Evolutionary probabilistic design for protocell

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Evolutionary probabilistic design for
protocell

• Ca Foscari group
• Irene Poli, Michele Forlin, Timoteo Carletti,
  Roberto Serra, Davide De March.
• in collaboration with ProtoLife group

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Outline

• The experimental problem
• the ProtoLife laboratory experiments
• The mixture class of designs and the simplex
  lattice designs
• Modeling data for redesign
• The evolutionary probabilistic design

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The experimental problem concerns the generation
of vesicles Vesicles are a basic tool of the
cell for organizing metabolism, transport, enzyme
storage, as well as being chemical reaction
chambers. From a statistical point of view it
is a design of experiments (DoE) problem, which
involves the identification of the experimental
space and the formulation and evaluation of
models for new designs.

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• Main features of Protolife experiments
• the technology chemical reacting processes
  develop in a parallel way on a plate with
  micro-wells, providing a response which can be
  read and measured by a fluorescent microscope (90
  micro-wells in each plate).
• the response, named Torbidity (T) ia a measure of
  both the number of evolving microstructures and
  the size of these microstructures ( T KNV2 e).
  
• This property emerges as a result of a
  chemical process involving a large number of
  experimental variables, of different and possibly
  high order interactions, and noise variables.

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the control variables (design factors), chosen
to generate and control the process, include both
compositional and process variables chemical
components, temperature, reaction time, etc The
candidate set of main factors is Xi,
i1,,90(?) which include amphiphilic molecules,
temperature and reaction time. the
experimental space, given by all possible
combinations of the factors and levels and
ranges. This space is a high dimensional
complex structure which can easily resist
exhaustive, or even accurate, exploration.
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Objective of the experiments find the
experimental design points , i.e. the set of
factors, their levels and their interactions,
which maximizes the torbidity and minimizes
noise. Constraint the response is a
function of the proportion of the components and
not of the total amount, In each experiment q
ingredients are chosen with proportions x1,,xq,
0 xi 1, i1,,q, ?
xi1 the Mixture Experiments
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The Simplex Lattice Design (SLD) The
proportions assumed by each components takes the
(m1) equally spaced values from 0 to 1 Xi 0,
1/m, 2/m,,1 i1,q and all possible
combinations (mixtures) of the proportions
summing to 1 are considered. The number of
design points (mixtures or simply experiments)
in a q, m simplex lattice design is N
(qm-1)!/m!(q-1)! For q16 and m5 we derive
N15,504.
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Example Consider a simplex lattice design 4,2,
Xi 0, 1/2, 1 i1,2,3,4 The design
consists of the following experiments (x1,x2,x3,x
4) (1,0,0,0)(0,1,0,0)(0,01,0)(0,0,0,1)
(1/2,1/2,0,0)(1/2,0,1/2,0)(1/2,0,01
/2) (0,1/2,
1/2,0)(0,1/2,0,1/2) With 4,2, N 5!/2!3! 10



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High dimensionality of the experiments When the
number of components is large, the simplex
lattice or the simple centroid designs or other
similar designs become unfeasible. Which
way the fractional designs (screening and
selection) . the evolutionary designs
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Selection of a sub-region of the space The
problem is to select a restricted area of the
experimental space for inferring the best
solution How Collecting information from some
explorative set of experiments.
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• Data analysis
• At the moment we have analyzed two sets of
  experiments
• with different components, different levels,
  different designs.
• Both the sets include
• repetitions
• no blocks
• randomizations

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The first set consists of 150 experiments
repeated 3 times (total experiments 450), where
each design point is a mixture with the
following structure with xi 0 xi 1,
i1,6, ? xi1. The choice of how many
molecules, which molecules and in which
proportion was an experimental choice, following
a principle of equal distance between components
(without a priori design). .
x1, x2, x3, x4, x5, x6
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The response of this set of experiments
exhibits a bimodal distribution The data
analysis we developed on this set of data did not
show relevant relation of the effect of each
single components and their interaction on the
resulting torbidity we learned a light positive
effect of x3 , the relevance of the presence of
x4 . The number of molecules considered was very
small and results not satisfactory.
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The second set of experiments the choice has
been to focus on a restricted area of the search
space and to sample the molecules in a random
way, starting an evolutionary walk. An initial
set of 30 experiments has the following mixture
from 16 molecules 5 have been randomly selected
receiving a proportion of .2 , fixing the
number of molecules (5) and the levels .2.
(random local search in HD)
x1, x2,,x16
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From this generation of experiments other 5
generations have been derived applying
proportional selection, and the genetic operators
of crossover, mutation and innovation. The
resulting torbidity (the mean value of the 3
replications) is
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Modelling We consider various classes of models
to achieve some understanding of the process and
hints on a better design The linear model, as
expected, gave bad results but showed immediately
the importance of three molecules in the mixture
the x13 , x12 , x4 j1,n. Model inference
was achieved via stepwise regression procedure,
with AIC.
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modelling molecules interactions From the binary
nonlinear model which involves terms of
interactions between molecules and where ?i
represents the expected response to the pure
blend, and ?ij represents either synergistic or
antagonist blending, we learned that the most
relevant interactions which affect the torbidity
are the ones which involve x13 in particular
x13 x12 x13 x4 x13 x14

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However, few tests on the model were not very
satisfactory, then we tried to identify
non-linear components building the following
model where ?(2) measures the average
deviation from linearity because of the mixing of
xi with other components (the second term
vanishes for xi1 and xi0).
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Applying this model to the data we could learn
that two components are hightly significant in
generating non linearity molecule x13 and
molecule x4 Then, on this information we
modeled the interactions (binary and ternary)
just of these molecules with others
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the residuals
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The selection and evolution of the model with a
GA for prediction confirmed some results, but
also discovered new relevant components great
effect of molecule x13 and its interaction with
molecule x4 and with molecules x10 and
x8 A negative role on torbidity played by x2
and by molecules x4 and x12 . A neural
network model confirmed the results. What did
we learn from this analysis?
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What next An evolutionary design with an
initial population of experiments generated by a
random selection of both molecules and
levels, with a pattern recognition procedure for
excellent bio-bricks, with families of
probability distributions to govern the evolution
of the best assemblies toward optimal
solutions.
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