Myocardial infarction (MI) is a leading cause of congestive heart failure (CHF) [1, 2]. In response to the MI stimulus, the left ventricle (LV) undergoes structural and functional adaptations that collectively have been termed as LV remodeling [3]. Adverse LV remodeling progresses to CHF in about 25% of post-MI patients, but the mechanisms that drive this progression remain poorly understood. During LV remodeling, both extracellular matrix (ECM) degradation and synthesis increase [4]. When ECM degradation dominates over synthesis, LV rupture can occur. When ECM synthesis dominates over degradation rates, fibrosis can occur. Fibrosis increases myocardial stiffness and further depresses LV function to culminate in CHF [5, 6]. Therefore, understanding what regulates the balance between ECM degradation and synthesis post-MI is critical to understand the mechanisms of LV remodeling and may allow us to target specific early diagnostic indicators to better guide treatment protocols.

Previous studies have shown that matrix metalloproteinases (MMPs) regulate ECM degradation and fibroblasts regulate ECM synthesis [7–9]. MMP-9, transforming growth factor-β₁ (TGF-β₁), tissue inhibitor of metalloproteinase-1 (TIMP-1), and collagen I levels are significantly elevated from day 1 to day 7 post-MI [4, 10, 11]. These increases are concomitant with increased infiltration of macrophages and activation of fibroblasts [12]. LV remodeling is a complex process that involves the spatiotemporal interactions among many biological components that remains poorly understood, in part due to the lack of complete sets of experimental data and computational models. Therefore, the objectives of this study were to 1) identify candidate biomarkers of LV remodeling post-MI from ECM gene expression and plasma analyte analyses, and 2) establish a mathematical model that incorporates experimental results to predict LV remodeling outcomes following different interventions. This model would provide a tool to elucidate LV regulatory mechanisms, estimate un-measurable variables, and predict outcomes following multiple therapeutic scenarios.

This study is the first investigation to integrate mathematical modeling with ECM and fibroblast gene array data and plasma analytes to predict ECM remodeling post-MI. We have integrated in vivo, in vitro, and in silico approaches to dissect the complicated interactions among multiple regulatory factors in LV remodeling. As such, this study provides a promising modeling approach for elucidating the complicated LV remodeling process. The most important findings of this study are highlighted as follows. 1) The balance between ECM construction and destruction kinetics is likely the key determinant of scar formation, and interventions to either the construction or destruction side lead to different remodeling outcomes. 2) Dynamic interactions among key factors in LV remodeling determine LV remodeling outcomes post-MI. Altering initial conditions, intervention strengths, or intervention times have significant effects on LV remodeling outcomes, and these effects could be simulated accurately by our model. 3) Collagen, MMP-9, TGF-β₁, and TIMP-1 are critical biomarker candidates of LV remodeling outcomes.

Our experimental results on microarray and plasma data provided the foundations to build our computational framework. We examined 84 ECM genes and chose the 17 genes that were most highly over-expressed in the infarct region compared to both control and non-infarcted groups (>2.5-fold over-expression). The expression levels of several of these factors were further verified by our plasma data at protein level. One interesting finding was that SPP1 (osteopontin) gene expression levels increased 206-fold in the infarct region compared to the control group at day 7 post-MI, suggesting strong macrophage activation. The plasma protein levels of osteopontin increased from 250 ± 60 ng/mL in controls to 390 ± 100 ng/mL in post-MI samples, which adds support for the critical role of macrophages in our mathematical model. Therefore, the primary selection of the most highly changed genes allowed us to focus on the most significant factors at gene level and predict the possible interactions at protein level and cellular level.

An interesting observation was that MMP-9 mRNA levels did not increase in our gene array analysis, but MMP-9 protein levels increased in the plasma data. It is well known that MMP-9 protein levels and activation were increased at day 7 post-MI. This conflicting phenomena is caused by pre-formed MMP-9 proteins stored in leukocytes, which do not rely on increased gene expression to induce MMP-9 secretion and activation [50]. In addition, the shift from a normal ventricle composed of cardiac myocytes, endothelial cells, and smooth muscle cells to an infarcted ventricle comprised primarily of cardiac fibroblasts and inflammatory cells could result in a quantitative no gain in gene expression level but qualitative increase in MMP-9 function due to increased activation and increased substrate availability. Karl Weber's group showed that MMP-9 protein levels increased early post-MI, but the mRNA levels were not elevated [51]. We have also shown that MMP-9 activation increases upon reperfusion in a dog model of cardiac ischemia/reperfusion [7]. These results support our observations in this study and highlight the fact that MMP-9 is primarily regulated at the post-translational level. Furthermore, the fact that MMP-9 gene levels do not change at day 7 post-MI also suggest that MMP-9 should be evaluated at the protein level.

There is limited data available to construct suitable functions of M(T _β ), F _g (T _β ), F _c (T _β ), and F _c (c). Wahl et al presented a set of in vitro data on monocyte chemotaxis induced by TGF-β with concentration ranges from 0.05 pg/mL to 10 pg/mL [17]. Their experiments also provided production of fibroblast growth activity induced with TGF-β concentration range from 10 pg/mL to 10 ng/mL. These data were used in this study to construct the functions of M (T _β ) and F _g (T _β ). Roberts et al have presented a set of data on in vitro collagen formation stimulated by TGF-β with the concentration range from 0.0825 pg/mL to 2.5 pg/mL [23]. Ignotz and Massague have examined the effects of TGF-β on collagenases in chick embryo fibroblasts stimulated by TGF-β at a concentration range of 1.25 ng/mL to 25 ng/mL [41]. We have done experiments to quantify the ECM production of cardiac fibroblast stimulated with TGF-β (10 ng/mL). These experimental data were used to build and justify the function, F _c (T _β ). Loftis and colleagues have studied effects of collagen density on cardiac fibroblast behavior and showed elevated fibroblast activities stimulated with higher collagen concentrations (750 μg/mL - 1250 μg/mL) [52]. Wu and colleagues showed that propeptides at lower levels caused about 80% decrease in collagen synthesis compared to control [53]. In this study, we used an in silico function F _c (c) provided by Waugh and colleagues [27, 28]. These experiments were done by different groups with different conditions and the in vitro experiments might not reflect the in vivo interactions. In addition, we established these functions using polynomial interpolation. It's likely that these functions are not the optimal forms to describe the in vivo interactions; however, they provide us a baseline for further study.

Our computational results demonstrated that altering the strength of TGF-β₁ altered LV remodeling outcomes. Elevated TGF-β₁ levels at the early stage (day 3 post-MI) led to elevated macrophage density and MMP-9 levels, decreased fibroblast secretion of collagen and collagen deposition, and thereby, prolonged the progression of remodeling. Wetzler and colleagues have shown that the prolonged persistence of macrophages at the late phase (after day 7 post-MI) impairs the wound healing process [54]. It has also been shown that elevated TGF-β₁ levels delays wound healing post-MI [55, 56]. Our simulation results are in agreement with these previously published studies.

Simulations of different TGF-β₁ strengths also shed light on the regulation scheme of ECM construction and destruction. For ECM construction regulation, active TGF-β₁ stimulated fibroblast proliferation and collagen secretion, which increased the crowding effect. The increased crowding coefficient ramped down fibroblast proliferation and TGF-β₁ secretion (negative feedback), which slowed down the stimulus for monocytes to migrate into the infarct region. The decrease of monocytes number led to less macrophage infiltration, which then reduced the crowding coefficient. Meanwhile, reduced macrophages lead to less TGF-β₁ secretion by macrophage, which further slowed down collagen synthesis. For collagen destruction regulation, TGF-β₁ induced macrophage infiltration, which lead to elevated MMP-9 secretion, elevated collagen degradation, and thereby reduced crowding coefficients. Smaller crowding coefficients lead to elevated fibroblast proliferation and collagen secretion. Notably, there are two types of negative feedback schemes in the mathematical model: degradation (apoptosis or emigration) rates associated with proteins (cells) and the crowding effects. Degradation rates are constants and determine how fast the proteins (cells) can respond to stimuli. Crowding effects are time varying impacts imposed by the environment. Through these regulation schemes, a dynamic balance of collagen construction and destruction can be maintained to generate a stable scar. Furthermore, profiles of crowding effects elucidated the transition from the normal LV to scar tissue with respect to cell types and collagen concentrations (Figure 3).

It is worth mentioning that there exist biological negative feedbacks in our mathematical model. For macrophage density regulation, there was a positive feedback loop containing macrophage and TGF-β₁: TGF-β₁ stimulated monocytes migration, leading to macrophage infiltration; macrophages secreted TGF-β₁ which might attract more macrophages to the infarct site. We observed elevated macrophage density and MMP-9 concentrations corresponding to increased TGF-β₁ levels (Figure 5). This positive feedback loop was inhibited by emigration of macrophages and degradation of TGF-β₁. In addition, Wahl et al pointed out that the monocyte chemotactic activity increased in response to low concentrations of TGF-β₁ stimuli, while the chemotactic activity decreased in response to higher concentrations of TGF-β₁[17]. Therefore, as TGF-β₁ levels continuously increased, infiltration speed of macrophages decreased as shown in figure 2 (M(T_β)), suggesting a secondary biological inhibition scheme of the TGF-β₁ -- macrophage positive feedback loop.

There are a few limitations of the mathematical model that resulted to a large degree from the model assumptions. More research is needed to address these limitations and further enhance the models. First, our model calls for accurate determination of MMP-9 activation and inhibition functions. Complete time-course measurements of TIMP-1 and the other three TIMPs (for MMP-9 inhibition) and MMP-3 (for MMP-9 activation) would provide additional details on the regulators of MMP-9 function. Second, the large differences between simulation results and experimental measurement of MMP-9 concentrations before day 4 post-MI in Figure 4 is likely due to the effect of neutrophils, an early source of MMP-9, indicating the need to investigate the role of neutrophils in the early stage (days 1-5) post-MI [7]. This inconsistency of the simulated MMP-9 concentrations and measurements from experimental results is one of the approaches for us to employ more biomarkers and key factors in model development. Third, Interleukin IL-1, IL-6, IL-10, and tumor necrosis factor-α profiles need to be included to better study macrophage activation phenotypes [57]. Fourth, the effects of other chemoattractants on monocyte migration on the LV remodeling need further investigation. The predicted fibroblast density at days 14-30 post-MI was lower than experimental measurements. This might be caused by assumption 2, that the increase of fibroblast numbers post-MI was contributed solely by proliferation of local cells. We will investigate the migration rates of fibroblasts in the future to refine our mathematical model. Regardless of the above limitations, we were able to use our model to compute the progression of macrophages, fibroblasts, and collagen density, MMP-9 and TGF-β₁ concentrations post-MI.

This systems biology study for LV remodeling can be expanded to include proteomics and cardiac functions in future studies. We employed plasma data in this study since plasma proteins reflect the process of LV remodeling and plasma data are more directly translatable to the clinic. However, we are well aware that measuring tissue protein levels will provide a more direct evaluation of LV remodeling. Further investigation on the ECM proteomics in cardiac samples has been planned in our future research to establish a more complete mathematical model for LV remodeling. Though it is beyond the scope of the current paper, we have previously reported some data on cardiac function [58–60] and our future study will integrate cardiac function into the mathematical model.

The computational model for post-MI LV remodeling developed here illustrated the dynamic interactions among critical factors in LV remodeling. This is the first mathematical model focusing on the protein and cellular interactions post-MI. Thus, this model provides a strong foundation for future studies to build a more comprehensive model that takes into account a more complete set of parameters. The model also provides a tool to guide experimental designs by identifying candidate factors to intervene, the proper intervention time, and doses for effective interventions to achieve the most beneficial outcomes. As an example, we have shown the effects of MMP-9 intervention time and doses on LV remodeling outcomes in this study. Though this model was established based on in vitro data and in vivo data from mice, the modeling approach can be used to develop models for other scenarios such as the LV remodeling of human MI and LV remodeling under reperfusion conditions.

In conclusion, we developed a set of differential equations to quantitatively model the dynamic interactions and temporal changes of the key components identified from our experimental results. Predictions of the mathematical model fell well within experimental measurements, particularly with regard to macrophage infiltration and matrix remodeling. This mathematical model provides a powerful tool to better understand how the dynamic balance between ECM construction and ECM destruction influences LV remodeling outcomes.