Type 2 Diabetes: One Disease, Many Pathways

Diabetes is a chronic, progressive disease that calls for longitudinal data and analysis. We introduce a longitudinal mathematical model that is capable of representing the metabolic state of an individual at any point in time during their progression from normal glucose tolerance to type 2 diabetes (T2D) over a period of years. As an application of the model, we account for the diversity of pathways typically followed, focusing on two extreme alternatives, one that goes through impaired fasting glucose (IFG) first, and one that goes through impaired glucose tolerance (IGT) first. These two pathways are widely recognized to stem from distinct metabolic abnormalities in hepatic glucose production and peripheral glucose uptake, respectively. We confirm this but go beyond to show that IFG and IGT lie on a continuum ranging from high hepatic insulin resistance and low peripheral insulin resistance to low hepatic resistance and high peripheral resistance. We show that IFG generally incurs IGT, and IGT generally incurs IFG on the way to T2D, highlighting the difference between innate and acquired defects and the need to assess patients early to determine their underlying primary impairment. We illustrate the relevance of this for patient stratification by simulating the effects of properly and improperly targeted therapies. The model also incorporates insulin granule exocytosis and accounts for both first and second phase secretion. Simulations suggest that the loss of first phase secretion in both the IGT-first and IFG-first pathways is only a marker of progression to diabetes, not a causative mechanism.

Diabetes is by definition a state of hyperglycemia, but its natural history is diverse. For example, some 30 individuals experience fasting hyperglycemia first (Impaired Fasting Glucose, IFG), followed by 31 hyperglycemia at the two-hour time point (2hPG) of an oral glucose tolerance test (OGTT), defined as 32 Impaired Glucose Tolerance (IGT), and some experience these in the opposite order. Eventually, all 33 people with diabetes will have both IFG and IGT (combined glucose impairment, CGI), so we refer to 34 these two pathways as "IGT-first" and "IFG-first", respectively. An important implication of these 35 observations is that the best period for determining differences in the underlying physiology of these 36 pathways is during the pre-diabetic stage, when the phenotypes are still distinct. 37 38 Prediabetes is also the stage in which progression to type 2 diabetes (T2D) can be markedly delayed or 39 prevented 1 , and interventions can plausibly be made even more effective by targeting the specific 40 metabolic defects of the patient. For example, IFG is generally thought to reflect insulin resistance at the 41 liver, resulting in elevated hepatic glucose production (HGP), whereas IGT is thought to reflect peripheral 42 insulin resistance, mainly in muscle, resulting in reduced glucose disposal. One would like to know 43 whether using drugs that primarily affect hepatic or peripheral insulin resistance makes a material 44 difference for patients on the IFG-first or IGT-first pathways, and whether any such benefit carries over 45 once T2D has begun. 46 and IVGTTs. A recent model 13 added the capability of following daily and post-challenge glucose 104 variations and was fit to OGTT data from the DPP. It also introduced a distinction between peripheral 105 and hepatic insulin resistance in order to account for the effects of drug and lifestyle interventions on 106 these parameters. 107 We also, using a different methodology, introduce simulations of OGTTs at selected points during 108 progression, and separate representations for hepatic and peripheral insulin resistance. We use these new 109 features to differentiate progression by either 2hPG or FPG. We perform IVGTTs as well to illustrate the 110 evolution of the acute insulin response to glucose (AIRg), often used to assess beta-cell function. This 111 requires the model to simulate first and second phase secretion, which we accomplish by incorporating a 112 previously published model for insulin granule exocytosis 18 . 113 This study focuses on mechanism and insight, rather than assessment. Instead of fitting parameters to 114 particular data sets, we assume parameters and investigate the trajectories of glycemia and insulin 115 secretion that result. We demonstrate that the model captures known features of diabetes pathogenesis 116 data and provides novel insights and interpretations of the data. We conceptualize this as building a 117 factory, not a product. Once the utility of the model is established, we expect that a wide variety of 118 applications to clinical data will become possible. 119 120

Materials and Methods 121 122
We briefly review the previous version of the model 6  (2) 132 133 The glucose (G) equation (Eq. 1) says that G increases on a time scale of hours as a result of meal influx 134 and hepatic glucose production (HGP) and decreases as a result of uptake, which has both insulin-135 independent and insulin-dependent components. The factor SI in the insulin-dependent term is closely 136 related to the well-known sensitivity to insulin reported by the Minimal Model. The insulin (I) equation 137 (Eq. 2) says that I decreases due to removal, mainly in the liver, with rate constant k, and increases due to 138 secretion by beta cells, where b is the beta-cell mass, ISR is the insulin secretion rate per unit mass, and V The parameter g in Eq.
(3) represents the effect of K(ATP) channel density to shift the glucose 145 dependence of secretion (the triggering pathway 21 ); when the channel density is low, g is high, and shifts 146 the dependence to the left, increasing secretion for the same level of M because Ca 2+ is higher. 147 Experiments in 22 showed that mouse beta cells in vitro adjust the K(ATP) channel density down in 148 response to sustained (overnight) elevated glucose. This has also been observed in vivo in humans 23-25 , 149 along with evidence of reduced insulin clearance, k, (19-21) which we omit here for simplicity. This can 150 be viewed as the first line of defense through enhanced beta-cell function against insulin resistance over a 151 time scale of days (e.g. holiday overeating). 152 The value of g depends on glucose, which is taken into account by adding a third differential equation to 153 the system: 154 where g∞ is an increasing sigmoidal function of G, andtg is the time constant.

157
Insulin resistance that persists over longer periods (months in humans) despite reduced K(ATP) channel 158 density, is assumed to trigger a further level of compensatory increased beta-cell function via s, the 159 maximal insulin secretion capacity (Eq. 3). This corresponds to the amplifying effects of metabolism 160 and/or modulators such as GLP-1 and ACh on the efficacy of Ca 2+ to drive insulin granule exocytosis. 161 This second aspect of beta-cell functional compensation entails a fourth differential equation: 162 We assume that increased ISR (workload in the sense of 26 ) leads to an increase in s whereas increased 164 M leads to a decrease in s.

165
The slowest and final form of compensation for insulin resistance is increased beta-cell mass, b, which 166 develops over years in humans. We assume that b is increased by proliferation, P, and decreased by 167 apoptosis, A. Following the data of 26 , we assume that P increases when ISR increases. We further 168 assume that apoptosis is largely driven by metabolic stress (e.g. through increased production of reactive 169 oxygen species) when glucose is high, so we make A an increasing function of M : The parameters defining P and A are chosen such that modest increases in G result in a net increase in b, 173 but large increases in G result in a net decrease in b. As in the predecessor model of 7 , this leads to a shift 174 from compensation (negative feedback) to decompensation (positive feedback). In 6 , we showed that this 175 can account for the threshold behavior observed in both rodents and humans, that is, nearly steady G 176 followed by a sharp, essentially irreversible increase 27,28 . We proposed this as an explanation for why 177 prevention of T2D is much easier than reversing it once it is established. The same dynamic properties 178 carry over in this study with the model enhanced as described next. 179 180

New features in the model 181
Modeling glucose flux during daily meals and glucose tolerance tests 182 In the previous version of the model 6 , G represented average daily glucose and insulin levels in response 183 to steady glucose input. To address IFG and IGT, we need to be able to dissociate fasting glucose from 184 post-challenge glucose. The first step is to introduce variable glucose influx from meals, represented by 185 the term MEAL in Eq. (1). Timing of meals is standardized to 6:00 AM, 12:00 Noon, and 6:00 PM. The In order to distinguish peripheral and hepatic insulin resistance and describe how they are related to each 193 other, we need to refine the model description of hepatic glucose production (HGP in Eq. 1). In the first 194 version of the model 6 , HGP was assumed to be constant, which is an acceptable approximation as long as 195 fasting plasma insulin is adequate to compensate perfectly for any hepatic insulin resistance. To study the 196 failure of compensation, however, we need to make HGP dependent on I (Eq. A4). This is sufficient to 197 give the typical drop and recovery of HGP after a meal (Fig. A4, A). Figure A6, E -H shows the 198 response of HGP and glucose disposal to a simulated hyperinsulinemic, euglycemic clamp, with steady-199 state values in good agreement with experimental data 29 . 200 Less obvious, but also important, we need to account for the correlation between hepatic and peripheral 201 insulin resistance, which we do by making two of the parameters in Eq. A4, hepamax and aHGP, functions 202 of SI (Eqs. A5, A6 and Fig. A4, B, C). If this is not done, then in a case of severe peripheral resistance 203 with strong compensatory insulin secretion, it is possible to have fasting hypoglycemia, which is not the 204 typical pattern (See Fig. A7). In more typical cases of progression to pre-diabetes or diabetes, the 205 relative impairment in insulin secretion would mask this effect: the level of glycemia would be reduced 206 but hypoglycemia would not result. We choose the parameters such that HGP remains normal when 207 insulin is elevated unless there is a defect in beta-cell mass or function. To represent hepatic insulin 208 resistance over and above the component related to peripheral insulin resistance, we decrease the 209 parameter hepaSI in Eq. A4, which increases HGP at any value of I. 210 211

Modeling insulin granule exocytosis 212
To study the dynamics of glucose and insulin under glucose challenges such as meals, OGTT, and 213 IVGTT, the model needs to account for the multiple kinetic components of insulin secretion. We adapted 214 an existing model of insulin granule exocytosis 18 , which was designed to capture the biphasic pattern of 215 ISR in response to a glucose step in vitro or a hyperglycemic clamp in vivo. The first phase is 216 characterized by a sharp peak of ISR during the first 10 minutes and the second phase by a steady increase 217 of ISR over the next hour. Figure A6 shows a simulated OGTT (panels A, B) and a simulated IVGTT 218 (panels, C, D) compared to experimental data. 219 The insulin secretion rate ISR in the first version 6 of the model (Eq. 3) is in the new version no longer a 228 function of glucose, but is calculated as an output of the exocytosis model (Eqs. A11), ISR thus now 229 depends on the history of exposure to G, as it should, not just the current value. The exocytosis model 230 requires as input the cytosolic Ca 2+ concentration, which is modeled as a sigmoidal function of the beta-231 cell metabolic rate M (Eq. A7), and the much higher Ca 2+ concentration in the microdomains of Ca 2+ 232 channels, which is modeled as a function of cytosolic Ca 2+ (Eq. A8). The dose response curve shift g, 233 previously included in Eq. 3, represents the dynamic changes in K(ATP) channel density as before, but 234 now explicitly alters cytosolic Ca 2+ at a given level of M (Eq. A7). Cytosolic calcium enhances the rates 235 of mobilization of the reserve pool to the plasma membrane (Eq. A10) and priming of docked vesicles (r2 236 in Eqs. A12), whereas vesicle fusion is primarily controlled by microdomain Ca 2+ . The amplifying effect 237 of glucose 21 is incorporated as a multiplicative factor in the rate of vesicle mobilization (GF in Eq. A9). 238 The effects of the incretins GLP-1 and GIP are effectively rolled into GF but could be broken out as 239 independent factors to study their dynamic changes over time or as targets of drug therapy, though we do 240 not use that feature in this paper. For IVGTT and hyperglycemic clamp simulations, we reduce GF by 241 about a factor of two to represent the lack of the incretin effect on vesicle mobilization and reduce P Q (Eq. 242 A12) about 10-fold to represent the lack of incretin effect on vesicle priming. The rate of mobilization 243 (Eq. A11) is also assumed to be proportional to the variable s (Eq. 6), which thus controls the magnitude 244 of second-phase insulin secretion. As a consequence, ISR implicitly includes s as a multiplicative factor,

Criteria of pre-diabetes and diabetes 249
Following the ADA criteria, we define IFG as FPG > 100 mg/dl but < 126 mg/dl, IGT as 2hPG > 140 250 mg/dl but < 200 mg/dl, and T2D as FPG ≥ 126 mg/dl or 2hPG ≥ 200 mg/dl. Parameters that were varied to make the figures are listed in Table S12A in the Appendix, and the initial 273 conditions for Figs. 1 -4 are in Table S12B.  insulin resistance progresses, 2hPG increases rapidly while FPG increases more slowly (Fig. 1C), 279 resulting in progression from normal glucose tolerance (NGT) to IGT, CGI and ultimately T2D (Fig. 1C). 280 Fasting plasma insulin (FPI) and 2-hour plasma insulin (2hPI) rise as the beta cells initially compensate 281 partially for the insulin resistance, then fall as the beta cells fail (Fig. 1D), following the classic "Starling 282 law" of the pancreas 31 . The initial rise in secretion results from an increase in beta-cell sensitivity to 283 glucose (the variable g increases, not shown), and the decline results from a fall in the slower component 284 of beta-cell function, s (Fig. 1E). Beta-cell mass (b) also rises and falls, but the variation is limited 285 because of the slowness of b, and the fall occurs only after T2D is already underway (Fig. 1F). This 286 accords with observations that beta-cell mass is elevated in insulin-resistant pre-diabetics but reduced in 287 long-standing diabetes 32, 33 . 288 289 A subtle but important point of this simulation is that insulin resistance in both the liver and peripheral 290 tissues reaches saturation (Fig. 1A, B) well before the advent of T2D. It is rather the continuing fall in 291 beta-cell function, s, that drives conversion to T2D. The same sequence was seen in the simulation of 292 T2D progression in Zucker diabetic fatty rats ( Fig. 6 in 6 ) and in data from monkeys 34 . 293 The fall in s is triggered by the hyperglycemia and glucotoxicity that follows the early loss of insulin 294 sensitivity ( Fig. 1D) but would not lead to T2D if the pre-existing capacity of beta-cell function to 295 compensate were stronger. This is illustrated by a simulation with the same degree of insulin resistance 296 as in Fig. 1, but a milder beta-cell defect, which mimics a non-diabetic subject with insulin resistance 297

IFG-first pathway 308
In Fig. 3 we illustrate a contrasting case to Fig. 1, dominant hepatic insulin resistance with minor 309 peripheral resistance (Fig. 3A, B); the same beta-cell function defect is assumed as in Fig. 1. Hepatic 310 insulin resistance drives FPG across the threshold for IFG, while 2hPG remains below the threshold for 311 IGT (Fig. 3C). After the initial threshold crossing, however, FPG and 2hPG continue to rise, and IFG 312 progresses to CGI as in Fig. 1. Insulin again rises with the help of g (not shown) and falls when the drop 313 in s becomes too great (Fig. 3E). As in the IGT-first pathway, the conversion to T2D is driven mainly 314 by reduced beta-cell function, s, because insulin resistance in both the liver and peripheral tissues 315 saturates well before T2D (or even CGI) begins. Beta-cell mass again plays a minor role (Fig. 3F). 316 In the BLSA some subjects who had progressed from NGT to IGT went on to T2D at the next follow-up, 317 which prompted the authors to ask whether CGI could be skipped 2 . Figure 4 demonstrates that this can 318 happen if peripheral insulin resistance is made much greater than hepatic resistance (compare Fig. 4A to 319 Fig. 1A). Extreme loss of peripheral insulin sensitivity causes 2hPG to rise dramatically, while FPG 320 remains in the normal range, converting NGT to IGT. 2hPG continues to deteriorate without a substantial 321 increase in FPG, resulting in progression of IGT to T2D without passing through CGI. Eventually, FPG 322 crosses the thresholds for IFG and T2D, but after the individual has already reached T2D based on 2hPG. 323 This is important both for designing clinical studies and for stratifying patients for treatment. The figure  334 suggests that the slope of the trajectory from two or more OGTTs spaced suitably far apart in time could 335 give a good indication of the future path of the patient. 336 We next look more closely at the pathogenesis process as it would appear clinically by simulating OGTTs 337 This indicates that even progression to CGI from IGT is mainly due to impaired beta-cell function. insulin resistance increases glucose at all time points during the OGTT (Fig. 6B). The increase in FPG is 355 greater than for 2hPG, so the threshold for IFG is crossed first in Fig. 3. Even though fasting insulin at 356 the IFG stage (Fig. 6D, dotted curve) is very high, it is not enough to maintain normal FPG, because of 357 the severe hepatic insulin resistance (Fig. 3B). However, 2hPG is maintained in the normal range because 358 peripheral insulin resistance is mild (Fig. 3A). Since both peripheral and hepatic insulin sensitivity 359 saturate before the onset of CGI (Fig. 3A, B), the decrease in insulin at all time points during the OGTT 360 ( Fig. 6D, dashed curve) due to falling beta-cell function (Fig. 3E) is the main contributor to the 361 progression to CGI from IFG and then to T2D. is widely considered a key early marker of future progress. For example, the classic paper 36 reported a 367 cross-sectional study of IVGTTs, and showed that AIRg declines as FPG rises and is nearly gone by the 368 time FPG reaches 115 mg/dl, well below the threshold for T2D. This supports the use of AIRg, and by 369 implication first-phase insulin secretion, as an early marker for T2D. We now show that the model can 370 reproduce the negative correlation between FPG and AIRg, but that rising FPG is not necessarily the sole 371 or proximal cause of the decline in AIRg. and IFG-first pathways, respectively. AIRg is blunted and then vanishes in both pathways as FPG rises, 374 as found in 36 , but 2hPG also rises at the same time, albeit to different degrees relative to FPG in the two 375 pathways. The decline of AIRg is more rapid than seen experimentally along both pathways 37 , but the 376 main point is that it results from the decline of RRP size (Figs. 7C, D), which is more fundamental than 377 the level of glycemia, as the next two paragraphs explain. 378 RRP size is controlled by two factors, the rate of secretion, which determines the rate of vesicle efflux 379 from the RRP and the rate of vesicle influx into the RRP from the docked pool. High FPG increases the 380 rate of efflux in the basal state, so the RRP will already be depleted when the IVGTT commences, and 381 AIRg will consequently be reduced. The rate of influx depends on the size of the docked pool and the 382 rate of priming of docked vesicles. The rate of priming does not vary much in our simulations, but the 383 size of the docked pool does, depending mainly on the rate of docking, which is proportional to one of our 384 beta-cell function variables, s. Although modest increases in glucose stimulate vesicle docking, larger 385 increases cause glucose toxicity, which reduces s and hence docking.

395
In summary, reduced AIRg can be a marker of impairment in either first-or second-phase secretion, and, 396 as glycemia progresses towards T2D, is likely to indicate both. 397 398

Targeted Drug Therapy 399
With the previous, simpler model 6 we showed that NGT and T2D were bistable states separated by a 400 threshold. This accounted for the well-known observation that it is easier to prevent T2D than to reverse 401 it. The new model retains these characteristics but raises the possibility that the response to therapeutic 402 interventions may vary depending on which pathway a patient follows to T2D. Figure 8 shows that this is 403 indeed the case, and that knowledge of a patient's subtype of insulin resistance can in principle lead to 404 more effective drug therapy. 405 Figures 8A, B contrast two drug therapies targeted to peripheral vs. hepatic insulin resistance in patients 406 in the early stages of diabetes. Figure 8A shows glucose for a patient on the IGT-first pathway with 407 dominant peripheral insulin resistance as in Fig. 1, in the absence of therapy (control, black curves) or in 408 response to a high dose of a drug targeted to peripheral insulin resistance (dashed curves) or a drug 409 targeted to hepatic insulin resistance (dotted). The high dose of the appropriately targeted drug only 410 transiently improves FPG and 2hPG and ultimately fails to reverse T2D. Nonetheless, it is more effective 411 at delaying progression than the mistargeted drug. The study in 13 found that it was necessary to assume that the efficacy of treatment wanes with time in 422 order to fit the data from lifestyle and drug interventions in the DPP. Here we have shown that even if the 423 efficacy of treatment is maintained, the intrinsic dynamics of progressive beta-cell dysfunction can cause 424 treatment to fail. 425 Caution should be used in interpreting the simulated treatments in Fig. 8 in terms of currently used drugs. 426 For example, in the DREAM study 38 it was found that rosiglitazone was effective in cases of isolated IFG 427 (IIFG), that is IFG in the absence of IGT. Although rosiglitazone is often thought of as primarily 428 improving peripheral insulin sensitivity, it also improves hepatic insulin sensitivity 39  We apply the model to analyze the diverse presentation of hyperglycemia, which may manifest first in 438 fasting glucose (IFG-first pathway) or two-hour glucose during an OGTT (IGT-first pathway). To carry 439 out this program, we modified the representation for beta-cell response to insulin resistance in the model 440 of 6 , enhancing it to differentiate between hepatic and peripheral insulin resistance. The simulations show 441 that heterogeneity in the degree of the two forms of insulin resistance can account for a wide variety of 442 observed patterns, supporting the idea of T2D as a unitary disease with quantitative variants. We have 443 focused on extreme cases to highlight the differences (e.g. Fig. 1 vs. Fig. 3), but the family of trajectories 444 in the FPG-2hPG plane (Fig. 5) shows that these lie on a continuum. Figure 5 also highlights that 445 differences in insulin resistance phenotype are most evident in the late NGT and early pre-diabetes stages, 446 which are thus most amenable to differential phenotyping and therapeutic stratification. 447 We have incorporated a description of insulin granule dynamics sufficient to account for both first-and 448 second-phase insulin secretion. This made it possible to simulate OGTT and IVGTT time courses and 449 show how they are transformed systematically during progression along the two canonical pathways to 450 diabetes (Figs. 6, 7). We also showed that sufficiently strong beta-cell function can prevent T2D even 451 when insulin resistance is severe, allowing individuals to maintain a permanent state of IGT (Fig. 2) or 452 even revert from IGT to NGT (not shown). Conversely, sufficient insulin sensitivity can prevent T2D 453 even when beta-cell function is somewhat impaired 6 . As discussed below, a fuller treatment of the 454 differences in the balance of insulin secretion and insulin action defects is needed to account fully for the 455 diverse patterns of T2D progression. 456 We summarize below the specific lessons learned and questions answered by this study and give a 457 preview of the clinical applications we anticipate for the model. The BLSA study 2 asked whether subjects who enter the IGT state necessarily pass through CGI on the 462 way to T2D. The model suggests (Fig. 4) that this is not the case, but skipping CGI happens only if the 463 peripheral insulin resistance is markedly greater than hepatic insulin resistance, so this is expected to 464 occur only rarely. An intermediate possibility predicted by the model is a short, but not absent, interval of 465

CGI that could escape detection if the follow-up interval is too long. 466
A parallel question is whether individuals can go directly from IFG to T2D without passing through CGI. 467 This is harder than going directly from IGT to T2D because 2hPG is much more labile than FPG; it is 468 difficult to get an increase in FPG sufficient to cross the threshold for T2D (125 mg/dl) without at the 469 same time having 2hPG cross the threshold for IGT (140 mg/dl). Indeed, we have not been able to 470 simulate this scenario just by choosing an appropriate mixture of hepatic and peripheral insulin sensitivity 471 using the other parameters as in Figs. 1 -4

, but model simulations (not shown) predict that it can happen 472
if a more severe beta-cell defect (in g∞, Eq. A15) is assumed. 473 The BLSA study also asked whether individuals can pass directly from NGT to T2D without passing 474 through any pre-diabetic state. Because glucose is in quasi-steady state with the much slower variables 475 representing beta-cell mass, beta-cell function and insulin sensitivity, this is not possible in the model 476 unless one of those slow variables undergoes a catastrophic, virtually discontinuous, change. 477 Pancreatectomy would be an example of this, but even type 1 diabetes, triggered by a rapid fall in beta-478 cell mass, has a distinct prediabetes phase. The cases observed in BLSA in which subjects were NGT at 479 baseline and T2D at first follow-up most likely reflected rapid progression or a long gap between visits. 480 Similarly, the model simulations indicate that it is unlikely for individuals to go from NGT to CGI 481 without passing through IFG or IGT. 482 The BLSA reported that IFG is generally followed by IGT and IGT is generally followed by IFG, and the 483 model suggests that each state induces the other. This happens because the initial rise in glucose during 484 IFG impairs beta-cell function, which causes 2hPG to rise, and vice versa. Another study raised the 485 question of whether CGI is a progressed state of IFG 40 ; the model simulations together with the BLSA 486 data show that CGI may instead be a progressed state of IGT, to which IFG has been added. 487 One can also ask whether crossing the threshold for FPG or 2hPG of pre-diabetes predicts whether T2D 488 will be reached by crossing the corresponding threshold. In Fig. 1, IGT is followed by T2D diagnosed 489 through 2hPG, and further simulations with the model (Fig. 5) suggest that this is typical. In Fig. 3, IFG  490 is followed by T2D diagnosed through FPG, but further simulations (not shown) indicate that this may or 491 may not be the case, depending on the degree of discrepancy between HIR and PIR and the strength of g 492 to control FPG. 493 Both the IFG-and IGT-first pathways exhibit elevated fasting insulin. This may account for the 494 observation that elevated fasting insulin was a better predictor of future diabetes in a prospective study 495 than fasting glucose, which is only elevated early on in the IFG-first pathway 41 ; it may not be necessary 496 to hypothesize a major causative role for high fasting insulin itself. Indeed, in the IGT-first pathway, 497 which is more common, fasting glucose may be suppressed by the compensatory increase in beta-cell 498 function (our variable s) induced by high post-load glucose (compare Figs. 1 and 4 to Fig. 3).

499
The suppression of fasting glucose in the context of a predominance of peripheral insulin resistance has 500 particular importance for pre-diabetes screening in populations that are prone to IGT but not IFG. This 501 applies notably to people of African descent, for whom fasting glucose has markedly reduced sensitivity 502 for detecting pre-diabetes and diabetes 42 . The problem is exacerbated for Africans living in Africa, 503 where measuring 2hPG with OGTTs is prohibitively expensive. The model suggests that in this and 504 similar cases, lowering the threshold for diagnosing pre-diabetes based on fasting glucose could be a cost-505 effective strategy. More generally, the model points to the need for population-and patient-specific 506 thresholds for diagnosis, which may contribute to resolving current debate on whether prediabetes is a 507 useful diagnosis 43 . 508 509

Peripheral and hepatic insulin resistance are not independent 510
We have varied peripheral and hepatic insulin resistance independently to study their contributions to 511 T2D progression, but in reality, they are related. Statistically, they are correlated with a coefficient of 512 about 0.7 44 . This is expected for several reasons. For one, they share major components of the insulin 513 signaling pathway. Also, there is evidence that an important determinant of hepatic insulin resistance is 514 excess supply of free fatty acid (FFA) substrate from adipose tissue 45 . Thus, insulin resistance in 515 adipose cells would increase lipolysis and FFA flux to the liver, which would drive increased 516 gluconeogenesis 46 . On the other hand, the liver has unique roles in glucose and lipid production not 517 shared with muscle, which may account for the fact that the correlation is imperfect. 518 The unique contribution of the model in this regard, however, is to reveal dynamic reasons for a 519 relationship between hepatic and peripheral resistance. Fasting HGP is primarily controlled by fasting 520 insulin concentration, but post-prandial HGP is suppressed by the post-prandial rise of insulin. If severe 521 peripheral insulin resistance is present, but the compensation in insulin is strong, it is possible to have 522 fasting hypoglycemia unless there is some degree of hepatic insulin resistance. This is illustrated in Fig.  523 A7. Since this is not typically observed, we have accounted for this by making HGP dependent on SI 524 (Eqs. A4 -A6, Fig. A4), reflecting the above-mentioned correlation between hepatic and peripheral 525 resistance. Note that we have omitted glucagon from the model for simplicity because we are not aware 526 of strong evidence that it is involved in the development of diabetes, though it is involved in worsening 527 hyperglycemia in established diabetes. It is possible that glucose may also contribute to avoiding 528 hypoglycemia under the conditions of severe insulin resistance and strong secretion described in this 529

paragraph. 530
To address hepatic insulin resistance above and beyond the component correlated with peripheral insulin 531 resistance, we have independently varied the affinity of HGP for insulin (parameter hepaSI in Eq. A4), the 532 effect of which is shown in Fig. A4. We have obtained similar results (not shown) by varying the 533 maximal rate of HGP (parameter hepamax). 534 535

Secretion defects 536
The simulations of progression to T2D (Figs. 1, 3, and 4) require some degree of secretion defect in 537 addition to the various combinations of insulin resistance. We assumed a defect only in the triggering 538 pathway (g ), but we have obtained similar results by assuming defects in the amplifying pathway (s ). 539 The assumed triggering defect represents a right shift in the glucose dose response curve, which 540 corresponds to a mild gain of function mutation of the K(ATP) channels, a prominent hit in GWAS 47 . 541 The model shows that defects in first-and second-phase secretion are not independent. Impairment in one 542 leads to impairment in the other because of the harmful effects of elevated glucose. The model accounts 543 for classic data 36 showing that the acute insulin response to glucose (AIRg), a surrogate for first phase 544 secretion, declines with even modest increases in FPG during the NGT and pre-diabetic stages. The 545 model shows, however, that second-phase insulin secretion declines in parallel, belying a privileged role 546 for first-phase secretion, as also shown in another modeling study 48

Limitations of the study 556
For simplicity and brevity, we addressed here only the contributions of hepatic and peripheral insulin 557 resistance in driving the IFG-first and IGT-first pathways. It has been shown, however, that non-insulin-558 dependent glucose uptake (glucose effectiveness) also plays a role 40 . The model can account for this if 559 the glucose effectiveness parameter EG0 in Eq. (1) is varied. We have also found that a right shift in the 560 sensitivity of the beta cells to glucose (our function g∞(G) in Eqs. (5, A15)) can by itself or in combination 561 with hepatic insulin resistance cause IFG and alter the trajectory of IGT. 562 The model as presented here is also oversimplified in that it only considers glucotoxicity and neglects 563 other factors that are likely to play a role, such as lipotoxicity 50 . In addition, we believe that prolonged 564 high secretion rate is probably harmful beyond the negative effect incorporated in the equation for s, 565 possibly because of ER stress and/or calcium toxicity 51 . Those factors were not included here because 566 they were not needed to account for the pathways considered, but they may be necessary to explain other 567 pathways to T2D and will be addressed elsewhere. 568 To capture the full range of patterns, it is necessary to consider as well pre-existing variation in beta-cell 569 function, not the moment-to-moment beta-cell function, which evolves in response to hyperglycemia, but 570 the innate, genetic capacity of beta-cell function to adapt to hyperglycemia. For example, changing the 571 parameters defining s∞ (Eqs. 6, A16) has marked effects on the speed of progression in IGT; we 572 neglected this because it doesn't change the likelihood of entering the IGT state much. 573 We have modeled the suppression of hepatic glucose production as a direct effect of insulin on the liver. 574 However, much if not all of the acute effect of insulin is indirect, mediated by suppression of lipolysis in 575 adipose tissue, which reduces the supply of free fatty acid (FFA) to the liver 45 . We consider this an 576 acceptable approximation for our purposes, as post-prandial suppression of lipolysis is roughly a mirror 577 image of the post-prandial rise in insulin. In future, if we want to account for FFA dynamics or adipose-578 tissue insulin resistance, the model would have to be augmented. 579 We have modeled insulin-dependent glucose uptake as linear in insulin, but it is likely to be non-linear 580 (sigmoidal) 52 and has been suggested to exhibit hysteresis 53 . We have not found these features to be 581 necessary to explain the data under consideration, but they can be easily added in the future if the need 582

arises. 583
We have included only a very simple representation of insulin clearance, assuming a first-order 584 dependence on insulin concentration. We have not distinguished portal from peripheral insulin 54 or 585 considered possible regulation by glucose 55 or free fatty acids 56 . 586 A question of particular current interest with regard to clearance that we have not investigated here is 587 what contribution clearance makes to the pathogenesis of T2D. There is considerable evidence that 588 insulin clearance is positively correlated with peripheral insulin sensitivity (e.g., 54,57 ), but the direction of 589 causation is not clear. If clearance is reduced secondary to reduced overall insulin sensitivity, then it 590 would contribute to the compensatory response, along with increased insulin secretion. However, it has 591 been suggested that the increased insulin resulting from reduced clearance may also contribute to insulin 592 resistance 58 . If that effect is modest in magnitude, it may reduce or even eliminate the compensatory 593 contribution of reduced clearance. 594 If the effect of hyperinsulinemia is great, or is even the primary cause of insulin resistance, as suggested 595 in 57 , it could possibly itself drive the pathogenesis of diabetes. Along those lines, it has been shown that 596 knocking out a key enzyme regulating insulin clearance, carcinoembryonic antigen-related cell adhesion 597 molecule 1 (CEACAM1), causes insulin resistance in mice 59 . The pathway involved is complicated, 598 involving direct effects on de novo lipogenesis in the liver and interactions with feeding circuits in the 599 hypothalamus in addition to hyperinsulinemia per se. It is beyond the scope of the present model but may 600 be an interesting topic for future modeling work. 601 602

Future directions 603
This paper has demonstrated that if the insulin resistance phenotype of an individual is known, their 604 future trajectory of hyperglycemia can be predicted (Figs. 1 -4) and drug choice can potentially be 605 optimized for the patient's insulin resistance phenotype (Fig. 8) or hepatic insulin sensitivity (modeled as a rapid increase in hepaSI; see Tables S13 -S16 for details). 866 The resistance, leading to IFG-first pathway as in Fig. 3. The appropriately targeted drug is more effective 869 than the inappropriately targeted drug in each case, but therapy is more effective when initiated during 870 prediabetes. T2D. In addition, some of the subjects who had initially progressed to IFG and IGT progressed further to 878 CGI (Fig. 3A of 2 ). Current ADA thresholds were used to define each category. 879     , where " = × u is the volume of distribution for glucose in dL, BW is body weight 947 in kg, u = 1.569 dL/kg 62 , and 948 The simulations in the paper were carried out assuming BW = 75kg, for a volume of distribution of 11.77 951 L, but this formulation makes the glucose load 75g independent of those choices. The values for ai are 952 given in Table S2. 953 954  and IVGTTbar is given in Table S3 along with the other parameters. As for the OGTT, the simulations 961 were carried out assuming BW = 75g. 962 peripheral insulin sensitivity SI using equations A4, A5, and A6. The model HGP is a decreasing function 966 of I (Eq. A4): As I increases during the post-prandial state, HGP is suppressed (Fig. A4A). hepamax and 967 aHGP are modeled as decreasing functions of peripheral insulin sensitivity SI, as shown in Figs.         Parameter adjustments for daily glucose responses. Some parameters in Tables S9 and S10 have been  1062 changed from 6 to accommodate daily glucose fluctuations.  Table S10. Parameters of s-dynamics for daily glucose fluctuations 1075