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1 This rtile ppered in journl pulished y Elsevier. The tthed opy is furnished to the uthor for internl non-ommeril reserh nd edution use, inluding for instrution t the uthors institution nd shring with ollegues. Other uses, inluding reprodution nd distriution, or selling or liensing opies, or posting to personl, institutionl or third prty wesites re prohiited. In most ses uthors re permitted to post their version of the rtile (e.g. in Word or Tex form) to their personl wesite or institutionl repository. Authors requiring further informtion regrding Elsevier s rhiving nd mnusript poliies re enourged to visit:

2 Author's personl opy Soil Biology & Biohemistry () 35 Contents lists ville t SieneDiret Soil Biology & Biohemistry journl homepge: Ammonium versus nitrte nutrition of Ze mys nd Lupinus lus: Effet on root-derived CO efflux Olg Gvrihkov, *, Ykov Kuzykov Deprtment of Forest Environment nd Resoures, University of Tusi, vi S. Cmillo de Lellis, 11 Vitero, Itly Deprtment of Agroeosystem Reserh, University of Byreuth, 95 Byreuth, Germny rtile info strt Artile history: Reeived 1 Jnury Reeived in revised form 9 July Aepted August Aville online 3 August Keywords: Lupinus lus Ze mys CO efflux Nitrogen fertiliztion Nitrte redution 1 C leling Root respirtion Rhizosphere Identifition of the mehnisms ontriuting to nitrogen (N) fertilizer-indued hnges in CO efflux from soil under griulturl rops hs een extremely hllenging euse of diffiulties in seprting root nd miroil ontriution to totl CO efflux. In this study we present the evidene tht high osts of nitrte redution result in strong inrese of root-derived respirtion nd the mgnitude of n inrese differs etween the speies with vrious ontriution of shoots nd roots to the nitrte redution proess. Fertiliztion of Lupinus lus nd Ze mys with nitrte or mmonium nd pulse leling of plnts in 1 CO tmosphere llowed evlution of the effet of N type on totl nd reently ssimilted CO efflux from soil. Addition of nitrte to plnted soil inresed reently ssimilted CO efflux y 1% in Lupinus lus (nitrte redution site in roots) nd y 11% in Ze mys (nitrte redution site oth, in shoots nd roots) in omprison with ontrol. Ammonium-indued CO inrese mounted for % in Lupinus lus nd for 73% in Ze mys. Cler diurnl hnges in CO efflux from plnted soil t onstnt dy/night temperture showed fst response of elow-ground proesses to photosynthesis. Both pprohes for root-derived CO ssessment: 1 C pulse leling nd differene of CO from plnted nd unplnted soil showed similr results: the form of N supply nd the lotion of the nitrte redution site hve strong signifint effet on the mount of root-derived CO respirtion. Ó Elsevier Ltd. All rights reserved. 1. Introdution The nitrogen (N) requirements of plnts n e met y oth nitrte (NO 3 ) nd mmonium (NH þ ) ion ssimiltion (Ls et l., ). Utiliztion of nitrogen in either form my ffet the rohydrte metolism nd energy eonomy of the plnt (Blquiere, 197). NO 3 ions n e umulted in vuoles, nd so most plnt speies n trnsport nitrtes to leves for redution nd ssimiltion nd re le to tolerte high nitrte onentrtions without ny sign of toxiity. However, NH þ slts sored y the plnt must e rpidly metolized into orgni nitrogen ompounds s mny plnts tolerte few or no exess mmonium ions (Brker et l., 199; Chillou et l., 199). So lmost ll NH þ ions re ssimilted in roots. This differene in the site for N ssimiltion leds to differene in the demnd of ron (C) skeletons, whih re provided in prt y the phosphorylting ytohrome (TCA) yle, nd hene to differene in the respirtion rte (Ls et l., ). However, there re still tive detes on the effet of the N soure on root respirtion, s ttempts to explin it experimentlly * Corresponding uthor. Tel.: þ ; fx: þ E-mil ddress: olhik@unitus.it (O. Gvrihkov). hve led to rgule results supporting different hypotheses. Some uthors suggest tht, when ompred to NO þ 3 nutrition, NH nutrition stimultes the rte of root respirtion, ttriuting this inrese to the stimultion of lterntive pthwy tivity (Brneix et l., 19; Blquiere, 197; Ls et l., ). There re two pthwys involved in respirtion: the phosphorylting ytohrome nd the non-phosphorylting lterntive pthwy. The physiologil role of the ltter is not ler ut severl uthors suggest tht this lterntive pthwy ould void the overredution of the eletron trnsport hin nd the susequent prodution of retive oxygen speies (Purvis nd Shewfelt, 1993). Thus, this pthwy ould llow oxidtion of TCA yle redutnt, mintining TCA yle ron flow for provision of iosyntheti intermedites for NH þ ion ssimiltion. On the other hnd, NO 3 oming to the plnt efore ssimiltion hve to e firstly redued to NH þ, nd this proess, together with ssimiltion, is mong the most energy-intensive proesses in plnts, in some ses followed y n dditionl CO evolution (Atkins et l., 1979; Aslm nd Huffker, 19; Ninomiy nd Sto, 19; Wrner nd Kleinhofs, 199; Blquiere, 197; Tishner, ). The proess proeeds in two steppes: onversion of NO 3 to NO nd the following onversion of NO to NH þ. In illuminted 3-717/$ see front mtter Ó Elsevier Ltd. All rights reserved. doi:1.11/j.soilio...3

3 Author's personl opy 3 O. Gvrihkov, Y. Kuzykov / Soil Biology & Biohemistry () 35 leves, these proesses re oupled to photosyntheti eletron trnsport. However, in roots nd during drkness, reduing equivlents re generted y oxidtion of rohydrtes with susequent evolution of CO (Aslm nd Huffker, 19; Ninomiy nd Sto, 19). Depending on the speies, the site of NO 3 redution ould e loted in shoots or roots (Andrews, 19; Oks nd Hirel, 195; Pte nd Lyzell, 199; Shilling et l., ; Silveir et l., 1; Vuylsteker et l., 1997). By this property, plnts re divided into three groups: speies reduing NO 3 predominntly in roots, speies reduing NO 3 predominntly in shoots, nd those tht do oth. The C osts for redution of NO 3 to NH þ depend on the site of nitrte redution in plnts. In this study we use the term root-derived CO for the sum of tul root respirtion nd CO derived from miroil tivity in the immedite viinity of the root (rhizomiroil respirtion) nd SOM-derived respirtion for CO evolved fter miroil deomposition of soil orgni mtter in root free soil. We seleted mize nd lupine sine the two speies hve different sites of nitrte redution: Ze mys redues hlf of the NO 3 in shoots nd hlf in roots nd Lupinus lus redues the mjor prt of the NO 3 in roots (Pte, 1973). The ojetive of the present work ws to onfirm or refute tht feeding lupine nd mize with NH þ redues rootderived efflux from soil ompred to feeding with NO 3. Three nitrogen tretments were pplied to eh speies: nitrte fertilizer, mmonium fertilizer, nd ontrol tretment without ny N fertilizer. A nitrifition inhiitor ws used to prevent miroil onversion of NH þ to NO 3 in soil. Pulse leling of plnts in 1 CO tmosphere ws pplied to quntify the effet of oth fertilizers on reently ( 1 C) nd totl ssimilted C. The differene etween totl CO efflux from the plnt-soil system nd miroil respirtion from re soil inuted t the sme onditions ws ompred with the results of the prinipl method of leling for root-derived CO quntifition.. Mterils nd methods.1. Soil The soil, lomy Hpli Luvisol, ws tken from the top 1 m (Ap horizon) of the Krlshof long-term field experimentl sttion of the University of Hohenheim. Soil smples were ir dried, mixed nd pssed through 5 mm sieve. The soil ontined 1.5% C tot nd.1% N tot, with.9% snd, 7.5% silt nd.% ly; its ph ws.5... Plnts nd growth onditions Centrifuge tues of 5 ml were filled with 5 g of soil eh nd were used for growing the plnts. Twenty four pots remined unplnted to mesure miroil respirtion from re soil. Seeds of mize (Ze mys L.) nd lupine (Lupinus lus L.) were germinted on moist filter pper in Petri dishes for dys. Germinted seedlings were trnsplnted to the PVC pots, with one seedling per pot, nd were grown under ontrolled lortory onditions with 1 h/1 h dy/night period t onstnt dy nd night temperture of 5.5 C, nd with photosynthetilly tive rdition (PAR) intensity of pproximtely mmol m 1 s 1 t the top of the plnt nopy. A onstnt dy/night temperture ws hosen to void the effets of hnging temperture on CO fluxes. During the experiment, soil wter ontent in eh pot ws mintined grvimetrilly t out % of the ville field pity y heking its weight dily. Before the leling, the wekest plnts were eliminted nd only twenty-four plnts similr in development nd height were hosen for the following tretments. Pots with re soil were exposed to the sme inuting onditions C leling nd N pplition Two speies were leled with 1 C: 1 plnts of mize were hosen nd leled in the morning on the th dy fter germintion; 1 plnts of lupine were leled on the 3th dy fter germintion. One dy efore the leling, the top of eh pot ws seled with silione pste (NG 317 from Thuer nd Co., Dresden, Germny). The sel ws tested for ir leks. Pumping the ir through the soil olumn flushed out the CO umulted in the soil during the plnt s growth. Three nitrogen tretments were pplied h efore 1 C leling: () nitrte tretment, with 15 NsK 15 NO 3 ; () n mmonium tretment, with 15 N s ( 15 NH ) SO ; nd () ontrol vrint without ny dded nitrogen. Four plnts of eh speies were exposed to eh N tretment ( 15 N enrihment 5 tom %). Diyndimide (DCD) t mg kg 1 soil ws pplied in solution with 15 N fertilizer to ll the tretments in order to hieve n effetive nitrifition inhiition throughout the soil olumn (in the mmonium tretment) nd to lne the side effets of the inhiitor (in the nitrte nd ontrol tretments). The mount of 15 N pplied to pot ws lulted to produe n verge onentrtion of mg of N kg 1 for eh N speies dded. Four unplnted pots were fertilized with hlf mount of nitrte or mmonium to estimte the effet of N fertiliztion on respirtion of soil miroorgnisms. The 1 C leling proess hs een desried in detil y Kuzykov et l. (1999) nd Kuzykov nd Cheng (1) nd Domnski et l. (1). Briefly, seled pots with plnts were put in plexigls hmer, 1 CO ws introdued to the hmer y dding 1 ml of 5 M H SO to N 1 CO 3 (1.5 MBq) solution. This llowed omplete evolution of 1 CO into the hmer tmosphere. After h-leling period, trpping of CO from the hmer through 1 ml of 1 M NOH solution ws strted to remove the remining unssimilted 1 CO. Then the hmer ws opened. Pots with the plnts were onneted to n output of memrne pumps y tues: ir ws pumped through every single pot from ottom to top. Another tue ws onneting eh pot to CO trpping tue, filled with 3 ml of 1 M sodium hydroxide (NOH) solution. The output of the trpping tue ws onneted to the input of the memrne pump. Therefore, the ir ontining CO evolved from the soil respirtion ws irulting in losed system: from the plnt-soil system to the trpping solution to the memrne pump nd k to the plnt-soil system... Smpling nd nlyses NOH in the trpping tues ws hnged for the first time h fter the leling nd then twie dy, in the morning nd in the evening, for dys fter the leling, with the im of olleting CO evolved in the rhizosphere during dy- nd night-periods. NOH trps were nlyzed for totl ronte ontent nd for 1 C tivity. The 1 C tivity ws mesured in 1 ml liquots of NOH with ml of the sintilltion oktil EoLite þ (ICN) fter the dey of hemiluminesene y liquid sintilltion ounter (MiroBet, TriLux). Totl ssimilted 1 CO ws determined s differene etween the 1 CO dded to the leling hmer nd the 1 CO reovered from the solution with the remining unssimilted 1 CO. To estimte totl CO efflux from the soil, CO trpped in NOH solution ws preipitted with.5 M rium hloride (BCl ) solution nd then NOH ws titrted with.1 M hydrohlori id (HCl) ginst phenolphthlein inditor (Ziilske, 199). On the th dy fter eh leling, ll the plnts were hrvested: eh shoot ws ut t the se, the lid of the pot ws opened, nd eh root-soil olumn ws pulled out of the pot. Roots were refully

4 Author's personl opy O. Gvrihkov, Y. Kuzykov / Soil Biology & Biohemistry () wshed with deionized wter to remove soil prtiles. Shoots nd roots were dried t 7 C, weighed nd ground with ll mill (F Retsh) for nlysis of C tot,n tot, nd 15 N ontent. A totl of 3 g of soil were tken from eh soil smple, dried t 7 C nd grounded for the sme purposes. C tot,n tot, nd the isotope rtio 15 N/ 1 N in plnt nd soil smples were determined using Crlo Er NA 15 gs hromtogrph (Crlo Er Instruments, Milno, Itly) oupled on isotope rtio mss spetrometer (Delt plus IRMS 51, Finnign Mt, Bremen, Germny)..5. Sttistis The experiment ws onduted with four replites. All replites were nlyzed for 1 C, C- nd N-ontents in shoots nd roots. 1 C dt re presented s the perentge of 1 C ssimilted during exposure of plnts to the pulse leling. All dt were nlyzed with SYSTAT 11. (SPSS In.). Effets of different N tretment (no N, NH þ -N nd NO 3 -N) nd smpling time (dy nd night) were tested using two-wy nlysis of vrine (ANOVA). We hve lulted the lest signifint differene (LSD.5) in post ho Newmn Keuls test to identify differing tretments. 3. Results 3.1. Dynmis of 1 CO efflux from soil omprtment with Lupinus lus nd Ze mys Lupinus lus The mximum of isotopilly enrihed respirtion ws registered within the first h fter the strt of the leling (Fig. 1). Soon fter, the emission rte delined from the mximum levels of 3.% for ontrol, 5.% for NH þ -N, nd 7.3% for NO 3 -N of totl ssimilted 1 Cd 1 to.9% C d 1 on the 3rd dy. Rhizosphere respirtion of reently ssimilted C ( 1 C) from the soil in ll N tretments showed ler diurnl dynmis. The diurnl dynmis of reently ssimilted 1 C in respired CO were strongly pronouned for non-fertilized plnts. This is espeilly ovious fter lultion of the differenes etween N nd ontrol tretments. The mximum differene etween ontrol nd soil with dded N ws found during the night periods nd minimum vlues were found during the dy (Fig. 1). The differene etween plnts fertilized y NO 3 -N nd NH þ -N in the quntity of 1 C respired, ws highest during the first dys fter the leling. After dys lredy no signifint differenes etween N tretments were mesured (Fig. 1). Cumultive 1 C respirtion of roots nd rhizosphere miroorgnisms during dys fter the leling rehed.% of ssimilted 1 C in soil without N fertiliztion,.3% for the NH þ -N tretment, nd 9.3% for the NO 3 -N tretment (Fig. 1), nd ws signifintly different (p <.1) etween ll N tretments. The 1 C losses from the soil were relulted per unit of root iomss (Fig. ) mesured dys fter the leling. Differenes etween the mximum 1 CO emissions were hosen for the omprison etween the N tretments, s it reltes diretly to the rootderived respirtion. Although there were no signifint differenes in root iomss etween tretments (p ¼.1) (Fig. ), strong effets of N fertiliztion on reently ssimilted C in CO were oserved. Tking the ontrol tretment without N s 1% referene, the respirtion losses of 1 C from the plnt-soil system with lupine fter dys mounted to 1% under NH þ -N nd % under NO 3 -N (p <.1) Ze mys For ll N tretments, the mximum intensity of 1 CO efflux ws rehed etween nd 3 h fter 1 CO pplition (Fig. 3). The emission rte delined rpidly from the mximum levels of 3.% for NH þ -N nd ontrol, nd 5.% for NO 3 -N of totl ssimilted 1 Cd 1, 1 CO efflux intensity (% of ssimilted) differene with ontrol, % 1 CO efflux (% of ssimilted) Control NH-N 7 NO3-N %.3%.% time sine leling (d) Fig. 1. () Dynmis of 1 CO from the soil (SE) with Lupinus lus under three N tretments: ontrol, NH þ -N, nd NO 3 -N for 5.5 dys fter 1 CO pulse leling of shoots; () differenes etween ontrol without N nd soil with NO 3 -N nd NH þ -N pplied, s % of ontrol. Dy (white) nd night (gry) periods re shown; () umultive 1 CO efflux (SE) from the soil with Lupinus lus under different N tretments. to the vlue of out.9% C d 1 on the th dy. The diurnl dynmi of respired 1 C ws more lerly oserved thn in the se of lupine. The differenes etween ontrol nd soil with pplied N repeted the shpe of the lupine urve (Figs. 1 nd 3), with mximum vlues t night nd minim during the dy. The solute differene in the quntity of 1 C respired etween plnts fertilized y NO 3 -N nd NH þ -N ws gin highest during the first dys fter the leling (Fig. 3). Cumultive 1 C respired y roots nd rhizosphere miroorgnisms during the dys of the experiment rehed.% for the ontrol, nd 5.% nd 7.% for the NH þ -N nd NO 3 -N tretments respetively (Fig. 3). The differene in umultive respirtion etween the two types of N pplied ws signifint (p <.1), ut no differene ws oserved etween NH þ -N nd the ontrol (p >.5). Different N fertilizers signifintly ffeted (p <.1) root iomss of mize with lowest vlues eing.3 g for NH þ -N fertilized plnts nd the highest eing.3 g for the ontrol (Fig. ). The rtio etween tretments in the quntity of respired 1 C, s relted per unit of root iomss (Fig. ), ws similr to tht

5 Author's personl opy 3 O. Gvrihkov, Y. Kuzykov / Soil Biology & Biohemistry () 35 root iomss, g 1 C losses (% of ontrol without N),,1,1,, of lupine. Losses of 1 C from the plnt-soil system with mize rehed 173% under the NH þ -N tretment nd 1% under the NO 3 -N tretment (p <.1), gin reltive to the ontrol. 3.. Totl CO efflux from plnted soil with Lupinus lus nd Ze mys The differene etween totl CO efflux from the root-soil system nd miroil respirtion from re soil inuted t the sme onditions ws used to lulte the CO respired y roots nd ssoited rhizosphere miroorgnisms (root-derived respirtion) nd to ompre with the results from 1 C leling for root-derived CO Lupinus lus Totl nd root-derived CO efflux from the soil in ll plnted tretments showed ler diurnl dynmi (Fig. 5,). Averge totl CO respired from the plnt-soil system ws lowest for the ontrol (3.13 mg C d 1 pot 1 ), nd mounted to.3 mg C d 1 pot 1 for NH þ -N nd 5.5 mg C d 1 pot 1 for NO 3 -N. The differene in totl CO respired from soils with different types of N pplied ws signifint during the whole mesurement period (p <.5) (Fig. 5). On the verge, the lrgest root-derived respirtion during the dy nd during the night ws oserved under NO 3 -N even if the differene with NH þ -N ws not signifint (Fig. 5). CO efflux from unplnted soil hd no diurnl hnges nd the differene etween N tretments ws not signifint (p ¼.7) (Fig. 5). The vlue of root-derived CO, lulted s differene etween totl CO efflux from soil with roots nd miroil respirtion from re soil, ws relulted per units of root iomss nd presented s perent of the ontrol (Fig. 5): root-derived CO from the plntsoil system with lupine ws found to e 33% for the NH þ -N tretment nd 31% for the NO 3 -N tretment (p <.1). Control NH-N NO3-N Control NH-N NO3-N Fig.. () Belowground iomss of Lupinus lus (SE) t the end of the experiment: 5.5 dys fter the leling; () 1 C (pek vlues) respired from root-soil system with Lupinus lus in % of ontrol without N, relted for the unit of root iomss. Letters ove indite the signifine of the differenes t p ¼.5 etween tretments. 1 1 CO efflux (% of ssimilted) differene with ontrol, % CO efflux intensity (% of ssimilted) ontrol NH-N NO3-N 7,% % 5.% time sine leling (d) Fig. 3. () Dynmis of 1 CO from the soil (SE) with Ze mys under three N tretments: ontrol, NH þ -N nd NO 3 -N for dys fter 1 CO pulse leling of shoots; () differenes etween ontrol without N nd soil with NO 3 -N nd NH þ -N pplied, s % of ontrol. Dy (white) nd night (gry) periods re shown; () umultive 1 CO efflux (SE) from the soil with Ze mys under different N tretments Ze mys A ler diurnl dynmi of totl nd root-derived CO from the soil for ll N tretments ws oserved lso for the plnt-soil system with mize (Fig.,). Averge totl CO respired from the plntsoil system ws lowest for the ontrol (3.9 mg C d 1 pot 1 ), while under NH þ -N, the efflux rte ws.79 mg C d 1 pot 1 nd under NO 3 -N, it ws 5.31 mg C d 1 pot 1. However, the differene etween the two N tretments ws not signifint (p >.5) (Fig. ). The lrgest verge root-derived respirtion in the dy nd in the night ws oserved under nitrte N (Fig. ). Reltive to the ontrol, the losses of CO from the plnt-soil system were 1% under the NH þ -N tretment nd 1% under the NO 3 -N tretment (Fig. ). However the differene etween the two N tretments ws not found to e signifint.

6 Author's personl opy O. Gvrihkov, Y. Kuzykov / Soil Biology & Biohemistry () root iomss, g Control NH-N NO3-N CO efflux (mg C dy -1 pot -1 ) 1 Control 1 NH-N NO3-N time sine leling (d) 1 C losses (% of ontrol without N) Control NH-N NO3-N CO efflux (mg C dy -1 pot -1 ) d dy night Control NH-N NO3-N Control NH-N NO3-N Fig.. () Belowground iomss of Ze mys (SE) t the end of the experiment: dys fter the leling; () 1 C (pek vlues) respired from root-soil system with Ze mys in % of ontrol without N, relted for the unit of root iomss. Letters ove indite the signifine of the differenes t p ¼.5 etween tretments N uptke y plnts Signifintly more 15 N ws reovered from shoots nd roots of lupine plnts under NH þ -N (p <.1) (Fig. 7). The mjor prt of the 15 N remined in roots (5% for NH þ -N nd % for NO 3 -N). Ze mys took up twie s muh 15 N s the lupine, the distriution of 15 N lso differed: round 7% of 15 N ws lloted in oveground iomss (Fig. 7). Signifintly more 15 N ws reovered from plnts grown under NH þ -N (p <.1). Mximum 1 CO efflux from plnt-soil systems ws relted to the unit of N uptke (Fig. 7, in the orner). 1 C respirtion under NO 3 -N ws. times higher thn the one under NH þ -N for lupine nd 1. times higher for mize.. Disussion.1. Root-derived CO omprison of two methods Two methods for estimting root-derived CO efflux were used in this study: (1) pulse leling in 1 C tmosphere with susequent tring of reently ssimilted 1 CO from soil; nd () omprison etween the CO efflux from soil with plnts nd tht from re soil, the differene eing epted here s equl to the ontriution of plnt roots to the totl CO efflux. In our experiment, oth methods showed very similr results, with plnts grown under NO 3 -N respiring more C thn those grown under NH þ -N: for lupine the method sed on 1 Cgven 7% inrese in respirtion for NO 3 -N reltive to NH þ -N while the seond method gve n 37% inrese (Figs. nd 5). For mize, oth methods were lso similr in mgnitude: the 1 C method CO efflux (% of ontrol without N) Control NH-N NO3-N Fig. 5. () Totl CO efflux (SE) from the soil with Lupinus lus under three N tretments: ontrol, NH þ -N nd NO 3 -N, dy (white) nd night (gry) periods re shown () positive vlues: root-derived CO (s differene etween totl nd miroil respirtion from ulk soil) (light gry), nd negtive vlues: miroil CO (drk gry) efflux from the soil under Lupinus lus y three N tretments: verges for dy nd night periods. Letters ove indite the signifine of the differenes t p ¼.5 etween the tretments, seprtely for root-derived nd soil-derived CO ; () root-derived CO (s differene etween totl nd miroil respirtion) from plntsoil system with Lupinus lus in % of ontrol without N, relulted for unit of root iomss. Letters ove indite the signifine of the differenes t p ¼.5 etween the tretments. giving 7% differene etween the two N fertilizer types nd the seond method giving 33% (Figs. nd ). The suitility of 1 Cor 13 C leling nd the following tring of reently ssimilted C in order to quntify root-originted CO hs een onfirmed y mny studies (Rygiewiz nd Andersen, 199; Kuzykov nd Cheng, 1; Kuzykov, ; Wng et l., 5; Crone nd Trumore, 7). Leling of plnts is one of few pprohes whih potentilly permit estimtion of root-originted respirtion minimizing the soil disturne. The seond pproh, ompring plnted nd unplnted soil, is hep nd simple one, ut it gives only rude estimte of rootderived CO nd SOM-derived CO from plnted soil (Kuzykov,

7 Author's personl opy O. Gvrihkov, Y. Kuzykov / Soil Biology & Biohemistry () 35 CO efflux (mg C dy -1 pot -1 ) CO efflux (mg C dy -1 pot -1 ) time sine leling (d),, d y night Control NH-N NO3-N Control NH-N NO3-N d Control NH-N NO3-N 15 N, mmol g dw mx 1C/ mmol of 15 N NH-N NO3-N d Lupine Lupine d Mize Mize roots shoots NH-N NO3-N NH-N NO3-N Fig N ontent (SE) in shoots (positive vlues, light gry rs) nd roots (negtive vlues, drk gry rs) of Lupinus lus nd Ze mys under two types of N fertilizers pplied: NH þ -N nd NO 3 -N. Letters ove indite the signifine of the differenes t p ¼.5 etween the tretments, seprtely for shoots nd roots. In the upper orner: 1 C (pek vlues) respired from plnt-soil system with Ze my nd Lupinus lus per unit of 15 N reovered from roots. Letters ove indite the signifine of the differenes t p ¼.5 etween tretments. In our study, we did not use the solute vlues of 1 CO nd unleled CO, ut insted relted them to the hnges in rootderived CO indued y the hnge in the form of N fertiliztion. Therefore, despite their mentioned differenes, oth pprohes for estimting the root-derived CO showed similr results. CO efflux (% of ontrol without N) Control NH-N NO3-N Fig.. () Totl CO efflux (SE) from the soil with Ze mys under three N tretments: ontrol, NH þ -N nd NO 3 -N, dy (white) nd night (gry) periods re shown; () positive vlues: root-derived CO (s differene etween totl nd miroil respirtion) (light gry), nd negtive vlues: miroil CO (drk gry) efflux from the soil under Ze mys y three N tretments: verges for dy nd night periods. Letters ove indite the signifine of the differenes t p ¼.5 etween the tretments, seprtely for root-derived nd soil-derived respirtion; () root-derived CO (s differene etween totl nd miroil respirtion) from plnt-soil system with Ze mys in % of ontrol without N, relulted for the unit of root iomss. Letters ove indite the signifine of the differenes t p ¼.5 etween tretments. ). Possile errors in the method ome from the ft tht it does not onsider possile intertions etween growing roots nd SOM deomposition (Cheng et l., 3), the so-lled rhizosphere priming effets (Kuzykov, ). The yling of nutrients, the wter regime, nd temperture lne in the plnted soil re lso different from tht in the unplnted soil (Fisher nd Gosz, 19; Ross et l., 1; Pterson, 3; Cheng nd Kuzykov, 5). Additionlly, it does not llow seprting the rhizomiroil respirtion, ssoited with miroil deomposition of rhizodeposits nd ded roots from the root respirtion, whih n e estimted using pulse leling in the form of the first CO evolved fter the pulse, ssuming the temporl differene etween the CO evolved from different soures... Diurnl hnges of totl nd 1 C-CO efflux from the soil Mny studies onfirm tht ssimiltion of CO nd the downwrd trnsport of C in plnts, s well s the utiliztion of ssimilted C y root respirtion, re very rpid proesses (Weixin et l., 1993; Gregory nd Atwell, 1991; Kuzykov et l., 1999, ; Kuzykov nd Cheng, 1; Nguyen et l., 1999; Swinnen et l., 199). The time lg etween photosyntheti CO uptke nd the ensuing relese of C through root respirtion vries mong studies from minutes to dys. For exmple, Kuzykov nd Cheng (1) found the first CO evolution from soil with Lolium perenne within the first h fter leling while Weixin et l. (1993) found the eginning of emission of CO from winter whet nd rye to our within the first 3 min. Field studies usully report lgs higher thn found in the lortory; Tng et l. (5) found evidene for time lgs from 7 to 1 h up to 5 dys, Horwth et l. (199) reported lg of 3 dys for tree-soil systems. We found the mximum 1 C efflux from soil within h fter the leling for lupine nd within 3 h for mize. As the growing onditions, whih ould influene the soil CO prodution rte nd soil ir vertil flow through the soil pot (soil wter ontent, soil temperture) (Tng et l., 3), were equl for oth speies, the differene in lgs is onneted to speies-speifi or growth-stge-speifi differenes in the trnsport rtes of ssimiltes in lupine nd mize. The differene in the lgs nnot e sried to differenes in pth length or plnt size (Frrr nd Jones, ; Crone nd Trumore, 7) s oth speies were of similr height t the leling. The lupine plnts were leled on the eleventh lef stge (v11) nd mize on the fifth (v5). The growth stge ould influene the metoli orienttion of plnts, influening soure (photosynthetilly tive leves, whih supply new C) sink (developing orgns of plnts, whih ompete for the new C) intertions. The flow of C to sinks depends on the strength of the sink, the sink size, nd the growth rte (Dikson, 1991; Frrr nd Jones, ). In the se of mize in the present growth stge, intensively growing shoot ells ould hve preferene

8 Author's personl opy O. Gvrihkov, Y. Kuzykov / Soil Biology & Biohemistry () 35 1 over roots in the ompetition for reently ssimilted C. The root/ shoot rtio of lupine ws.3, inditing possile intensive rootgrowing proess, ompred to 1. for mize with n lredy wellestlished root system. Its worth noting tht the differene in the N quisition strtegy etween lupine nd mize mkes the omprison etween these speies prtiulrly omplex. As n exmple other studies showed tht symiosis of lupine with rhizoteri inreses the C sink nd so my elerte downwrd trnsport of ssimiltes ompred to non-legume plnts like mize (Lyzell et l., 1979), however the nodultion of lupine ws not quntified here. Diurnl hnges in 1 CO nd totl efflux from plnted soil were oserved for oth speies nd ll N tretments (Figs. 1, 3, 5 nd ). In our experiment, plnts were grown t single onstnt temperture during oth dy nd night. As CO efflux from unplnted soil ws independent of dy/night hnges (Figs. 5 nd ), the dytime inrese in 1 C evolution is ttriuted to the ssimiltion of C y photosynthesis nd the ensuing rpid trnslotion to roots, with n ssoited signl in the root-derived CO. This oservtion ws onfirmed lso y Kuzykov nd Cheng (1)..3. Cron osts of nitrte redution omprison etween speies nd different N supplies We hose two speies with different sites of nitrte redution. Aording to Pte (1973), Lupinus lus redues the mjor prt of inoming nitrte in roots. On the ontrry, Ze mys redue only hlf of the nitrte in roots nd the other hlf trnslotes to the shoots for redution. This differene in the redution site ould led to differenes in the quntity of CO respired per unit of N sored, given tht in non-green root ells nd in drkness, the proess of nitrte redution is supplied y reduing equivlents from the degrdtion of rohydrtes with n dditionl CO prodution (Aslm nd Huffker, 19; Ninomiy nd Sto, 19), wheres the sme proess performed in leves during the dy is oupled diretly with photosyntheti eletron trnsport (Aslm nd Huffker, 19; Atkins et l., 1979; Wrner nd Kleinhofs, 199) without dditionl CO evolution. Following these oservtions, we expeted to oserve differenes in the quntity of CO respired y given speies for different types of N supply nd etween two different speies grown using either NO 3 -N or NH þ -N fertilizer. As no effet of N form ws oserved on the respirtion from unplnted soil we n onlude tht the form of N (NO 3 or NH þ ) ffeted minly root-derived respirtion nd not SOM-derived one. But, mjor question in this work is whether the differenes in respirtion reflet tul root respirtion rther thn exudtion nd miroil respirtion in the rhizosphere. Its ler tht N form ffets respired C, ut oth plnts nd miroes hve to redue NO 3 to NH þ efore ssimilting it, nd the C osts might e similr, mking it diffiult to simply onlude tht ny extr C respired hs rootorigin. Thus, while we nnot estlish the nswer to the question definitively, we elieve tht the time ourse of respirtion, s viewed in the light of previous studies, strongly suggests the oserved differenes re due to hnges in root respirtion rther thn miroil one. After Kuzykov et l. (1999) nd Kuzykov nd Domnski () the 1 CO efflux fter pulse leling originting from different soures ppers t different time fter the leling: 1 CO from root respirtion ours erlier thn 1 CO from miroil respirtion y deomposition of root exudtes euse the ltter onsists of hin of suessive proesses: exudtion from the root, intke y miroorgnisms, nd only then respirtion y miroorgnisms. It ws shown on Lolium perenne tht the tul root respirtion ffets the 1 CO efflux urve only during the first h fter pulse leling nd the mximum effet of exudtion on rhizomiroil respirtion predomintes in the 1 CO efflux only fter out 1 dys fter the pulse leling (Kuzykov et l., 1; Kuzykov nd Domnski, ). In our study, for oth plnt speies, N tretment ffeted 1 CO efflux most during periods when the dominnt soure of 1 CO ws likely root respirtion. Therefore, the results re onsistent with N form hving signifint effet on respirtory osts of plnts whih is ssoited with NO 3 -N redution nd ssimiltion. Additionlly, the results of the 15 N nlyses in shoots nd roots demonstrted tht ll plnts took up muh more 15 N under NH þ -N thn under NO 3 -N, mking the differene etween two types of N pplied in the quntity of the respired C even more drmti. This ould e used s n extr prove of the ostliness of nitrte redution. Adding this, its worth to note tht we re operting with totl mount of reovered 15 N, the plnts were hrvested on the th dy fter the fertilizing nd the distriution of 15 N etween shoots nd roots during this period ould hnge signifintly. Between speies omprisons demonstrted signifint differene in the mount of CO evolved under NO 3 -N nd NH þ -N supply: respirtion under NO 3 -N reltive to tht under NH þ -N ws. times higher for lupine nd 1. times higher for mize. Although miroes lso py the ost for ssimiltion of NO 3 -N nd might use n inrese in 1 C respired, the effet would e the sme ross plnt speies nd so we onsider the oserved vrition in respired 1 C to e determined y plnt physiology. A higher differene etween the two N fertilizers in the se of lupine ould e explined y the ft tht lupine is referred to the plnts reduing the mjor quntity of nitrtes in roots, resulting in n enhned demnd for reduing equivlents of the rohydrtes degrdtion-origin with susequent evolution of CO (Pte, 1973; Ninomiy nd Sto, 19). The result hieved y 1 C pulse leling ws supported lso y n independent method sed on the mesurements of unleled totl CO respired from plnted nd unplnted soil, lthough etween speies vrition ws not so pronouned (Figs. 5 nd ). It should e mentioned lso tht the lotion of the nitrte redution site is not speies- ut rther ultivrs-dependent (Shilling et l., ; Silveir et l., 1). Moreover, environmentl onditions nd the quntity of N ould lso ffet nd hnge the proportion of nitrte redued in root nd shoots. Atkins et l. (1979, 19) nd Osrson nd Lrsson (19) oserved n inresed portion of nitrte redution in shoots when more NO 3 eme ville. So, ttention must e pid when hoosing the speies nd ultivtion onditions. We onlude tht the form of N supply hs strong effet on the mount of root-derived CO respired from two plnts hrterized y different nitrte redution sites. This ws determined from two plnt speies using two independent methods sed on reently ssimilted ( 1 C leled) nd totl (unleled) CO... Conlusions Fertiliztion of lupine nd mize with leled nitrte (K 15 NO 3 ) nd mmonium (( 15 NH ) SO ), omined with pulse leling of plnts in 1 CO tmosphere llowed evluting the effet of N form on reently respired CO efflux from the rhizosphere. In respet to mmonium, nitrte ddition signifintly ugments root-derived respirtion from oth plnts, influening lso the ontriution of utotrophi respirtion to the totl CO efflux. This mkes essentil to ount for the form in whih the soil N ws ville for plnt uptke nd for the lotion of nitrte redution site in plnts in modeling nd while seprting estimtion of individul CO soures whih ontriute to totl soil CO efflux. Aknowledgements We thnk Dr. Rik Wehr for reviewing the mnusript nd useful omments whih improved the originl vrint.

9 Author's personl opy O. Gvrihkov, Y. Kuzykov / Soil Biology & Biohemistry () 35 Referenes Andrews, M., 19. The prtitioning of nitrte ssimiltion etween root nd shoot of higher plnts. Plnt Cell Environment 9, Aslm, M., Huffker, R.C., 19. In vivo nitrte redution in roots nd shoots of rley (Hordeum vulgre L.) seedlings in light nd drkness. Plnt Physiology 7, Atkins, C.A., Pte, J.S., Lyzell, D.B., Assimiltion nd trnsport of nitrogen in non nodulted (NO_3 grown) Lupinus lus L. Plnt Physiology, Atkins, C.A., Pte, J.S., Griffiths, G.J., White, S.T., 19. Eonomy of ron nd nitrogen in nodulted nd non nodulted (NO_3 grown) ow pe [Vign unguiult (L.) Wlp. Plnt Physiology, Brker, A.V., Volk, R.J., Jkson, W.A., 199. Growth nd nitrogen distriution ptterns in en plnts Phseolus vulgris L. sujeted to mmonium nutrition: I Effets of rontes nd idity ontrol. Soil Siene Soiety of Ameri Proeedings 3, 3. Brneix, A.J., Breteler, H., Siee, C., Vn de Geijn, S.C., 19. Gs nd ion exhnges in whet roots fter nitrogen supply. Physiologi Plntrum 1, Blquiere, T., 197. Ammonium nd nitrte nutrition in Plntgo lneolt nd P. mjor ssp. mjor. II: Effiieny of root respirtion nd growth. Comprison of mesured nd theoretil vlues of growth respirtion. Plnt Physiology nd Biohemistry 5, Crone, M.S., Trumore, S.E., 7. Contriution of new photosyntheti ssimiltes to respirtion y perennil grsses nd shrus: residene times nd llotion ptterns. New Phytologist 1, Chillou, S., Rideout, J.W., Rper, C.D., Morot-Gudry, J.F., 199. Responses of soy en to mmonium nd nitrte supplied in omintion to the whole root system or seprtely in split root system. Physiologi Plntrum 9, 59. Cheng, W., Kuzykov, Y., 5. Root effets on soil orgni mtter deomposition. In: Wright, S., Zoel, R. (Eds.), Roots nd Soil Mngement: Intertions etween Roots nd the Soil. Agronomy Monogrph, Amerin Soiety of Agronomy, Mdison, Wisonsin, USA, pp Cheng, W., Johnson, D.W., Fu, S., 3. Rhizosphere effets on deomposition ontrols of plnt speies, phenology nd fertiliztion. Soil Siene Soiety of Amerin Journl 7, Dikson, R.E., Assimilte distriution nd storge. In: Rghvendr, A.S. (Ed.), Physiology of Trees. Wiley, J. nd Sons. In., New York, USA, pp Domnski, G., Kuzykov, Y., Sinikin, S.V., Sthr, K., 1. Cron flows in the rhizosphere of Lolium perenne. Journl of Plnt Nutrition nd Soil Siene 1, Frrr, J.F., Jones, D.L.,. The ontrol of ron quisition y roots. New Phytologist 17, Fisher, F.M., Gosz, J.R., 19. Effets of trenhing on soil proesses nd properties in New Mexio mixed-onifer forest. Biology nd Fertility of Soils, 35. Gregory, P.J., Atwell, B.J., The fte of ron in pulse leled rops of rley nd whet. Plnt Soil 13, Horwth, W.R., Pretziger, K.S., Pul, E.A., 199. C llotion in tree-soil systems. Tree Physiology 1, Kuzykov, Y.,. Review: ftors ffeting rhizosphere priming effets. Journl of Plnt Nutrition nd Soil Siene 15, Kuzykov, Y.,. Soures of CO efflux from soil nd review of prtitioning methods. Soil Biology nd Biohemistry 3, 5. Kuzykov, Y., Cheng, W., 1. Photosynthesis ontrols of rhizosphere respirtion nd orgni mtter deomposition. Soil Biology nd Biohemistry 1, Kuzykov, Y., Domnski, G.,. Model of rhizodeposition nd CO efflux from plnted soil nd its vlidtion y 1 C pulse leling of ryegrss. Plnt nd Soil 39, 7 1. Kuzykov, Y., Kretzshmr, A., Sthr, K., Contriution of Lolium perenne rhizodeposition to ron turnover of psture soil. Plnt nd Soil 13, Kuzykov, Y., Ehrenserger, H., Sthr, K., 1. Cron prtitioning nd elowground trnslotion y Lolium perenne. Soil Biology nd Biohemistry 33, 1 7. Ls, B., Frehill, S., Apriio-Tejo, P.M., Lmsfus, C.,. Alterntive pthwy respirtion is ssoited with mmonium ion sensitivity in spinh nd pe plnts. Plnt Growth Regultion 37, Lyzell, D.B., Rinird, R.M., Atkins, C.A., Pte, J.S., Eonomy of photosynthte use in nitrogen fixing legume nodules. Oservtions on two ontrsting symioses. Plnt Physiology, 91. Nguyen, C., Todorovi, C., Roin, C., Christophe, A., Gukert, A., Continuous monitoring of rhizosphere respirtion fter lelling of plnt shoots with 1 CO. Plnt Soil 1, Ninomiy, Y., Sto, S., 19. A ferredoxin-like eletron rrier from non-green ultured too ells. Plnt Cell Physiology 5, Oks, A., Hirel, B., 195. Nitrogen metolism in roots. Annul Review of Plnt Physiology 3, Osrson, P., Lrsson, C.M., 19. Reltions etween uptke nd utiliztion of NO_3 in Pisum growing exponentilly under nitrogen limittion. Physiologi Plntrum 7, Pte, J.S., Uptke, ssimiltion nd trnsport of nitrogen ompounds y plnts. Soil Biology nd Biohemistry 5, Pte, J.S., Lyzell, D.B., 199. Energeti nd iologil osts of nitrogen ssimiltion. In: Miflin, B.J., Le, P.J. (Eds.), The Biohemistry of Plnts. A Comprehensive Tretise. Ademi Press, Sn Diego, New York, Boston, London, Sydney, Tokyo, Toronto, pp. 1. Pterson, E., 3. Importne of rhizodeposition in the oupling of plnt nd miroil produtivity. Europen Journl of Soil Siene 5, Purvis, A.C., Shewfelt, R.L., Does the lterntive pthwy meliorte hilling injury in sensitive plnt tissues? Physiologi Plntrum, Ross, D.J., Sott, N.A., Tte, K.R., Rodd, N.J., Townsend, J.A., 1. Root effets on soil ron nd nitrogen yling in Pinus rdit D.Don plnttion on ostl snd. Austrlin Journl of Soil Reserh 39, Rygiewiz, P.T., Andersen, C.P., 199. Myorrhize lter qulity nd quntity of ron lloted elow ground. Nture 39, 5. Shilling, G., Adgo, E., Shulze, J.,. Cron osts of nitrte redution in rod een (Vii f L.) nd pe (Pisum stivum L.) plnts. Journl of Plnt Nutrition nd Soil Siene 19, Silveir, J.A.G., Mtos, J.C.S., Cetto, V.M., Viegs, R.A., Oliveir, J.T.A., 1. Nitrte redutse tivity, distriution, nd response to nitrte in two ontrsting Phseolus speies inoulted with Rhizoium spp. Environmentl nd Experimentl Botny, 37. Swinnen, J., Vn Veen, J.A., Merkx, R., C pulse leling of field-grown spring whet: n evlution of its use in rhizosphere ron udget estimtion. Soil Biology nd Biohemistry, Tng, J., Bldohi, D., Qi, Y., Xu, L., 3. Assessing soil CO efflux using ontinuous mesurements of CO profiles in soils with smll solid-stte sensors. Agriulturl nd Forest Meteorology 11, 7. Tng, J., Bldohi, D.D., Xu, L., 5. Tree photosynthesis modultes soil respirtion on diurnl time sle. Glol Chnge Biology 11, Tishner, R.,. Nitrte uptke nd redution in higher nd lower plnts. Invited review. Plnt. Cell nd Environment 3, Vuylsteker, C., Leleu, O., Rmour, S., Influene of BAP nd NAA on the expression of nitrte redutse in exised hiory roots. Journl of Experimentl Botny, Wng, Z.P., Li, L.H., Hn, X.G., Li, Z.Q., Chen, Q.S., 5. Dynmis nd llotion of reently photo-ssimilted ron in n Inner Mongoli temperte steppe. Environmentl nd Experimentl Botny 59, 1 1. Wrner, R.L., Kleinhofs, A., 199. Genetis nd moleulr iology of nitrte metolism in higher plnts. Physiologi Plntrum 5, 5 5. Weixin, C., Colemn, D.C., Crroll, C.R., Hoffmn, C.A., In situ mesurement of root respirtion nd solule C onentrtions in the rhizosphere. Soil Biology nd Biohemistry 5, Ziilske, L.M., 199. Cron minerliztion. In: Wever, R.W., Angle, S., Bottomley, P., Bezdiek, D., Smith, S., Tti, A., Wollum, A. (Eds.), Methods of Soil Anlysis, Prt. Miroiologil nd Biohemil Properties. Soil Siene Soiety of Ameri, Mdison, pp. 35.

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