4. Resilience as a systems biology measure from transcriptome model

Development of a resilience measure from transcriptome RNAs could improve basic knowledge of the transcriptome and responses to stress. Transcriptome size and overall variation have been documented across cell cycle stages, tissue types, developmental stages, diurnal cycles, sexes, and environment [50]. Despite the ubiquity of transcriptome size variation, its potential to introduce systematic bias into expression profiling has been largely overlooked and this study uncovers responses of the transcriptome to stress.

#### 4.1. Formalization of metric for resilience in biological systems using STIC metrics

Insight into structural determinants of robustness and resilience can guide the understanding of systems that go through transitions. Systems engineering research has developed methodologies to measure the functionality and complexity of engineered systems for designing and assessing system resilience. While system functions, resilience, functionality, and complexity are widely used concepts in systems engineering, there is significant diversity in definitions and no unified approach to measurement in the systems biology area [51]. One method for measuring impacts on functionality in dynamic engineered systems is based on changes in kinetic energy [52]. This metric can be applied at particular levels of abstraction and system scales, consistent with the established multiscale nature of biological systems.

#### 4.2. Measuring complexity

A difficulty in complexity theory is the lack of a clear definition for complexity, particularly one that is measurable [53]. Underlying cause for this lack of a unified complexity definition is that there are numerous conceptual types of complexity. The first formal treatment of complexity focused on algorithmic complexity, which reflects the computation requirements for a mathematical process [54]. Senge [55] and Sterman [56] expand the scope of definition to include dynamic complexity, which is primarily characterized by difficult-to-discern and hard-to-measure cause-effect relations. A recent workable definition is that of thermodynamic depth, which essentially asserts that complexity is a "measure of how hard it is to put something together" [57]. Several variations on this approach share the commonality that complexity should disappear for both ordered and purely stochastic systems [58]. Additionally, Bar-Yam [59] defined complexity as the length of the shortest string that can represent the properties of a physical system. This string could be the result of measurements and observations over time.

An energy-based metric was proposed by Chaisson [60] measuring the energy rate density, where Φm is energy rate density, E is energy flow through a system, τ is the time frame, and m is system mass. Chaisson obtains results that correlate well with other notions of complexity, and below we add our proposed relation from this transcriptome model framework

$$\mathcal{O}m = \mathbb{E}/\tau m \text{ or which we propose is :}\\a(\Sigma^S \text{NAM} + \Sigma^S \text{RCM})/N \tag{5}$$

from the extracellular space (EC) in the form of microparticles and exosomes TEC

<sup>α</sup> <sup>þ</sup> <sup>T</sup>IN

Figure 3. Framework for deriving transcriptome interactions and resilience. Data source is from RNA expression experiments using RNA-seq or microarray values, or randomized sets for controls. From input sets, the aligned gene ID and frequency of the extracted words are populated into a dictionary. Gene ID is used to calculate solvent-accessible (A) and inaccessible (I) word probabilities from full length transcripts in silico. The dictionary can be queried for any sequence S to find probability distribution of S in the dictionary. Changes in the transcriptome will change the distribution due to changes in A/I for affected words. Overall metrics of the dictionary measure resilience using Eq. (8) in the text.

where F is a filter function with parameters S (transcript sequence), RC (reverse complement of transcript sequence), n sequence length of S, and "a" is a fitting parameter with suitable dimensions, derived from: F α NAM/(RCM \* n) proportionality. Thus the extracellular pool is composed of transcripts with greater similarity S, and less reverse complementarity RC to the transcriptome of origin and also have smaller size n. The filter functions fS(S) and fRC(S,RC) operate on sequences S and RC, and essentially is a semantic selection filter on transcripts by affecting diffusion. We propose that resilience of the cell is proportional to size of the transcriptome filter F, then

such that |fS| is sum of all similarity matches, |fRC| is sum of all reverse complement interac-

EC � <sup>T</sup>OUT

OUT <sup>¼</sup> <sup>T</sup><sup>α</sup> � <sup>F</sup>½S, RC, n� <sup>≈</sup> <sup>T</sup><sup>α</sup> � ½<sup>a</sup> � <sup>f</sup> <sup>S</sup>ðSÞ=ð<sup>f</sup> RCðS,RCÞ � <sup>n</sup>Þ� <sup>ð</sup>7<sup>Þ</sup>

Models of RNA Interaction from Experimental Datasets: Framework of Resilience

http://dx.doi.org/10.5772/intechopen.69452

95

Resilience ¼ ðjf <sup>S</sup>jþjf RCjÞ=N ð8Þ

depletion as microparticle or exosome export to the extracellular space with T<sup>α</sup>

<sup>T</sup><sup>α</sup> <sup>¼</sup> <sup>T</sup><sup>0</sup>

resilience α |F|, where |F| ¼ |fS| þ |fRC|, or normalized for transcriptome size,

tions, and N is the total nucleotide size of the transcriptome.

with

Tα

IN, and

OUT. Or,

<sup>α</sup> ð6Þ

A practical difficulty in using the Φm metric is determining the appropriate mass and energy. In measuring the Φm of a transcriptome, we can use the mass of RNA production and the total energy processed by the system. Energy in this framework could be the total sum of all possible RNA-RNA interactions, which is just the count of all NAM and RCM in W as a sum of overall transcript sequences S. However, the total energy of a transcriptome does not flow just through its cell, but also exported to the extracellular space and captured from that external source of transcripts, the mass of which is difficult to measure.

While higher functionality can be associated with increased resiliency and robustness, the concepts are not synonymous. As defined by the INCOSE Resilient Systems Working Group, "Resilience is the capability of a system with specific characteristics before, during, and after a disruption to absorb the disruption, recover to an acceptable level of performance, and sustain that level for an acceptable period of time" [61]. Robustness is the ability of a system to reject disturbances without altering its state. A system is robust when it can continue functioning in the presence of internal and external challenges without fundamental changes to the original system. In relation to previous section on energy availability, robustness is the ability for a system to retain reachable states in the event of falling available energy.

#### 4.3. Framework for measuring resilience

Instead, complexity in the presented framework can be derived from properties of W or T as in Figure 3. Consider a transcriptome from a cell type alpha to be represented as Tα, such that it is the sum of all RNAs, including mRNA, miRNA, lncRNA, and rRNA within the cell (Table 1). This set is the result of transcripts produced from the cellular DNA, T<sup>α</sup> 0 , transcripts captured

Figure 3. Framework for deriving transcriptome interactions and resilience. Data source is from RNA expression experiments using RNA-seq or microarray values, or randomized sets for controls. From input sets, the aligned gene ID and frequency of the extracted words are populated into a dictionary. Gene ID is used to calculate solvent-accessible (A) and inaccessible (I) word probabilities from full length transcripts in silico. The dictionary can be queried for any sequence S to find probability distribution of S in the dictionary. Changes in the transcriptome will change the distribution due to changes in A/I for affected words. Overall metrics of the dictionary measure resilience using Eq. (8) in the text.

from the extracellular space (EC) in the form of microparticles and exosomes TEC IN, and depletion as microparticle or exosome export to the extracellular space with T<sup>α</sup> OUT. Or,

$$T\_{\alpha} = T\_{\alpha}^{0} + T\_{\text{EC}}^{\text{IN}} - T\_{\alpha}^{\text{OUT}} \tag{6}$$

with

4.2. Measuring complexity

A difficulty in complexity theory is the lack of a clear definition for complexity, particularly one that is measurable [53]. Underlying cause for this lack of a unified complexity definition is that there are numerous conceptual types of complexity. The first formal treatment of complexity focused on algorithmic complexity, which reflects the computation requirements for a mathematical process [54]. Senge [55] and Sterman [56] expand the scope of definition to include dynamic complexity, which is primarily characterized by difficult-to-discern and hard-to-measure cause-effect relations. A recent workable definition is that of thermodynamic depth, which essentially asserts that complexity is a "measure of how hard it is to put something together" [57]. Several variations on this approach share the commonality that complexity should disappear for both ordered and purely stochastic systems [58]. Additionally, Bar-Yam [59] defined complexity as the length of the shortest string that can represent the properties of a physical system. This string could be the result of measurements and observations over time.

94 Applications of RNA-Seq and Omics Strategies - From Microorganisms to Human Health

An energy-based metric was proposed by Chaisson [60] measuring the energy rate density, where Φm is energy rate density, E is energy flow through a system, τ is the time frame, and m is system mass. Chaisson obtains results that correlate well with other notions of complexity,

A practical difficulty in using the Φm metric is determining the appropriate mass and energy. In measuring the Φm of a transcriptome, we can use the mass of RNA production and the total energy processed by the system. Energy in this framework could be the total sum of all possible RNA-RNA interactions, which is just the count of all NAM and RCM in W as a sum of overall transcript sequences S. However, the total energy of a transcriptome does not flow just through its cell, but also exported to the extracellular space and captured from that

While higher functionality can be associated with increased resiliency and robustness, the concepts are not synonymous. As defined by the INCOSE Resilient Systems Working Group, "Resilience is the capability of a system with specific characteristics before, during, and after a disruption to absorb the disruption, recover to an acceptable level of performance, and sustain that level for an acceptable period of time" [61]. Robustness is the ability of a system to reject disturbances without altering its state. A system is robust when it can continue functioning in the presence of internal and external challenges without fundamental changes to the original system. In relation to previous section on energy availability, robustness is the ability for a

Instead, complexity in the presented framework can be derived from properties of W or T as in Figure 3. Consider a transcriptome from a cell type alpha to be represented as Tα, such that it is the sum of all RNAs, including mRNA, miRNA, lncRNA, and rRNA within the cell (Table 1).

0

, transcripts captured

<sup>Φ</sup><sup>m</sup> <sup>¼</sup> <sup>E</sup>=τ<sup>m</sup> or which we propose is : <sup>α</sup>ðΣ<sup>S</sup>NAM <sup>þ</sup> <sup>Σ</sup><sup>S</sup>RCMÞ=<sup>N</sup> <sup>ð</sup>5<sup>Þ</sup>

and below we add our proposed relation from this transcriptome model framework

external source of transcripts, the mass of which is difficult to measure.

system to retain reachable states in the event of falling available energy.

This set is the result of transcripts produced from the cellular DNA, T<sup>α</sup>

4.3. Framework for measuring resilience

$$T\_a \, ^{\rm OUT} = T\_a \ast \mathcal{J} [\text{S}, \, \text{RC}, n] \approx T\_a \ast \left[ a \ast f\_{\text{S}}(\text{S}) / (f\_{\text{RC}}(\text{S}, \text{RC}) \, \ast n) \right] \tag{7}$$

where F is a filter function with parameters S (transcript sequence), RC (reverse complement of transcript sequence), n sequence length of S, and "a" is a fitting parameter with suitable dimensions, derived from: F α NAM/(RCM \* n) proportionality. Thus the extracellular pool is composed of transcripts with greater similarity S, and less reverse complementarity RC to the transcriptome of origin and also have smaller size n. The filter functions fS(S) and fRC(S,RC) operate on sequences S and RC, and essentially is a semantic selection filter on transcripts by affecting diffusion. We propose that resilience of the cell is proportional to size of the transcriptome filter F, then resilience α |F|, where |F| ¼ |fS| þ |fRC|, or normalized for transcriptome size,

$$\text{Resiliente} = (|f\_S| + |f\_{\text{RC}}|)/N \tag{8}$$

such that |fS| is sum of all similarity matches, |fRC| is sum of all reverse complement interactions, and N is the total nucleotide size of the transcriptome.
