Potentially applicable to cancer chemotherapy
 Although cancer drugs are notorious for narrow therapeutic window

Practical Limitations in Clinical Practice
 Best resistance management is at one extreme of therapeutic window
 In practice clinicians cautiously avoid these extremes (margin for error)
 More aggressive than minimum effective dose
 Ensures no patients fail treatment
 Less aggressive than maximum tolerable dose
 Ensures no patients have drug toxicity

Practical Limitations in Clinical Practice
 Best resistance management is at one extreme of therapeutic window
 In practice clinicians cautiously avoid these extremes (margin for error)
 More aggressive than minimum effective dose
 Ensures no patients fail treatment
 Less aggressive than maximum tolerable dose
 Ensures no patients have drug toxicity
 Is this caution clinically justified or perceived?
 “Better Safe than Sorry” … when lives are at stake
 Need to consider low dose / short courses – promise some in clinical trials
 Need to accurately determine the therapeutic window (esp. for new drugs)

Evolutionary Theory for Drug Treatment
CL = Lowest Effective Dose; CU = Highest Safe Dose
Probability of Evolving (Untreatable) Resistance

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