Motivación de individuos

Over the last two decades, purely structural metabolic models have become increasingly prevalent. However, a survey of the curated models hosted by the Biomodels database [159] reveals that since 2010 at least 200 kinetic models have been published. While this number includes models other than metabolic models (e.g. [225,226]), it also includes a variety of relatively large metabolic models (e.g. [227–229]). Regardless of the size of the model, how- ever, after publication many of these models are not utilised in further investigations. This represents a significant waste of resources as, in our opinion, model construction is only the first step of the “modelling approach”. As stated in the introduction of this text (Chapter1), a fundamental goal of systems biology is to reach a system-level understanding of biology by concerning itself with how the properties of, and non-linear interactions between, the molec- ular components of biological systems give rise to higher levels of function. Throughout the remainder of this text we have endeavoured to reach system-level understanding by develop- ing software implementations of metabolic analysis frameworks, by applying these tools in a novel manner, and by uncovering previously unknown behaviour of two metabolic models.

While the methods contained within

_{PySCeSToolbox}

have been utilised in the past, and it is technically possible in principle to apply them in model analysis without using

PySCeSToolbox

, the development of specific software implementations of the thermody- namic/kinetic analysis framework, symbolic control analysis, and generalised supply-demand analysis have unlocked the potential of these frameworks in a way that was previously inac- cessible. One notable strength of these software implementations is that they are completely

general. This means that, while there are some limitations in terms of the size of the mod- els that can comfortably be approached (see discussion below), each of the tools provided by

PySCeSToolbox

can be utilised to investigate metabolic models of arbitrary size and complexity using essentially the same procedure. Secondly, all three of

_RateChar

,

_SymCa

, and

ThermoKin

are to a large extent automated, which means that minimal user interven- tion is required when utilising these tools. These two features abolish the need to develop specialised solutions for individual models, thus greatly reducing the time-investment and technical barrier for performing the analyses provided by

PySCeSToolbox

.

A second advantage stems from the fact that

_{PySCeSToolbox}

is implemented as a Python library. While this decision may be a point of contention among potential users of the soft- ware, as it necessitates a scripting approach to model analysis, we believe that it is one of the most powerful assets of this software. Together with the fact that the tools of

_{PySCeSToolbox}

are general and automated, a key benefit to this approach is the high degree of reproducibil- ity and repeatability that it imparts to modelling experiments; by removing all need for user intervention after a script is developed, in silico experiments and analyses may be executed multiple times on the same computer, or on different computers, with no variation in out- put. Thus, assuming the original analysis script is correct, the produced results will always be accurate. In contrast, these highly sought-after traits of reproducibility and repeatability are much more difficult to achieve in simulators and tools that require user guided analysis through continuous interaction with a graphical user interface or a command-line interface, as this process is prone to user-error.

In Chapters 4 and 5, the features described in the above two paragraphs were indis- pensable to our own analyses. In Chapter 4 the scripting approach allowed us to perform practically the same analysis on models of completely different systems (pyruvate branch metabolism vs. aspartate-derived amino-acid synthesis) using the largely the same scripts with only minor alterations. Moreover, in the case where different versions of the same model were investigated (such as the various knockout models of Chapter4, or the fixed moiety ratio and free moiety ratio models of Chapter5), alterations to scripts were even more sparse. This greatly simplified the execution of modelling experiments, thus freeing up mental energy for interpreting results, rather than generating them.

Each of the metabolic analysis frameworks implemented in

PySCeSToolbox

has distinct uses for uncovering various properties of metabolic systems that might not be accessible using other techniques. GSDA, for instance, was originally developed in order to give researchers an entry point into the investigation of metabolic models. It achieves this by giving a broad overview of the behaviour, control, and regulation of a system, and by highlighting its most important regulatory features. Thus, while this framework relies on the principles of MCA,

it offers a more comprehensive view than what is achievable through investigation of the control and elasticity coefficients of a system. In Chapter 4, we have specifically used it to illuminate the regulatory role of multiple routes of interaction between reaction blocks in two distinct metabolic models. While it would have been possible to generate these results purely through the application of MCA, this process would also have been much more laborious as it would have involved using different versions of the models (one for each fixed variable intermediate) and a large number of calculations.

Similarly, symbolic control analysis offers advantages over numeric control coefficient analysis. In addition to indicating the degree of control that reaction steps have over the metabolic variables of a pathway, it illuminates the source of this control. Thus symbolic control analysis has far greater explanatory power than “conventional” MCA. In Chapter 5, this framework was central to uncovering the chains of local effects that resulted in the neg- ative response of the acetyldehyde dehydrogenase NADH/NAD+ _{demand block towards an}

increase in its substrate presented in Chapter 4. Here the control coefficient expressions themselves provided insight into a variety of phenomena. Firstly, they indicated that differ- ent chains of local effects determined the control properties of the system under different conditions. Secondly, by investigating and comparing the properties of the components of these chains, they allowed us to understand why different chains of local effects were dom- inant under different conditions. Finally, performing these same comparisons between the chains of local effects of different control coefficients pointed out that the source of their dif- ferent values were related to the composition of their control patterns (and subsequently the properties of the components of these control patterns). In summary, the symbolic control coefficient expressions are able to quantify the control of a system in terms of its components and composition.

While software providing functionality for performing symbolic control analysis has ex- isted for more than 20 years (albeit in a much more limited capacity than presented here), very few studies have, to our knowledge, utilised these tools. In the few cases where they have been used, the symbolic control coefficient expressions were never used in an explana- tory capacity to the extent presented here. For instance, in a previous study by Thomas et al. [27],

MetaCon

[22] (see Section2.4) was used to generate expressions for the control coeffi- cients of glycolysis in Solanum tuberosum. These authors subsequently substituted the values of the elasticity coefficient of the steps of the system into the control coefficient expressions to determine their values. By varying the value of a particular elasticity coefficient they could determine its effect on important control coefficient values. While keeping in mind that these results were generated nearly two decades ago, it is noteworthy that the same results could have been achieved through inversion of different numeric E-matrices for each set of elas-

ticity coefficients [57]. Thus, in this case the control coefficient expressions were not really essential to the study. This is in stark contrast to the manner in which control coefficient expressions were utilised in Chapter5and in the case studies performed by Akhurst [24] in his thesis on the development of the original incarnation of

_SymCa

. In both of these cases, the control coefficient expressions and their control patterns were used to relate higher level sys- tem behaviour to the chains of interactions between the physical components of the system. We therefore believe that this framework has been severely underutilised in the past.

While the thermodynamic/kinetic analysis framework of Rohwer and Hofmeyr [16] of- fers an arguably more justified demarcation between far-from and near-equilibrium reactions than that suggested by Rolleston [135], it also provides a more rigorous approach to inves- tigating the effects of intrinsic mass-action and enzyme binding and catalysis. In contrast to approaches that rely only on the “distance-from-equilibrium” metric to classify a reaction rate as being determined by mass-action or by enzyme kinetics, this framework utilises elas- ticity coefficients to quantify the specific effects of these components. In our investigation presented in Chapter 5, we used this technique to explain the differences observed in the elasticity coefficient components of the partial response coefficients of the acetyldehyde de- hydrogenase NADH/NAD+ _{demand block towards NADH/NAD}+ _{of Chapter4. In this case,}

however, the kinetic contribution towards determining the reaction sensitivity was zero, due to the fact that the elasticity coefficients were determined with respect the ratio of substrate to product rather than for an individual intermediate.

As previously mentioned, a particular strength of above-mentioned tools is their potential for complementing one another. In this dissertation this is exemplified in our analysis of the pyruvate branch metabolism model presented in Chapters4 and5. GSDA was used as an entry point in determining the behaviour of this system, and subsequently followed by analyses using

SymCa

and

ThermoKin

, which revealed finer details. Ultimately, this strategy uncovered high-level system behaviour and explained this behaviour in terms of both the interactions between system reactions, and the individual properties of the reactions. We believe that this fulfils the criteria for a mechanistic explanation of a biological system where neither the individual components, nor the complete system itself, is privileged [230].

This is not to say that these techniques are without limitations or caveats. In GSDA the intermediates are fixed and varied over a range to generate rate characteristic plots. This process has two important implications. Firstly, it prevents communication between reac- tion blocks through this intermediate, which results in different control properties for the “fixed” vs. “unfixed” models. Secondly, this artificial perturbation cannot be counteracted by the system as would be expected in regular dynamically stable systems. In our analysis in Chapter4we utilised two fixed intermediate models as part of a GSDA to investigate the flux-

responses of different reaction blocks towards the fixed intermediates, and to subsequently explain these flux-responses in terms of the different routes of interaction between the fixed intermediates and the reaction blocks. In this case, parametrisation of the intermediates was necessary to isolate the effect of changes in their concentrations on the system without the system counteracting these changes. Similarly, in Chapter 5the chains of local effects that comprise the control coefficient components of the flux-responses investigated in the previous chapter were analysed using a model in which the NADH/NAD+_{ratio was fixed. As described}

in Section5.3.6, we justified our use of the fixed model in two ways. Firstly, we wanted to extend the analysis of the previous chapter, thus warranting the use of the same model. Sec- ondly, in spite of altering the control properties of the system, very similar behaviour and dominant control patterns were observed in the reference model when modulating of the activity of NADH oxidase. However, it is important not to overextend this approach and to be mindful of the consequences of the technique; in other models, parametrising an intermedi- ate of the system may lead to vastly different behaviour and control properties compared to the reference model, thus limiting the usefulness of the “fixed” model for explaining actual biological phenomena.

A possible issue with symbolic control analysis is the practicability of the task of sifting through and making sense of the generated control patterns that constitute the control coef- ficients of a system. For instance, while the model of pyruvate branch metabolism consists of only 14 reactions, more than 200 control patterns were generated in the reference model for CJ6

v6 (Chapter5), and one can therefore expect an enormous number of patterns for larger

models. Our solution was to utilise backbone and multiplier patterns to simplify the task of analysing and comparing control patterns. Moreover, by focusing on the model where the NADH/NAD+ _{ratio was fixed, the number of control patterns was significantly reduced.}

Nevertheless, this technique might not be viable in all cases due to the previously described issues. Finally, all control patterns containing elasticity coefficients of zero value (indicating insensitivity of a reaction towards a substrate or product) were disregarded, which further decreased the number of control patterns. This strategy can be extended to disregarding control patterns that contain elasticity coefficients known to be very close to zero under the conditions pertinent to a specific investigation. Another viable option may be to consider groups of reactions as single units using group elasticities as originally suggested by Hofmeyr [121]. In this strategy multiple reactions are effectively regarded as a single reaction with a single elasticity coefficient. Utilising the concept of monofunctional units, which are groups (or blocks) of reactions that only interact with the rest of the system through a single degree of freedom [231], can also be useful as they will most probably result in the simplest con- trol coefficient expressions. Thus, analysis of a model could proceed in stages where the full

complexity is abstracted until there is a specific need for investigating the specific chains of local effects contained within the block of reactions represented by a group elasticity.

Finally, one should also be mindful of the fact that the results produced by these tech- niques are to a large extent only a reflection of the properties of the system under the specific configuration and conditions when they were generated. In other words, while they explain why a system behaves as it does, they cannot always reliably be used to predict the outcome of an alteration to the system. An example of such a case can be found in our investigation of the differences between control patterns 063 and 071 of CJ6

v3 in the pyruvate branch model

in Section 5.3.5. Here, replacing one reaction with another with the goal of modifying the control properties of the system was unsuccessful, as the system-level effect of our alteration was ultimately counteracted by the system. Thus, while we could successfully explain the behaviour of the system in terms of its component properties and interactions, manipulations based on this information did not result in system behaviour matching our expectations. One must therefore avoid the temptation to fall into the reductionist trap of traditional molecular biology of attempting to attribute system behaviours to single components by disregarding that these components themselves are affected by the system as a whole.

In document El papel de la cultura y de la innovación en el diseño y desarrollo de los nuevos modelos de negocio (página 91-97)