Shaping and Dilating the Fitness Landscape for Parameter Estimation in Stochastic Biochemical Models
Abstract
:Featured Application
Abstract
1. Introduction
2. Materials and Methods
2.1. Reaction-Based Modeling and Stochastic Simulation Algorithm
- The set of molecular species;
- The set of the biochemical reactions describing all interactions among the species in .
- ;
- ;
- .
2.2. Fuzzy Self-Tuning Particle Swarm Optimization
2.3. Dilation Functions
2.4. Evolving Dilation Functions
2.5. Surrogate Fourier Modeling with surF
- 1.
- Discrete Cosine Transform.
- 2.
- Reducing the number of samples.
- If is in the convex hull defined by the points , then is obtained by a linear interpolation;
- otherwise, a linear interpolation is not possible and is defined as , where is the point among nearest to .
- 3.
- Parameters of surF.
- , which is the number of samples from f used to build ;
- , which is the “density” of samples from to obtain the points used to calculate the DFT; and
- , which controls the number of low frequencies preserved.
3. Results
3.1. Effect of DFs on the PE Problem
3.2. Combining DFs and Fourier Surrogate Modeling
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
ABF | Average Best Fitness |
BF | Basis Function |
DCT | Discrete Cosine Transform |
DF | Dilation Function |
E | Enzyme |
ES | Enzyme–Substrate complex |
FRBS | Fuzzy Rule-Based System |
FST-PSO | Fuzzy Self-Tuning Particle Swarm Optimization |
MM | Michaelis–Menten |
P | Product |
PE | Parameter Estimation |
PSO | Particle Swarm Optimization |
RBM | Reaction-Based Model |
S | Substrate |
SSA | Stochastic Simulation Algorithm |
surF | Fitness Landscape Surrogate Modeling with Fourier Filtering |
Mathematical Notation | |
stoichiometric coefficients associated with the n-th reactant | |
stoichiometric coefficients associated with the m-th reaction | |
vector of stochastic constants | |
stochastic (kinetic) constant | |
cognitive attractor of FST-PSO | |
social attractor of FST-PSO | |
D | number of dimensions of the search space |
number of distinct combinations of the reactant molecules | |
f | original fitness function |
dilated fitness function | |
, | surrogate fitness functions |
folding operator | |
number of lower frequencies to not be zeroed | |
I | number of sampled points to compute the dilated landscape |
lower and upper bounds of the search space | |
linear basis function | |
the experimental (target) amount of measured at time | |
p | parameter of the linear basis function |
coefficient representing the amplitude of -th frequency | |
r | parameter of the folding operator |
set of biochemical reactions | |
m-th biochemical reaction | |
number of equally spaced points to build the surrogate function | |
set of molecular species | |
i-th molecular specie | |
number of samples used to construct the surrogate | |
t | time of the system |
vector of time points | |
k-th time point | |
waiting time | |
maximum velocity of the FST-PSO particles | |
minimum velocity of the FST-PSO particles | |
inertia factor of FST-PSO | |
simulated amount of the species at time | |
vector representing the state of the system at time t | |
amount of the n-th molecular specie | |
control point | |
Q-th control point | |
length of the individuals representing the DFs | |
vector of control points | |
fitness value of the -th point of the surrogate | |
-th point of the search space to build the surrogate function | |
random number sampled from an uniform distribution | |
random number sampled from an uniform distribution |
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Molecular Species | Amount |
---|---|
S (substrate) | 200 |
E (enzyme) | 100 |
(enzyme–substrate complex) | 0 |
P (product) | 0 |
ID | Name | Semantics |
---|---|---|
0 | Identity | |
1 | Linear transformation | |
2 | ||
3 | Folding operators | |
4 |
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Nobile, M.S.; Papetti, D.M.; Spolaor, S.; Cazzaniga, P.; Manzoni, L. Shaping and Dilating the Fitness Landscape for Parameter Estimation in Stochastic Biochemical Models. Appl. Sci. 2022, 12, 6671. https://doi.org/10.3390/app12136671
Nobile MS, Papetti DM, Spolaor S, Cazzaniga P, Manzoni L. Shaping and Dilating the Fitness Landscape for Parameter Estimation in Stochastic Biochemical Models. Applied Sciences. 2022; 12(13):6671. https://doi.org/10.3390/app12136671
Chicago/Turabian StyleNobile, Marco S., Daniele M. Papetti, Simone Spolaor, Paolo Cazzaniga, and Luca Manzoni. 2022. "Shaping and Dilating the Fitness Landscape for Parameter Estimation in Stochastic Biochemical Models" Applied Sciences 12, no. 13: 6671. https://doi.org/10.3390/app12136671
APA StyleNobile, M. S., Papetti, D. M., Spolaor, S., Cazzaniga, P., & Manzoni, L. (2022). Shaping and Dilating the Fitness Landscape for Parameter Estimation in Stochastic Biochemical Models. Applied Sciences, 12(13), 6671. https://doi.org/10.3390/app12136671