# Incorporating Heuristics in a Swarm Intelligence Framework for Inferring Gene Regulatory Networks from Gene Expression Time Series

## Summary (2 min read)

### 1 Introduction

- Certain genes code for special proteins called transcription factors, which are responsible for regulating the expression of other genes .
- The authors model a GRN as a graph, upon which the ant colony optimization (ACO) meta-heuristic is implemented for the selection of putative GRN architectures.
- The selected structure is then modelled as a recurrent neural network (RNN), whose parameters (weights and bias terms) are optimized using particle swarm optimization (PSO), so as to minimize the error between the model’s output and the actual time series.
- In the next section, the authors present an overview of existing approaches to the problem of GRN inference from time course gene expression data.

### 2 Existing Approaches

- The earliest approaches to the problem of inferring gene relationships from time course gene expression data, were cluster analysis methods, mostly based on global correlation metrics, such as Pearson correlation coefficient, mutual information etc., that extracted co-regulation information out of co-expressed gene clusters [5][6].
- Nevertheless, cluster analysis is still useful, primarily as a technique to reduce the search space and improve the performance of algorithms.
- Their strength in representing noisy, stochastic processes due to their probabilistic nature, makes them good candidates for addressing the problem of inferring gene regulatory networks [9].
- Ressom et al. [4] implement a swarm intelligence framework where an ant system, driven only by pheromone amplification, is used for the selection of putative network structures.
- After a structure has been formed, the corresponding model (RNN) is optimized using PSO, in order to evaluate the quality of the selected structure.

### 3 Methods

- Network architectures are constructed using the ACO meta-heuristic [14], whereby artificial ants navigate a graph of N nodes, where N is the number of genes in the time series.
- After the threshold of maximum allowed PSO iterations has been reached, the minimum achieved error ǫ(wS) is returned to the ACO algorithm as the quality of the selected structure S.
- These expression changes in a gene’s temporal profile are encoded as ‘events’, by calculating the slope of the expression profile at every time interval and classifying it as either ‘R’ , ‘F’ or ‘C’ .
- This is done by swapping ‘R’s with ‘F’s, while ‘C’s remain intact.

### 4 Results

- The authors selected 5 cyclin genes that are known to be involved in cell cycle regulation, from the S. cerevisiae data set published in Spellman et al. [18], for the purpose of comparing their results to those of Ressom et al. [4].
- The yeast data set contains multiple time series from the yeast cell cycle; the authors chose the cdc15 time series, consisting of 24 time points (more than the others).
- The authors performed 10 such experiments and recorded the number of times each edge was selected.
- The incorporation of the selected heuristic metric does not seem to influence structure selection in a decisive manner.

### 5 Further Work

- The reported early results that have been presented in this paper, form part of an ongoing study into a swarm intelligence perspective to the problem of reverseengineering gene regulatory networks.
- The proposed framework allows for the incorporation of an arbitrary number of problem-specific heuristics, perhaps with an appropriately defined weighting scheme, to a model-based optimization approach.
- Furthermore, the authors note that their experiments have used a hand-picked subset of temporal gene expression profiles.
- An investigation of the algorithm’s scalability is necessary, particularly when considering the full set of genes, whose expression levels are captured in a real world data set.

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##### Citations

59 citations

33 citations

### Cites methods from "Incorporating Heuristics in a Swarm..."

...In [11], an ant system is implemented to generate candidate network structures, and in [22], the bees algorithm is used to generate Boolean network examples to support a theorem presented in that work....

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21 citations

### Cites methods from "Incorporating Heuristics in a Swarm..."

...In [22], an ant system is implemented to generate candidate network structures and in [23] the bees algorithm is used to generate Boolean network examples to support a theorem presented in that work....

[...]

13 citations

1 citations

### Cites background from "Incorporating Heuristics in a Swarm..."

...Research in this direction has already been done, for example in [27, 23, 13], but no analysis of the underlying fitness landscape had been performed before....

[...]

...Many mathematical models exist in the literature to describe gene regulatory interactions: Relevance Networks [17], Boolean Networks [16], Dynamic Bayesian Networks [6] and systems of additive or differential equations, being them linear [1], ordinary nonlinear [7, 13, 23, 25, 28, 27] (including recurrent neural networks) or S-systems [21, 14, 24]....

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##### References

35,104 citations

### "Incorporating Heuristics in a Swarm..." refers methods in this paper

...Optimization of the model’s parameters is performed using a PSO algorithm [15], where each particle’s position is encoded as a vector wS of size N(K + 1) that contains the weights of the selected edges, as well as the bias terms....

[...]

16,371 citations

### "Incorporating Heuristics in a Swarm..." refers background in this paper

..., that extracted co-regulation information out of co-expressed gene clusters [5][6]....

[...]

11,844 citations

### "Incorporating Heuristics in a Swarm..." refers methods in this paper

...A variation of the Needleman-Wunsch algorithm for sequence alignment [17] is then used to determine the best possible alignment for a pair of event strings, by using the event scoring matrix shown in Table 1....

[...]

5,822 citations

### "Incorporating Heuristics in a Swarm..." refers methods in this paper

...Network architectures are constructed using the ACO meta-heuristic [14], whereby artificial ants navigate a graph of N nodes, where N is the number of genes in the time series....

[...]

5,176 citations

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##### Frequently Asked Questions (12)

###### Q2. What is the definition of a dynamic Bayesian network?

Dynamic Bayesian networks are models of joint, multivariate probability distributions that attempt to represent conditional independence relationships between variables.

###### Q3. How is the quality of a candidate structure assessed?

After a candidate structure S has been constructed, its quality is assessed by tuning the corresponding model’s parameters in order to compare its predicted output with the actual time series.

###### Q4. Why are swarms of ants good candidates for inferring gene regulatory networks?

Their strength in representing noisy, stochastic processes due to their probabilistic nature, makes them good candidates for addressing the problem of inferring gene regulatory networks [9].

###### Q5. What are some of the popular models used in the literature?

Such models include Boolean networks, Bayesian networks, linear additive models, systems of differential equations, power law systems etc. [7]

###### Q6. What is the proposed framework for a swarm intelligence perspective?

The proposed framework allows for the incorporation of an arbitrary number of problem-specific heuristics, perhaps with an appropriately defined weighting scheme, to a model-based optimization approach.

###### Q7. How does the approach extend the work by Ressom et al.?

Their approach extends the work by Ressom et al. [4], first by changing the way candidate architectures are constructed by individual artificial ants and, second, by introducing a heuristic metric with the intention to bias the probabilistic edge selection process towards biologically plausible relationships.

###### Q8. What is the pheromone matrix of a candidate structure?

After the threshold of maximum allowed PSO iterations has been reached, the minimum achieved error ǫ(wS) is returned to the ACO algorithm as the quality of the selected structure S. The pheromone matrix is then updated according to:τij = 1ǫ(wS) ∀eji ∈ S (4)The incorporation of heuristics to probabilistic structure selection offers a way of enriching a domain-agnostic procedure with problem-specific insights.

###### Q9. What is the meaning of events in a gene’s temporal profile?

These expression changes in a gene’s temporal profile are encoded as ‘events’, by calculating the slope of the expression profile at every time interval and classifying it as either ‘R’ (rising), ‘F’ (falling) or ‘C’ (constant).

###### Q10. What is the probability of selection of node j as a potential regulator of node?

The probability of selection of node j as a potential regulator of node i is given by:pij = ταijη β ij∑Nj=1 τ α ijη β ij(2)where τij is the pheromone value of edge eji, ηij is the selection desirability of edge eji based on a suitably defined heuristic function and α, β are their respective relative influences.

###### Q11. What is the way to determine the alignment for a pair of event strings?

A variation of the Needleman-Wunsch algorithm for sequence alignment [17] is then used to determine the best possible alignment for a pair of event strings, by using the event scoring matrix shown in Table 1.

###### Q12. What is the probability of selection of a potential regulator of node i?

Each artificial ant probabilistically selects K regulator nodes for each target node in the graph, resulting in a candidate network structure S = {eji} of NK connections.