C1 metabolism is essential for all organisms to provide one-carbon units for methylation and other types of modifications, as well as for nucleic acid, amino acid, and other biomolecule syntheses. In particular, C1 metabolism process provides the one-carbon units essential for DNA methylation, which controls plant growth and development, with a particular involvement in regulation of gene expression and DNA replication [3] .

DNA methylation in plants, similar to that in animals, affects the ability of specific proteins to bind to the DNA and chromatin based transcription complex formation, and also related to histone modifications. Methylation in plants is species-, tissue-, organelle- and age-specific. In plants, DNA is highly methylated; containing 5- methylcytosine (m5C) and N 6-methyladenine (m6A) [3] .

C1 metabolism in plants, however, differs in fundamental ways from that in bacteria, fungi, and mammals. In plants, one carbon transfer is very critical for plant specific metabolic pathways such as photorespiration, mitochondrial formate metabolism, glyoxylate metabolism, and the methylation cycle.

Perturbations to C1 metabolism, therefore, may likely affect the control mechanisms of DNA methylation, which itself is modulated by phytohormones and changes on seed germination, flowering and under the influence of various pathogens (viral, bacterial, fungal). At the enzymatic level, the common enzymes that plants share with other organisms have been shown to have different roles in plants. Formaldehyde dehydrogenase and s-formylglutathione hydrolase, for example, are known to metabolize endogenous formaldehyde and not exogenous formaldehyde from the environment [2] .

C1 metabolism is a complex system of molecular pathway systems. The three major molecular pathway systems of C1 metabolism, aforementioned, are summarized from the previous systematic literature review to provide the reader a background to appreciate the in silico modeling efforts herein.

One of the three systems of C1 metabolism is methionine biosynthesis. Methionine biosynthesis is comprised of set of reactions that are folate-dependent as shown in Figure 2 [4] . The starting point for methionine synthesis is the addition of either serine [7] or the formate molecule [8] to tetrahydrofolate (THF), followed by several interconversions that lead to methionine biosynthesis [9] . Formate can also get oxidized to carbon dioxide (CO₂) or dimerize to yield glyoxylate [10] . The last step in this set of molecular pathways is the synthesis of methionine. Reaction between homocysteine and a THF derivative catalyzed by methionine synthase leads to the formation of methionine in either the cytosol or chloroplast [11] .

The major vehicles of one carbon unit transfer are various complexes of THF present mostly in cytosol [12] - [14] , as well as the mitochondria and chloroplast [15] . The synthesis of THF spans the chloroplast, cytosol, and mitochondrion. The precursor of THF, dihydropterin, is synthesized in cytosol whereas p-aminobenzoic acid is synthesized in chloroplast. They are translocated into the mitrochondrion for completion of THF synthesis [16] [17] .

Another important system of C1 metabolism is the activated methyl cycle, as shown in Figure 3. Of the total methionine synthesized from the methionine biosynthesis pathway, 20% is utilized for protein synthesis [18] . The remaining methionine may be the used in theactivated methyl cycle.

Methionine in the activated methyl cycle is converted to S-adenosylmethionine (SAM) in the cytosol [11] [19] - [21] and can be translocated to chloroplast for methylation [11] . Methyltransferase enzymes bind to SAM, which binds to enzymes [22] to form a complex. This SAM-bound enzymes subsequently transfers the methyl group to methylate DNA, RNA, proteins, and other biomolecules to complete the methylation process. Loss of methyl group from SAM yields s-adenosylhomo-cysteine which dissociates into adenosine and homocysteine [23] . Homocysteine is then converted back to methionine [23] and recycled.

Within C1 metabolism, formaldehyde detoxification as shown in Figure 4, is a critical system for modulating formaldehyde levels. Formaldehyde is a toxic compound produced during plant C1 metabolism. The detoxification of formaldehyde therefore is essential to normal cellular function in plants.

The main sources of formaldehyde in plants are 5, 10-methylene-THF, methanol, and sarcosine [24] [25] . The detoxification of formaldehyde results in either formate or a THF derivative [4] . Formate can either be further oxidized to CO₂ [26] or utilized as a carbon source in C1 metabolism.

In this process, formaldehyde may bind to either to glutathione (to form hydroxylmethylglutathione (HM- glutathione)) [27] or to a THF derivative. Conversion of HM-glutathioneto formate involves its catalysis by for- maldehyde dehydrogenase (FALDH) to formylglutathione (formyl-GSH). In the final steps, formylglutathione is converted to formate and glutathione which is catalyzed by s-formylglutathione hydrolase [28] - [31] .

CytoSolve, developed in earlier work by Ayyadurai and Dewey (2011) [5] , provides a scalable computational systems biology platform for the dynamic integration of complex and large-scale molecular pathway models [5] [6] [32] . CytoSolve was selected for use in this research since, it allows for complex and scalable integration of multiple molecular pathway models.

CytoSolve aggregates existing peer-reviewed scientific literature and mines this literature to extract molecular pathways of biological processes. Mathematical models derived from these pathways are integrated to create a validated and integrative model. This method provides a computational architecture, as shown in Figure 5, for coupling individual molecular pathway models dynamically without the need to create a monolithic model.

This approach provides a scalable methodology for integration of systems of systems of molecular pathway models. Other computational approaches are not scalable as they have not considered the intractability that

emerges from maintaining a single large monolithic model, wherein each model, within a system of molecular pathway model may require constant updates and changes, given the dynamic nature of biological research [6] .

In silico modeling benefits greatly through a high level architecture, which provides a blueprint on how the elemental pathway systems integrate as well as an understanding of how such systems may interact with related systems. This effort results in the development of a systems architecture map. This systems architecture map provides a cogent approach not only to produce an integrative model, but also to appreciate how other related systems, in future research, can be integrated to expand more complex understanding of the phenomena of interest.

The CytoSolve platform enables the development of three in silico molecular pathway models: 1) methionine biosynthesis, 2) activated methyl cycle, and 3) formaldehyde detoxification. For each individual pathway, relevant literature is identified, reviewed and prioritized. Key reactions in the individual pathways are identified from the relevant literature along with appropriate kinetic information, as well as the biomolecular species and their concentration information.

In the Supplementary Materials, are provided the sources of the kinetic information used in deriving the individual molecular pathway models. Tables S1-S3 of the Supplementary Material contain the kinetic information for methionine biosynthesis, activated methyl cycle, and formaldehyde detoxification models, respectively. The Supplementary Materials also provides the literature references from which the kinetics are obtained for developing the in silico models.

The three validated molecular pathway models of methionine biosynthesis, activated methyl cycle and formaldehyde detoxification are integrated in the CytoSolve platform to create an integrative and comprehensive in silico model of C1 metabolism. This integration is modular and dynamic, meaning the individual models remain in their native formats, and intelligent computational engine afforded by CytoSolve provides a mechanism to dynamically integrate the individual models, based on identification of common biomolecular species across a plurality of a system of models. For example, in one case, the two molecular species: homocysteine and methionine are common species across the two molecular pathway systems of methionine biosynthesis and active methyl cycle models. In another example, 5,10-methylene THF and formate are the common molecular species across the molecular pathway systems of methionine biosynthesis and formaldehyde detoxification pathways.

The integrative model resulting from the coupling of the three molecular pathway systems of C1 metabolism can be used for executing simulations through CytoSolve, which performs mass balance and simultaneously couples and solves the systems of systems of differential equations to estimate the rate curves for each biomolecular species within the C1 metabolism system to estimate the concentration profiles of biomolecules in C1 metabolism. All simulations were executed for a simulation time period of 800,000 seconds (~9 days). These simulations provide the insights for conducting in silico modeling and testing of biological phenomena to support in vitro and in vivo research.

The systems architecture map of C1 metabolism is shown in Figure 6. This figure is the schematic illustration of how the three major molecular systems of methionine biosynthesis, activated methyl cycle and formaldehyde detoxification illustrated in Figures 2-4, respectively, interconnect and interface with one another.

The schematic illustration in Figure 6 shows that each molecular pathway system of C1 metabolism interacts with the other two. Methionine biosynthesis, shown in Figure 2, communicates with formaldehyde detoxification, shown in Figure 4, via the common molecular specie of THF and 5,10-methylene-THF. Methionine biosynthesis communicates with activated methyl cycle, shown in Figure 3, via the common molecular specie of methionine and homocysteine. The activated methyl cycle communicates with formaldehyde detoxification via the common molecular species of sarcosine.

In addition to the core elements of C1 metabolism illustrated in Figure 6, Figure 7 illustrates, based on the current literature review, other molecular pathway systems that may likely interact with C1 metabolism. These systems include: THF biosynthesis, oxidative stress metabolism, catalase activity, shikimic acid metabolism, adenosine metabolism, glyphosate metabolism, formate biosynthesis, and serine biosynthesis.

The key biomolecular species of interest in the methionine biosynthesis model are methionine and formaldehyde. The methionine biosynthesis model was simulated for a simulation time period of 800,000 seconds (~9 days). There are three important results that emerged from this simulation.

First, the model predicts that methionine concentrations reach saturation levels of 1000 nM, near instantaneously relative to the simulation time of period of 800,000 seconds (~9 days), as shown in Figure 8(a). The individual model of methionine biosynthesis only considers the reaction of formation of methionine and not its consumption in downstream pathways; therefore, the methionine concentrations reacha plateau and achieve a steady state. The steady state value 1000 nM of methionine resultsfromthe complete conversion of homocysteine, which is reported to have 1000 nM in physiological conditions [33] . The results indicate that all of the homocysteine is converted to methionine in the methionine biosynthesis model.

The second result is concerning formaldehyde formation in the methionine biosynthesis model as shown in Figure 8(b). Formaldehyde is produced from 5, 10-methylene THF [13] [34] in the methionine biosynthesis model. A steady state concentration of 0.06 nM of formaldehyde is achieved near instantaneously in methionine biosynthesis model.

The third result is concerning formate concentrations in the methionine biosynthesis model as shown in Figure 8(c). Formate is produced from formylglutathione (formyl-GSH) and consumed in the methionine biosynthesis model [28] [35] . Formate rapidly increases as it synthesized from formylglutathione and is converted to CO₂ and water in the methionine biosynthesis model which explains the near instantaneous rise in formate concentrations followed by decrease in its concentrations with time. Since the formate concentrations are obtained from the mass balance of formate, the reduction in formate concentrations over time indicates that the conversion of formate to CO₂ is dominant relative to the formation of formate from formylglutathione.

There is one important result that emerges from this simulation as shown in Figure 9. One of the key reactions in activated methyl cycle is the transfer of methyl group from glycine to an acceptor such as sarcosine [36] [37] . Since sarcosine is an important mediator in the transfer of methyl group, observing its temporal change in simulation provides us critical insights into the state of the activated methyl cycle. The activated methyl cycle model was simulated for a simulation time period of 800,000 seconds (~9 days).

The model predicts that the sarcosine concentrations reach steady state levels of 2000 nM near instantaneously. This is likely since sarcosine is synthesized and not consumed in activated methyl cycle model. Even though glycine is present in excess amounts [33] , sarcosine concentration does not increase with time as there is a limited amount of methyl-group transfer from s-adenosylhomocysteine, which is required for sarcosine production.

Formaldehyde (HCHO), which is synthesized in the methionine biosynthesis cycle, enters the formaldehyde detoxification model where it is eventually converted to CO₂ and water (H₂O) [38] . The sources of formaldehyde synthesis include 5, 10-methylene-THF, methanol and sarcosine [24] [39] [40] . Detoxification of formaldehyde is glutathione (GSH) dependent [41] . GSH-formaldehyde adduct undergoes series of inter-conversions catalyzed by FALDH resulting in formate [28] [42] . Formate is then converted to CO₂ and water by formate dehydrogenase.

The formaldehyde detoxification model was simulated for a simulation time period of 800,000 seconds (~9 days). Two biomolecular species are of particular interest in this simulation: formaldehyde and glutathione.

As shown in Figure 10, formaldehyde starts initially at a low, non-zero level, and decays, detoxified, within ~120,000 seconds (~1.5 days) to zero. These results indicate that during normal plant metabolism, formaldehyde is efficiently cleared in the formaldehyde detoxification pathway.

Since glutathione (GSH), an important antioxidant, is necessary for clearance of formaldehyde in the formaldehyde detoxification pathway, simulation results of glutathione’s temporal dynamics are generated. The simulation results, in Figure 11, indicate that during normal plant metabolism, glutathione levels are stable and static and maintain a steady state level of 5 mM.

The individual models representing methionine biosynthesis, activated methyl cycle and formaldehyde detoxification arecoupled using CytoSolve to produce an integrative model of C1 metabolism. The earlier results in Sections 3.2, 3.3 and 3.4 are based on simulations of individual models. The results in this section are from simulations executed on the integrative C1 metabolism model. In the integrated model, the interconnections between individual models can provide insights into how the biomolecular species in one individual model affect the biomolecular species in the other individual model. As before, the simulation time period is maintained at 800,000 seconds (~9 days).

There are three important results that emerge from this integrative simulation: 1) formaldehyde is detoxified completely in C1 metabolism (Section 3.5.1), 2) sarcosine is completely depleted in C1 metabolism (Section 3.5.2), and 3) glutathione is maintained at steady state levels in C1 metabolism (Section 3.5.3).

The results from the in silico modeling of C1 metabolism have provided insights on key biomolecular species, such as formaldehyde, formate, sarcosine and glutathione. These simulation results are highly dependent on the integrity of the literature reviewed and in particular on the kinetic rate constants used in the modeling. Parameter sensitivity analysis provides a method to appreciate the relative significance of critical parameters.

Given the importance of formaldehyde synthesis and clearance in C1 metabolism, parameter sensitivity analysis was performed on the following three critical parameters:

1. kFTD―Rate constant for conversion of 5,10-methylene-THF to formaldehyde;

2. VCAT―Rate of formaldehyde production from methanol;

3. kGSH-HCHO―Binding rate constant of glutathione (GSH) and formaldehyde (HCHO).

Three sets of results emerge from the sensitivity analysis. First, kFTD, is varied from 1.4 to 5.6 s⁻¹ and the resulting formaldehyde concentrations are simulated and observed for the integrated model of C1 metabolism in Figure 15. The results indicate that, formaldehyde concentrations are not sensitive to kFTD in the integrative C1 metabolism model.

VCAT is varied from 22 to 100 nM/s, and the resulting formaldehyde concentrations are simulated and observed for the integrated model of C1 metabolism in Figure 16. The results indicate that, formaldehyde concentrations are not sensitive to VCAT in the integrative C1 metabolism model.

Third, kGSH-HCHO is varied from 0.000864 to 0.00864 nM⁻¹∙s⁻¹, and the resulting formaldehyde concentrations are simulated and observed for the integrated model of C1 metabolism in Figure 17. The results indicate that, as kGSH-HCHO is increased, the formaldehyde concentration is decreased over time. Therefore, from a parameter sensitivity standpoint, unlike kFTD and VCAT, formaldehyde concentrations are highly sensitive to variations in kGSH-HCHO in the integrative C1 metabolism model. Although the parameter value varies across one order of magnitude, formaldehyde is completely detoxified in all cases.