A mathematical model for ketosis-prone diabetes suggests the existence of multiple pancreatic β-cell inactivation mechanisms
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eLife assessment:
This theoretical study makes a useful contribution to our understanding of a subtype of type 2 diabetes – ketosis-prone diabetes mellitus (KPD) – with a potential impact on our broader understanding of diabetes and glucose regulation. The article presents an ordinary differential equation-based model for KPD that incorporates a number of distinct timescales – fast, slow, as well as intermediate, incorporating a key hypothesis of reversible beta cell deactivation. The presented evidence is solid and shows that observed clinical disease trajectories may be explained by a simple mathematical model in a particular parameter regime.
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Abstract
Ketosis-prone diabetes mellitus (KPD) is a subtype of type 2 diabetes, which presents much like type 1 diabetes, with dramatic hyperglycemia and ketoacidosis. Although KPD patients are initially insulin-dependent, after a few months of insulin treatment, ∼ 70% undergo near-normoglycemia remission and can maintain blood glucose without insulin, as in early type 2 diabetes or prediabetes. Here, we propose that these phenomena can be explained by the existence of a fast, reversible glucotoxicity process, which may exist in all people but be more pronounced in those susceptible to KPD. We develop a simple mathematical model of the pathogenesis of KPD, which incorporates this assumption, and show that it reproduces the phenomenology of KPD, including variations in the ability for patients to achieve and sustain remission. These results suggest that a variation of our model may be able to quantitatively describe variations in the course of remission among individuals with KPD.
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eLife assessment:
This theoretical study makes a useful contribution to our understanding of a subtype of type 2 diabetes – ketosis-prone diabetes mellitus (KPD) – with a potential impact on our broader understanding of diabetes and glucose regulation. The article presents an ordinary differential equation-based model for KPD that incorporates a number of distinct timescales – fast, slow, as well as intermediate, incorporating a key hypothesis of reversible beta cell deactivation. The presented evidence is solid and shows that observed clinical disease trajectories may be explained by a simple mathematical model in a particular parameter regime.
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Reviewer #1 (Public review):
The goal of this work is to understand the clinical observation of a subgroup of diabetics who experience extremely high levels of blood glucose levels after a period of high carbohydrate intake. These symptoms are similar to the onset of Type 1 diabetes but, crucially, have been observed to be fully reversible in some cases.
The authors interpret these observations by analyzing a simple yet insightful mathematical model in which β-cells temporarily stop producing insulin when exposed to high levels of glucose. For a specific model realization of such dynamics (and for specific parameter values) they show that such dynamics lead to two distinct stable states. One is the relatively normal/healthy state in which β-cells respond appropriately to glucose by releasing insulin. In contrast, when enough β-cells …
Reviewer #1 (Public review):
The goal of this work is to understand the clinical observation of a subgroup of diabetics who experience extremely high levels of blood glucose levels after a period of high carbohydrate intake. These symptoms are similar to the onset of Type 1 diabetes but, crucially, have been observed to be fully reversible in some cases.
The authors interpret these observations by analyzing a simple yet insightful mathematical model in which β-cells temporarily stop producing insulin when exposed to high levels of glucose. For a specific model realization of such dynamics (and for specific parameter values) they show that such dynamics lead to two distinct stable states. One is the relatively normal/healthy state in which β-cells respond appropriately to glucose by releasing insulin. In contrast, when enough β-cells "refuse" to produce insulin in a high-glucose environment, there is not enough insulin to reduce glucose levels, and the high-glucose state remains locked in because the high-glucose levels keep β-cells in their inactive state. The presented mathematical analysis shows that in their model the high-glucose state can be entered through an episode of high glucose levels and that subsequently the low-glucose state can be re-entered through prolonged insulin intake.
The strength of this work is twofold. First, the intellectual sharpness of translating clinical observations of ketosis-prone type 2 diabetes (KPD) into the need for β-cell responses on intermediate timescales. Second, the analysis of a specific model clearly establishes that the clinical observations can be reproduced with a model in which β-cells dynamics reversibly enter a non-insulin-producing state in a glucose-dependent fashion.
The likely impact of this work is a shift in attention in the field from a focus on the short and long-term dynamics in glucose regulation and diabetes progression to the intermediate timescales of β-cell dynamics. I expect this to lead to much interest in probing the assumptions behind the model to establish what exactly the process is by which patients enter a 'KPD state'. Furthermore, I expect this work to trigger much research on how KPD relates to "regular" type 2 diabetes and to lead to experimental efforts to find/characterize previously overlooked β-cell phenotypes.
In summary, the authors claim that observed clinical dynamics and possible remission of KPD can be explained through introducing a temporarily inactive β-cell state into a "standard model" of diabetes. The evidence for this claim comes from analyzing a mathematical model and clearly presented. Importantly, the authors point out that this does not mean their model is correct. Other hypotheses are that:
- Instead of switching to an inactive state, individual β-cells could adjust how they respond to high glucose levels. If this response function changes reversibly on intermediate timescales the clinical observations could be explained without a reversible inactive state.
- Kidney function is indirectly impaired through chronic high glucose levels. The apparent rapid glucose increase might then not highlight a new type of β-cell phenotype but would reflect rapid changes in kidney function.
- In principle, the remission could be due to a direct response of β-cells to insulin and not mediated through the lowering of glucose levels.
Crucially, the hypothesized reversibly inactive state of β-cells remains to be directly observed. One of the key contributions of this theoretical work is directing experimental focus towards looking for reversible β-cell phenotypes.
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Reviewer #2 (Public review):
In this manuscript, Ridout et al. present an intriguing extension of beta cell mass-focused models for diabetes. Their model incorporates reversible glucose-dependent inactivation of beta cell mass, which can trigger sudden-onset hyperglycemia due to bistability in beta cell mass dynamics. Notably, this hyperglycemia can be reversed with insulin treatment. The model is simple, elegant, and thought-provoking.
Concerning the grounding in experimental phenomenology, it would be beneficial to identify specific experiments to strengthen the model. In particular, what evidence supports reversible beta cell inactivation? This could potentially be tested in mice, for instance, by using an inducible beta cell reporter, treating the animals with high glucose levels, and then measuring the phenotype of the marked …
Reviewer #2 (Public review):
In this manuscript, Ridout et al. present an intriguing extension of beta cell mass-focused models for diabetes. Their model incorporates reversible glucose-dependent inactivation of beta cell mass, which can trigger sudden-onset hyperglycemia due to bistability in beta cell mass dynamics. Notably, this hyperglycemia can be reversed with insulin treatment. The model is simple, elegant, and thought-provoking.
Concerning the grounding in experimental phenomenology, it would be beneficial to identify specific experiments to strengthen the model. In particular, what evidence supports reversible beta cell inactivation? This could potentially be tested in mice, for instance, by using an inducible beta cell reporter, treating the animals with high glucose levels, and then measuring the phenotype of the marked cells. Such experiments, if they exist, would make the motivation for the model more compelling. For quantitative experiments, the authors should be more specific about the features of beta cell dysfunction in KPD. Does the dysfunction manifest in fasting glucose, glycemic responses, or both? Is there a "pre-KPD" condition? What is known about the disease's timescale?
The authors should also consider whether their model could apply to other conditions besides KPD. For example, the phenomenology seems similar to the "honeymoon" phase of T1D. Making a strong case for the model in this scenario would be fascinating.
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Author response:
Response to Public Comment of Reviewer 1: We thank the Reviewer for the positive assessment of the manuscript. We also are grateful to the Reviewer for pointing out that providing alternatives to our model is a strength, and not a weakness, potentially stimulating future experiments that could falsify our model.
Response to Public Comment of Reviewer 2: We thank the Reviewer for the positive assessment of the manuscript.
In our manuscript, we already provide some references to evidence supporting reversible β-cell inactivation in a high-glucose environment. In the revision, we will expand this discussion, emphasize it, and add additional references that we have discovered recently.
In the revision, we will additionally expand our discussion of what is and is not known about the features of β-cell dysfunction in KPD, the …
Author response:
Response to Public Comment of Reviewer 1: We thank the Reviewer for the positive assessment of the manuscript. We also are grateful to the Reviewer for pointing out that providing alternatives to our model is a strength, and not a weakness, potentially stimulating future experiments that could falsify our model.
Response to Public Comment of Reviewer 2: We thank the Reviewer for the positive assessment of the manuscript.
In our manuscript, we already provide some references to evidence supporting reversible β-cell inactivation in a high-glucose environment. In the revision, we will expand this discussion, emphasize it, and add additional references that we have discovered recently.
In the revision, we will additionally expand our discussion of what is and is not known about the features of β-cell dysfunction in KPD, the relevant timescales, and so on. We will expand on how little is known about the possible pre-KPD state: individuals with KPD usually show up in a hospital with a new onset of diabetes, and often have had little access to medical care prior to this presentation. Thus, prior medical records are often unavailable. We hope this theoretical work will help justify appropriate future studies of the clinical history of KPD patients.
In the revision of the manuscript, we plan to briefly discuss how our model might, indeed, account for the honeymoon phase of type 1 diabetes, as well as for some phenomenology of gestational diabetes, and progression of type 2 diabetes in youth. In other words, the model developed for explaining KPD is potentially much broader, explaining many other phenomena. However, we prefer to leave the detailed modeling of these conditions, and comparisons to alternate hypotheses of their pathogenesis, to a future publication.
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