A mathematical model of N-linked glycosylation

Metabolic engineering of N-linked oligosaccharide biosynthesis to produce novel glycoforms or glycoform distributions of a recombinant glycoprotein can potentially lead to an improved therapeutic performance of the glycoprotein product. A mathematical model for the initial stages of this process, up to the first galactosylation of an oligosaccharide, was previously developed by Umana and Bailey (1997) (UB1997). Building on this work, an extended model is developed to include further galactosylation, fucosylation, extension of antennae by N-acetyllactosamine repeats, and sialylation. This allows many more structural features to be predicted. A number of simplifying assumptions are also relaxed to incorporate more variables for the control of glycoforms. The full model generates 7565 oligosaccharide structures in a network of 22,871 reactions. Methods for solving the model for the complete product distribution and adjusting the parameters to match experimental data are also developed. A basal set of kinetic parameters for the enzyme-catalyzed reactions acting on free oligosaccharide substrates is obtained from the previous model and existing literature. Enzyme activities are adjusted to match experimental glycoform distributions for Chinese Hamster Ovary (CHO). The model is then used to predict the effect of increasing expression of a target glycoprotein on the product glycoform distribution and evaluate appropriate metabolic engineering strategies to return the glycoform profile to its original distribution pattern. This model may find significant utility in the future to predict glycosylation patterns and direct glycoengineering projects to optimize glycoform distributions.     

A mathematical model of sialylation of N-linked oligosaccharides in the trans-Golgi network

A mathematical model is developed of the compartmentalized sialylationof N-linked oligosaccharides in order to understand and predictthe outcome of sialylation reactions. A set of assumptions arepresented, including Michaelis-Menten-type dependency of reactionrate on the concentration of the glycoprotein substrate. Theresulting model predicts the heterogeneous outcome of a posttranslationaloligosaccharide biosynthesis step, a critical aspect that isnot accounted for in the modeling of the cotranslational attachmentof oligosaccharides to glycosylation sites (Shelikoff et al.,Biotech. Bioeng., 50, 73–90, 1996) or general models ofthe secretion process (Noe and Delenick, J. Cell Sci, 92, 449–459,1989). In the steady-state for the likely case where the concentrationof substrate is much less than the K_m of the sialyltransferase,the model predicts that the extent of sialylation, x, will dependupon the enzyme concentration, enzyme kinetic parameters andsubstrate residence time in the reaction compartment. The valueof x predicted by the model using available literature datais consistent with the values of x that have been recently determinedfor the glycoproteins CD4 (Spellman et al, Biochemistry, 30,2395–2406, 1991) and t-PA (Spellman et al, J. Biol Chem.,264, 14100–14111, 1989) secreted by Chinese hamster ovarycells. For the unsaturated case, the model also predicts thatx is independent of the concentration of secreted glycoproteinin the Golgi. The general modeling approach outlined in thisarticle may be applicable to other glycosylation reactions andposttranslational modifications. model sialylation N-linked glycosylation     

A mathematical model of kinetics of the biosynthesis of tetracyclines

Summary A mathematical model simulating the behaviour or Streptomyces aureofaciens in batch culture under conditions when tetracyclines are synthesized in excessive amounts has been formulated. The response of the mathematical model to the experimental conditions applied corresponds with data obtained in the experiments. The mathematical model demonstrated that the level of tetracycline production is determined during the period of culture growth beginning with exhaustion of inorganic phosphate from the medium and ending with inhibition of the synthesis of enzymes caused by the synthesized tetracyclines. Further tetracycline synthesis is then proportional to the amount of enzymes synthesized in this interval.List of symbols E Activity of ACT-oxygenase (10×nkat/g) - P Product concentration (mg/l) - k ₁-k ₆ Rate constants - K _S Saturation constant (g sugar/l) - K _I1 Inhibition constant (mg product/l) - K _I2 Inhibition constant (mM phosphate/l) - K _I3 Inhibition constant (mg product/l) - S ₁ Substrate sucrose (g sugar/l) - S ₂ Substrate concentration — phosphate (mM/l) - r _P Specific rate of product formation (mg product/g · h) - r _E Specific rate of enzyme synthesis (10×nkat/g² · h), Expressed by activity units - t Cultivation time (hour) - X Biomass dry weight (g/l) - Y _S/X Yield coefficient - Specific growth rate (h^-1)     

N-linked glycan of a sperm CD52 glycoform associated with human infertility.

In a benchmark study, Isojima and colleagues established H6-3C4, the first successful heterohybridoma immortalized from the peripheral blood lymphocytes of an infertile woman who exhibited high sperm-immobilizing antibody titers. The present report demonstrates the identity between the glycoprotein antigens recognized by the human H6-3C4 monoclonal antibody (mAb) and the murine S19 mAb, generated in our laboratory to sperm agglutination antigen-1 (SAGA-1). Both mAb's recognize N-linked carbohydrate epitopes on the 15-25 kDa, polymorphic SAGA-1 glycoprotein that is localized to all domains of the human sperm surface. Treatment with phosphatidylinositol-specific phospholipase C demonstrated that SAGA-1 is anchored in the sperm plasmalemma via a GPI-lipid linkage. Immunoaffinity purification and microsequencing indicated that the core peptide of the SAGA-1 glycoprotein is identical to the sequence of CD52, a GPI-anchored lymphocyte differentiation marker implicated in signal transduction. Comparison of anti-SAGA-1 and anti-CD52 immunoreactivities revealed that the sperm form of CD52 exhibits N-linked glycan epitopes, including the epitope recognized by the infertility-associated H6-3C4 mAb, which are not detected on lymphocyte CD52. Thus, the two populations of the CD52 glycoprotein on lymphocytes and spermatozoa represent glycoforms, glycoprotein isoforms with the same core amino acid sequence but different carbohydrate structures. Furthermore, mAb's to the unique carbohydrate epitopes on sperm CD52 have multiple inhibitory effects on sperm function, including a cytotoxic effect on spermatozoa in the presence of complement. These results are the first to implicate unique carbohydrate moieties of a sperm CD52 glycoform as target epitopes in the anti-sperm immune response of an infertile woman. Furthermore, localization of CD52 on all domains of the sperm surface coupled with the multiple sperm-inhibitory effects of antibodies to its unique carbohydrate moieties suggest opportunities for immunocontraceptive development.     

A dynamic mathematical model for monoclonal antibody N-linked glycosylation and nucleotide sugar donor transport within a maturing Golgi apparatus

Monoclonal antibodies (mAbs) are one of the most important products of the biopharmaceutical industry. Their therapeutic efficacy depends on the post-translational process of glycosylation, which is influenced by manufacturing process conditions. Herein, we present a dynamic mathematical model for mAb glycosylation that considers cisternal maturation by approximating the Golgi apparatus to a plug flow reactor and by including recycling of Golgi-resident proteins (glycosylation enzymes and transport proteins [TPs]). The glycosylation reaction rate expressions were derived based on the reported kinetic mechanisms for each enzyme, and transport of nucleotide sugar donors [NSDs] from the cytosol to the Golgi lumen was modeled to serve as a link between glycosylation and cellular metabolism. Optimization-based methodologies were developed for estimating unknown enzyme and TP concentration profile parameters. The resulting model is capable of reproducing glycosylation profiles of commercial mAbs. It can further reproduce the effect gene silencing of the FucT glycosylation enzyme and cytosolic NSD depletion have on the mAb oligosaccharide profile. All novel elements of our model are based on biological evidence and generate more accurate results than previous reports. We therefore believe that the improvements contribute to a more detailed representation of the N-linked glycosylation process. The overall results show the potential of our model toward evaluating cell engineering strategies that yield desired glycosylation profiles. Additionally, when coupled to cellular metabolism, this model could be used to assess the effect of process conditions on glycosylation and aid in the design, control, and optimization of biopharmaceutical manufacturing processes.     

N-linked glycoprotein biosynthesis in the developing mouse embryo

We have developed microenzymic assays that have, for the first time, enabled analysis of several enzymes in the pathway for N-linked glycoprotein biosynthesis in pre- and peri-implantation mouse embryos. The in vitro activities of the glycosyl transferases responsible for the formation of N-acetylglucosaminylpyrophosphoryldolichol,N, N'-diacetyl-chitobiosylpyrophosphoryldolichol, mannosylphosphoryldolichol, and glucosylphosphoryldolichol were found to decrease after fertilization before increasing significantly at the blastocyst stage, a stage that was also found to be highly sensitive to the glycosylation inhibitor, tunicamycin. The observed elevation in the activities of these enzymes in blastocysts still occurred when ebbryos were cultured in alpha-amanitin, indicating that de novo mRNA synthesis is unnecessary for the observed increase in their activities. Thus, an elevated capacity for N-glycosylation exists at the blastocyst stage, a time when dramatic increases in cell-cell interactions are known to occur.     

Inhibitors of the biosynthesis and processing of N-linked oligosaccharides

A number of glycoproteins have oligosaccharides linked to protein in a GlcNAc----asparagine bond. These oligosaccharides may be either of the complex, the high-mannose or the hybrid structure. Each type of oligosaccharides is initially biosynthesized via lipid-linked oligosaccharides to form a Glc3Man9GlcNAc2-pyrophosphoryl-dolichol and transfer of this oligosaccharide to protein. The oligosaccharide portion is then processed, first of all by removal of all three glucose residues to give a Man9GlcNAc2-protein. This structure may be the immediate precursor to the high-mannose structure or it may be further processed by the removal of a number of mannose residues. Initially four alpha 1,2-linked mannoses are removed to give a Man5 - GlcNAc2 -protein which is then lengthened by the addition of a GlcNAc residue. This new structure, the GlcNAc- Man5 - GlcNAc2 -protein, is the substrate for mannosidase II which removes the alpha 1,3- and alpha 1,6-linked mannoses . Then the other sugars, GlcNAc, galactose, and sialic acid, are added sequentially to give the complex types of glycoproteins. A number of inhibitors have been identified that interfere with glycoprotein biosynthesis, processing, or transport. Some of these inhibitors have been valuable tools to study the reaction pathways while others have been extremely useful for examining the role of carbohydrate in glycoprotein function. For example, tunicamycin and its analogs prevent protein glycosylation by inhibiting the first step in the lipid-linked pathway, i.e., the formation of Glc NAc-pyrophosphoryl-dolichol. These antibiotics have been widely used in a number of functional studies. Another antibiotic that inhibits the lipid-linked saccharide pathway is amphomycin, which blocks the formation of dolichyl-phosphoryl-mannose. In vitro, this antibiotic gives rise to a Man5GlcNAc2 -pyrophosphoryl-dolichol from GDP-[14C]mannose, indicating that the first five mannose residues come directly from GDP-mannose rather than from dolichyl-phosphoryl-mannose. Other antibodies that have been shown to act at the lipid-level are diumycin , tsushimycin , tridecaptin, and flavomycin. In addition to these types of compounds, a number of sugar analogs such as 2-deoxyglucose, fluoroglucose , glucosamine, etc. have been utilized in some interesting experiments. Several compounds have been shown to inhibit glycoprotein processing. One of these, the alkaloid swainsonine , inhibits mannosidase II that removes alpha-1,3 and alpha-1,6 mannose residues from the GlcNAc- Man5GlcNAc2 -peptide. Thus, in cultured cells or in enveloped viruses, swainsonine causes the formation of a hybrid structure.(ABSTRACT TRUNCATED AT 400 WORDS)     

A mathematical model of cleavage

In the present paper, we propose a mathematical model of cleavage. Cleavage is a process during the early stages of development in which the fertile egg undergoes repeated division keeping the cluster size almost constant. During the cleavage process individual cells repeat cell division in an orderly manner to form a blastula, however, the mechanism which achieves such a coordination is still not very clear. In the present research, we took sea urchin as an example and focused on the diffusion of chemical substances from the animal and vegetal pole. By considering chemotactic motion of the centrosomes, we constructed a mathematical model that describes the processes in the early stages of cleavage.     

A mathematical model of mitochondrial swelling

Background

Salmonid alphavirus (SAV) is a widespread pathogen in European aquaculture of salmonid fish. Distinct viral subtypes have been suggested based on sequence comparisons and some of these have different geographical distributions. In Norway, only SAV subtype 3 have so far been identified. Little is known about viral mechanisms important for pathogenesis and transmission. Tools for detailed exploration of SAV genomes are therefore needed.

Results

Infectious cDNA clones in which a genome of subtype 3 SAV is under the control of a CMV promoter were constructed. The clones were designed to express proteins that are putatively identical to those previously reported for the SAVH20/03 strain. A polyclonal antiserum was raised against a part of the E2 glycoprotein in order to detect expression of the subgenomic open reading frame (ORF) encoding structural viral proteins. Transfection of the cDNA clone revealed the expression of the E2 protein by IFAT, and in serial passages of the supernatant the presence of infectious recombinant virus was confirmed through RT-PCR, IFAT and the development of a cytopathic effect similar to that seen during infection with wild type SAV. Confirmation that the recovered virus originated from the infectious plasmid was done by sequence identification of an introduced genetic tag. The recombinant virus was infectious also when an additional ORF encoding an EGFP reporter gene under the control of a second subgenomic alphavirus promoter was added. Finally, we used the system to study the effect of selected point mutations on infectivity in Chinook salmon embryo cells. While introduced mutations in nsP2₁₉₇, nsP3₂₆₃ and nsP3₃₂₃ severely reduced infectivity, a serine to proline mutation in E2₂₀₆ appeared to enhance the virus titer production.

Conclusion

We have constructed infectious clones for SAV based on a subtype 3 genome. The clones may serve as a platform for further functional studies.     

A mathematical model of glutathione metabolism

Background and hypothesis

Based on neurochemical and genetic evidence, we suggest that both prevention and treatment of multiple addictions, such as dependence to alcohol, nicotine and glucose, should involve a biphasic approach. Thus, acute treatment should consist of preferential blocking of postsynaptic Nucleus Accumbens (NAc) dopamine receptors (D1-D5), whereas long term activation of the mesolimbic dopaminergic system should involve activation and/or release of Dopamine (DA) at the NAc site. Failure to do so will result in abnormal mood, behavior and potential suicide ideation. Individuals possessing a paucity of serotonergic and/or dopaminergic receptors, and an increased rate of synaptic DA catabolism due to high catabolic genotype of the COMT gene, are predisposed to self-medicating any substance or behavior that will activate DA release, including alcohol, opiates, psychostimulants, nicotine, gambling, sex, and even excessive internet gaming. Acute utilization of these substances and/or stimulatory behaviors induces a feeling of well being. Unfortunately, sustained and prolonged abuse leads to a toxic" pseudo feeling" of well being resulting in tolerance and disease or discomfort. Thus, a reduced number of DA receptors, due to carrying the DRD2 A1 allelic genotype, results in excessive craving behavior; whereas a normal or sufficient amount of DA receptors results in low craving behavior. In terms of preventing substance abuse, one goal would be to induce a proliferation of DA D2 receptors in genetically prone individuals. While in vivo experiments using a typical D2 receptor agonist induce down regulation, experiments in vitro have shown that constant stimulation of the DA receptor system via a known D2 agonist results in significant proliferation of D2 receptors in spite of genetic antecedents. In essence, D2 receptor stimulation signals negative feedback mechanisms in the mesolimbic system to induce mRNA expression causing proliferation of D2 receptors.

Proposal and conclusion

The authors propose that D2 receptor stimulation can be accomplished via the use of Synapatmine?, a natural but therapeutic nutraceutical formulation that potentially induces DA release, causing the same induction of D2-directed mRNA and thus proliferation of D2 receptors in the human. This proliferation of D2 receptors in turn will induce the attenuation of craving behavior. In fact as mentioned earlier, this model has been proven in research showing DNA-directed compensatory overexpression (a form of gene therapy) of the DRD2 receptors, resulting in a significant reduction in alcohol craving behavior in alcohol preferring rodents. Utilizing natural dopaminergic repletion therapy to promote long term dopaminergic activation will ultimately lead to a common, safe and effective modality to treat Reward Deficiency Syndrome (RDS) behaviors including Substance Use Disorders (SUD), Attention Deficit Hyperactivity Disorder (ADHD), Obesity and other reward deficient aberrant behaviors. This concept is further supported by the more comprehensive understanding of the role of dopamine in the NAc as a "wanting" messenger in the meso-limbic DA system.     

A mathematical model of iron metabolism

A mathematical model of iron metabolism is presented. It comprises the following iron pools within the body: transferrin-bound iron in the plasma, iron in circulating red cells and their bone marrow precursors, iron in mucosal, parenchymal and reticuloendothelial cells. The control exerted by a hormone, called erythropoietin, on bone marrow utilization of iron for hemoglobin synthesis is taken into account. The model so obtained consists of a system of functional differential equations of retarded type. Most model parameters can be estimated from radiotracer experiments, others can be measured and numerical values can be assigned to the remaining ones making few reasonable assumptions according to the available physiological knowledge. Iron metabolism behavior under different therapeutical treatments was simulated. Model predictions were compared to experimental data collected in clinical routine.This work has been partially supported by C.N.R. (Italy) through grants N. 80.01227.07 and N. 81.00888.07     

A mathematical model of the urethra

Models having the form of surfaces of revolution may be used to represent the urethra under pre-voiding pressure. From such models are derived formulas for calculating muscle tension from the shape of a urethragram.     

A mathematical model of canine granulocytopoiesis

Summary The granulocyte cell renewal system of the dog is represented by a mathematical model consisting of the following compartments: The pool of pluripotential stem cells, the committed stem cell pool, divided into a blood and a bone marrow compartment, the proliferation pool, the maturation pool, the reserve pool and the blood pool of functional granulocytes. This chain of compartments is described by a system of non-linear differential equations. Cell losses anyplace in the system provoke increased production in all pools containing cells capable to divide. A reduced number of granulocytes in the blood pool stimulates production of a granulocyte releasing factor which mobilizes a rising number of cells to transit from the marrow reserve into the blood pool.The model was simulated on a digital computer. It was found to be capable to reproduce the steady state conditions and it also fits the data of two distinct experimental perturbations of the system both equally well. These perturbations are a loss of proliferating cells as it occurs after the administration of cytostatic drugs and losses of functional cells as they are induced by leukapheresis experiments of differing leukapheresis rates.This study was supported by the Deutsche Forschungsgemeinschaft (SFB 112)     

A mathematical model of biological evolution

In order to understand generally how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dN _n (t)/dt=(m _n (t-)N _n (t)+N _n-1(t) (n=0,1,2,3...), where N _n (t) and m _n (t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t and is the mutation rate, assumed to be a positive constant. The step number of each replicon is defined as either equal to or larger by one than that of its parent, the latter case occurring when and only when mutation has taken place. The average evolution rate defined by is rigorously obtained for the case (i) m _n (t)=m _n is independent of t (constant fitness model), where m _n is essentially periodic with respect to n, and for the case (ii) (periodic fitness model), together with the long time average m of the average Malthusian parameter . The biological meaning of the results is discussed, comparing them with the features of actual molecular evolution and with some results of computer simulation of the model for finite populations.An early version of this study was read at the International Symposium on Mathematical Topics in Biological held in kyoto, Japan, on September 11–12, 1978, and was published in its Procedings.