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Linear nonisothermal, single-step, stability studies of dried preparations of influenza virus
(‘KYoInoLow,
9, 34-47 (1972)
Linear
Nonisothermal, Single-Step, Stability Studies Dried Preparations Of Influenza Virus1
(/‘I’) (r/Y/t/t) for the left’ side of Eq. (1) and intcgratinp wr obtain
We have shown recently t’hat a m&ematic model bawd on isothermal kinetics can be used t)o predict the st,abilities of viruses dried b,- sublimitation of ice in vacua (S-10). The mcthodologies developrd for viruses have been used also to determine the stabilities of dried bacterial prcparations (4, 5). IJnfortunatela-, isothermal inactiT~ations require 3-G wreks t,o prrform and it is frequently necessary t,o carry out several preliminary experiments to det)ermine the fixed low and high temperatures of inactivation. A more rapid means of thermal inactivation requiring a single experiment, for estimating stabilit,ies of drird preparations would he advantageous. Since first introduced in 1963 to answer the objections above (12), the field of nonisothermal kinetic~s has grown considerably (2, 3, G, 11, 13). The prcsrnt studies were undertaken to test, the feasibility of application of t,lif constructs of nonisot,hcrmal kinetics to prcdictjing the stabilitics of dried preparations of biologic ent,ities (influenza virus)
1,) ?I! = - ; 2/l
k(T)y,
1972 by .\cudemir
Press.
Inc.
(2)
in Eq. (3) ~iclcls
(1)
taking the anti-log of both sides of Eq. (5) and substituting T for 7’, and k(T) for X:(7’,), we obtSain
(6)
Received December 6, 1971. ‘These studies were support,ed, in part, by Contract NIH-69-2070 from t,he Infectious Disease Branch, National Institute of Allergy and Infectious Diwases of the National Institutes of Health. 0
lit
where: HI t’erm is t,he increase in cnthnlpy per mole necessary to raise the rew+ants to n state of activation. -4ssuming that a,+, nctivntion energy, has a const,ant value for a given virus and is independent, of tcmperat,urc and wing the identit,!;
where d!/ is t,he change in concentration of active virus, dt is the change in time, k(T) is the rcnction rat,c constant as a funct’ion of absolute temperature (2’)) and y is titer of virus at a given time (t). Substituting the identity -(dy/
Copyright
k(T) J T1
(3)
Because the reaction rate constant (A) of the equation for a first-order renct’ion is a function of temperature, this relat.ionship may be expressed as =
T2
In the prcscnt irivcstjigation our wvnt,er baths wcrc heated in :I linear manner. Therefore, t,he term dT/tlt is equal to the heating rate constant (6). It, is important’ to not,e that. any heating rate (linear, exponential, logarithmic, etc.) ma? be used. provided dT/dt can lw cvalnatctl for :I given temperature. Starting with the Van’t Hoff rcluation for the tc~mpcrnt~urr ~orffi&iit~ of the equilibrium constant, Arhennius pointed out that a reasonable csl)ression of the relation of t,lie rate constant to tcmpcmture ww
THEORETICAL
--(dy/rlt
Of
mhirh gives the reaction rate constant,, k(T) as a function of temperature and the initial reaction rate constant, li (T,) . 34
Y2 t2
Y2
El
zy, 13~ iutc~gr:ating the equation for :I first-order reaction, WC obtain tlw value for k (T,) of tllo initial iwt~hcrm:il portion of tlic cwrvc of dcgr;ldntiou of dried virus:
----
YIJ O to toq
I
lc(T3) = (In u. - In ?/2)l12
(0)
Bcc:u~~c Eq. (i) clots not have a closed form whit ion, :I Fortrnn IV program TVXS written which mlmcricnll~ int,egrates t,he right-hand side of Eq. (7) for :L trial wlue of H:/‘R. The opcr;\for wmp:wes tjhc t,rial wluc of HQR used in t,lle right-hand side of Eq. (i) with the experimentally determined value of the left,-hand side of Kq. (7) This procedure is rcpcnted imt~il :\ vnluc for ZIf/R is found which sntisfies the rquality csprcsscd by Eq. (i). The wluc of H:/‘R found to ,wtkt”y Eq. (T) is used in Eq. (6) to determilw I: (7’) The flow dingr:lm for computer solution of the cquntions giwii :d~ovc~ i:: :lvaihlh from thr author (D.G.)
y,t*
I:
TO
Tlw initinl reaction rate conhnt. 1;(T,), rccpkwl to sat,isfy Eq. (8) depends on dntj:l derived from isothermal inartivnt,ion. It wx? ncwxs;:trv. tlicwforc. to develop nn aI~prosimntion for tllc initial rat,e constant bawd on nonisothermal tl:lt:L. To do t,his, we :wsumcd tjllatj k (T,) is :I linc:rr fwwtion of tcmpcrxture. From our cht:l we plotted the contiguous t,ime-tempernturc sots vcr~us virus titer (Fig. 1). The arex of the gr:\ril delimited by t,, yl, !/,C,, t2, k proportional to tlic :trtivation energ\- at isot~lwrmnl tcmperntllrcls: the are:1 clelimit,ed 1,~ t,,, y.‘fs, t, proportional to activation euerg~ at8 iioiiiiothrmnl cwnditions. The areas under each curve are (~p11 proviclrd: (1) ?‘,, and T, are rchtivcl) r~losc!; (2) TL = [(T? - T,,)/“] + T,,; :1nd (3) t, = [(t- - r,,)/2] + t,,. If the vonditious nbovcl arc s:~tisfied, :\d thy wcw iti tlic prowit ~liitl!~,
-----
5 T To < T, < T2
t,Tlme T2 Temp Yo>Y 12'Y
Frc:. 1. Kolntionshi~~ of nctivation enfvgirs ior isothcrm:il :mtl nonkothermnl tcmpc~rnturrs in wlniion lo tlcclinrs in litvra of dried influc~nxn view. TV:ISdcrivr~tl from tlic mctl~odolog~ usccl for cnlcwlating the hlf-life of r:\tlio:~ctix m:~tcri:~l.
To test th mntl~rm:~tirnl procedures outlined previously, ;I w-atcr hnt~li progr:u~imed to licnt in ;t line;tr m:mucr WS dcvc~lopcd. This wn~ acromplishr~tl I,\- att:rching n syncllronorw Telcchron motor to’ tlic rcqlating lw:~tl of the Bronwill :rpp:rratus tlicrmorcgul:ltor - licntcr - circuht or (Fig. 2). Tlw Tckchron motor used in the prescwt studies incrtwcd the tcmlwratjurc of the 1~111at th ratr of 0.0135°C/min. Oiw-milliliter wnplcs of influriiz:i virus su+ peuclcd iu cxlcium lactobionnte I%, + serum all)umin. human. 1’; wrr dried by anhlimat~ion of ice ill ~YKU~ to a rwidunl mokturc cvntcnt ol’ 0.65/o (!)) The witcr bath ws lientcd to 35°C :iritl all ~:~niplcs i;ihmc~rgerl xt this tcmprr:tturr. Tllc wnpka rtm:\incd at 1hid tcmlwraturc for 30 miu to allow them to come‘ into cvluilibirum with the thrm;tl environment of the bnth; nt, the cwtl of 30 mill, tlirc>c a:miplcs ww rcmovrd. After tlw wmo\-nl of th initial wmplcs, (0 timcx), tllca :11)I):ir;\tus was i;tnrtccl :rncl the s:implw wcLr(’ rcmowd 3s wcpicnti:d temperntjurc incare:ldcsof 5°C (400 niiri clnpml hrnc) All snmpies wcw Aored at :I -iO”C until teAed for xctivitiw. Th results are shown in Table 1. .4pl)l+ig the mtlthem:itic nnnl\-sk outlined I)wvioll~l~. tlics li (?‘) v:llllw for ~cwral trmpern-
3G
CREIFF
AND GREIFF test based on isothermal kinetics for predicting the &abilities of preparations of influenza virus dried to different contents of residual moist,ure and sealed under vacuum (9). To test the total syst,em developed for predict,ing the stabilities of dried preparations of influenza virus inactivated in a linearly programmed tcmpcrature bat)h, snmplcs of dried virus were placed at +lO”, +20”, and +4O”C and removed at, the t,imes predicted for thrse sampler to losr 1 log of titer, 38 days, lS.6 days, :and 6.8 days, rcspectivcly. Within the experimcnt’nl error of the method used for determining titers, t)he sample:: tested lost 1 log of titer at the timcz: prcdictrd for a prrstkt~ed temperature of storagcb. I)ISCIJSSIOS
Fro. 2. Appnralns for nonisothermal heating (linear) of dried influenza virus preparation. A. Water bath. 13. Thcnnor~gul:rtor-hrntcr-circ,ulntor apIxw:ltw (Bromnill). C. S,vnclrronous Telwhron motor. TABLE
1
THIS: TITERS OF DRIED PRIW.LR.~TIOLVS OF INFLUISNZS VIRUS AFTER IMMERSION IN .I LINFXI~ NONISOTHERM.\L TEMPRR.ZTUILI~: BETH .ZND RI.:MOVED AT 5°C INCREMI~XT INCRX~SES IN TE:MPER.kTURE --
--
The method of exaggerating tjempcratures to accelerate the degradation of biologic entities or organic compounds is used frequently to compile data necessary to predict mathematically the stabilities of these materials. The literature is replete with examples of both the use and usefulness of this tcchniyue. The basic procedure, that of determining the concentration indepcndcnt, rat,e constant at several t8cmperaturcs, calculating art,ivation energies, and then predicting t,he rates of chnnge when stored at different temperatures, has changed or improved little since first developed (1, 7). Classical isothermic kinetic studies for determining the energies of nctivation have several drawbacks: (a) t’he relaTABL15 2 C.ILCUL.ZTED VALUES FOR k(T) .\ND THE PIMP+ DICTED TIMES TO LOSE 1 LOG OF TITEH BASED ON EONISOTHI<;RMAL KIXI~:TICS
~~ 0 400 805 1200 1595 2000
35 40 45 50 55 60
10-7.“” 10-7.00 10-6.5” 10-G.5:* 10-4.3” 10-3.A8
tures in the times predicted for our preparations to lose 1 log of titer if stored at these temperatures were calculated (Table 2). The values for k(T) and t_, ,Opwere within the range of values found in our studies using an accelerated storage
Isothermal (P:q. 9) +40 Nonisothermal (I
+20 +10 0 -10 -20
0.339 6) 0.523 0.333 0.206 0.123 0.071 0.039 0.021 0.010
6.89 4.39 6.89 11.14 18.60 32.20 58.03 109.36 216.69
9, 34-47 (1972)
Linear
Nonisothermal, Single-Step, Stability Studies Dried Preparations Of Influenza Virus1
(/‘I’) (r/Y/t/t) for the left’ side of Eq. (1) and intcgratinp wr obtain
We have shown recently t’hat a m&ematic model bawd on isothermal kinetics can be used t)o predict the st,abilities of viruses dried b,- sublimitation of ice in vacua (S-10). The mcthodologies developrd for viruses have been used also to determine the stabilities of dried bacterial prcparations (4, 5). IJnfortunatela-, isothermal inactiT~ations require 3-G wreks t,o prrform and it is frequently necessary t,o carry out several preliminary experiments to det)ermine the fixed low and high temperatures of inactivation. A more rapid means of thermal inactivation requiring a single experiment, for estimating stabilit,ies of drird preparations would he advantageous. Since first introduced in 1963 to answer the objections above (12), the field of nonisothermal kinetic~s has grown considerably (2, 3, G, 11, 13). The prcsrnt studies were undertaken to test, the feasibility of application of t,lif constructs of nonisot,hcrmal kinetics to prcdictjing the stabilitics of dried preparations of biologic ent,ities (influenza virus)
1,) ?I! = - ; 2/l
k(T)y,
1972 by .\cudemir
Press.
Inc.
(2)
in Eq. (3) ~iclcls
(1)
taking the anti-log of both sides of Eq. (5) and substituting T for 7’, and k(T) for X:(7’,), we obtSain
(6)
Received December 6, 1971. ‘These studies were support,ed, in part, by Contract NIH-69-2070 from t,he Infectious Disease Branch, National Institute of Allergy and Infectious Diwases of the National Institutes of Health. 0
lit
where: HI t’erm is t,he increase in cnthnlpy per mole necessary to raise the rew+ants to n state of activation. -4ssuming that a,+, nctivntion energy, has a const,ant value for a given virus and is independent, of tcmperat,urc and wing the identit,!;
where d!/ is t,he change in concentration of active virus, dt is the change in time, k(T) is the rcnction rat,c constant as a funct’ion of absolute temperature (2’)) and y is titer of virus at a given time (t). Substituting the identity -(dy/
Copyright
k(T) J T1
(3)
Because the reaction rate constant (A) of the equation for a first-order renct’ion is a function of temperature, this relat.ionship may be expressed as =
T2
In the prcscnt irivcstjigation our wvnt,er baths wcrc heated in :I linear manner. Therefore, t,he term dT/tlt is equal to the heating rate constant (6). It, is important’ to not,e that. any heating rate (linear, exponential, logarithmic, etc.) ma? be used. provided dT/dt can lw cvalnatctl for :I given temperature. Starting with the Van’t Hoff rcluation for the tc~mpcrnt~urr ~orffi&iit~ of the equilibrium constant, Arhennius pointed out that a reasonable csl)ression of the relation of t,lie rate constant to tcmpcmture ww
THEORETICAL
--(dy/rlt
Of
mhirh gives the reaction rate constant,, k(T) as a function of temperature and the initial reaction rate constant, li (T,) . 34
Y2 t2
Y2
El
zy, 13~ iutc~gr:ating the equation for :I first-order reaction, WC obtain tlw value for k (T,) of tllo initial iwt~hcrm:il portion of tlic cwrvc of dcgr;ldntiou of dried virus:
----
YIJ O to toq
I
lc(T3) = (In u. - In ?/2)l12
(0)
Bcc:u~~c Eq. (i) clots not have a closed form whit ion, :I Fortrnn IV program TVXS written which mlmcricnll~ int,egrates t,he right-hand side of Eq. (7) for :L trial wlue of H:/‘R. The opcr;\for wmp:wes tjhc t,rial wluc of HQR used in t,lle right-hand side of Eq. (i) with the experimentally determined value of the left,-hand side of Kq. (7) This procedure is rcpcnted imt~il :\ vnluc for ZIf/R is found which sntisfies the rquality csprcsscd by Eq. (i). The wluc of H:/‘R found to ,wtkt”y Eq. (T) is used in Eq. (6) to determilw I: (7’) The flow dingr:lm for computer solution of the cquntions giwii :d~ovc~ i:: :lvaihlh from thr author (D.G.)
y,t*
I:
TO
Tlw initinl reaction rate conhnt. 1;(T,), rccpkwl to sat,isfy Eq. (8) depends on dntj:l derived from isothermal inartivnt,ion. It wx? ncwxs;:trv. tlicwforc. to develop nn aI~prosimntion for tllc initial rat,e constant bawd on nonisothermal tl:lt:L. To do t,his, we :wsumcd tjllatj k (T,) is :I linc:rr fwwtion of tcmpcrxture. From our cht:l we plotted the contiguous t,ime-tempernturc sots vcr~us virus titer (Fig. 1). The arex of the gr:\ril delimited by t,, yl, !/,C,, t2, k proportional to tlic :trtivation energ\- at isot~lwrmnl tcmperntllrcls: the are:1 clelimit,ed 1,~ t,,, y.‘fs, t, proportional to activation euerg~ at8 iioiiiiothrmnl cwnditions. The areas under each curve are (~p11 proviclrd: (1) ?‘,, and T, are rchtivcl) r~losc!; (2) TL = [(T? - T,,)/“] + T,,; :1nd (3) t, = [(t- - r,,)/2] + t,,. If the vonditious nbovcl arc s:~tisfied, :\d thy wcw iti tlic prowit ~liitl!~,
-----
5 T To < T, < T2
t,Tlme T2 Temp Yo>Y 12'Y
Frc:. 1. Kolntionshi~~ of nctivation enfvgirs ior isothcrm:il :mtl nonkothermnl tcmpc~rnturrs in wlniion lo tlcclinrs in litvra of dried influc~nxn view. TV:ISdcrivr~tl from tlic mctl~odolog~ usccl for cnlcwlating the hlf-life of r:\tlio:~ctix m:~tcri:~l.
To test th mntl~rm:~tirnl procedures outlined previously, ;I w-atcr hnt~li progr:u~imed to licnt in ;t line;tr m:mucr WS dcvc~lopcd. This wn~ acromplishr~tl I,\- att:rching n syncllronorw Telcchron motor to’ tlic rcqlating lw:~tl of the Bronwill :rpp:rratus tlicrmorcgul:ltor - licntcr - circuht or (Fig. 2). Tlw Tckchron motor used in the prescwt studies incrtwcd the tcmlwratjurc of the 1~111at th ratr of 0.0135°C/min. Oiw-milliliter wnplcs of influriiz:i virus su+ peuclcd iu cxlcium lactobionnte I%, + serum all)umin. human. 1’; wrr dried by anhlimat~ion of ice ill ~YKU~ to a rwidunl mokturc cvntcnt ol’ 0.65/o (!)) The witcr bath ws lientcd to 35°C :iritl all ~:~niplcs i;ihmc~rgerl xt this tcmprr:tturr. Tllc wnpka rtm:\incd at 1hid tcmlwraturc for 30 miu to allow them to come‘ into cvluilibirum with the thrm;tl environment of the bnth; nt, the cwtl of 30 mill, tlirc>c a:miplcs ww rcmovrd. After tlw wmo\-nl of th initial wmplcs, (0 timcx), tllca :11)I):ir;\tus was i;tnrtccl :rncl the s:implw wcLr(’ rcmowd 3s wcpicnti:d temperntjurc incare:ldcsof 5°C (400 niiri clnpml hrnc) All snmpies wcw Aored at :I -iO”C until teAed for xctivitiw. Th results are shown in Table 1. .4pl)l+ig the mtlthem:itic nnnl\-sk outlined I)wvioll~l~. tlics li (?‘) v:llllw for ~cwral trmpern-
3G
CREIFF
AND GREIFF test based on isothermal kinetics for predicting the &abilities of preparations of influenza virus dried to different contents of residual moist,ure and sealed under vacuum (9). To test the total syst,em developed for predict,ing the stabilities of dried preparations of influenza virus inactivated in a linearly programmed tcmpcrature bat)h, snmplcs of dried virus were placed at +lO”, +20”, and +4O”C and removed at, the t,imes predicted for thrse sampler to losr 1 log of titer, 38 days, lS.6 days, :and 6.8 days, rcspectivcly. Within the experimcnt’nl error of the method used for determining titers, t)he sample:: tested lost 1 log of titer at the timcz: prcdictrd for a prrstkt~ed temperature of storagcb. I)ISCIJSSIOS
Fro. 2. Appnralns for nonisothermal heating (linear) of dried influenza virus preparation. A. Water bath. 13. Thcnnor~gul:rtor-hrntcr-circ,ulntor apIxw:ltw (Bromnill). C. S,vnclrronous Telwhron motor. TABLE
1
THIS: TITERS OF DRIED PRIW.LR.~TIOLVS OF INFLUISNZS VIRUS AFTER IMMERSION IN .I LINFXI~ NONISOTHERM.\L TEMPRR.ZTUILI~: BETH .ZND RI.:MOVED AT 5°C INCREMI~XT INCRX~SES IN TE:MPER.kTURE --
--
The method of exaggerating tjempcratures to accelerate the degradation of biologic entities or organic compounds is used frequently to compile data necessary to predict mathematically the stabilities of these materials. The literature is replete with examples of both the use and usefulness of this tcchniyue. The basic procedure, that of determining the concentration indepcndcnt, rat,e constant at several t8cmperaturcs, calculating art,ivation energies, and then predicting t,he rates of chnnge when stored at different temperatures, has changed or improved little since first developed (1, 7). Classical isothermic kinetic studies for determining the energies of nctivation have several drawbacks: (a) t’he relaTABL15 2 C.ILCUL.ZTED VALUES FOR k(T) .\ND THE PIMP+ DICTED TIMES TO LOSE 1 LOG OF TITEH BASED ON EONISOTHI<;RMAL KIXI~:TICS
~~ 0 400 805 1200 1595 2000
35 40 45 50 55 60
10-7.“” 10-7.00 10-6.5” 10-G.5:* 10-4.3” 10-3.A8
tures in the times predicted for our preparations to lose 1 log of titer if stored at these temperatures were calculated (Table 2). The values for k(T) and t_, ,Opwere within the range of values found in our studies using an accelerated storage
Isothermal (P:q. 9) +40 Nonisothermal (I
+20 +10 0 -10 -20
0.339 6) 0.523 0.333 0.206 0.123 0.071 0.039 0.021 0.010
6.89 4.39 6.89 11.14 18.60 32.20 58.03 109.36 216.69