Conclusion - Development of an integrated metabolic analysis toolbox

In this chapter we have revisited results generated in a previous study in order to provide a demonstration of the analysis of the regulation of a system in terms of the properties of its components. Previously, we have shown that the negative flux-response of the acetaldehyde dehydrogenase flux due to an increase in the ratio of NADH to NAD+ _{was a result of interac-}

tions of these intermediates with other reactions within a model of L. lactis pyruvate branch metabolism. We subsequently explained the influence of these reactions on the acetaldehyde dehydrogenase flux in terms of their sensitivities towards this metabolite ratio, and in terms of the control of these reactions over the acetaldehyde dehydrogenase flux. Here, we dissected these reaction sensitivities and flux-control coefficients in order to arrive at a mechanistic explanation of the previously described flux response. We have also derived some general conclusions regarding the use of control patterns in the investigation of metabolic systems.

Our analysis of control patterns of this system was greatly simplified by using the concepts of backbone and multiplier patterns, which provided a descriptive language for comparing and contrasting control patterns that is much more digestible than considering the full control pattern expressions. We have seen that certain combinations of interactions between components in a system are more important than others for determining the control of a reaction over a system variable, thus the number of control patterns to consider is reduced to only those that actually contribute to the control. The importance of these control patterns is not static, and shifts as parameters are changed; however, certain control patterns never contribute significantly towards the control regardless of a specific parameter value. We also found that different reactions have similar control patterns for the same metabolic variables. In addition to describing the control coefficients in terms of chains of physical effects, we could, in a select few cases, explain certain aspects of their behaviour in terms of the properties and behaviour of single reactions. The information gleaned from describing control in terms of a single elasticity coefficient can probably not be used reliably to alter the control properties of a system, as we have seen. However, by zooming out and considering the general trends that groups of elasticity coefficients indicate (in the form of control patterns), these techniques could aid in metabolic engineering by guiding towards rational engineering strategies.

Many of the general findings described here are certainly not limited to the model we have used, as they are based on the well established principles of metabolic control analysis, simply seen from a different perspective. This work was made possible by software implementations

Table 5.4: Numerator expressions of the dominant control patterns of CJ6

v₃ in the free-φN model in

terms of the CJ6

v3 control patterns in the fixed-φN model. Each dominant control pattern of the free-

φN model is, to some degree, equivalent to a dominant control pattern in the fixed-φNmodel and is

expressed in terms of that pattern and the factors which account for the differences between the two expressions, considering only the numerators of the control patterns. Control patterns are divided into groups based on their dominant φN value range, which correspond with those of the dominant

control patterns in the fixed-φNmodel. Group 2 is divided into smaller groups A and B, as there is

a difference between the shape of the patterns in these groups (See Fig.C.4). Control patterns are arranged in descending order of relative importance within their group.

Group Control Pattern Expression

1 CP003 CP001 · J₁₃"_φv13 N CP027 CP011 ·J₁₃"_φv13 N 2A CP177 CP064 ·J₁₃"_φv13 N CP088 CP031 · J₁₃"_φv13 N CP116 CP042 ·J13"_φv13 N 2B CP181 CP064 · J₂"_φv2 N CP092 CP031 ·J2"_φv2_N CP120 CP042 · J₂"_φv2 N 3 CP176 CP063 ·J₁₃"_φv13 N CP214 CP063 ·2J4"_φv4_C"_φv6_N/"_φv6_C CP069 CP063 ·−2J4"_φv4_C"_Acalv6 "_φv7_N/("_φv6_C"_Acalv7 ) CP087 CP030 · J₁₃"_φv13 N 4 CP216 CP071 ·2J4"_φv4_C"_φv6_N/"_φv6_C CP067 CP036 ·2J₄"v4 φC" v6 φN/" v6 φC CP071 CP071 ·−2J4"_φv4_C"_Acalv6 "_φv7_N/("_φv6_C"_Acalv7 ) CP212 CP058 ·2J₄"v1 φN" v5 φA/" v1 φA CP191 CP071 ·J13"_φv13 N CP211 CP036 · −2J4"_φv4_C"Acalv6 " v7 φN/(" v6 φC" v7 Acal) CP098 CP036 ·J13"_φv13 N CP124 CP045 · J₁₃"_φv13 N

of theoretical tools that were not available 10 years ago and we believe that the techniques described here can lead to a richer understanding of why and how other systems behave the way that they do. In our case, the application of these techniques not only led to biological insight, but also to new insights regarding the further development of our analysis software (as will be discussed in Section6.3).

Chapter 6

General Discussion

This final chapter offers a broad overview and consolidated discussion of the work presented thus far. In Section6.1a summary of the main results of Chapters 3–5 is presented, whereafter this work is critically appraised and discussed in terms of its general implications within the context of systems biology and metabolic pathway analysis in Section6.2. In Section6.3sug- gestions are made for possible future developments, before finally concluding in Section6.4.

6.1 Synopsis

There were two interrelated primary motivations for the work presented in this dissertation. Firstly, we wanted to develop a software “toolbox” of implementations of various previously conceived metabolic analysis frameworks. Each of these tools had to be individually useful for exposing previously unknown properties of metabolic models relating to their behaviour, control, and regulation; however, a key envisioned strength of these tools was their potential for being applied to complement each other in this undertaking. Secondly, as we perceived most of the analysis frameworks included in our software toolbox as being underutilised in the investigation of models of real metabolic systems within the literature, we wanted to explore the practical utility of our tools in this domain. Thus, we set out to utilise these tools in the analysis of previously published kinetic models in order better understand the systems they represent.

After a review of the relevant literature, we presented our software package

PySCeSToolbox

in Chapter3. This software includes three main tools, with each being a software implemen- tation of a conceptual framework that can be utilised for model analysis. These three tools are

RateChar

SymCa

, and

ThermoKin

RateChar

automatically generates rate-characteristic plots of the supply and demand blocks of the variable intermediates of metabolic models in

order to perform generalised supply-demand analysis [15].

SymCa

is used to determine the symbolic expressions of the control coefficients of a metabolic system in terms of the elasticity coefficients of its steps; therefore this tool provides the functionality to perform symbolic metabolic control analysis [23,24] and control pattern analysis [17,119,121]. Finally,

ThermoKin

can be used to determine the contributions of the thermodynamic and kinetic aspects of rate equations towards the rates of the reactions they describe in a metabolic pathway [16]. Additionally it can determine the degree to which these terms control the reaction rate, as well as the distance of the reaction from equilibrium. While each of the software tools provided by

_{PySCeSToolbox}

can be used in isolation, they are designed in a way that facilitates their combined use in metabolic model analysis.

In Chapter4, we utilised

RateChar

to perform generalised supply-demand analysis on two previously published metabolic models. One of these models was of pyruvate branch metabolism in Lactococcus lactis [86], whereas the other was of aspartate-derived amino-acid synthesis in Arabidopsis thaliana [85]. Here we focussed specifically on elucidating the regulatory effects of multiple routes of interaction between various reaction blocks in each model. In the pyruvate branch model we explored the regulatory effects of the moiety-conserved cycles of ATP/ADP and NADH/NAD+_{. One notable result was that a demand block of NADH/NAD}+

(with the demand enzyme acetyldehyde dehydrogenase) exhibited a response reminiscent of substrate inhibition towards in increase in the ratio NADH to NAD+_{. This effect was, however,}

shown rather to be a result of the interaction of the members of this moiety-conserved cycle with pyruvate dehydrogenase upstream from acetyldehyde dehydrogenase.

In the aspartate-derived amino acid synthesis model, we concentrated on the regulation of the aspartate semialdehyde supply block by this intermediate itself. This supply block was found to respond negatively towards a positive perturbation of aspartate semialdehyde due to the interaction of this intermediate with its demand blocks, rather than through the expected product inhibition of the supply enzyme. This phenomenon was a result of an increase in the concentration of intermediates within the aspartate semialdehyde demand blocks, which act as upstream inhibitors of the supply block. Thus, for both models investigated within this chapter, the presence of multiple routes of interaction between reaction blocks resulted in unexpected regulatory phenomena that were uncovered with, and subsequently quantified using, generalised supply-demand analysis.

The analysis involving the pyruvate branch model was extended in Chapter5. Here we first used

_SymCa

to explore the control properties of this system, focussing specifically on the flux control of the acetyldehyde dehydrogenase NADH/NAD+ _{demand block. By focussing}

on the steps that dominated the overall flux control of this block, our analysis revealed that, out of the large variety of possible chains of local effects that can propagate from these steps,

only a select few control patterns were actually responsible for the observed flux control. Fur- thermore, there was a degree of overlap between the chains of local effects of the dominant control patterns, i.e., the most important paths for propagating perturbations in terms of their contributions towards the observed control coefficients were closely related, and they could therefore be categorised into groups of related patterns. Secondly, we utilised

ThermoKin

to investigate the thermodynamic and kinetic aspects of the constituent elasticity coefficients of a selection of the aforementioned dominant control patterns. In these modelling experiments we demonstrated how the differences in some control coefficients can be traced to the properties of specific individual enzyme-catalysed reactions. By making appropriate alterations to these reactions according to their thermodynamic and kinetic properties, we were able to alter the flux control in one case, but not in another. Ultimately, the analyses in this chapter revealed the underlying mechanistic basis of the observed flux responses of the previous chapter.

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