1. Ronald JW Lambert PhD PhD FRSC, Cranfield University, UK; rjwlambert@gmail.com
Synergy: From E.coli to Cancer. R. Lambert
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][][][
exp
nnnnn
P
Propionic
P
Acetic
P
H
RTD
Synergy of combined weak acids ?
An checkerboard experiment
with 100 different combinations
of acetate and propionate
(preservatives) at pH 6 was
carried out. The time taken for
Escherichia coli to grow to a
given level in each well of the
micro-titre plate was obtained.
The 3D plot shows the
observed (red spheres) and the
fitted model – black grid.
Conclusions and Summary
• Since 1926 models of synergy have been based on the Loewe conjecture; modern models (>1958) have used the supposition that
linear isobols mean ‘additive’ behaviour, curved isoboles mean synergy (or antagonism).
• Majority of models ignore the effect of dose response. Those that attempt to incorporate the dose response do so empirically.
• The new model for combining factors has the Loewe model as a special case; curved isoboles are a natural consequence of mixing
drugs with different dose responses.
• The new method gives a simple graphical and statistical output.
•Why is this important?
• The majority of patents/papers on synergy have never looked at the dose response, or are based on erroneous effect models
• This means a lot of research money and time is wasted looking for the reason for ‘the synergy’ where none exists!
• Real Interest is the exploitation of this new knowledge…BUT, can we achieve a paradigm shift
Combined anti-cancer: Cisplatin, Taxol, Topotecan
Eg., treatment of advanced ovarian
cancer: a triple treatment of cisplatin,
taxol and topotecan: rationale based
partially on the study and conclusions of
Synergy by Chou 1994.
New Model
• Each therapeutic had enough published
data to produce a Hill model for each.
• This gave three Hill exponents
• cisplatin < paclitaxel < tapotecan
• By the previous arguments any study
based on Loewe will result in a
conclusion of synergy, because curved
isoboles will occur.
• A plot of the observed against the effective concentration for the
triple combination ((comb)g), will follow the basic Hill plot if it is
additive. If, however, there is a real synergy between
components it will not.
Conclusion: There is no synergy between any of the three
components of this mixture, even although the literature
abounds with synergy in weak acids.
 g
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combf
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Two parameters are required to describe the effect of a single bioactive.
For two bio-actives in combination a description of an additive effect must only use 4 parameters.
Any expression of synergy must require additional parameters.
A mathematically correct model (for a mix
of two) which allows for different dose
responses (but can also be expanded for
multiple components) is given by
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lasParo EC
lasalocid
EC
nParomomyci
5050
1
100
100
/
This new model leads to the Loewe conjecture if the dose responses are equal ( = , i.e. straight line isoboles). Mixing
compounds with different dose responses leads to a failure of Loewe (curved isoboles- for the additive effect).
New Model
In combination a mixture follows
the Hill model
Synergy is a highly patentable concept, e.g. combined antibiotics, antivirals, anti-cancer, food preservatives, etc. Although the basis of
synergy analysis is the Loewe additive model (1926), synergy is often treated as a user defined definition. Modelling combined effects
commonly uses the Median effect method of Chou & Talalay or the Greco flagship model, both based on the ‘standard’ Hill model– but
these are difficult to use and interpret. A singular problem is the failure to address the dose response. Here we suggest a different
paradigm for synergy/addition and also a new, easy to use and interpret, model.
Combined Drugs against Cryptosporidium
parvum. You et al (1998) J Antimic. Chemother.
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yx
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EC
y
EC
x
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,
A classic study, using the median effect, by the CDC, on the
synergy between two drugs against a serious pathogen.
A standard ray design was
used to obtain inhibition data.
Analysis using the new model
suggested there were no
statistically significant
interactions between the two
drugs. The original work
suggested that the synergy
reported be investigated
further. This work suggests
not to.
Model – red
Observed-blue
The triple combination which is synergistic according to Chou is
simply additive – there is no statistical evidence of any
interactions between any of the components.
A graphical representation of the median effect model’s
conclusions, from Chou 1994.
• The new ‘Extended Hill model’ was applied to twin combinations
and then to the triple combination.