Patent Application: US-201213628611-A

Abstract:
this invention provides a quantitative analysis of glycan biosynthesis along meta pathways using computer simulation for comparing a computer generated spectrum to experimental data to quantitatively track the biosynthesis . computer simulating the mass spectra of isotopic detection of aminosugars with glutamine experiments allows modeling the glycan biosynthesis over time , via changes in the 14 n and 15 n isotope abundance levels , to estimate the relative abundance of molecules involved in glycan biosynthesis , from experimental mass spectra . gradient search optimization is used to maximize the coefficient of determination between the experimental spectrum and the simulated spectrum . these relative abundances are then fed into a pathway simulation model to analyze glycan biosynthesis . simulating a mass spectrum allows reconfirming the identification , quantifying the isotopic configurations and obtaining the relative abundance of each as samples are taken at periodic intervals , which is then organized to allow tracking the changes in abundance levels over time .

Description:
mass spectrometry ( ms ) is “ a microanalytical technique that can be used selectively to detect and determine the amount of a given analyte ” ( watson and sparkman 2007 , ref . 27 ). besides the quantitation of analytes , ms “ is also used to determine the elemental composition and some aspects of the molecular structure of an analyte ” ( watson and sparkman 2007 , ref 27 ). for its high sensitivity and fast speed , ms “ has evolved to become an irreplaceable technique in the analysis of biologically related molecules ” ( glish and vachet 2003 ) ( ref . 8 ). a typical ms procedure involves generation of charged molecular ions and measurement of their mass - to - charge ( m / z ) ratios and relative abundance . the output data from the mass spectrometers , namely , mass spectra , can be represented as a plot of intensity vs . m / z value and stored in a file as a sequence of [ m / z , intensity ] pairs . the development of the idawg ™ technique (“ isotopic detection of aminosugars with glutamine ”) relates to the incorporation of differential mass tags into the glycans of cultured cells . in this method , culture media containing amide - 15 n - gln is used to metabolically label cellular aminosugars with heavy nitrogen . ( orlando et al . 2009 ). in idawg ™ experiments , a “ light ” form ( natural abundance 14 n ) and a “ heavy ” form ( 15 n - enriched ) of glutamine are used to prepare otherwise identical culture media . natural abundance or 15 n - enriched nitrogen from the glutamine is incorporated into all newly synthesized aminosugars . after a number of cell divisions , each instance of particular aminosugar is replaced by a family of isotopologues , which contains the identical elements in the elemental composition except that the number of 14 n and 15 n atoms do not correspond to natural abundance . if the number of nitrogen atoms is n , the number of isotopologue families for this elemental composition is ( n + 1 ). for an elemental composition of h x c y n n o z , the ( n + 1 ) families of isotopologues can be represented as h x c y ( 15n ) i ( 14n ) j o z , where i + j = n . for each family , the abundances of the isotopes of other elements in the composition , such as hydrogen , carbon and oxygen , remain the same as the occurrence in nature since no enriched sources of these elements are introduced in idawg ™ experiments . consider a sodiated ion of reduced permethylated ( gal ) 1 ( galnac ) 1 ( neunac ) 2 as an example , its elemental composition is c 55 h 99 n 3 o 27 na + . because it contains three nitrogen atoms , the possible isotopologue families include the following : c 55 h 99 15 n 0 14 n 3 o 27 n | , c 55 h 99 15 n 1 14 n 2 o 27 na | , c 55 h 99 15 n 2 14 n 1 o 27 na | , and c 55 h 99 15 n 3 14 n 0 o 27 na + . for brevity , each of these sets of isotopologues is represented as a tuple of [ 15 n , 14 n ] ∈ {[ 0 , 3 ], [ 1 , 2 ], [ 2 , 1 ], [ 3 , 0 ]} because the number of the other elements is identical , namely c 55 h 99 o 27 na − . fig1 shows a simplified pathway representing how ( gal ) 1 ( galnac ) 1 ( neunac ) 2 is synthesized in an idawg ™ experiment . this pathway is described in : ( i ) the lab page of dr . kelley moremen under the “ galnac ( mucin - type ) core synthesis / branching ” section ( see http :// www . ccrc . uga . edu /˜ moremen / glycomics /) and ( ii ) o - glycan biosynthesis pathway section of kegg ( kyoto encyclopedia of genes and genomes ) ( see reaction r05908 , r05913 and r05914 in http :// www . genome . jp / kegg - bin / show_pathway ? bta00512 ). the graphical format used to represent these structures is described in http :// glycomics . scripps . edu / cfgnomenclature . pdf . the sole nitrogen sources of experiments are amide - 14 n - gln ( light medium ) or amide - 15 n - gln ( heavy medium ) as indicated by the arrows starting from them . after three reactions , which are marked with 1 , 2 and 3 , occur following the controlled biosynthetic pathway , ( gal ) 1 ( galnac ) 1 ( neunac ) 2 is synthesized as the final product . due to the existence of both light and heavy media , positions with puzzle mark in fig1 will contain either 15 n or 14 n . therefore , considering the combinations of numbers of 15 n and 14 n , four isotopologue families of ( gal ) 1 ( galnac ) 1 ( neunac ) 2 , namely [ 0 , 3 ], [ 1 , 2 ], [ 2 , 1 ] and [ 3 , 0 ], will be generated during the biosynthesis process . furthermore , for each isotopologue family with a fixed number of 14 n and 15 n , e . g . 15 n 1 14 n 2 , many different isotopomers exists , in part because 14 n and 15 n atoms may be present at the different positions , which are denoted by puzzle marks . these isotopomers have the same number of each isotopic atom but differing in their positions . in fig1 , udp ( uridine diphosphate ) and cmp ( cytosine monophosphate ), classified as sugar nucleotides , donate sugar residues to the growing glycan , as discussed more fully below . the cultures were grown in the media for a total of 36 hours and mass spectra were recorded using aliquots sampled at time points of hr — 0 , hr — 6 , hr — 12 , hr — 24 and hr — 36 for the subsequent simulation and modeling . chemical composition can be represented as a residue composition or an elemental composition . in idawg ™ experiments , the residue composition and the corresponding monoisotopic mass are in one - to - one mapping and stored in a pre - defined configuration file . the residue / elemental composition is identified by looking up monoisotopic mass ( mass ) in the configuration file , while mass is calculated from both charge state ( z ) and ( m / z ) value of the monoisotopic peak in the experimental spectrum via the formula m / z = mass / z . the monoisotopic peak , which corresponds to the isotopomer containing the most abundant isotopes for each element ( all 1 h , 12 c , 14 n , and 16 o , etc .) is used to identify the elemental composition of each ion . the charge state ( z ) is an integer , typically in range of − 5 to + 5 , that indicates the electrical charge of the molecular ion . mass spectrometers use an ionization process ( e . g ., electro - spray or uv light ) to put a charge on molecules in order to accelerate them toward the detector . the value of the charge state is specified in the same configuration file as the mapping between residue compositions and masses , and the default is + 1 . for a molecule containing n atoms , its population of isotopologues follows multinomial distribution . for each possible isotopologue , the mass and probability can be computed via equation 1 . for example , the oxygen element has three significantly populated ( stable ) isotopes in nature , namely , 16 o , 18 o and 17 o . from the table of isotopes , the three isotopes &# 39 ; relative abundances are p i = 0 . 99762 , p 2 = 0 . 00200 and p 3 = 0 . 00038 and their atomic masses are m 1 = 15 . 9949146 , m 2 = 17 . 9991604 and m 3 = 16 . 9991315 , respectively . ( see http :// www . matpack . de / info / nuclear / nuclids /). carbon , hydrogen and nitrogen each have two stable isotopes . by substituting x i with the number of atoms of each isotope and m i is the corresponding isotopic mass , the mass contributed to the isotopologue and probability ( p ( x 1 , x 2 , x 3 ) or probiso ) that a particular molecule is that isotopologue can be calculated via equation 1 . where n is the number of atoms in the molecule such that σx i = n and x i ∈ { 0 , 1 , . . . , n } is the number of atoms of each stable isotope in the isotopologue ; m i and p i are obtained from the table of isotopes . since the number of possible combinations is large , a probability threshold is used to limit the number of isotopomers calculated . after an array of [ probiso , massiso ] pairs is calculated ( one pair for each isotopologue that is consistent with the chemical formula ), a segment of the mass spectrum [ m / z vs . abundance ] is simulated using an algorithm that uses a joint probability formula to generate gaussian and / or lorentzian line shapes as a function of m / z , based on the array [ probiso , massiso ]. besides those elements with natural abundance isotopes , idawg ™ experiments introduce 15 n - enriched precursors into the cultivation media . the population of isotopologues in molecules that incorporate nitrogen from 15 n - enriched precursors also follows a multinomial distribution . if the isotopic purity of 15 n is purity , then the abundance of 14 n in the enriched precursor is ( 1 - purity ). this is addressed computationally by defining “ pseudoelements ” that consist of isotopes in non - natural ratios . 15 n - enriched nitrogen is defined as the pseudoelement ñ . for example 98 % 15 n - enriched nitrogen consists of the same isotopes as n , except that 98 % of the ñ atoms are 15 n and 2 % of the ñ atoms are 14 n . in this way , the “ pseudochemical ” formula of an isotopically enriched precursor or a biomolecule that incorporates atoms from that precursor can be specified . that is , natural abundance glutamine has the chemical formula c 5 h 10 n 2 o 3 while 98 % amide - 15 n - enriched glutamine has the pseudochemical formula c 5 h 10 no 3 ñ . specification of such a formula allows the masses and populations of isotopologues for isotopically labeled molecules to be calculated using equation 1 . this also allows arrays describing the isotopologue populations and masses [ probiso , massiso ] of biomolecules ( such as glycans ) whose atoms are derived from both natural abundance and isotopically - enriched precursors to be calculated explicitly . for example , a glycan that contains n nitrogen atoms can be represented as a combination of the following n + 1 pseudochemical formulae : c c h h n n o o , c c h h n n − 1 o o ñ 1 , . . . , c c h h o o ñ n , where c , h and o indicate the number of c , h and o atoms in the molecule . each pseudochemical formula corresponds to a unique set of isotopologues . the experimental spectrum corresponds to a linear combination of these n + 1 sets of isotopologues , and this combination can be described as a vector t =( t 0 , t 1 , . . . t n ), where each number t j represents the proportion of the molecules that contain j atoms of the pseudoelement ñ . each t j also describes the population of molecules that contain j nitrogen atoms from the enriched precursor pool and n − j nitrogen atoms from the natural abundance precursor pool thus , the time - dependent evolution of t during cell growth provides key information regarding the metabolic fate of isotopically enriched precursors and thereby sheds light on the biochemical process that led to the formation of the glycan . the idawg ™ experimental data may be recorded using an orbital trapping method ( hu et al . 2005 , ref . 11 ) and post - processed using a fast fourier transform ( fft ). the resulting spectral features have line shapes that are a combination of lorentzian and gaussian shapes , depending on the parameters used for data processing . the ratio of gaussian to lorentzian is thus a parameter that must be optimized for accurate spectral simulation . furthermore , to obtain a high quality fit to the experimental peaks , some additional spectral parameters need to be considered for optimization . peak width : the peak width ( pw ) of the mixed gaussian and lorentzian curve is related to the standard deviation ( σ ) of the curve &# 39 ; s probability density function ( pdf ) as σ = 0 . 4247 × pw , which is given in section 9 . 2 . 3 . 3 of ( inczédy et al . 1998 , ref . 12 ). delta : delta is the shifting parameter between the experimental and theoretical spectra . due to errors in calibrating m / z for the experimental data , the m / z values for the experimental spectrum may be shifted slightly to the left or right side with regard to the theoretical mass value . normalization threshold : when the experimental spectrum is generated in the mass spectrometer , very low intensity values are cut out ( set to zero ) by the instrument and rejected as noise . however , there is no noise in the theoretical simulation , so a normalization threshold is used to cut off the simulated spectrum in order to mimic the experimental data collection process . in summary , using the array of [ prob , mass ] pairs for each isotopomer , the simulated spectral peaks as a combination of lorentzian and gaussian shapes is calculated by the computer processor using equation 2 . where σ is calculated from the peak width of the mixed gaussian and lorentzian curve , both prob and mass with index j are theoretical mass and probability values in [ prob , mass ] array of each isotopologue , mass with index i is calculated by the computer processor from charge state and m / z value from experimental spectrum . after both curves are simulated , the complete simulated spectrum for one isotopologue is computed via equation 3 . simuspec i = r × f g ( i )+( 1 − r )× f l ( i ) equation 3 where simuspec is an array of spectral data points with index i and r is the gaussian fraction of the total . after the computer processor calculates simulated spectral signatures for every isotopologue in equation 4 , the complete simulated idawg ™ mass spectrum is a weighted sum of sub - spectral signature from all the ( n + 1 ) isotopologues based on the concentration level of each , if the number of nitrogen atoms in the elemental composition is n . in summary , the algorithm used by the computer for generating the simulated idawg ™ mass spectrum is listed in table 1 . this leads to a multi - dimensional optimization problem , in which the difference between the simulated and the experimental spectra should be minimized . the simulation parameters are divided into two sets : experiment parameters : ( i ) isotopic purity of 15 n , ( ii ) relative abundances of the ( n + 1 ) isotopologues spectral parameters : ( i ) peak widths of gaussian and lorentzian shapes , respectively , ( ii ) fraction of gaussian shape of the total , ( iii ) delta and ( iv ) normalization threshold it is not feasible to perform an exhaustive search to find an optimal solution for the following reasons : ( i ) there are ( n + 5 ) independent parameters where n is the number of nitrogen atoms , ( ii ) the search space is continuous , and ( iii ) the experimental data is high resolution with 4 to 5 significant digits . the approach is to optimize the parameters via a gradient ascent method . it is difficult to perform a gradient search for all parameters at once , because the gradient of all parameters will often lead to divergence rather than to convergence . therefore , parameters are grouped and optimized separately . the effects of noise in fitting the spectral parameters are minimized as these parameters are fitted using a small region of the monoisotopic peak within the complete experimental spectral window . furthermore , using a small window makes optimization of the spectral parameters much faster . then , fitting the experimental parameters such as the isotopic purity of 15 n will also be faster , as the dimensionality of the problem is reduced and diversions from the optimal solution that occur as a result of inappropriately adjusting peak width and delta ( which have relatively large effects and which have already been optimized ) do not occur when the derivative purity ( which has a small effect ) is varied . the hr — 0 data of idawg ™ experiments only contains the “ heavy ” 15 n media , therefore the concentration levels of isotopologues are all 0s except for the one containing all 15 n , which is 100 %. another tuple [ pool — 1 , pool — 2 ] in ([ 3 , 0 ], [ 2 , 1 ], [ 1 , 2 ], [ 0 , 3 ]) is defined here to indicate the number of nitrogen atoms in the ion that originate from the 15 n - enriched and natural abundance glutamine pools , respectively . thus , the tuple [ 3 , 0 ] corresponds to ions in which all three of the nitrogen atoms originate from the 15 n - enriched glutamine precursor pool . ( please note that not all of the nitrogen in an ion composed of 100 % [ 3 , 0 ] is 15 n , as the isotopic purity of the precursor pool is always less than 100 %.) this tuple reflects the metabolic history of the ion while taking into account the isotopic purity of the precursor pool . the coefficient of determination ( r ) is used as a measure of how well the simulated spectrum fits the experimental spectrum . using a correlation coefficient in comparing the goodness - of - fit of simulated spectrum was proposed in ( maccoss et al . 2003 , ref 17 ). after the simulated spectrum is generated , the intensity of both the simulated and experimental spectra are compared . if the pattern of both spectra matches well , the coefficient of determination is close to 1 . the optimization result shows that the optimization algorithm reaches the expected outcome . gradient ascent optimization : gradient ascent optimization ( fletcher and powell 1963 ) ( ref . 5 ) is applied to search for a near optimal solution because the search space is continuous and multi - dimensional . the typical procedure of gradient ascent optimization is as follows : changing the parameters by a small δ , calculating the gradient via where x is a vector of parameters , adjusting the value of parameter after each iteration by a small step to the direction that would most increase the fitness value . in order to handle constraints of parameter , penalty function is used by assigning penalty = min [ 0 , value - lowerlimit ]+ min [ 0 , upperlimit - value ] when updating the parameter value . line search is used to change step size adaptively for faster convergence . the gradient ascent routine utilized herein is shown in table 2 . given the experimental spectra at five time points and their monoisotopic peaks , the steps of the computer simulation optimization algorithm are implemented in two phases : phase 1 processes data at hr — 0 while phase 2 processes the rest . in phase 1 , the concentration levels for all isotopologues of [ 0 , 3 ], [ 1 , 2 ], [ 2 , 1 ] and [ 3 , 0 ] are always 0 , 0 , 0 and 100 %. based on the monoisotopic peak , the peak width of gaussian and lorentzian are grouped with delta and optimized separately assuming there is only one curve constituting the whole peak . after obtaining the peak width of both curves , delta and fraction of gaussian are grouped together and optimized . with all of the spectral parameters optimized , experiment parameters are optimized based on the complete experimental spectrum . the spectral parameters and derivative purity at hr — 0 are saved for phase 2 . in phase 2 , firstly , the concentration levels are guessed via the saved parameters of hr0 ; and then the guessed concentration levels are applied to estimate the spectral parameters following the steps in phase 1 ; thirdly , estimate the experiment parameters to obtain the optimized concentration levels , which are to be used in the pathway modeling . idwag ™ experiments follow the hexosamine biosynthetic pathway ( an introduction can be found in fantus et al . 2006 , ref 4 ). in order to synthesize ( galnac ) 1 ( gal ) 1 ( neuac ) 2 , three reactions involved in the biosynthetic pathway shown in fig1 are listed in equation 4 including the reactants , products and enzymes . for brevity , the enzymes are represented by ec number used in kegg . the job of cmp - and udp - is to transfer the glycan attached to it to another acceptor . for example , in the first reaction , udp - gal conveys gal to ( galnac ) 1 so that ( galnac ) 1 ( gal ) 1 is produced . fig3 shows the pathway model of three reactions synthesizing ( galnac ) 1 ( gal ) 1 ( neuac ) 2 . in the preliminary pathway model , the first two reactions in equation 5 are not covered and the last reaction is discussed in detail for illustration purposes only . because all of the reactions contain cmp -( neuac ) 1 and cmp as reactant and product ( in blue box ), they are shown for how they are numbered and omitted from the other reactions with bidirectional arrows . the pathway model starts with ( galnac ) 1 ( gal ) 1 , ends with ( galnac ) 1 ( gal ) 1 ( neuac ) 2 and the intermediate product is ( galnac ) 1 ( gal ) 1 ( neuac ) 1 . due to the existence of both the heavy 15 n and light 14 n sources , the glycans containing nitrogen atoms , e . g ., galnac and neuac will have different isotopologues for different positions where 14 n i and 15 n j are attached . although different isotopomers exist for one isotopologue , they are identified as the same isotopologue in the mass spectrometer . for example ( galnac ) 1 ( gal ) 1 ( neuac ) 2 &# 39 ; s have four isotopologues . there is only one isotopomer for [ 0 , 3 ] and [ 3 , 0 ] since the three positions will be all 15 n or all 14 n , while [ 2 , 1 ] and [ 1 , 2 ] have three different isotopomers for each as indicated in fig3 . the reactants and products that are going to be modeled are numbered as x i , i ∈ { 1 , . . . , 10 }: three isotopologues of ( gal ) 1 ( galnac ) 1 ( neunac ) 1 : [ 2 , 0 ] as x 1 , [ 1 , 1 ] as x 2 and [ 0 , 2 ] as x 3 ; four isotopologues of ( gal ) 1 ( galnac ) 1 ( neunac ) 2 : [ 3 , 0 ] as x 4 , [ 2 , 1 ] as x 5 , [ 1 , 2 ] as x 6 and [ 0 , 3 ] as x 7 ; two isotopologues of cmp -( neuac ) 1 : [ 1 , 0 ] as x 8 and [ 0 , 1 ] as x 9 ; cmp is numbered as x 10 . because of complexity and lack of data differentiating some of the isotopomers , the individual low level reactions were not modeled , but were aggregated into the meta - pathways . after all the reactants and products are numbered , the reactions are grouped as follows : at this stage , the effects of enzyme concentrations are not analyzed , so a pseudo reaction rate is essentially introduced to derive the following set of ordinary differential equations ( odes ) as listed in equation 5 . { dot over ( x )} 1 = k [ 4 → 1 ] [ x 4 ][ x 10 ]+ k [ 5 → 1 ] [ x 5 ][ x 10 ] { dot over ( x )} 2 = k [ 5 → 2 ] [ x 5 ][ x 10 ]+ k [ 6 → 2 ] [ x 6 ][ x 10 ] { dot over ( x )} 3 = k [ 6 → 3 ] [ x 6 ][ x 10 ]+ k [ 7 → 3 ] [ x 7 ][ x 10 ] { dot over ( x )} 4 = k [ 1 → 4 ] [ x 1 ][ x 8 ] { dot over ( x )} 5 = k [ 1 → 5 ] [ x 1 ][ x 9 + k [ 2 → 5 ] [ x 2 ][ x 8 ] { dot over ( x )} 6 = k [ 2 → 6 ] [ x 2 ][ x 9 ]+ k [ 3 → 6 ] + k [ 3 → 6 ] [ x 3 ][ x 8 ] { dot over ( x )} 7 = k [ 3 → 7 ] [ x 3 ][ x 9 ] equation 5 there are 12 constants ( starting with k ) as pseudo reaction rate and 7 variables x i , i ∈ { 1 , 2 , . . . , 7 } as time derivative of concentration level . from the result of simulation optimization , the concentration level of isotopologues of ( galnac ) 1 ( gal ) 1 ( neuac ) 1 and ( galnac ) 1 ( gal ) 1 ( neuac ) 2 at five time points will be used as the initial values . based on the experimental spectrum of ( neuac ) 2 ( gal ) 1 ( galnac ) 1 from the time points of hr — 0 , hr — 6 , hr — 12 , hr — 24 and hr — 36 , the optimized simulated spectra are shown in fig5 . the optimized results for the coefficient of determination of simulated and experimental spectra are 0 . 9891 , 0 . 9799 , 0 . 9309 , 0 . 9858 and 0 . 9919 for five time points , from which we can see that simulation algorithm can reach satisfactory results . even with the existence of noise , as indicated in fig4 , the simulated spectrum fits the experimental spectrum well , which shows the robustness . fig5 shows the concentration levels of isotopologues of ( neuac ) 2 ( gal ) 1 ( galnac ) 1 at five time points . it can be seen that the concentration level of each isotopologue changes over time . although the available time points are limited , the time - series data can be used to model the isotopologues &# 39 ; behavior in the biosynthesis process , such as how a residue that contained 15 n gets replaced by 14 n and vice versa . modeling biosynthesis pathway dynamics by looking into the reaction rates , concentration levels and other parameters that affect the biosynthesis pathways in idawg ™ experiments will follow . the [ 3 , 0 ] curve rapidly drops over the 36 hr period . this has two causes : first more molecules with 14 n are being synthesized , so the percentage of [ 3 , 0 ] naturally drops . however , it seems to drop more than would be expected and this is possibly due to molecular remodeling ( e . g . a reverse reaction followed by a forward reaction ). another interesting curve is [ 2 , 1 ] which can be created as shown in fig5 by either new biosynthesis or molecular remodeling . as more data is collected and the pathway modeling is refined , this question will be addressed . in any event , the invention provides a computer system for simulating spectral patterns for isotope labeled glycans for use in a quantitative analysis of glycans which includes a database containing experimental spectral patterns of the isotope labeled glycans , a processor for identifying the elemental composition from the experimental spectrum patterns , calculating the number of labeled atoms from the elemental composition and generating a list of elemental compositions for all possible isotopologues , and for each isotopologue , calculating an array of [ probability , mass ] for the isotopologue , generating a simulated spectrum for each isotopic analog , based on a concentration level , and normalizing the simulated spectrum . in yet another embodiment of the invention , a method for the isotope detection of aminosugars with glutamine and the quantitative analysis thereof comprises the steps of providing a computer system for simulating spectral patterns for isotope labeled glycans having a database containing experimental spectral patterns of the isotope labeled glycans , a processor for identifying the elemental composition from the experimental spectrum patterns , calculating the number of labeled atoms from the elemental composition and generating a list of elemental compositions for all possible isotopologues , and for each isotopic analog , calculating an array of [ probability , mass ] for the isotopic analog , and generating a simulated spectrum for each isotopic analog , based on a concentration level , and normalizing the simulated spectral pattern . the method can also include obtaining a biological material and growing the biological material in the presence of isotope labeled glutamine , the biological material thereby producing labeled glycans , performing a spectral analysis of the labeled glycans and obtaining actual spectral patterns therefrom , and , comparing the actual spectral patterns to the simulated spectral patterns and extracting quantitative information that is encoded in the spectral patterns . cell surface complex carbohydrates play a critical role in cell recognition and adhesion , with carbohydrate - dependent interactions being essential for normal embryonic development and the function of the immune system . carbohydrate modification has also been implicated in a number of different pathological conditions , including cancer . for example , human colon cancer is associated with antigenic and structural changes in mucin - type carbohydrate chains ( o - glycans ). genetic diseases that affect the biosynthesis of protein o - glycans are also being found . many patients with an unsolved defect in n - glycosylation have been found to have an abnormal o - glycosylation , with the defect not necessarily localized in one of the glycan - specific transferases , but can possibly be found in the biosynthesis of nucleotide sugars , their transport to the endoplasmic reticulum ( er )/ golgi , and in golgi trafficking . in view of the number of genes involved in o - glycosylation processes and the increasing scientific interest in congenital disorders of glycosylation , it is expected that the number of identified diseases where tracking glycan biosynthesis can be used to develop treatments will likely grow rapidly in the future . understanding glycoprotein biosynthesis is important to many biological phenomena , and should eventually lead to the development of new drugs that will help to control pathological processes involving carbohydrate - mediated interactions . in the area of simulation optimization , much research work has been done . azadivar ( 1999 ) ( ref . 1 ) gave a tutorial on methods and techniques applied in the field of simulation optimization , e . g ., gradient based search method , stochastic approximation methods , sample path optimization , response surface methods and heuristic search methods . fu et al . ( 2005 ) ( ref 6 ) presented a survey of theoretical development in simulation optimization area and gave a list of available software and several illustrative applications . kim ( 2006 ) ( ref 13 ) provided a review of two gradient - based techniques for simulation optimization ( stochastic approximation and sample average approximation methods ). kleinstein et al . ( 2006 ) ( ref . 15 ) exploited how nonuniform sampling can help make the global optimization converge faster in the problem of parameter estimation in biological pathway . in this work , a steepest gradient ascent algorithm of finite difference estimation is utilized , in which line search is used in controlling the step size for fast convergence and penalty function is applied to restrict the values of parameters when they violates the constraints . because there are many ways to improve the performance and accuracy of gradient search , the gradient ascent algorithm may be modified to be faster and more robust . because the success of gradient search depends on the shape of the surface , the feasibility of applying other meta - heuristic global optimization algorithms , such as genetic algorithm and particle swarm optimization , will also be explored . systems biology approach , as introduced in ( kitano 2002 ), ( ref . 14 ) has been widely applied to model the biological systems and to gain insight into the interactions and operations within the system . battogtokh et al . ( 2002 ) ( reference 2 ) proposed a chemical reaction network for qa gene cluster and developed an efficient monte carlo simulation method by randomly walking in the search space . ( rajasimha et al . 2004 ) ( ref . 20 ) modeled the effects of the cell divisions on the dna drift and simulated activities such as mdna replication and degradation , cell division and death . funahashi et al . ( 2006 ) ( ref . 7 ) introduced celldesigner , a process diagram editor for gene - regulatory and biochemical networks featuring graphical representation and integration of standardized technologies . with regard to the approach utilized in simulation of systems biology , most previous work concentrated on building the logic model for the target biological system . uhrmacher and priami ( 2005 ) ( ref . 26 ) presented a discrete event systems specification in systems biology using π - calculus and added another modeling formalism to support micro - macro modeling in cell biology in ( uhrmacher et al . 2007 , ref . 25 ). mazemondet et al . ( 2009 ) ( ref . 18 ) investigated how to apply imperative π - calculus to model signaling pathway . busi and zandron ( 2006 ) ( ref . 3 ) applied brane calculi and membrane systems to model the behavior of a biological process , the ldl cholesterol degradation pathway . however , due to lack of experimental data , the verification of the model remains a big challenge . harris et al . ( 2009 ) ( ref . 9 ) extended the rule - based modeling language ( bngl ) to enable explicit modeling of the compartmental organization of the cell and its effects on system dynamics . instead of starting from formalism and then trying to verify the model , starting from the experimental data was used here , with parameters estimated via simulation of mass spectrum and then a meta - reaction model was built using system dynamics based on the optimized results . taking a closer look at the simulation of biosynthesis pathway , most of the previous work focused on modeling simple reactions . sahle et al . ( 2006 ) ( ref . 23 ) presented copasi , a new software tool for simulating and analyzing biochemical networks in the form of a + e ae → b + e . kwiatkowska et al . 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