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Mathematical Modeling of Early Cellular Innate and Adaptive Immune Responses to Ischemia/Reperfusion Injury and Solid Organ Allotransplantation.

Day JD, Metes DM, Vodovotz Y - Front Immunol (2015)

Bottom Line: We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft.These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response.An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of Tennessee , Knoxville, TN , USA ; National Institute for Mathematical and Biological Synthesis , Knoxville, TN , USA.

ABSTRACT
A mathematical model of the early inflammatory response in transplantation is formulated with ordinary differential equations. We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft. These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response. In simulations of this model, resolution of inflammation depends on the severity of the tissue damage caused by these events and the patient's (co)-morbidities. We augment a portion of a previously published mathematical model of acute inflammation with the inflammatory effects of T cells in the absence of antigenic allograft mismatch (but with DAMP release proportional to the degree of graft damage prior to transplant). Finally, we include the antigenic mismatch of the graft, which leads to the stimulation of potent memory T cell responses, leading to further DAMP release from the graft and concomitant increase in allograft damage. Regulatory mechanisms are also included at the final stage. Our simulations suggest that surgical injury and I/R-induced graft damage can be well-tolerated by the recipient when each is present alone, but that their combination (along with antigenic mismatch) may lead to acute rejection, as seen clinically in a subset of patients. An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies. We suggest that mechanistic mathematical models might serve as an adjunct for patient- or sub-group-specific predictions, simulated clinical studies, and rational design of immunosuppression.

No MeSH data available.


Related in: MedlinePlus

Interaction diagram. The diagram provides an abstract, high-level view of the immune and inflammatory processes involved in solid organ transplant that we include in our mathematical model. Four dynamic immune variables are defined: I, A, TP, and TA as described in the figure legend next to their respective graphic marker. Also tracked is host tissue damage and graft tissue damage via the dynamic variables, D and DG, which are represented in the diagram by the shape labeled “Surgical, Ischemia/Reperfusion, and Graft Injury” at the top of the diagram, along with DAMP release as a result of this injury. Arrows represent induction/activation of a target variable (connected at the arrow head) by an initiating variable (connected at the arrow tail). Inhibitory effects are indicated by the presence of an inhibitory variable marker resting atop the middle part of an arrow. For example, A inhibits the activation of I from DAMPs released by tissue damage. Multiple arrows coalescing into a target variable at the same point indicate that all initiating variables are required to complete that particular induction/activation process. For instance, I and A are both needed to activate TA. Circulating/resting source populations of T cells and innate immune components, T0 and IR, respectively, are required for all processes that induce/activate these into the variables TP or TA and I, respectively. To keep the diagram uncluttered, the source populations are not shown in all of the processes in which they are required. Instead a representative example is given for each, as seen in the activation of IR into I by TP and in the activation of T0 into TP (alternatively, into TA) by TP (alternatively, by TA). The presence of allo-Ag of the graft is indicated with a red cross and represents another excitatory factor of the pro-inflammatory arms of the system as is the DAMP release by damaged tissue. Some activation processes require the presence of allo-Ag and these are represented by a red cross at the initiating (tail) end of an arrow.
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Figure 1: Interaction diagram. The diagram provides an abstract, high-level view of the immune and inflammatory processes involved in solid organ transplant that we include in our mathematical model. Four dynamic immune variables are defined: I, A, TP, and TA as described in the figure legend next to their respective graphic marker. Also tracked is host tissue damage and graft tissue damage via the dynamic variables, D and DG, which are represented in the diagram by the shape labeled “Surgical, Ischemia/Reperfusion, and Graft Injury” at the top of the diagram, along with DAMP release as a result of this injury. Arrows represent induction/activation of a target variable (connected at the arrow head) by an initiating variable (connected at the arrow tail). Inhibitory effects are indicated by the presence of an inhibitory variable marker resting atop the middle part of an arrow. For example, A inhibits the activation of I from DAMPs released by tissue damage. Multiple arrows coalescing into a target variable at the same point indicate that all initiating variables are required to complete that particular induction/activation process. For instance, I and A are both needed to activate TA. Circulating/resting source populations of T cells and innate immune components, T0 and IR, respectively, are required for all processes that induce/activate these into the variables TP or TA and I, respectively. To keep the diagram uncluttered, the source populations are not shown in all of the processes in which they are required. Instead a representative example is given for each, as seen in the activation of IR into I by TP and in the activation of T0 into TP (alternatively, into TA) by TP (alternatively, by TA). The presence of allo-Ag of the graft is indicated with a red cross and represents another excitatory factor of the pro-inflammatory arms of the system as is the DAMP release by damaged tissue. Some activation processes require the presence of allo-Ag and these are represented by a red cross at the initiating (tail) end of an arrow.

Mentions: Figure 1 provides a schematic of all the components and interactions included in the model equations. Table 1 provides a description of the dynamic model variables and Table 3 in the Section “Materials and Methods” explains the auxiliary model variables. The dynamic model variables are those whose rates change over time and are modeled with an ordinary differential equation (ODE); whereas auxiliary variables are functions of dynamic variables. We first discuss the interactions that are pro-inflammatory and then discuss how these processes initiate and/or are inhibited by the anti-inflammatory components, all based on the immunology discussed in Section “Inflammation and Immunity in Solid Organ Transplantation.” The model does not currently take into consideration explicitly the immunosuppressive therapies given before/during the transplantation procedure, though the effect of immunosuppression is in a sense contained in the concept of apparent antigenic mismatch. We envision testing specific immunosuppression mechanisms (e.g., killing of all inflammatory cells vs. specific killing of T cells) in future iterations of this model.


Mathematical Modeling of Early Cellular Innate and Adaptive Immune Responses to Ischemia/Reperfusion Injury and Solid Organ Allotransplantation.

Day JD, Metes DM, Vodovotz Y - Front Immunol (2015)

Interaction diagram. The diagram provides an abstract, high-level view of the immune and inflammatory processes involved in solid organ transplant that we include in our mathematical model. Four dynamic immune variables are defined: I, A, TP, and TA as described in the figure legend next to their respective graphic marker. Also tracked is host tissue damage and graft tissue damage via the dynamic variables, D and DG, which are represented in the diagram by the shape labeled “Surgical, Ischemia/Reperfusion, and Graft Injury” at the top of the diagram, along with DAMP release as a result of this injury. Arrows represent induction/activation of a target variable (connected at the arrow head) by an initiating variable (connected at the arrow tail). Inhibitory effects are indicated by the presence of an inhibitory variable marker resting atop the middle part of an arrow. For example, A inhibits the activation of I from DAMPs released by tissue damage. Multiple arrows coalescing into a target variable at the same point indicate that all initiating variables are required to complete that particular induction/activation process. For instance, I and A are both needed to activate TA. Circulating/resting source populations of T cells and innate immune components, T0 and IR, respectively, are required for all processes that induce/activate these into the variables TP or TA and I, respectively. To keep the diagram uncluttered, the source populations are not shown in all of the processes in which they are required. Instead a representative example is given for each, as seen in the activation of IR into I by TP and in the activation of T0 into TP (alternatively, into TA) by TP (alternatively, by TA). The presence of allo-Ag of the graft is indicated with a red cross and represents another excitatory factor of the pro-inflammatory arms of the system as is the DAMP release by damaged tissue. Some activation processes require the presence of allo-Ag and these are represented by a red cross at the initiating (tail) end of an arrow.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4585194&req=5

Figure 1: Interaction diagram. The diagram provides an abstract, high-level view of the immune and inflammatory processes involved in solid organ transplant that we include in our mathematical model. Four dynamic immune variables are defined: I, A, TP, and TA as described in the figure legend next to their respective graphic marker. Also tracked is host tissue damage and graft tissue damage via the dynamic variables, D and DG, which are represented in the diagram by the shape labeled “Surgical, Ischemia/Reperfusion, and Graft Injury” at the top of the diagram, along with DAMP release as a result of this injury. Arrows represent induction/activation of a target variable (connected at the arrow head) by an initiating variable (connected at the arrow tail). Inhibitory effects are indicated by the presence of an inhibitory variable marker resting atop the middle part of an arrow. For example, A inhibits the activation of I from DAMPs released by tissue damage. Multiple arrows coalescing into a target variable at the same point indicate that all initiating variables are required to complete that particular induction/activation process. For instance, I and A are both needed to activate TA. Circulating/resting source populations of T cells and innate immune components, T0 and IR, respectively, are required for all processes that induce/activate these into the variables TP or TA and I, respectively. To keep the diagram uncluttered, the source populations are not shown in all of the processes in which they are required. Instead a representative example is given for each, as seen in the activation of IR into I by TP and in the activation of T0 into TP (alternatively, into TA) by TP (alternatively, by TA). The presence of allo-Ag of the graft is indicated with a red cross and represents another excitatory factor of the pro-inflammatory arms of the system as is the DAMP release by damaged tissue. Some activation processes require the presence of allo-Ag and these are represented by a red cross at the initiating (tail) end of an arrow.
Mentions: Figure 1 provides a schematic of all the components and interactions included in the model equations. Table 1 provides a description of the dynamic model variables and Table 3 in the Section “Materials and Methods” explains the auxiliary model variables. The dynamic model variables are those whose rates change over time and are modeled with an ordinary differential equation (ODE); whereas auxiliary variables are functions of dynamic variables. We first discuss the interactions that are pro-inflammatory and then discuss how these processes initiate and/or are inhibited by the anti-inflammatory components, all based on the immunology discussed in Section “Inflammation and Immunity in Solid Organ Transplantation.” The model does not currently take into consideration explicitly the immunosuppressive therapies given before/during the transplantation procedure, though the effect of immunosuppression is in a sense contained in the concept of apparent antigenic mismatch. We envision testing specific immunosuppression mechanisms (e.g., killing of all inflammatory cells vs. specific killing of T cells) in future iterations of this model.

Bottom Line: We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft.These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response.An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of Tennessee , Knoxville, TN , USA ; National Institute for Mathematical and Biological Synthesis , Knoxville, TN , USA.

ABSTRACT
A mathematical model of the early inflammatory response in transplantation is formulated with ordinary differential equations. We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft. These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response. In simulations of this model, resolution of inflammation depends on the severity of the tissue damage caused by these events and the patient's (co)-morbidities. We augment a portion of a previously published mathematical model of acute inflammation with the inflammatory effects of T cells in the absence of antigenic allograft mismatch (but with DAMP release proportional to the degree of graft damage prior to transplant). Finally, we include the antigenic mismatch of the graft, which leads to the stimulation of potent memory T cell responses, leading to further DAMP release from the graft and concomitant increase in allograft damage. Regulatory mechanisms are also included at the final stage. Our simulations suggest that surgical injury and I/R-induced graft damage can be well-tolerated by the recipient when each is present alone, but that their combination (along with antigenic mismatch) may lead to acute rejection, as seen clinically in a subset of patients. An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies. We suggest that mechanistic mathematical models might serve as an adjunct for patient- or sub-group-specific predictions, simulated clinical studies, and rational design of immunosuppression.

No MeSH data available.


Related in: MedlinePlus