Glycated Hemoglobin, Plasma Glucose, and Erythrocyte Aging

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1 659885DSTXXX / Journal of Dabetes Scence and TechnologyBeltran del Ro et al research-artcle2016 Orgnal Artcle Glycated Hemoglobn, Plasma Glucose, and Erythrocyte Agng Journal of Dabetes Scence and Technology 2016, Vol. 10(6) Dabetes Technology Socety Reprnts and permssons: sagepub.com/journalspermssons.nav DOI: / dst.sagepub.com Manuel Beltran del Ro, PhD 1,2, Mukesh Twar, MD 1, Leo I Amodu, MD 1, Joaqun Caglan, MD 2, and Horaco Lus Rodrguez Rlo, MD 1 Abstract Background: The relatonshp between HbA1c and blood glucose averages has been characterzed many tmes, yet, a unfyng, mechanstc descrpton s stll lackng. Methods: We calculated the level of HbA1c from plasma glucose averages based solely on the n vvo rate of hemoglobn glycaton, and the dfferent turnover rates for erythrocytes of dfferent ages. These calculatons were then compared to the measured change of HbA1c due to changes n mean blood glucose (MBG), to complex models n the lterature, and our own experments. Results: Analyss of data on erythrocyte ageng patterns revealed that 2 separate RBC turnover mechansms seem to be present. We calculated the mean red blood cell (RBC) lfe span wthn ndvduals to le between 60 and 95 days. Comparson of expected HbA1c levels to data taken from contnuous glucose montors and fnger-stck MBG yelded good agreement (r =.87, P <.0001). Experments on the change wth tme of HbA1c nduced by a change of MBG were n excellent agreement wth our calculatons (r =.98, P <.0001). Conclusons: RBC turnover seems to be domnated by a constant rate of cell loss, and a mechansm that targets cells of a specfc age. Average RBC lfe span s 80 ± 10.9 days. Of HbA1c change toward treatment goal value, 50% s reached n about 30 days. Many factors contrbute to the rato of glycated hemoglobn, yet we can make accurate estmatons consderng only the n vvo glycaton constant, MBG, and the age dstrbuton of erythrocytes. Keywords glycated hemoglobn, erythrocyte lfe span, blood sugar control, contnuous glucose montor Glycated HbA has stood as a clncal marker of long term glycemc control for well over 4 decades, and remaned for the past 20 years, alongsde fastng glucose, as the golden standard for dabetes control. 1-6 The status of ths clncal assay has motvated much research, partcularly about ts relatonshp wth blood glucose levels, and ts reacton tme to changes n ther mean values. 3,7-17 Many of these studes have focused on fndng an emprcal relatonshp between HbA1c ratos and mean blood glucose concentraton. It s clear that there s such a relatonshp, but there s certanly no agreement as to a sngle algebrac form for t. 16,18 Recently, models have been proposed to nfer ths form, 3,6,14 and have collectvely ncorporated fne detals of hemoglobn glycaton and turnover, such as the contrbuton from retculocyte glycaton n bone marrow, the rate of dssocaton of glucose from hemoglobn, the effect of hgh glucose concentratons on RBC lfe span, etc. Yet, n each case, the man components are always the n vvo glycaton rate of hemoglobn, and some model of erythrocyte lfe cycle. The mechansm of hemoglobn glycaton, especally at the amno-termnal of the β subunts, has been extensvely studed and many experments have been desgned to calculate ts reacton rate On the other hand, and despte numerous efforts, not untl recently has detaled data on human erythrocyte turnover cycles been made avalable. 26 In our study, we analyze the experments on botnylated RBCs from Cohen et al 26 and ncorporate our fndngs to a 1 Pancreas Dsease Center, Department of Surgery, Northwell Health System, Manhasset, NY, USA 2 Fensten Insttute for Medcal Research, Manhasset, NY, USA Correspondng Author: Beltran del Ro, Manuel. PhD, Fensten Insttute for Medcal Research, 350 Communty Drve, Manhasset, NY 11030, USA. Emal: mbeltrande@northwell.edu

2 1304 Journal of Dabetes Scence and Technology 10(6) the daly rate of glycaton per Mol glucose. We then calculate the same proporton for erythrocytes that are 2 days old; ths s equal to the proporton of HbA1c n RBCs 1 day old, plus a contrbuton gven by the probablty that a (nonglycated) HbA molecule wthn a 1-day-old RBC s glycated by the second day, all multpled by a factor equal to the probablty that an erythrocyte age 1 day survves 24 hours. We then terate ths process to calculate the contrbuton to total HbA1c from RBCs of every age, and obtan the total HbA1c rato by addng each contrbuton (see Appendx B for detals). It should be noted that although such frst order knetcs have been used extensvely before, 3,27 couplng t wth a nontrval treatment of RBC clearance from emprcal data makes the desgn novel. It would seem, also, that what Tahara and Shma called the Weght Functon n ther semnal work, 3 was an ndrect measurement of RBC survval. Fgure 1. Example of botnylated RBC survval curve (data from Cohen et al 26 ). Damonds are botynlated RBC survval ratos. The followng fts are shown: a constraned quadratc 2 ( f ()= t at + bt + 1 R 2 =.998, sold lne), lnear (homogeneous lfe-span model, R 2 =.979, dot-dashed lne), and exponental (random death model, R 2 =.976, dashed lne). straghtforward method to calculate the percentage of HbA1c from a steady-state mean blood glucose value. Research Desgn and Methods Erythrocyte Survval We extracted data on day to day, n vvo survval of botnylated RBCs from Cohen et al 26 usng a MATLAB scrpt developed by our group (verson 8.6.0, R2015b; MathWorks Inc, Natck, MA, USA). The dgtzed survval curves, shown n the thrd fgure n the source publcaton, belong to 6 dabetc patents and 6 nondabetc controls. From the survval curves we can nfer the proporton of RBCs of a specfc age to the total, the mean RBC age, the average RBC lfe span, etc (mathematcal detals n Appendx A). Whle Cohen et al used a cubc functon to characterze these curves, we found that a restrcted quadratc form (ax 2 +bx+1) ftted the data well n every case (R 2 >.99). A randomly chosen example s shown n Fgure 1. HbA Glycaton Knowng the general shape of RBC survval curves we can calculate the total HbA1c usng an expermental estmate of the n vvo glycaton rate of hemoglobn (here we use the constant (mmol h) -1 reported by Mortensen et al 21 ). To do so, we frst calculate the proporton of glycated to non glycated HbA molecules wthn RBCs 1 day old, whch s roughly the product of glucose concentraton and Mean Blood Glucose and HbA1c Rato To test the accuracy of our method of calculatng HbA1c to total HbA we used 4 sets of data: our own, prevously publshed data of contnuous glucose montor (CGM) readngs and HbA1c n 45 patents wth chronc pancreatts and 9 healthy volunteers, 28 a set extracted from a study on 22 dabetc patents and 3 healthy controls, 16 a larger, CGM-based study, 17 and a large set (>600) of self-measured blood glucose and HbA1c percentages extracted from Kovatchev et al. 10 Varaton n tme of HbA1c Wth a mnor varaton of the procedure descrbed above to calculate the rato of glycated to total hemoglobn, we can estmate the rate of change of HbA1c due to a sudden change n mean blood glucose levels. Tahara et al 3 descrbe such stuaton on a seres of trals n whch 9 patents were montored closely after hosptalzaton for dabetes treatment. We used ther data for valdaton of our estmatons on the tme course of HbA1c. In addton, we compared our output to a smlar scenaro modeled by Osterman-Golkar et al. 14 Results In many of the prevous models of MBG and HbA1c, a daly turnover of only the oldest fracton of RBCs has been used, 1,3,14 the so called homogeneous lfe-span model. 29 The patent curvature of the erythrocyte survval functon suggests a dfferent approach and has mportant clncal consequences. Manly, t contradcts the seemngly prevalent noton of a homogeneous RBC lfe span of about 120 days; 4,30 whle the nterndvdual average survval of the most longevous RBCs (maxmum erythrocyte lfe span, ) s ndeed about 120 days (116.6 ± 12.7 days), the botnylated RBC measurements we analyzed yelded an average erythrocyte lfe span (AEL) of 80 ± 10.9 days. Ths means that n

3 Beltran del Ro et al 1305 addton the well documented senescence-medated clearance, 31,32 contrbutons to RBC turnover from non agerelated mechansms should be ncluded n calculatng HbA1c ratos. Fgure 1 shows an example of an expermental survval curve, our quadratc ft, a lnear ft (homogeneous lfespan model), and an exponental ft (random death model). The average age of crculatng erythrocytes was 49 ± 6 days. Unlke a general quadratc, a 2-parameter constraned form lke the one we chose s not expected to be a de facto mprovement over a lnear functon, whch was our case for every ft. We further found that the 2 parameters, a and b, whch descrbe each curve were not ndependent (the exponental ft a = αe -βx yelded R 2 =.98). Therefore, survval curves of human erythrocytes can be characterzed by a sngle parameter. In the followng we use to completely characterze an ndvdual s RBC turnover. Self-measured, fnger-stck MBG has 2 man nherent dffcultes: the bas ntroduced by perodc rather than random measurements, and the nablty of the subject to perform measurements durng sleep. The former problem was addressed by Kovatchev et al. 10 To assess possble bases from the latter, we compared separate CGM averages for awake and sleep perods on our healthy volunteers. In most cases the dfference between averages was sgnfcant (10 of 11, ANOVA at α = 0.05), though t was not systematc (greater durng sleep n only 7 out of 10 ), and only 1 presented a dfference of more than 10 mg/dl (0.56 mmol). We then decded to append fnger-stck measurements to CGM data. We calculated 1-day movng averages of our CGM data (not shown) to confrm the plausblty of consderng a 24 hour glycemc steady-state for our calculatons. In Fgure 2 we plot the expermental HbA1c-MBG pars alongsde our estmatons of HbA1c for a human wth = 90, 117, and 140 days. The curve belongng to the mean (117 days) agrees wth the overall data poston (r =.87, P <.0001), whle the envelopng curves ( = 90 and 140 days, the 2 extreme values reported n Cohen et al ) spread toward the greater glucose densty ranges, also n agreement wth the experments heteroscedastcty (a Kolmogorov-Smrnov test faled to reject the hypothess that the data were standard Gaussan when normalzed to a mean of = 117 d, and spread of = 134 d). It should be noted that expermental ponts n the hgher MBG ranges group slghtly closer to the lower ( = 90 d) estmate. Ths fact consttutes a nod to the sentment that hyperglycema reduces erythrocyte lfe span, 18,25,29 though botnylated RBC experments faled to confrm such a noton. 6,26 Ths nablty of the botnlated RBC experments to resolve a dfference between nondabetc and dabetc RBC lfe spans does not allow us to treat these 2 cases separately. A lkely consequence of ths s the fact that the predcted varablty of HbA1c n the nondabetc cohort s slghtly hgher than the one reported n the lterature (9.9% vs. 8.1%). Fgure 2. Calculated and expermental values of HbA1c % vs MBG (chronc pancreatts patents from Beltrán del Río et al, 28 crcles; Healthy volunteers from Beltrán del Río et al, 28 damonds; dabetes melltus from Kovatchev et al, 10 dots; dabetes melltus from Nathan et al, 17 crosses; dabetes melltus from Nathan et al, 16 squares). The 3 predctons correspond to dfferent values of erythrocyte lfe spans: = 117d, sold lne; = 140d, dashed lne; = 97d, dot-dashed lne. The nset shows the correlaton between expermental and expected HbA1c values ( = 117d) of all combned data (dots n nset). We calculated the expected change n tme of HbA1c after a stepwse decrease n blood sugar average for 3 cases: a medan of 117 days, and 2 extreme cases = 140 and 97 days. We normalzed these calculatons to percentage change and compared them to the equvalent experment descrbed n Tahara and Shma. 3 The ft yelded qute good agreement: (r =.98, P <.0001), see Fgure 3. Also, the HbA1c half-lfe we predcted (31 days) s consstent wth values reported by Osterman-Golkar and Vesper, and Tahara and Shma. 3,14 Fnally, we found that equvalent calculatons usng a much more complcated model, shown n the ffth graph n Osterman-Golkar et al, 14 are not only consstent but completely overlap our estmates (not shown, R 2 >.999, P <.0001). Conclusons The analyss done on RBC survval curves from Cohen et al 26 suggests an average erythrocyte crculaton tme of 80 ± 11 days. It was found that n the populaton examned, a sngle parameter (, AEL, etc ) was enough to fully characterze an ndvduals RBC turnover. The shape of the survval functons speaks of 2 man mechansms for RBC turnover: a constant, seemngly random loss (not dependent on RBC age), and a sudden, senescence-medated cutoff around a defnte age. From our calculatons we nferred that

4 1306 Journal of Dabetes Scence and Technology 10(6), () t = at + bt б. 0, t > AEL s calculated through the lfe span probablty densty: λ(t)= 1 β + βδ ( t ) where β = б ()/ б (0) s the probablty that an erythrocyte survves untl maxmum lfe span, and δ s a Drac densty functon. Appendx B HbA1c Estmaton Fgure 3. Rate for change of HbA1c % after a stepwse change n MBG. The 3 estmates correspond to calculatons based on dfferent erythrocyte lfe spans: = 117d, sold lne; = 140d, dashed lne; = 97d, dot-dashed lne. Data n damonds are measurements from Tahara and Shma. 3 only about 38 ± 9.6% of erythrocytes survve to reach ths actve clearance age. The small sample (N = 12) reported n Cohen et al, 26 s substantal enough for us to conclude that erythrocyte survval s more complex than what the commonly used homogeneous lfe span model descrbes, but not to draw a detaled pcture of the dstrbuton of RBC lfe spans n the general populaton, less so n smaller cohorts of clncal relevance. Our estmatons provded an accurate and parsmonous portrayal of HbA1c dynamcs through a mechanstc approach, rather than the more common lnear descrptons n the lterature. 18 The method presented nherently ncorporates a mean and a spread, from whch we nferred a maxmum RBC lfe span average and standard devaton of 117 ± 12 days. Measurements yelded an HbA1c half-lfe between 25 and 35 days, and 50 to 70 days to reach 80% of an HbA1c goal value. Appendx A Erythrocyte Turnover Analyss From a survval curve S(t) we obtan the RBC age densty functon (t), through the relatonshp: S() t = ρ ( ξ ) d ξ, б t under the assumpton of steady erythropoess. Average RBC age per ndvdual s therefore: RBCAge For quadratc S(t) we nferred: = ξρ ( ξ ) d ξ To calculate HbA1c we used a smple Markov model: f ρ 1 s the rato of RBCs aged to RBCs aged 1, and ρ 1 = 1, then the probablty that an RBC survves day j s p j = ρ j + 1 / ρ. j The contrbuton to HbA1c percentage by erythrocytes aged 1 day s α1 = ρ1γσ where γ s the per-day, per Mol, n vvo glycaton rate, and σ s the MBG concentraton. The contrbuton to HbA1c from RBCs aged j days s then: α j = p j 1 ( α j 1 + γσ ( ρj 1 α j 1 )), the contrbuton of already glycated hemoglobn molecules n survvng erythrocytes plus the contrbuton from newly formed HbA1c. Total rato s then calculated wth: α HbA1 C = 100 ρ Abbrevatons AEL, average erythrocyte lfe span; CGM, contnuous glucose montor; MBG, mean blood glucose;, maxmum erythrocyte lfe span; RBC, red blood cell. Acknowledgments MBDR thanks the revewers of ths manuscrpt for ther valuable nput and tme. Declaraton of Conflctng Interests The author(s) declared no potental conflcts of nterest wth respect to the research, authorshp, and/or publcaton of ths artcle. Fundng The author(s) receved no fnancal support for the research, authorshp, and/or publcaton of ths artcle. References 1. Bunn HF, Haney D, Kamn S, Gabbay K, Gallop P. The bosynthess of human hemoglobn A1c. Slow glycosylaton of hemoglobn n vvo. J Cln Invest. 1976;57(6): Dabetes Control and Complcatons Tral Research Group. The effect of ntensve treatment of dabetes on the development

5 Beltran del Ro et al 1307 and progresson of long-term complcatons n nsuln-dependent dabetes melltus. N Engl J Med. 1993;329(14): Tahara Y, Shma K. Knetcs of HbA1c, glycated albumn, and fructosamne and analyss of ther weght functons aganst precedng plasma glucose level. Dabetes Care. 1995;18(4): Freeman DL. Harrson s prncples of nternal medcne. JAMA. 2001;286(8): Internatonal Expert Commttee. Internatonal Expert Commttee report on the role of the A1C assay n the dagnoss of dabetes. Dabetes Care. 2009;32(7): Lledó-García R, Mazer NA, Karlsson MO. A sem-mechanstc model of the relatonshp between average glucose and HbA1c n healthy and dabetc subjects. J Pharmacoknet Pharmacodyn. 2013;40(2): Sh K, Tahara Y, Noma Y, Yasukawa K, Shma K. The response of glycated albumn to blood glucose change n the crculaton n streptozotocn-dabetc rats comparson of theoretcal values wth expermental data. Dabetes Res Cln Pract. 1992;17(3): Tahara Y, Shma K. The response of GHb to stepwse plasma glucose change over tme n dabetc patents. Dabetes Care. 1993;16(9): Gould BJ, Dave SJ, Yudkn JS. Investgaton of the mechansm underlyng the varablty of glycated haemoglobn n non-dabetc subjects not related to glycaema. Cln Chm Acta. 1997;260(1): Kovatchev BP, Cox DJ, Straume M, Farhy LS. Assocaton of self-montorng blood glucose profles wth glycosylated hemoglobn n patents wth nsuln-dependent dabetes. Methods Enzymol. 1999;321: Cohen RM, Holmes YR, Chener TC, Joner CH. Dscordance between HbA1c and fructosamne evdence for a glycosylaton gap and ts relaton to dabetc nephropathy. Dabetes Care. 2003;26(1): Derr R, Garrett E, Stacy GA, Saudek CD. Is HbA1c affected by glycemc nstablty? Dabetes Care. 2003;26(10): Nuttall FQ, Gannon MC, Swam WR, Adams MJ. Stablty over tme of glycohemoglobn, glucose, and red blood cell survval n hematologcally stable people wthout dabetes. Metabolsm. 2004;53(11): Osterman-Golkar SM, Vesper HW. Assessment of the relatonshp between glucose and A1c usng knetc modelng. J Dabetes Complcatons. 2006;20(5): Inaba M, Okuno S, Kumeda Y, et al. Glycated albumn s a better glycemc ndcator than glycated hemoglobn values n hemodalyss patents wth dabetes: effect of anema and erythropoetn njecton. J Am Soc Nephrol. 2007;18(3): Nathan D, Turgeon H, Regan S. Relatonshp between glycated haemoglobn levels and mean glucose levels over tme. Dabetologa. 2007;50(11): Nathan DM, Kuenen J, Borg R, Zheng H, Schoenfeld D, Hene RJ. Translatng the A1C assay nto estmated average glucose values. Dabetes Care. 2008;31(8): Makrs K, Spanou L. Is there a relatonshp between mean blood glucose and glycated hemoglobn? J Dabetes Sc Technol. 2011;5(6): Hggns PJ, Bunn HF. Knetc analyss of the nonenzymatc glycosylaton of hemoglobn. J Bol Chem. 1981;256(10): Mortensen HB, Chrstophersen C. Glucosylaton of human haemoglobn a n red blood cells studed n vtro. Knetcs of the formaton and dssocaton of haemoglobn A 1c. Cln Chm Acta. 1983;134(3): Mortensen HB, Vølund A, Chrstophersen C. Glucosylaton of human haemoglobn a. dynamc varaton n HbA 1c descrbed by a boknetc model. Cln Chm Acta. 1984;136(1): Svendsen PA, Chrstansen JS, Søegaard U, Nerup J. Synthess of glycosylated haemoglobn n vvo. Dabetologa. 1981;21(6): Russo V, Barker-Gear R, Gates R, Franco R. Studes wth botnylated RBC: (1) use of flow cytometry to determne posttransfuson survval and (2) solaton usng streptavdn conjugated magnetc beads. In: Magnan M, DeLoach JR, eds. The Use of Resealed Erythrocytes as Carrers and Boreactors. New York, NY: Sprnger; 1992: Kumpel B, Austn E, Lee D, Jackson D, Judson P, Chapman G. Comparson of flow cytometrc assays wth sotopc assays of 51chromum-labeled cells for estmaton of red cell clearance or survval n vvo. Transfuson. 2000;40(2): Vrtue MA, Furne JK, Nuttall FQ, Levtt MD. Relatonshp between GHb concentraton and erythrocyte survval determned from breath carbon monoxde concentraton. Dabetes Care. 2004;27(4): Cohen RM, Franco RS, Khera PK, et al. Red cell lfe span heterogenety n hematologcally normal people s suffcent to alter HbA1c. Blood. 2008;112(10): Beach KW. A theoretcal model to predct the behavor of glycosylated hemoglobn levels. J Theoret Bol. 1979;81(3): Beltrán del Río M, Georgev GI, Cercone R, Twar M, Rlo HL. Contnuous glucose montorng analyss as predctor of slet yeld and nsuln requrements n autologous slet transplantaton after complete pancreatectomy. J Dabetes Sc Technol. 2014;8(6): Lledó-García R, Kalck RM, Uehlnger DE, Karlsson MO. Modelng of red blood cell lfe-spans n hematologcally normal populatons. J Pharmacoknet Pharmacodyn. 2012;39(5): Ladyżyńsk P, Wójcck JM, Bak M, et al. Valdaton of hemoglobn glycaton models usng glycema montorng n vvo and culturng of erythrocytes n vtro. Ann Bomed Eng. 2008;36(7): Kefer CR, Snyder LM. Oxdaton and erythrocyte senescence. Curr Opn Hematol. 2000;7(2): Lutz H. Innate mmune and non-mmune medators of erythrocyte clearance. Cell Molec Bol. 2004;50(2):