Post on 03-May-2020
Haugh Model and Modification 1
December 12, 2017
Haugh Model and Modification
I. INTRODUCTION
Human growth hormone (hGH) is a peptide hormone that is required for several
important signaling pathways in the human body, including cellular growth and
metabolism. These pathways also promote aging, genomic instability, as well as
impacting sleep cycles (Guevara-Aguirre 2011). Consequently, an understanding of the
interaction between hGH and its receptor protein on the cell surface is vital.
hGH has two binding sites, site 1 and site 2, and both sites bind to the same receptor.
This signaling acts through receptor homodimerization. However, each site has a
different affinity for the receptor. Site 1 has a much higher affinity for the hGH receptor
than site 2. The sequence of reactions can then be stated as followed. hGH binds to a
receptor on the cell surface at site 1. The unbound site 2 of hGH in this complex then
binds to another receptor on the cell surface, forming a homodimer made of 1 hGH
protein and 2 receptors. This dimer then promotes downstream signaling pathways by
recruiting Janus kinase 2 (Jak2) tyrosine kinases to other receptors.
The pathway is more complex and involves many other cellular mechanisms,
involving internalizations of cell-surface proteins, recycling of internalized receptors, and
synthesis of receptors. The model developed by Jason M. Haugh was created to
incorporate these ligand and receptor trafficking mechanisms (Haugh 2004). He sought to
match dose response data reported in literature by modeling proliferation signal
depending on the amount of hGH introduced to the cell, as well as including the ability to
model and predict inhibition and different mutations in hGH. Rate constants used in this
Haugh Model and Modification 2
model were determined from previous literature and by adjusting the parameters so as to
minimize the differences between the model and raw data. Initial conditions were set at
2000 receptor proteins per cell. Consequently, the model developed accurately
represented the raw data and predicted limitations.
II. MODEL
The Haugh model uses 4 ordinary differential equations to calculate dimer formation
and thus signaling. The ODEs used describe the hGH receptors on the cell surface (R),
the complexes bound to site 1 of hGH on the cell surface (C), dimers made of 1 hGH and
2 receptor proteins (D), and internalized receptor proteins (Ri) (Figure 1B). The ODEs
account for receptor and complex endocytosis, internalized receptor recycling, receptor
degradation, and binding at the cell surface (Figure 1A). Dimer degradation is assumed to
happen the instant a dimer is internalized, captured in the rate constant ke. Rate constants
used were of that in the Haugh paper.
The model was successfully used to describe the effect of changing the affinity of site
1 in hGH on the proliferation signal produced, calculated as per equation A5 in the
Haugh model (Figure 2). As expected, the general shape of the curve is a bell curve; the
proliferation signal increases as hGH concentration increases because dimer formation
increases, until so much hGH is added that instead of forming dimers, multiple hGH
proteins bind receptors at site 1, which has a higher affinity for the receptor. When the
affinity of site 1 is mutated to be higher (blue dashed line), the maximum proliferation
signal is about the same, but the range of hGH variant that can hold that maximum
decreases (Figure 2). This happens because as hGH increases, because the affinity at site
Haugh Model and Modification 3
1 is higher the protein is more inclined to bind at site 1. When site 1 affinity is decreased
(red dashed line), the maximum proliferation signal decreases, but this maximum is
achieved at much higher concentrations of hGH (Figure 2). This is because with a lower
affinity, the protein is not pushed as hard to bind at site 1, so more hGH must be added to
force multiple hGH proteins to be bound only at site 1.
Similarly, the model was also able to predict the effect on proliferation signal by
changing the site 2 affinity for the receptor by changing the value of the rate constant kx2
(Figure 4). Increasing the affinity by a factor of 10 (dashed blue line) relative to wildtype
hGH resulted in a slightly increased maximum proliferation signal because this is the rate
constant leading to dimer formation, thus at steady state more dimer can be formed
(Figure 4). The higher affinity also allowed the maximum proliferation signal to be
achieved for a greater range of hGH variant concentration because it increased the
likelihood of hGH binding two receptors. Decreasing the affinity of site 2 for the receptor
by 10-fold (dashed red line) similarly decreases the maximum proliferation rate and the
range of hGH concentration this maximum can be held out for. However, both variants
and wildtype hGH reach their maximum proliferation signal at 1 nM hGH (variant),
indicating that changing the affinity of site 2 does not have an impact on the amount of
hGH required for maximum dimer formation.
The model was also able to predict the relationship between proliferation signal and
receptor downregulation, which was almost linear (Figure 3). This means that as the
dimers forming increases, there is a linear increase in proliferation signal. This
conclusion can help in interpreting other results as well, by drawing the relationship
between dimer formation and signaling.
Haugh Model and Modification 4
Antagonistic effects of hGH variants were also successfully described by
implementation of the Haugh model (Figure 5). Antagonism by K172A/F176A (blue
line) showed that much higher levels of hGH variant needed to be added to decrease
proliferation signal, as expected because the affinity of K172A/F176A is about 650x
lower than the site 1 affinity of wildtype hGH. A defective site 2 of the hGH antagonist
showed a decease in proliferation signal at lower concentration of hGH variant, because
of the inability of the antagonist to dimerize (red and yellow lines). Furthermore, a higher
site 1 affinity of the antagonist was confirmed to decrease dimerization as lower
concentrations of hGH as seen in the difference between H21A/R64K/E17A/G120R and
G120R (red and yellow lines).
Using anti-hGH antibodies, Fab fragments were also modeled as antagonists because
of their inability to form dimers (Figure 7). Proliferation signal was calculated for
different concentrations of Fab 5 (red line) and Fab 13E1 (blue line), and Fab 5 decreases
proliferation signal (and thus dimerization) at lower concentrations of Fab than Fab 13E1.
Fab 5 antagonism decreases the kx2 of hGH binding rather than inhibiting, which proved
to be a more dramatic antagonistic effect because kx2 is the only rate contributing to dimer
formation.
Furthermore, the agonistic effect of anti-hGH antibodies as monoclonal antibodies, or
MAbs, on the proliferation signal was also demonstrated by the model (Figure 6). MAb 5
(purple line) cannot form dimers, so the proliferation signal was always 0. MAb 3D9
(yellow line) and 263 (red line) both reach their maximum proliferation signal at 10 nM
MAb, which indicates that the fact both have the same site 1 affinity is important to when
max proliferation occurs. However, the maximum proliferation signal with MAb 263 is
Haugh Model and Modification 5
much higher than that of MAb 3D9, indicating that higher rate constants, like kf1 and kx2,
result in increased dimerization. MAb 13E1 (blue line) has the highest proliferation
signal but requires a higher MAb concentration, indicating that a higher KD needs a
higher MAb concentration for maximum dimerization and confirms that a higher kf1 and
kx2 result in increased dimer formation.
Dimer fraction versus time and hGH concentration was also calculated using the
Haugh model and gave expected results (Figure 6).
The model employed several key assumptions upon implementation. To begin with,
hGH was assumed to have been in excess, so that [L] ~ [L]0. This assumption is valid
because enough hGH (or hGH variant) is added to the system to be able to ignore ligand
depletion, and was confirmed to cause no change in proliferation signal by the simple
addition of a differential equation (Figure 9A). Additionally, the internalized pool of
receptors was ignored by setting the krec/kdeg fraction to 0; thus, krec = 0 and the value of
kdeg is irrelevant. This assumption serves to simplify the model but may not be as accurate
a representation of signaling as it could be. Furthermore, the model depends upon
receptor proteins and complexes being internalized at the same rate, as well as dimers
being degraded upon internalization at a different rate.
The model also makes several assumptions about the binding of hGH to the receptor
proteins. Haugh assumes that hGH first binds at site 1, which makes sense because this
site has a higher affinity. The model also depends upon site 1 dissociating to break up the
dimer, followed by the “fast” dissociation of hGH and receptor protein at site 2.
Haugh Model and Modification 6
ODEs were written using standard mass action methods, indicating an assumption that
the solution is well-mixed (although a common assumption, this may not be the most
accurate representation).
Although several assumptions were made and many rate constants fit to the data, the
model well represented the data and gave insight into the mechanism.
III. CONCLUSION
Generally, the Haugh model fit the data provided. However, this good fit was brought
about by starting with rate constants determined by data, and then “adjusting” them to
give a better fit—essentially fitting the data, which takes away from the significance of
how good the fit is. Additionally, while the ODEs incorporated recycling and degradation
of internalized receptor, krec was set to 0, which neglected this entire portion of the model.
This means that the entire point of modeling receptor protein is mute and leaves a huge
hole in what this model could do. There is also room for improvement in the basic
assumption of the solution being well-mixed, where one could factor in different
compartments. Furthermore, the representation of the dissociation of the complex formed
after dissociation of the dimer, i.e. receptor bound to hGH at site 2, as “fast” leaves room
for modification. What exactly is “fast,” how can that truly be modeled, and what is the
mechanism behind it?
That being said, the assumptions made allowed for the model to be easily (more or
less) implemented to provide insight into the mechanism, including what rate constants
were important, how binding sites affected signaling, and antagonist agonist by anti-hGH
antibodies. Without the simplifications made by Haugh, this model would have been at
Haugh Model and Modification 7
worst impossible and at best much more complex to implement and understand, and
could have less significance in determining the mechanisms at play.
IV. MODIFICATION
The Haugh model presents an opportunity for modification where it models the
irreversible dissociation of the complex formed upon dissociation of the dimer (receptor
bound to hGH at site 2) as “fast.” “Fast” is not a rate and is likely missing steps in
between, and no truly irreversible reaction exists in biology. This modification
incorporates reversible dissociation of the dimer to form a second complex (C2), where
receptor protein is bound to site 2 of hGH, which can also reversibly dissociate to
unbound receptor and ligand (Figure 10A). This model accounts not only for reversible
reactions and a more specific method of dimer formation and dissociation but also for the
binding of receptor protein to the lower-affinity site 2 of hGH first. This modification is
an important addition because it provides another mechanistic insight and possible
explanation; even if it does not prove to be as accurate as the Haugh model, it could be
adjusted and applied to other mechanisms. The ODEs used to implement the modification
can be found in Figure 10B. I hypothesize that this modification will as a general trend
increase the dimer formation and thus proliferation signaling.
The actual results of the implementation of the modified model proved to be more
complex than my simple hypothesis. The modification has no noticeable effect on the
dimer fraction formed at different time points and hGH concentrations (Figure 11).
Additionally, the relationship between receptor downregulation and proliferation signal
Haugh Model and Modification 8
remains the same, but this makes sense as it only shows the relationship between dimer
and signaling (Figure 12).
However, once the changes in the affinities of the binding sites are modeled, we see
interesting changes with the modification. With site 1, with a higher affinity the
modification does not change the initial increase in proliferation signal at lower
concentrations of hGH variant or the maximum cell proliferation. However, the
modification does change the range of hGH concentration that this maximum can be held
for (Figure 13). At a higher affinity, the modification shortens it, but at a lower affinity
the modifications lengthens this range. Furthermore at a low site 1 affinity, the
modification increases both the range of hGH concentration at maximum proliferation
signal as well as increases the maximum proliferation signal.
Analysis of site 2 affinity reveals an analogous trend. The modification did not impact
the increase in proliferation signal as hGH concentration increases at low concentrations,
which makes sense because the modification includes site 2 affinity binding for dimer
formation, but that does not greatly impact formation since the affinity is lower than that
of site 1. However, at high kx2 values, the modification decreases the range of hGH
variant that achieve maximum proliferation signal, while at low values of kx2 this range is
increased. Perhaps at high values of kx2 although more dimer could potentially be formed,
more dimer could dissociate through the modified mechanism.
Although the results did not necessarily agree with my hypothesis, they brought about
interesting insight that could prove useful in future modeling.
dR/dt = vs + krec[Ri] – kt[R] – kf1[L][R] + kr1[C] – kx2[C][R] + k-x2[D] + 2k-x1[D]
dC/dt = kf1[L][R] - kr1[C] – kt[C] – kx2[C][R] + k-x2[D]
dD/dt = kx2[C][R] - k-x2[D] – k-x1[D] – ke[D]
dRi/dt = kt([R] + [C]) – krec[Ri] – kdeg[Ri]
Haugh Model and Modification 9
V. FIGURES
Figure 1: The Haugh Model. Shown is the model developed and by Jason M. Haugh
and used to model hGH signaling data. Shown in red brackets is an illustration of a
reaction that is defined by Haugh as happening at a “fast” rate. Consequently, this
reaction is assumed to happen instantaneously once the dimer has unbound hGH at site 1.
(A) An illustration of the model is presented. (B) The ODEs used to implement the
mathematical model are shown.
hGH variant (nM)
Proliferation signal Haugh Model and Modification 10
Figure 2: Effect of site 1 affinity on proliferation signal. The Haugh model was
implemented to model the proliferation signal as a function of initial ligand (hGH
variant) concentration. Proliferation signal at steady state as a function of initial
concentration of wildtype hGH (solid black curve; site 1 KD = 1.5 nM), a high-affinity
hGH variant (dashed blue curve; H21A/R64K/E174A; site 1 KD = 0.05 nM), and a low
affinity hGH variant (dashed red curve; K172A/F176A; site 1 KD = 1.0 uM) were
modeled. The high affinity variant increases proliferation signal at a lower than wildtype
hGH, but this higher affinity also makes the proliferation signal remain high for a shorter
amount of time than wildtype. The lower affinity requires a much higher concentration of
hGH variant for maximum proliferation signal, and this maximum is lower than that of
wildtype hGH.
Receptor downregulation (%)
Proliferation signal
Haugh Model and Modification 11
Figure 3: The relationship between proliferation signal and receptor
downregulation in wildtype hGH. Receptor downregulation is equal to initial receptor
proteins on the cell surface – the sum of the complex, dimer, and recepetor proteins on
the cell surface at steady state. This relationship between proliferation signal and
downregulation is almost linear and shows that maximum proliferation signal is achieved
at about 90% receptor downregulation.
Haugh Model and Modification 12
Figure 4: Effect of site 2 affinity on proliferation signal. The proliferation signal at
steady state was calculated using the Haugh model for wildtype hGH (solid black line; kx2
= 0.0024, k-x2 = 0.016) and hypothetical hGH variants with changed site 2 affinities: one
with a 10x higher affinity (dashed blue line; kx2 = 0.024, k-x2 = 0.016) and one with a 10
times lower affinity (dashed red line; kx2 = 0.00024, k-x2 = 0.016). All 3 variants reach
peak proliferation signal around the same concentration of hGH, but the lower the affinity
(or the higher the kx2) at site 2 the higher the maximum proliferation signal. Furthermore,
lower affinity at site 2 also showed that a higher proliferation signal meant that more
hGH variant had to be added in order to decrease proliferation signal (due to self-
antagonism).
Proliferation signal
hGH variant (nM)
Haugh Model and Modification 13
Figure 5: Antagonistic effect of hGH variants on proliferation signal. Proliferation
signal at steady state was calculated for cells with 1 nm hGH and different concentrations
of hGH variants. The variants used were K172A/F176A (blue line; site 1 KD = 1 uM),
wildtype hGH (purple line; site 1 KD = 1.5 nm), G120R (yellow line; site 1 KD = 1.5 nm,
kx2 = 0), and H21A/R64K/E17A/G120R (red line; site 1 KD = 0.5 nm, kx2 = 0). The higher
affinity site 1 with defective site 2 variant (H21A/R64K/E17A/G120R) requires less hGH
variant to be added than the normal affinity site 1 with defective site 2 variant (G120R).
Additionally, a defective site 2 shows less hGH variant required to decrease proliferation,
as shown by the difference between G120R and wildtype hGH. Contrarily, a normal site
2 but decreased affinity at site 1 requires more hGH variant to be added to decrease cell
proliferation, shown by the difference between wildtype hGH and K172A/F176A.
hGH variant (nM)
Proliferation signal
Haugh Model and Modification 14
Antibody kf1 kr1 kx2 k-x2 k-x1
13E1 0.0024 0.042 0.0108 0.0042 0.0042
263 0.006 0.03 7.95x10^(-4) 0.003 0.003
3D9 0.002 0.01 2.04x10^(-5) 0.001 0.001
5 0.004 0.002 0 0.002 0.002
Figure 6: Effect of monoclonal antibodies as agonists on proliferation signal. (A)
Kinetic rates for the antibodies selected were calculated. (B) Proliferation signal was
calculated for four monoclonal antibodies, where dimers formed with the monoclonal
antibodies also contribute to the proliferation signal. The four selected anti-hGH
antibodies were 13E1, 263, 3D9, ad 5 (kinetic rates given in chart). MAb 5 cannot form
A.
Proliferation signal
Monoclonal antibody (nM)
B.
Haugh Model and Modification 15
dimers (kx2 = 0), so the proliferation signal remained at 0 no matter the MAb
concentration. MAbs 3D9 and 263, both of which do not bind specifically at the hGH
binding site, reach peak proliferation signal around 10 nm MAb, but MAb 263 requires
much more monoclonal antibody added to decrease proliferation signal from its
maximum. Furthermore MAb 3D9 has a lower maximum proliferation signal.
Additionally, MAb 13E1 does not reach its peak maximum proliferation signal until 100
nM MAb, and this maximum is the highest of the four MAbs.
Haugh Model and Modification 16
Figure 7: Effect of Fab fragments as antagonists on proliferation signal. Proliferation
signal at steady state was calculated at 1 nM hGH and varying concentrations of Fab
fragments. 2 Fab fragments were examined in particular: Fab 13E1 (red line; inhibition
with rate constants in chart with kf1/2 and kx2 = 0) and Fab 5 (blue line; changes the kx2 of
wildtype hGH). Fab 5 decreases proliferation signal at lower concentrations than Fab
13E1.
Proliferation signal
Fab concentration (nM)
Haugh Model and Modification 17
Figure 8: Receptor dimer formation at different at different time points and hGH
concentrations. Dimers formed were calculated using the Haugh model at 1 minute, 10
minutes, 45 minutes, and steady state. At each time, hGH concentration was 0.01 (dark
blue), 0.1 (cerulean blue), 1 (light blue), 10 (teal), 100 (light green), 103 (orange), and 104
(yellow) nM. At 0.01 nM hGH, the dimer fraction does not increase significantly until 10
minutes, and the increases slightly at 45 minutes until it reaches its steady state value. At
0.1 nM, dimer fraction increases 5x between 1 and 10 minutes, and remains at a dimer
fraction of 0.1 between 10 minutes and 45 minutes, but then eventually decreases about
50% to its steady state value. At 1 nM, the dimer fraction peaks at 10 minutes at a value
Haugh Model and Modification 18
of 0.45, but then decreases to 0.075 at 45 minutes, and then again to about 0.03 at steady
state. At 10 nM hGH, the dimer fraction peaks at 1 minute at a value of 0.6, but decreases
slightly to 0.4 at 10 minutes, then decreases to about 0.3 for steady state. At 100 nM
hGH, the dimer fraction remains relatively constant for the first 10 minutes at 0.3, then
drops to 0.75 at 45 minutes, and then again to about 0.025 at steady state. At 103 nM
hGH, the dimer fraction increases slightly after one to ten minutes to 0.6 but hovers
around its steady state value. At 104 nM hGH, there is not much of a difference between
the dimer fraction at steady state and 1 minute. Steady state dimer fraction is at a
maximum at 1 and 10 nM hGH.
Haugh Model and Modification 19
Figure 9: Ignoring ligand depletion is a valid assumption in the Haugh Model. To
check the ligand depletion assumption, an adjustment of the Haugh model was made and
hGH variant (nM)
Proliferation signal
A.
B.
Haugh Model and Modification 20
compared to the original. (A) Proliferation signal at steady state was calculated at varying
concentrations of hGH using the original Haugh model (black line) and with an adjusted
model that factors for ligand depletion. Proliferation signal factoring in ligand depletion
plotted against the initial hGH concentration (blue circles) and plotted against the actual
concentration (subtracting the hGH depleted; red crosses) were also calculated. This
adjustment was no different than the original Haugh model, demonstrating this was a
valid assumption. The actual difference in cell proliferation was on the order of 10-30. (B)
The adjusted ODEs to factor in ligand depletion are shown. The added ODE is for hGH
(L), where Nav = Avogadro’s number and Ce = cells/mL, assumed to be 4 x 1012.
Haugh Model and Modification 21
Figure 10: Modification of the Haugh Model. Shown is a modification of model
developed and by Jason M. Haugh. (A) The modification is shown in red brackets.
Instead of a “fast” and irreversible dissociation of hGH bound to receptor at site 2, this
modification accounts for a reversible reaction with a rate constant associated with it.
This modification also allows for complex and dimer formation for when hGH binds to
the receptor at site 1 first. (B) The ODEs used to implement the modified model are
shown. This modification assumes the same values for rate constants as in the Haugh
paper and also assumes that affinity of site 1 for the receptor remains unchanged whether
or not site 2 is bound, and vice versa. Thus, it is assumed that k-x3 = kr1, kx3 = kf1, k-x4 = k-
x2, and kx4 = kx2.
dR/dt = vs + krec[Ri] – kt[R] – kf1[L][R] + kr1[C] – kx2[C][R] + k-x2[D] + k-x3[D] – kx3[R][C2] + k-x4[C2] – kx4[R][L]
dC/dt = kf1[L][R] - kr1[C] – kt[C] – kx2[C][R] + k-x2[D]
dD/dt = kx2[C][R] - k-x2[D] – k-x3[D] + kx3[R][C2] – ke[D]
dRi/dt = kt([R] + [C] +[C2]) – krec[Ri] – kdeg[Ri]
dC2/dt = -kt[C2] + kx4[R][L] – k-x4[C2] – kx3[R][C2] + k-x3[D]
Haugh Model and Modification 22
A.
B.
Haugh Model and Modification 23
Figure 11: Modified Haugh model does not noticeably change dimers fraction at
different times and hGH concentraions. Dimers formed were calculated 1 minute, 10
minutes, 45 minutes, and steady state. At each time, hGH concentration was 0.01 (dark
blue), 0.1 (cerulean blue), 1 (light blue), 10 (teal), 100 (light green), 103 (orange), and 104
(yellow) nM. (A) As shown in Figure 8, the original Haugh model was used to calculate
the dimer fractions. (B) The modified Haugh model was used to calculate dimer
fractions, which appear the same as those of the original Haugh model.
Haugh Model and Modification 24
Figure 12: Modification of Haugh model does not change the relationship between
proliferation signal and receptor downregulation. Receptor downregulation was
calculated as per equations provided by Jason M. Haugh where receptor downregulation
equals initial receptor proteins on the cell surface – the sum of the complex, dimer, and
recepetor proteins on the cell surface at steady state. The proliferation signal versus
downregulation calculated by the original Haugh model (light blue line) perfectly
overlaps with that of the modified model (dashed red line).Proliferation signal
Receptor downregulation (%)
Haugh Model and Modification 25
Figure 13: Comparison of the effect of site 1 affinity on proliferation signal in the
modified and original Haugh model. Proliferation signal at steady state was calculated
for different concentrations of hGH variant using the original Haugh or modified model,
as labeled. In black is the wildtype hGH (site 1 KD = 1.5 nM), where the solid line
represents the original model and the dashed line represents the modified model. In blue
is the hGH variant H21A/R64K/E174A with a high affinity site 1 (KD = 0.05 nM), where
the solid line represents the original model and the dashed line represents the
modification. In red is the hGH variant K172A/F176A with a low affinity site 1 (KD = 1.0
uM), where the solid line represents the original model and the dashed line represents the
modification.
hGH variant (nM)
Proliferation signal
Haugh Model and Modification 26
Figure 14: Comparison of the effect of site 2 affinity on proliferation signal in the
modified and original Haugh model. The proliferation signal at steady state was
calculated for wildtype hGH (black lines; kx2 = 0.0024, k-x2 = 0.016) and hypothetical
hGH variants with changed site 2 affinities: one with a 10x higher affinity (blue lines; kx2
= 0.024, k-x2 = 0.016) and one with a 10 times lower affinity (red lines; kx2 = 0.00024, k-x2
= 0.016). Solid lines represent calculations done using the original Haugh model, and
dashed lines represent calculations done using the modified Haugh model.
hGH variant (nM)
Proliferation signal
Haugh Model and Modification 27
References
Jason M. Haugh. “Mathematical Model of Human Growth Hormone (hGH)-Stimulated
Cell Proliferation Explains the Efficacy of hGH Variants as Receptor Agonists or
Antagonists.” Biotechnology Progress 20 (2004): 1337-1344.
Jaime Guevara-Aguirre, Priya Balasubramanian, Marco Guevara-Aguirre, Min Wei,
Federica Madia, Chia-Wei Cheng, David Hwang, Alejandro Martin-Montalvo, Jannette
Saavedra, Sue Ingles, Rafael de Cabo, Pinchas Cohen, Valter D. Longo. “Growth
Hormone Receptor Deficiency Is Associated with a Major Reduction in Pro-Aging
Signaling, Cancer, and Diabetes in Humans.” Science Translational Medicine 3 (2011):
1-9.