Viva la ResistanceDoes High-Dose Antimicrobial Chemotherapy

Prevent the Evolution of Resistance?Tom Kelly – PhD candidate approx. 2 yearsSupervised by Mik Black & Parry Guilford (Biochemistry Dept)Genetics Journal Club 2016

Antibiotic ResistanceSource: 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 issueSource: Nature 431:892-893 (2004)

Source: dfwhc Foundation

Source: The Atlanic

A serious health issue

A serious (global) health issue

Source: BBC Health

A serious (global) health issue

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.1004689Published 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)

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

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 High level resistance (HLR) strains have resistance so high the drug is

ineffective Resistant to drug concentrations above those tolerable / feasible in the clinic

The “Hit Hard” Hypothesis

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)

Evolutionary Processes

H(Infected

)

Evolutionary Processes

H(Infected

)

H(Cured)

Killed by Treatment

Evolutionary Processes

H(Infected

)

H(Cured)

Wild-typeKilled by

Treatment H(Hidden)

Mutation

H(Hidden)

H(Hidden)

Evolutionary Processes

H(Infected

)

H(Cured)

H(Hidden)

H(Emerge

)

MutationEscape / Release

At high doses

H(Hidden)

H(Emerge

)

Wild-typeKilled by

Treatment

Evolutionary Processes

H(Infected

)

H(Cured)

H(Hidden)

Mutation

Suppression / Outcompeted

At low doses

H(Hidden)

H(Hidden)

Wild-typeKilled by

Treatment

Evolutionary Processes

H(Infected

)

H(Cured)

H(Hidden)

H(Emerge

)

MutationEscape / Release

Suppression / Outcompeted

At low doses

At high doses

Wild-typeKilled 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

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 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).

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 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]

Highly resistant HLR is one mutational step from wild-type Mutation to HLR occurs from wildtype population as it goes extinct at rate

λ(p(t,c),c) HLR strain has a metabolic or replicative cost

Probability of escape from competitive suppression π(x(t,c),c)

Assumptions and parameters

Highly resistant HLR is one mutational step from wild-type 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) HLR strain has a metabolic or replicative cost

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

Rate of Risk of Resistance Evolving

Derivatives(initial rate of change)

Derivative

Rate of Risk of Resistance Evolving

Emergence of rare resist strains (to clinically significant levels)

Depends on drug concentration

Rate of Risk of Resistance Evolving

Change in de novo mutation

(towards highly resistant)

Rate of Risk of Resistance Evolving

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)

Rate of Risk of Resistance Evolving

Change in de novo mutation

(towards highly resistant)

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)

Rate of Risk of Resistance EvolvingReplication of newly

emerged highly resistant strains

Change in de novo mutation

(towards highly resistant)

Rate of Risk of Resistance EvolvingReplication of newly

emerged highly resistant strains

Change in de novo mutation

(towards highly resistant)

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

Rate of Risk of Resistance EvolvingReplication of newly

emerged highly resistant strains

Change in de novo mutation

(towards highly resistant)

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

considered

Rate of Risk of Resistance EvolvingReplication of newly

emerged highly resistant strains

Change in de novo mutation

(towards highly resistant)

Replication of pre-existing highly resistant strains

Rate of Risk of Resistance EvolvingReplication of newly

emerged highly resistant strains

Change in de novo mutation

(towards highly resistant)

Replication of pre-existing highly resistant strains

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)

Rate of Risk of Resistance EvolvingReplication of newly

emerged highly resistant strains

Change in de novo mutation

(towards highly resistant)

Replication of pre-existing highly resistant strains

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

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

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 Straightforward to compute, scale, and simulate on a computer

Rectangle Rule

Source: Khurram Wadee (CC) Wikipedia

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 Straightforward to compute, scale, and simulate on a computer

Rectangle Rule

Trapezium Rule

Source: Khurram Wadee (CC) Wikipedia

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 Straightforward to compute, scale, and simulate on a computer

Rectangle Rule

Simpson’s Method

Trapezium Rule

Source: Khurram Wadee (CC) Wikipedia

General Findings

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 or the smallest clinically effective 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 appearsResistant strain emerges

Specific Examples – Strain Outbreak

Specific Examples – Strain Outbreak

Implications – balance of opposing forces

Derivatives(initial rate of

change)

Replication of newly emerged highly resistant

strains

Change in de novo mutation

(towards highly resistant)

Replication of pre-existing highly resistant strains

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 or the smallest clinically effective 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 tooBetter idea

Counterproductive

Empirical Evidence for Unimodal Distribution23.Negri MC, Morosini MI, Loza E, Baquero F. In-vitro selective antibiotic concentrations of beta-lactams for penicillin-resistant Streptococcus-pneumoniae populations. Antimicrobial Agents and Chemotherapy. 1994;38:122–125. doi: 10.1128/AAC.38.1.122. pmid:8141563 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:1295135226.Jumbe N, Louie A, Leary R, Liu WG, Deziel MR, Tam VH, et al. Application of a mathematical model to prevent in vivo amplification of antibiotic-resistant bacterial populations during therapy. Journal of Clinical Investigation. 2003;112:275–285. doi: 10.1172/JCI16814. pmid:1286541527.Gumbo T, Louie A, Deziel MR, Parsons LM, Salfinger M, Drusano GL. Selection of a moxifloxacin dose that suppresses drug resistance in Mycobacterium tuberculosis, by use of an in vitro pharmacodynamic infection model and mathematical modeling. Journal of Infectious Diseases. 2004;190:1642–1651. doi: 10.1086/424849. pmid:1547807028.Firsov AA, Vostrov SN, Lubenko IY, Arzamastsev AP, Portnoy YA, Zinner SH. ABT492 and levofloxacin: comparison of their pharmacodynamics and their abilities to prevent the selection of resistant Staphylococcus aureus in an in vitro model. Journal of Antimicrobial Chemotherapy. 2004;54:178–186. doi: 10.1093/jac/dkh242. pmid:1519004129.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 human therapy. Antimicrobial Agents and Chemotherapy. 2004;48:1699–1707. doi: 10.1128/AAC.48.5.1699-1707.2004. pmid:1510512330.Etienne M, Croisier D, Charles PE, Lequeu C, Piroth L, Portier H, et al. Effect of low-level resistance on subsequent enrichment of fluoroquinolone-resistant Streptococcus pneumoniae in rabbits. Journal of Infectious Diseases. 2004;190:1472–1475. doi: 10.1086/423853. pmid:1537844031.Tam VH, Schilling AN, Neshat S, Poole K, Melnick DA, Coyle EA. Optimization of meropenem minimum concentration/MIC ratio to suppress in vitro resistance ofPseudomonas aeruginosa. Antimicrobial Agents and Chemotherapy. 2005;49:4920–4927. doi: 10.1128/AAC.49.12.4920-4927.2005. pmid:16304153

32.Tam VH, Louie A, Deziel MR, Liu W, Leary R, Drusano GL. Bacterial-population responses to drug-selective pressure: examination of Garenoxacin’s effect on Pseudomonas aeruginosa. Journal of Infectious Diseases. 2005;192:420–428. doi: 10.1086/430611. pmid:15995955 33.Firsov AA, Smirnova MV, Lubenko IY, Vostrov SN, Portnoy YA, Zinner SH. Testing the mutant selection window hypothesis with Staphylococcus aureus exposed to daptomycin and vancomycin in an in vitro model. Journal of Antimicrobial Chemotherapy. 2006;58:1185–1192. doi: 10.1093/jac/dkl387. pmid:1702809434.Cui JC, Liu YN, Wang R, Tong WH, Drlica K, Zhao XL. The mutant selection window in rabbits infected with Staphylococcus aureus. Journal of Infectious Diseases. 2006;194:1601–1608. doi: 10.1086/508752. pmid:1708304735.Tam VH, Louie A, Deziel MR, Liu W, Drusano GL. The relationship between quinolone exposures and resistance amplification is characterized by an inverted U: a new paradigm for optimizing pharmacodynamics to counterselect resistance. Antimicrobial Agents and Chemotherapy. 2007;51:744–747. doi: 10.1128/AAC.00334-06. pmid:1711667936.Gumbo T, Louie A, Deziel MR, Liu WG, Parsons LM, Salfinger M, et al. Concentration-dependent Mycobacterium tuberculosis killing and prevention of resistance by rifampin. Antimicrobial Agents and Chemotherapy. 2007;51:3781–3788. doi: 10.1128/AAC.01533-06. pmid:1772415737.Bourgeois-Nicolaos N, Massias L, Couson B, Butel MJ, Andremont A, Doucet-Populaire F. Dose dependence of emergence of resistance to linezolid in Enterococcus faecalis in vivo. Journal of Infectious Diseases. 2007;195:1480–1488. doi: 10.1086/513876. pmid:1743622838.Goessens WHE, Mouton JW, ten Kate MT, Bijll AJ, Ott A, Bakker-Woudenberg I. Role of ceftazidime dose regimen on the selection of resistant Enterobacter cloacae in the intestinal flora of rats treated for an experimental pulmonary infection. Journal of Antimicrobial Chemotherapy. 2007;59:507–516. doi: 10.1093/jac/dkl529. pmid:1728976539.Stearne LET, Goessens WHF, OlofssonCars JW, Gyssens IC. Effect of dosing and dosing frequency on the efficacy of ceftizoxime and the emergence of ceftizoxime resistance during the early development of murine abscesses caused by Bacteroides fragilis and Enterobacter cloacae mixed infection. Antimicrobial Agents and Chemotherapy. 2007;51:3605–3611. doi: 10.1128/AAC.01486-06. pmid:1764641640.Zhu YL, Mei Q, Cheng J, Liu YY, Ye Y, Li JB. Testing the mutant selection window in rabbits infected with methicillin-resistant Staphylococcus aureus exposed to vancomycin. Journal of Antimicrobial Chemotherapy. 2012;67:2700–2706. doi: 10.1093/jac/dks280. pmid:2280970341.Schmalstieg AM, Srivastava S, Belkaya S, Deshpande D, Meek C, Leff R, et al. The antibiotic resistance arrow of time: Efflux pump induction is a general first step in the evolution of Mycobacterial drug resistance. Antimicrobial Agents and Chemotherapy. 2012;56:4806–4815. doi: 10.1128/AAC.05546-11. 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)

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.1004689Published 28 January 2016

Evolutionary Theory for Drug Treatment

CL = Lowest Effective Dose; CU = Highest Safe Dose

Probability of Evolving (Untreatable) Resistance