**2.6.2 G93A feasibility study structure**

The dynamic meta-analysis structure is best illustrated like an engineering process flow diagram. Here we show in Figure 1 the categories of outcome measures (boxes) and their interactions (lines). Based on the presented study structure, we determined that there are minimally 72 interactions between the 10 categories of outcome measures. Thus, the minimum number of primary studies to be included in the feasibility study is 72, one for each interaction. Note that we define a primary study as an experiment that measures the interaction between two outcome measures. Therefore, a single published primary experimental article can, and often does, contain more than one primary study. However, it is easier to think of each interaction as needing at least one primary article, and thus, approximately 72 primary articles are need for data extraction to complete a minimalistic feasibility study. The differences between the full and feasibility study structure are shown in Figure 2.

Even for a feasibility study, an "n" of one for each interaction may not sound like metaanalysis, but keep in mind that there are multiple interactions contributing to the effect and prediction of each category. For example, in the structure presented in Figure 1, there are 3-10 interactions for each category. Therefore, 3-10 primary studies contribute to the prediction of each category of outcome measures. That range is in line with the number of primary studies per outcome measure that we might expect for a traditional metaanalysis.

### **2.7 Extracting data**

Quantifiable data is extracted from included primary study figures and tables. Figure 3 shows a hypothetical example of the type of data figure one typically seen in the G93A literature. The Y-axis is typically the affected measure (in this case, percent of cargos travelling retrogradely) and the X-axis is typically the controlled measure (glutamate concentration in our hypothetical example). Additionally, the measure is usually quantified in both the wild-type and G93A mice populations.

Upon extraction, data is normalized to make it unitless. That is, we only look at the relative changes between measures. In this example data, the wild-type retrograde transport went down by ~20% with a 40% increase in glutamate concentration, whereas the SOD1 retrograde transport went down by ~25% with a 40% increase in glutamate concentration.

*Free radicals:* encompasses measures of oxidation or inflammation-induced nitric oxide, but particularly the accumulation of reactive oxygen species, such as the superoxides and peroxides that are associated with mitochondrial dysfunction or failure. Free radicals initiate

*Necro-apoptosis*: encompasses the measures of cell death, including the signaling cascades, their constituents, and machinery, which promote cell death. The final destination of an ALS affected motoneuron is cell death either through inflammation-induced necrosis or more likely through apoptosis (Mattson and Duan 1999) via the activation of stress response and

*Systemic:* encompasses invivo measures of function in the G93A mouse model (Derave, Van Den Bosch et al. 2003). It includes measures of muscle weakness, atrophy, fasiculations, denervation and ultimately loss of function that decreases essential stimulatory retrograde

The dynamic meta-analysis structure is best illustrated like an engineering process flow diagram. Here we show in Figure 1 the categories of outcome measures (boxes) and their interactions (lines). Based on the presented study structure, we determined that there are minimally 72 interactions between the 10 categories of outcome measures. Thus, the minimum number of primary studies to be included in the feasibility study is 72, one for each interaction. Note that we define a primary study as an experiment that measures the interaction between two outcome measures. Therefore, a single published primary experimental article can, and often does, contain more than one primary study. However, it is easier to think of each interaction as needing at least one primary article, and thus, approximately 72 primary articles are need for data extraction to complete a minimalistic feasibility study. The differences between the full and feasibility study structure are shown

Even for a feasibility study, an "n" of one for each interaction may not sound like metaanalysis, but keep in mind that there are multiple interactions contributing to the effect and prediction of each category. For example, in the structure presented in Figure 1, there are 3-10 interactions for each category. Therefore, 3-10 primary studies contribute to the prediction of each category of outcome measures. That range is in line with the number of primary studies per outcome measure that we might expect for a traditional meta-

Quantifiable data is extracted from included primary study figures and tables. Figure 3 shows a hypothetical example of the type of data figure one typically seen in the G93A literature. The Y-axis is typically the affected measure (in this case, percent of cargos travelling retrogradely) and the X-axis is typically the controlled measure (glutamate concentration in our hypothetical example). Additionally, the measure is usually quantified

Upon extraction, data is normalized to make it unitless. That is, we only look at the relative changes between measures. In this example data, the wild-type retrograde transport went down by ~20% with a 40% increase in glutamate concentration, whereas the SOD1 retrograde transport went down by ~25% with a 40% increase in glutamate concentration.

reactions that damage DNA (Pehar, Vargas et al. 2007).

caspase pathways (Beere 2004; Gifondorwa, Robinson et al. 2007).

signaling, causing further progression of the diseased state.

**2.6.2 G93A feasibility study structure** 

in Figure 2.

analysis.

**2.7 Extracting data** 

in both the wild-type and G93A mice populations.

Therefore, the slope or gain (dY/dX) for wild-type is -0.2 for the interaction from glutamate to retrograde transport. Correspondingly, the gain, for SOD1, is -0.25. Because we only calculate relative changes in dynamic meta-analysis, the magnitude of the gain utilized is actually the relative difference between the wild-type and SOD1 gain magnitudes, (|SOD1| – |wild-type|)/|wild-type|, or [(0.25) – (0.20)]/(0.25) = 0.25, and the sign of this final gain value for this example is net negative (-). Applying the gain of the experimental outcome measures to the category measures, the interaction *from* the category outcome measure of excitotoxicity *to* the category outcome measure of axonal transport is -0.25. Finally, we divide the gain by the time point (or in the case of a feasibility study, the *to* category time constant) to obtain the interaction coefficient (B) used in Equation 2.

Fig. 2. Scope of dynamic meta-analysis study for the G93A SOD1 mouse model of ALS: feasibility study versus a full study.

Dynamic Meta-Analysis as a Therapeutic Prediction Tool for Amyotrophic Lateral Sclerosis 69

Apoptosis M + (Collard, 1995; Ackerley, 2004) Inflammation S - (Brooks,1991; Sasaki, 1996) Chemistry Systemic M + (Tiwari, 2005; Ludolph, 2006; Watanabe,

> Transport S - (LaMonte, 2002; Strom, 2008) Excitotoxicity S + (Kawahara, 2004; Sasabe, 2007) Energetics S - (Wendt, 2002; Lee, Shin, 2008) Free Radicals S + (Poon, 2005; Furukawa, 2006)

Apoptosis M + (Elam, 2003; Kiaei, 2007; Lee, Shin, 2008) Proteomics M + (Lindberg, 2002; Bergemalm, 2006; Rumfeldt, Stathopulos,2006)

Transport S - (Hiruma, 2003; Tateno, 2008; Stevenson, Yates. 2009) Excitotoxicity M + (Rothstein, 1990; Rothstein, 1995; Kuo, 2004;

Energetics L - (Beal, 1992; Nicholls, 1998; Jabaudon, 2000; Ellis, 2003) Free Radicals L + (Kruman, 1999; Kruman, 1999; Carriedo,

Apoptosis L + (Liu, 1999; Sun, 2006; Gibb, 2007; Boutahar, 2008)

Systemic S + (Bittigau, 1997; Corona, 2007)

Transport M + (Sickles, 1990; Magrane, 2009)

Energetics M + (Mattson, 1999; Mattiazzi, 2002) Free Radicals L + (Mattson, 1999; Liu, 2002; Cassina, 2008)

Inflammation M + (Levine, 1999; Bilsland, 2008)

Chemistry S + (Poon, 2005; Furukawa, 2006)

Systemic M + (Verstreken, 2005)

Excitotoxicity L + (Beal, 1992; Agrawal, 1996; Ellis, 2003;

Transport S - (Chou, 1996; Chou, 1996; Ferrante, 1997)

Excitotoxicity S + (Kruman,1999; Kruman, 1999; Ellis, 2003) Energetics L - (Liu, 1996; Liu, 1999; Mattson, 1999; Liu, 2002; Cassina, 2005) Free Radicals M - (Liu 1996; Liu. 1999; Cookson, 2002; Cassina,

2000; Ellis, 2003) Inflammation L + (Hewett, 1994; Cholet, 2002; Barbeito, 2004)

Nicholls, 2003)

2007; Knudson, 2008)

Pehar 2005; Pehar 2007)

Transport M - (Kieran, 2005; De Vos, 2007; Zhang, Strom 2007) Energetics S - (Sakama, 2003; Miller , 2004; De Vos, 2007) Excitotoxicity S - (Hiruma, 2003; Stevenson, 2009; Tateno, Kato, 1999)

2007; Hozumi, 2008)

Damiano, Starkov, 2006; Kuwabara, 2007)

(Kruman, 1999; Kaal, 2000; Guegan, 2001; Dupuis, Gonzalez de Aguilar, 2004; Ilzecka,

**From To Size Sign Primary Reference(s)** 

Axonal

Necro-

Axonal

Necro-

Necro-

Necro-

Apoptosis L +

Excitotoxicity Axonal

Energetics Axonal

Free Radicals Axonal

Axonal Transport

Fig. 3. Example data from a prototypical primary study.

### **2.8 Quantified data aggregation**

For a category-level feasiblity study, such as presented here, it is appropriate to take a non-parametric approach to aggregating the quantitative experimental measures, as the aggregated relationships too disparate to make normalization practical. Consequently, gains were first qualitatively grouped into "small," "medium," or "large". Based on the overall range and resolution of the quantified category interaction magnitudes obtained from the primary studies, numerical gain values for small, medium, and large were set to 0.33, 1, and 3, respectively. However, other values were also explored (e.g. 0.5, 1, and 2; 0.25, 0.5, and 1 etc.) with no qualitative change in result. Table 1 lists the relative magnitude and sign of the category relationships and the primary references from which data was extracted.

Additionally, the corresponding time points for each category utilize a qualitative grouping of small, medium, and large. Based on our mathematical implementaiton of the time points, which is analagous to that used with time constants, we refer to the time points as time constants. Their numerical values and scaling are chosen based on the average onset of associated changes documented for a particular category using the G93A SOD1 mouse model time course. For example, measurable changes are occurring by day 40 in axonal transport, such as the appearance of aggregates and changes in cargo distribution (Kieran, Hafezparast et al. 2005; Teuchert, Fischer et al. 2006); thus, 40 days is used as the time constant for that category. Using the range and resolution of documented changes in G93A over all of the categories, the small, medium, and large time constants are set to 40, 80, and 120 days, respectively (Table 2).

For a category-level feasiblity study, such as presented here, it is appropriate to take a non-parametric approach to aggregating the quantitative experimental measures, as the aggregated relationships too disparate to make normalization practical. Consequently, gains were first qualitatively grouped into "small," "medium," or "large". Based on the overall range and resolution of the quantified category interaction magnitudes obtained from the primary studies, numerical gain values for small, medium, and large were set to 0.33, 1, and 3, respectively. However, other values were also explored (e.g. 0.5, 1, and 2; 0.25, 0.5, and 1 etc.) with no qualitative change in result. Table 1 lists the relative magnitude and sign of the category relationships and the primary references from which

Additionally, the corresponding time points for each category utilize a qualitative grouping of small, medium, and large. Based on our mathematical implementaiton of the time points, which is analagous to that used with time constants, we refer to the time points as time constants. Their numerical values and scaling are chosen based on the average onset of associated changes documented for a particular category using the G93A SOD1 mouse model time course. For example, measurable changes are occurring by day 40 in axonal transport, such as the appearance of aggregates and changes in cargo distribution (Kieran, Hafezparast et al. 2005; Teuchert, Fischer et al. 2006); thus, 40 days is used as the time constant for that category. Using the range and resolution of documented changes in G93A over all of the categories, the small, medium, and large time constants are set to 40, 80, and

Fig. 3. Example data from a prototypical primary study.

**2.8 Quantified data aggregation** 

data was extracted.

120 days, respectively (Table 2).


Dynamic Meta-Analysis as a Therapeutic Prediction Tool for Amyotrophic Lateral Sclerosis 71

Systemic M + (Turner, 2005; Bucher, 2007)

Energetics S - (Wendt, 2002; Zhao, 2006) Free Radicals S + (Mahoney, 2006; Pierce, 2008)

Apoptosis S + (Martin, 2000; Patel, 2010) Systemic S - (Nagano, 2005; Deforges, 2009)

Table 1. Parametric gains for category interactions. Interactions are listed directionallyoriented *from* the category imposing the effected *to* the category being affected. The sign indicates whether the interaction is increasing or decreasing the category, and size (small,

Table 2. Feasibility study time constants utilized for the calculation of the interaction term

Differential equations, in the form shown in Equation 2, are use to construct the dynamic meta-analysis computations. Thus, each category has its own first order differential equation, which includes the effects of each interaction as well as the category time point (or in the case of a feasibility study, a time constant). Each interaction gain coefficient (B) in Equation 2 is simply the change in the affected interaction measure divided by the time point (or in the case of a feasibility study, the category time constant). Because the effect of time is included, the dynamic meta-analysis can predict outcome measures at multiple time points over the entire disease course. Thus, a dynamic meta-analysis can be "simulated" much like a traditional mechanistic model. Because the time-based differential equation computations of dynamic meta-analysis are inherently more complicated than the algebraic regression equations of traditional meta-analysis, the use of a computer simulator assists in

(B), as shown in Equation 2. Time points are aggregated from primary studies.

medium, large) qualitatively represents the gain magnitude (see Extracted Data

Category Time Point (days)

Axonal Transport 40 Chemistry 40 Excitotoxicity 80 Energetics 80 Free Radicals 80 Genetic Damage 40 Inflammation 120 Necro-Apoptosis 120 Proteomics 40 Systemic 120

Proteomics S - (Puttaparthi, 2007; Morimoto, 2007; Cheroni, 2009)

**From To Size Sign Primary Reference(s)** 

Systemic Excitotoxicity S + (Kuner, 2005 ; Pieri, 2008)

Necro-

Aggregation).

**2.9 Implementation** 



Table 1. Parametric gains for category interactions. Interactions are listed directionallyoriented *from* the category imposing the effected *to* the category being affected. The sign indicates whether the interaction is increasing or decreasing the category, and size (small, medium, large) qualitatively represents the gain magnitude (see Extracted Data Aggregation).


Table 2. Feasibility study time constants utilized for the calculation of the interaction term (B), as shown in Equation 2. Time points are aggregated from primary studies.

### **2.9 Implementation**

70 Amyotrophic Lateral Sclerosis

Genetic Damage M + (Aguirre, 2005; Mitsumoto, 2008)

Proteomics S + (Dalle-Donne, 2007; Poon, 2005)

Genetic Damage Excitotoxicity M + (Kawahara, 2004; Ignacio, Moore, 2005;

Apoptosis M + (Locatelli, 2007; Lu, 2000)

Inflammation M + (Hensley, 2006; Liu, 2008; Nagai, 2007; Pehar, 2005)

Pehar, 2007; Wood, 1995)

(Dalle-Donne, 2007; Poon, 2005; Kato, 2005; Mahoney, 2006; Mitsumoto, 2008; Sohmiya,

Apoptosis L + (Chen, 2009; Estevez, 1999; Pehar, 2005;

2005)

Free Radicals S + (Armon, 2005; Wiedau-Pazos, 1996) Genetic Damage M - (Armon, 2005; Jiang, 2005; Muller, 2008) Inflammation S - (Puttaparthi, 2005; Di Giorgio, 2007;

Transport S - (Chou, 1996; Kaasik, 2007; King, 2009;

Excitotoxicity M + (Hewett, 1994; Cholet, 2002; Pehar, 2004) Energetics S - (Cassina, 2008; Cassina, 2005; Takeuchi, 2005; Bilsland, 2008)

Free Radicals L + (Hensley, 2006; Nagai, 2007; Pehar, 2007) Inflammation M - (Gowing, 2008; Puttaparthi, 2005; Schiffer, 1996)

Apoptosis L - (Gonzalez de Aguilar, 2000; Gonzalez de Aguilar, 1999)

Proteomics M + (Gal, 2007; Gal, 2009; Yamashita, 2007)

Transport M + (Eaton, 2005; De Vos, 2007; Sasaki, 2005)

Free Radicals S + (Aquilano, Rotilio et al. 2003; Clement, 2003)

Apoptosis M + (Urushitani, 2008; Atkin, 2008; Gal, 2007)

Systemic M + (Li, 2007; Narai, 2005)

Inflammation M + (Stieber, 2000)

Chemistry M + (Rumfeldt, 2009; Atkin, 2006) Excitotoxicity S + (Rothstein, 2005; Vanoni, 20040

Apoptosis L + (Collard, 1995; Ackerley, 2004) Systemic S + (Hall, 1998; Cassina, 2005; Cho, 1999)

Transport S + (Ackerley, 2004; Collard, 1995) Chemistry S - (Kiaei, 2007; Elam, 2003; Lee, 2009) Excitotoxicity L + (Gibb, 2007; Sun, 2002; Liu, 1999) Energetics L - (Guegan, 2001; Guegan, 2002) Free Radicals M + (Raoul, 2002; Raoul, 2005) Genetic Damage S + (Muller, 2007; Raoul, 2006) Inflammation L + (Hall, 1998; Cassina, 2005)

Kawahara, 2006)

Puttaparthi, 2007)

Morimoto, 2007)

**From To Size Sign Primary Reference(s)** 

Systemic S +

Necro-

Necro-

Necro-

Axonal

Necro-

Necro-

Proteomics Axonal

Inflammation Axonal

Necro-Apoptosis

> Differential equations, in the form shown in Equation 2, are use to construct the dynamic meta-analysis computations. Thus, each category has its own first order differential equation, which includes the effects of each interaction as well as the category time point (or in the case of a feasibility study, a time constant). Each interaction gain coefficient (B) in Equation 2 is simply the change in the affected interaction measure divided by the time point (or in the case of a feasibility study, the category time constant). Because the effect of time is included, the dynamic meta-analysis can predict outcome measures at multiple time points over the entire disease course. Thus, a dynamic meta-analysis can be "simulated" much like a traditional mechanistic model. Because the time-based differential equation computations of dynamic meta-analysis are inherently more complicated than the algebraic regression equations of traditional meta-analysis, the use of a computer simulator assists in

Dynamic Meta-Analysis as a Therapeutic Prediction Tool for Amyotrophic Lateral Sclerosis 73

Table 3. Standard meta-analysis result table illustrating the effect of each category on disease

Next, we examine the relative changes in the category outcome measures over time in order to get a better feel of the system dynamics. As shown in Figure 4, initially, the system exhibits a period of relative quiescence (days 0-80) in which there appears to be little variation from the baseline operating point. However, closer examination reveals a few fluctuations, which appear as small oscillations from baseline (Figure 5). Over time each oscillation grows in magnitude, with the first notable oscillation starting around day 40. However, the component trajectories do eventually explode at approximately

These qualitative system features of ALS align well with the characterization of the G-93A SOD-1 experimental paradigm. In fact, the first large oscillation corresponds to the average onset of measurable functional deficits and the final explosion aligns with the average time of death for the G-93A SOD-1 mouse model (Xu, Jung et al. 2004; Kieran, Hafezparast et al. 2005; Gould, Buss et al. 2006; Teuchert, Fischer et al. 2006). It should be noted that the oscillations of this system do not necessarily represent the relapsing and remitting of functional deficits, such as is seen with multiple sclerosis, but rather the oscillations of individual mechanisms and pathways. In fact, such oscillations could be responsible for small fluctuations sometimes seen within and among mechanistic studies, such as those examining axonal transport (De Vos, Chapman et al. 2007) and protein aggregation (Stieber, Gonatas et al. 2000; Gould, Buss et al. 2006). How oscillations correlating with specific losses in muscle function remains to be seen. It is likely that the overall loss of systemic control aligns with what is typically seen as continuously degenerating function or degenerative

From a system dynamics point of view, it is likely that the exploding oscillations of ALS are the result of an unstable system. Initially, the regulatory systems, including excitability, ionic and axonal transport, cellular energetics and others, are able to maintain partial control, as evidenced by the smaller oscillations, which are an attempt to regulate. However, as the disease progresses the control mechanisms simply fail to keep

outcome measures (survival and function).

function with intermixed plateaus.

day 150.

up.

**3.1 Dynamics of the G93A SOD1 mouse pathology** 

**Category Avg Stdev Min Max N**  Axon Transport -1% 12% -21% 16% 6 Chemistry 11% 27% -6% 71% 7 Energetics -19% 71% -98% 102% 7 Excitotoxicity 0% 39% -80% 36% 7 Free Radical 2% 24% -53% 44% 10 Genetics 3% 6% -3% 12% 5 Inflammation 14% 21% -6% 49% 7 Necro-Apoptosis 16% 26% -35% 59% 10 Proteomics 13% 24% -17% 56% 8 Systemic -2% 5% -10% 2% 5

its implementation. For this feasibility study, the dynamic meta-analysis was coded, simulated, and analyzed in Matlab (Mathworks, Inc.).

### **2.10 Post-result analysis and prediction**

The basic results of dynamic meta-analysis are quantitative predictions of each outcome measure or category outcome measure changes over time. Additional, higher level results can be obtained by performing sensitivity analyses, which perturb the system and measure the resulting affects. Perturbation can include varying the initial conditions of each category individually or en masse, or varying the interaction gain coefficients (B). Changing initial conditions provides an assessment of the effect size whereas varying specific or category gains provides an assessment of their sensitivity/specificity. For more detail on sensitivity analyses, see (Mitchell, Feng et al. 2007; Mitchell and Lee 2007; Mitchell and Lee 2009).

Traditional meta-analysis analytical tools, such as statistical linear regression and effect size prediction, are still useful to analyze dynamic meta-analysis results. However, the dynamic and multi-variate nature of dynamic meta-analysis also provides possibilities for richer analyses like those typically seen in the analysis of complex or dynamical systems. Given that the two greatest advantages of dynamic analysis are the implicit inclusion of interactions and explicit inclusion of time, analyses that examine how relationships change over time are particularly telling. Analyses such as cross-correlation (or landscapes) of outcome measures or category outcome measures at specific disease time points, such was done in (Mitchell and Lee 2008) and (Mitchell and Lee 2007), provide a overview of what the system is doing without becoming mired in detail.

Finally, the implicit inclusion of interactions allows combination treatments to be examined. All clinical treatments, in some form, exploit a cellular interaction at some level. For example, pharmaceutical modulators typically exploit the interaction between a receptor and its ligand. Thus, every potential interaction within the dynamic meta-analysis structure can be evaluated as a hypothetical treatment possibility. Furthermore, the structure of dynamic meta-analysis allows every single interaction (whether between outcome measures or between categories of outcome measures) to be varied and simulated individually and in combination. Measuring the resultant effect size of an interaction or combination of interactions predicts its potential treatment efficacy. For more methodological detail on simulating combination therapies, see our previous work with combination treatments and spinal cord injury (Mitchell and Lee 2008).

### **3. Results of a G93A SOD1 feasibility study**

We begin by examing the effect size of each category, an analysis that is typically seen with traditional meta-analysis. Table 3 reveals the average, standard deviation, maximum, and minimum effect size of each category based on a sensitivity analysis that perturbed the intial conditions. Note that "N'' is the connectivity, or number of interactions (as shown in Figure 1), affecting the category measure. This examination reveals that the average effect of, for example, treating energetics is a relatively unimpressive 19% outcome change for a 100% treatment effect on energetics itself. (Note that a "real" treatment would have effects substantially smaller than 100%, often only 10% or so.). However, this type of analysis misses the potential for interactions completely and to some extent even minimizes the potential significance of targeted treatments by averaging.


Table 3. Standard meta-analysis result table illustrating the effect of each category on disease outcome measures (survival and function).

### **3.1 Dynamics of the G93A SOD1 mouse pathology**

72 Amyotrophic Lateral Sclerosis

its implementation. For this feasibility study, the dynamic meta-analysis was coded,

The basic results of dynamic meta-analysis are quantitative predictions of each outcome measure or category outcome measure changes over time. Additional, higher level results can be obtained by performing sensitivity analyses, which perturb the system and measure the resulting affects. Perturbation can include varying the initial conditions of each category individually or en masse, or varying the interaction gain coefficients (B). Changing initial conditions provides an assessment of the effect size whereas varying specific or category gains provides an assessment of their sensitivity/specificity. For more detail on sensitivity analyses, see (Mitchell, Feng et al. 2007; Mitchell and Lee 2007; Mitchell and Lee 2009). Traditional meta-analysis analytical tools, such as statistical linear regression and effect size prediction, are still useful to analyze dynamic meta-analysis results. However, the dynamic and multi-variate nature of dynamic meta-analysis also provides possibilities for richer analyses like those typically seen in the analysis of complex or dynamical systems. Given that the two greatest advantages of dynamic analysis are the implicit inclusion of interactions and explicit inclusion of time, analyses that examine how relationships change over time are particularly telling. Analyses such as cross-correlation (or landscapes) of outcome measures or category outcome measures at specific disease time points, such was done in (Mitchell and Lee 2008) and (Mitchell and Lee 2007), provide a overview of what the

Finally, the implicit inclusion of interactions allows combination treatments to be examined. All clinical treatments, in some form, exploit a cellular interaction at some level. For example, pharmaceutical modulators typically exploit the interaction between a receptor and its ligand. Thus, every potential interaction within the dynamic meta-analysis structure can be evaluated as a hypothetical treatment possibility. Furthermore, the structure of dynamic meta-analysis allows every single interaction (whether between outcome measures or between categories of outcome measures) to be varied and simulated individually and in combination. Measuring the resultant effect size of an interaction or combination of interactions predicts its potential treatment efficacy. For more methodological detail on simulating combination therapies, see our previous work with combination treatments and

We begin by examing the effect size of each category, an analysis that is typically seen with traditional meta-analysis. Table 3 reveals the average, standard deviation, maximum, and minimum effect size of each category based on a sensitivity analysis that perturbed the intial conditions. Note that "N'' is the connectivity, or number of interactions (as shown in Figure 1), affecting the category measure. This examination reveals that the average effect of, for example, treating energetics is a relatively unimpressive 19% outcome change for a 100% treatment effect on energetics itself. (Note that a "real" treatment would have effects substantially smaller than 100%, often only 10% or so.). However, this type of analysis misses the potential for interactions completely and to some extent even minimizes the

simulated, and analyzed in Matlab (Mathworks, Inc.).

system is doing without becoming mired in detail.

spinal cord injury (Mitchell and Lee 2008).

**3. Results of a G93A SOD1 feasibility study** 

potential significance of targeted treatments by averaging.

**2.10 Post-result analysis and prediction** 

Next, we examine the relative changes in the category outcome measures over time in order to get a better feel of the system dynamics. As shown in Figure 4, initially, the system exhibits a period of relative quiescence (days 0-80) in which there appears to be little variation from the baseline operating point. However, closer examination reveals a few fluctuations, which appear as small oscillations from baseline (Figure 5). Over time each oscillation grows in magnitude, with the first notable oscillation starting around day 40. However, the component trajectories do eventually explode at approximately day 150.

These qualitative system features of ALS align well with the characterization of the G-93A SOD-1 experimental paradigm. In fact, the first large oscillation corresponds to the average onset of measurable functional deficits and the final explosion aligns with the average time of death for the G-93A SOD-1 mouse model (Xu, Jung et al. 2004; Kieran, Hafezparast et al. 2005; Gould, Buss et al. 2006; Teuchert, Fischer et al. 2006). It should be noted that the oscillations of this system do not necessarily represent the relapsing and remitting of functional deficits, such as is seen with multiple sclerosis, but rather the oscillations of individual mechanisms and pathways. In fact, such oscillations could be responsible for small fluctuations sometimes seen within and among mechanistic studies, such as those examining axonal transport (De Vos, Chapman et al. 2007) and protein aggregation (Stieber, Gonatas et al. 2000; Gould, Buss et al. 2006). How oscillations correlating with specific losses in muscle function remains to be seen. It is likely that the overall loss of systemic control aligns with what is typically seen as continuously degenerating function or degenerative function with intermixed plateaus.

From a system dynamics point of view, it is likely that the exploding oscillations of ALS are the result of an unstable system. Initially, the regulatory systems, including excitability, ionic and axonal transport, cellular energetics and others, are able to maintain partial control, as evidenced by the smaller oscillations, which are an attempt to regulate. However, as the disease progresses the control mechanisms simply fail to keep up.

Dynamic Meta-Analysis as a Therapeutic Prediction Tool for Amyotrophic Lateral Sclerosis 75

**Stabilizing Treatments:** If pathological progression is driven by, or is the result of, system instability, then one potential therapeutic strategy is to develop treatments that rectify the instability. We tested single treatments that targeted individual category interactions as well as combination treatments that simultaneously targeted up to 3 category interactions. A small percentage of the over 44,000 different combinations treatments investigated rectified the system instability (See example in Figure 6), thereby preventing the "explosion" typically seen between days 150-200 at the average time of death. That is, these treatments have the potential to greatly extend the life span of the typical G-93A

Of note is that many of the most successful treatment combinations did not include the component that was responsible for the initiating perturbation. Also in some cases, the directions (sign of the relationship) that components best treated the system could be non-

Fig. 6. Dynamics of ALS predicted by dynamic analysis of the G93A SOD1 mouse model. ALS dynamics are unstable, (dashed lines) characterized by growing oscillations that "explode" near the average time of death. Dynamic meta-analysis of potential treatment combinations predicts that a small percentage of 3-way treatment combinations can assist in

**Treatment synergism:** Whether stabilizing or not, or just purely interaction-based, many of the ALS treatments have a synergistic effect. That is, their combined effects are substantially greater than the sum of their individual effects. For two-way treatments (treatments addressing two category interactions), 16% of the total possible 10,000 combinations are synergistic. (Note that treatment direction was made in the more favorable direction.) For three-way combinations, approximately 22% of the possible 900,000 combinations are

re-stabilization of the system (solid lines).

synergistic (Figure 7).

intuitive, again likely owing to the highly interactive nature of the ALS system.

mouse.

Fig. 4. Unstable, oscillatory dynamics of ALS predicted by dynamic meta-analysis .

Fig. 5. Expansion of oscillations initiating during the pre-symptomatic quiescent period.

#### **3.2 Combination therapy predictions**

We examine how hypothetical therapeutics that exploit single and multi-category interactions can potentially "treat" the system. We utilize the systemic category as our primary outcome measure since it includes known functional metrics. Two different combination treatment types are examined: 1.) combination treatments that stabilize the system (e.g. dampen the oscillations) and 2.) synergistic combination treatments.

Fig. 4. Unstable, oscillatory dynamics of ALS predicted by dynamic meta-analysis .

Fig. 5. Expansion of oscillations initiating during the pre-symptomatic quiescent period.

system (e.g. dampen the oscillations) and 2.) synergistic combination treatments.

We examine how hypothetical therapeutics that exploit single and multi-category interactions can potentially "treat" the system. We utilize the systemic category as our primary outcome measure since it includes known functional metrics. Two different combination treatment types are examined: 1.) combination treatments that stabilize the

**3.2 Combination therapy predictions** 

**Stabilizing Treatments:** If pathological progression is driven by, or is the result of, system instability, then one potential therapeutic strategy is to develop treatments that rectify the instability. We tested single treatments that targeted individual category interactions as well as combination treatments that simultaneously targeted up to 3 category interactions. A small percentage of the over 44,000 different combinations treatments investigated rectified the system instability (See example in Figure 6), thereby preventing the "explosion" typically seen between days 150-200 at the average time of death. That is, these treatments have the potential to greatly extend the life span of the typical G-93A mouse.

Of note is that many of the most successful treatment combinations did not include the component that was responsible for the initiating perturbation. Also in some cases, the directions (sign of the relationship) that components best treated the system could be nonintuitive, again likely owing to the highly interactive nature of the ALS system.

Fig. 6. Dynamics of ALS predicted by dynamic analysis of the G93A SOD1 mouse model. ALS dynamics are unstable, (dashed lines) characterized by growing oscillations that "explode" near the average time of death. Dynamic meta-analysis of potential treatment combinations predicts that a small percentage of 3-way treatment combinations can assist in re-stabilization of the system (solid lines).

**Treatment synergism:** Whether stabilizing or not, or just purely interaction-based, many of the ALS treatments have a synergistic effect. That is, their combined effects are substantially greater than the sum of their individual effects. For two-way treatments (treatments addressing two category interactions), 16% of the total possible 10,000 combinations are synergistic. (Note that treatment direction was made in the more favorable direction.) For three-way combinations, approximately 22% of the possible 900,000 combinations are synergistic (Figure 7).

Dynamic Meta-Analysis as a Therapeutic Prediction Tool for Amyotrophic Lateral Sclerosis 77

*System dynamics revealed.* Conventional wisdom in ALS research has been that there is a single, specific root cause. However, dynamic meta-analysis predicts that a system-level instability is the actual problem (see oscillations in Figure 4). Lending credence to the predictions of dynamic meta-analysis is the mounting evidence from recent studies that indicates that multiple mutations or underlying mechanisms can result in the symptoms

*Novel treatment strategies identified.* In this small scale feasibility study of ALS, dynamic metaanalysis predicts that reducing the overall feedback gain will be more effective than identifying and ameliorating a single "source" or point of initiation (Mitchell and Lee 2010). That is, inducing small changes across multiple categories of mechanisms is more effective than inducing a large change in a single category. Additionally, treatments that target the underyling system dyanmics, such as stabilizing oscillations, could be another potentially

*Combination treatment prediction enabled.* Another key opportunity afforded by dynamic meta-analysis is an innovative approach to predicting combination treatment effectiveness in a high-throughput manner. The interacting differential equations of dynamic metaanalysis implicitly include all possible treatment interactions. Thus, potential synergistic combinations can be identified before they are explicitly examined experimentally. For example, in spinal cord injury, a sweep of all possible combinations of virtual treatments revealed that none were synergistic (Mitchell and Lee 2008). While disappointing, we were at least able to discover treatments that combined linearly. On the other hand, in our initial evaluation of ALS, a small percentage of treatment combinations show very profound synergism! It appears that in ALS, the broader the treatment the more effective it becomes. (Figure 6 illustrates an example of a 3-way combination that appears to arrest the oscillatory explosion observed in the control case.) Finally, dynamic meta-analysis is not only well suited to identify promising combinations but can be used to prioritize them

This work was supported by the National Institute of Health (NS069616 and NS062200).

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phosphorylates neurofilaments and is associated with neurofilament pathology in

**4. Conclusions** 

effective path.

as well.

**5. Acknowledgments** 

**6. References** 

characterized as ALS (Rothstein 2009).

Fig. 7. Percentage of total treatment combinations belonging to each efficacy type.

Tables 4 and 5, show the efficacies of 2-way and 3-way synergistic combination treatments. A linearly additive treatment (combination A&B effect = A effect + B effect) was assigned an efficacy factor of 1.0. Thus, synergistic treatments have efficacy factors >1 and sub-additive treatments have efficacy factors <1. Therefore, categories with higher average and maximum efficacy factors have a tendency to produce greater synergistic effects in combination.


Table 4. Synergistic two-way combination treatment predictions.


Table 5. Synergistic three-way combination treatment predictions.
