Biology subjects

Udema, I. I.

Publications and source records attributed to Udema, I. I..

5 recordsLinked to original sources

bioRxiv2023

Where Initial rates are directly proportional to Substrate concentrations with Application in Molar-mass Determination, Zero-order Specificity constant is Inappropriate

Background"High-ranking scientists" employ the initial rate (vi), expression without consideration for the conditions under which the vi expression can be used. The consequence is the suggestion that the vi is equal to the product of maximum velocity, Vmax, and substrate concentration [S0] divided by the Michaelis-Menten constant, KM. ObjectivesThe main objectives are: 1) to show that vi is not equal to Vmax[S0]/KM; 2) to show that the equilibrium dissociation constant, Kd, is strictly proportional to the concentration ([E0]) of the enzyme; and 3) to show that the two standard quasi-steady-state assumptions (sQSSA) and reverse QSSA (rQSSA) have a limited domain of validity. MethodsThe study was experimental and theoretical, supported by the Bernfeld method of enzyme assay. ResultKd is directly proportional to [E0], and vi is not equal to Vmax[S0]/KM.. A KM-like value that is greater than the putative Kd value, 2.482 g/L, is equal to 2.569 g/L. The KM-like values in other situations are 2.396 and 2.407 g/L; the corresponding equilibrium dissociation constant (Kd) values are, respectively, 2.288 and 2.299 g/L; the molar mass of insoluble potato starch ranges between 62.296 and 65.616 exp. (+6) g/mol. ConclusionThe equations that invalidate the assumption that vi is equal to Vmax[S0]/KM whenever [S0] is much less than KM were derived; the proposition that Kd is strictly proportional to [E0] was confirmed; the molar mass of starch could be calculated from the derived equation; and it was shown graphically and mathematically that both the sQSSA and rQSSA domains have a limit of validity; the equation with which to calculate the second order rate constant based on the conditions that validate the rQSSA is not applicable to the sQSSA. A KM-like value that is greater than the putative Kd value is possible. GRAPHICAL ABSTRACT O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=95 SRC="FIGDIR/small/535898v1_ufig1.gif" ALT="Figure 1"> View larger version (16K): org.highwire.dtl.DTLVardef@5eff08org.highwire.dtl.DTLVardef@b97aecorg.highwire.dtl.DTLVardef@13557d2org.highwire.dtl.DTLVardef@118bb62_HPS_FORMAT_FIGEXP M_FIG The graphical abstract illustrates three zones: the zone in which the sQSSA is valid, the zone in which the rQSSA is valid, and the zone in which neither assumption is exclusively valid. The curved arrow (oxblood) pointing to the red line depicts a tendency towards conditions that validate the rQSSA if the assay is conducted with an appropriate [S0]/[E0] ratio (< 1 to <<1) while the red curved arrow pointing to the blue line depicts a tendency towards conditions that validate the sQSSA if the assay is conducted with an appropriate [S0]/[E0] ratio (>1 to >>1). The enzyme-substrate complex (ES) is in a quasi-steady state with respect to S as depicted by {partial} [ES]/ {partial}t{approx}0, the sQSSA case, while in the rQSSA, it is the S that is in a quasi-steady state with respect to ES as depicted by {partial}[S0]/{partial}t{approx}0. The double-headed arrow merely shows, artistically, the limit of the data points. C_FIG

biochemistry↗

bioRxiv2023

Alternative equations and "pseudo-statistical" approaches that enhance the precision of initial rates for the determination of kinetic parameters

A burning concern among researchers studying enzyme kinetics has been ways of improving the accuracy of initial rates (v) with much greater precision. The goal of this study was to establish a formal (mathematical) way of achieving more accurate v values in enzyme assay. By adopting Bernfeld method of assay, the v values generated and other values in the literature were explored with two main objectives:1) to derive equations for a correctional calculation of initial rates and for the calculation of Michaelis-Menten (MM) parameters and 2) to evaluate the derived equations. The results of study showed that the maximum velocity (Vmax) and the MM constant (KM) obtained from a robust nonlinear regression (RNR) using v values in the literature were respectively between 21 and 26-fold and 6.56 to 61.2-fold greater than values generated from other method such as double reciprocal plot (drp), reciprocal variant of direct linear plot (RVDLP), and new method (z-model) derived based on MM equation; the Vmax and KM values (for alpha-amylase) calculated based on the RVDLP using the uncorrected v values were respectively 1.26- and 1.264-fold greater than the values using corrected v values; based on the z method, the Vmax and KM values using the uncorrected v values were 179.8- and 9.35-fold greater than the values using their corrected counterparts. In conclusion, the erroneous initial rates can be corrected using new equations before fitting RNR, RVDLP, drp, and any other equation to the corrected v values for the determination of MM parameters. Graphical Abstract figure O_FIG O_LINKSMALLFIG WIDTH=122 HEIGHT=200 SRC="FIGDIR/small/524223v1_ufig1.gif" ALT="Figure 1"> View larger version (22K): org.highwire.dtl.DTLVardef@2d6dcborg.highwire.dtl.DTLVardef@833f08org.highwire.dtl.DTLVardef@9f4648org.highwire.dtl.DTLVardef@bf2e9f_HPS_FORMAT_FIGEXP M_FIG C_FIG The implication of the result in b (i) is that the Vmax and KM should either be a negative value or infinite value according to the equations unlike b (ii).

biochemistry↗

bioRxiv2023

The life span of steps in the enzyme-catalyzed reaction, its implications, and matters of general interest

There is increasing recognition for steps and their life span (LS) in the enzyme-catalyzed reaction pathway; the need for rate constants, activation parameters, and transition states (TS) has assumed preeminence in the literature. The determination of the life span of complexes, enzyme-product (EP) complexes in particular, is not a regular feature in most studies. The study aims to show that there is LS for EP and TS destined for irreversible product formation and release. The cognate objectives are to: 1) derive the equation for the graphical determination of the first-order rate constant (FORC) of EP dissociation into E and P as well as the FORC of ES dissociation to free enzyme, E, and free substrate, S; 2) derive a FORC equation for the TS to EP conversion; 3) calculate the duration; and 4) calculate the FORC for the TS to EP conversion. Using mesophilic alpha-amylase and the Bernfeld method of assay, the velocities of catalysis were used to generate first the Michaelian parameters and then the rate constants. The LS of the TS and the FORC for the conversion of the enzyme-substrate (ES) complex to TS are 4.321 exp. (-6) min and 2.314 exp. (+5)/min, respectively; the LS of the TS destined for backward conversion (deactivation) to ES and its FORC are 7.525 exp. (-7) min and 1.387 exp. (+6)/min, respectively; the LS of the EP and its FORC for dissociation to E and P are 1.33 exp. (-5) and 7.52 exp. (+4)/min respectively. In conclusion, there are always steps in an enzyme-catalyzed reaction in the catalytic cycle; the LS of each step is shorter than the total LS of deactivation and dissociation processes; this is applicable to forward reactions. Thermodynamic activation parameters must account for all FORC in accordance with the additivity principle.

biochemistry↗

bioRxiv2022

Directly and indirectly determinable rate constants in Michaelian enzyme-catalyzed reactions

Backed by kinetic schemes, attempts had been made to derive equations for the calculation of all zero-order first-order rate constants (ZOFORC) for the activation of the enzyme-substrate (ES) complex and its deactivation, k+2 and k -2, respectively. The values of ZOFORC, including the kind for the dissociation of the enzyme-product complex (EP) to free enzyme (E) and product (P), are hardly reported. The methods of research were primarily Bernfeld and Lineweaver methods. The goal of the research was to determine ways for the utilization of experimental data for the determination of verifiable and quantifiable rate constants, with the following objectives: 1) To derive equations for the first order rate constants, k+2 and k-2, for the activation of ES and its deactivation, respectively; 2) to quantify by calculation the first order rate constant for product release; 3) ultimately quantify the rate constants, k-2 and k+2; and 4) to advise the reactor, process, chemical engineers, etc. in different industrial concerns on the usefulness of k-2 and k+2. The value of ZOFORC for the dissociation of EP to free E and P is 3.155 exp. (+5)/min; the values of k+2 and k-2 are 3.513 exp. (+4) and 2.377 exp. (+8)/min, respectively. Ultimately, it is imperative for all stakeholder groups to devise means of controlling the enzymatic rate of catalysis by manipulating the magnitudes of k+2 and k-2 in particular. The derived equations can be fitted to the experimentally generated and calculated data. A future research project should entail conducting the assay under optimum conditions so as to verify possible variations in the ZOFORC values when compared with values generated outside optimum conditions.

biochemistry↗

bioRxiv2022

Derivation of Steady-State First-order Rate Constant Equations for Enzyme-Substrate Complex Dissociation, as well as Zero-order Rate Constant Equations in Relation to Background Assumptions

The maximum velocity (Vmax) of catalysis and the substrate concentration ([ST]) at half the Vmax, the KM, are regarded as steady-state (SS) parameters even though they are the outcomes of zero-order kinetics (ZOK). The research was aimed at disputing such a claim with the following objectives: To: 1) carry out an overview of issues pertaining to the validity of assumptions; 2) derive the needed steady-state (SS) equations distinct from Michaelian equations that can be fitted to both experimental variables and kinetic parameters; 3) calculate the SS first-order rate constant for the dissociation of enzyme-substrate complex (ES) to free substrate, S and enzyme, E; 4) derive the equation of rate constant as a function of the reciprocal of the duration of each catalytic event in the reaction pathway. The experimental values of the data were generated by Bernfeld and Lineweaver-Burk methods. The calculated SS 1st order-order rate constant was << the zero-order Michaelian value, and the difference is {approx} 97.59 % of the zero-order value; the SS catalytic rate differed from the zero-order catalytic rate by {approx} 76.41 % of the latter value; and it was {approx} 93.87 % with respect to the 2nd order rate constant for the formation of enzyme-substrate complex. The equations of time-dependent rate constants, KM, and dissociation constants were derived. The concentration [ST] of the S must be > the concentration ([E0]) of the E for the quasi-steady-state assumption (or approximation) to hold. The SS kinetic parameters are not equivalent to zero-order parameters.

biochemistry↗