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ABSTRACT The Monod equation has been widely applied as the general rate law of microbial growth, but its applications are not always successful. By drawing on the frameworks of kinetic and stoichiometric metabolic models and metabolic control analysis, the modeling reported here simulated the growth kinetics of a methanogenic microorganism and illustrated that different enzymes and metabolites control growth rate to various extents and that their controls peak at either very low, intermediate, or very high substrate concentrations. In comparison, with a single term and two parameters, the Monod equation only approximately accounts for the controls of rate-determining enzymes and metabolites at very high and very low substrate concentrations, but neglects the enzymes and metabolites whose controls are most notable at intermediate concentrations. These findings support a limited link between the Monod equation and methanogen growth, and unify the competing views regarding enzyme roles in shaping growth kinetics. The results also preclude a mechanistic derivation of the Monod equation from methanogen metabolic networks and highlight a fundamental challenge in microbiology: single-term expressions may not be sufficient for accurate prediction of microbial growth. IMPORTANCE The Monod equation has been widely applied to predict the rate of microbial growth, but its application is not always successful. Using a novel metabolic modeling approach, we simulated the growth of a methanogen and uncovered a limited mechanistic link between the Monod equation and the methanogen’s metabolic network. Specifically, the equation provides an approximation to the controls by rate-determining metabolites and enzymes at very low and very high substrate concentrations, but it is missing the remaining enzymes and metabolites whose controls are most notable at intermediate concentrations. These results support the Monod equation as a useful approximation of growth rates and highlight a fundamental challenge in microbial kinetics: single-term rate expressions may not be sufficient for accurate prediction of microbial growth. 

The Monodequationhasbeenwidelyappliedasthegeneralratelaw of microbialgrowth,butitsapplicationsarenotalwayssuccessful.Bydrawingon the frameworksofkineticandstoichiometricmetabolicmodelsandmetaboliccon- trol analysis,themodelingreportedheresimulatedthegrowthkineticsofametha- nogenic microorganismandillustratedthatdifferentenzymesandmetabolitescon- trol growthratetovariousextentsandthattheircontrolspeakateitherverylow, intermediate, orveryhighsubstrateconcentrations.Incomparison,withasingle term andtwoparameters,theMonodequationonlyapproximatelyaccountsforthe controls ofrate-determiningenzymesandmetabolitesatveryhighandverylow substrate concentrations,butneglectstheenzymesandmetaboliteswhosecontrols are mostnotableatintermediateconcentrations.These findings supportalimited link betweentheMonodequationandmethanogengrowth,andunifythecompet- ing viewsregardingenzymerolesinshapinggrowthkinetics.Theresultsalsopre- clude amechanisticderivationoftheMonodequationfrommethanogenmetabolic networks andhighlightafundamentalchallengeinmicrobiology:single-termexpres- sions maynotbesufficient foraccuratepredictionofmicrobialgrowth. 

For many decades, educational communities, including computing education, have debated the value of telling students what they need to know (i.e., direct instruction) compared to guiding them to construct knowledge themselves (i.e., constructivism). Comparisons of these two instructional approaches have inconsistent results. Direct instruction can be more efficient for short-term performance but worse for retention and transfer. Constructivism can produce better retention and transfer, but this outcome is unreliable. To contribute to this debate, we propose a new theory to better explain these research results. Our theory, multiple conceptions theory, states that learners develop better conceptual knowledge when they are guided to compare multiple conceptions of a concept during instruction. To examine the validity of this theory, we used this lens to evaluate the literature for eight instructional techniques that guide learners to compare multiple conceptions, four from direct instruction (i.e., test-enhanced learning, erroneous examples, analogical reasoning, and refutation texts) and four from constructivism (i.e., productive failure, ambitious pedagogy, problem-based learning, and inquiry learning). We specifically searched for variations in the techniques that made them more or less successful, the mechanisms responsible, and how those mechanisms promote conceptual knowledge, which is critical for retention and transfer. To make the paper directly applicable to education, we propose instructional design principles based on the mechanisms that we identified. Moreover, we illustrate the theory by examining instructional techniques commonly used in computing education that compare multiple conceptions. Finally, we propose ways in which this theory can advance our instruction in computing and how computing education researchers can advance this general education theory. 

Using laser excitation, expression microdissection (xMD) can selectively heat cancer cells targeted via immunohistochemical staining to enable their selective retrieval from tumor tissue samples, thus reducing misdiagnoses caused by contamination of noncancerous cells. Several theoretical models have been validated for the photothermal effect in highly light absorbing and scattering media. However, these models are not generally applicable to the physics behind the process of xMD. In this study, we propose a thermal model that can analyze the transient temperature distribution and heat melt zone in an xMD sample medium composed of a thermoplastic film and a tumor tissue sample sandwiched between two glass slides. Furthermore, we experimentally examined the model using an ink layer with controllable optical properties to serve as a microscale-thin, tissue-mimicking phantom and found the experimentally measured film temperature is in good agreement with the model predictions. The validated model can help researchers to optimize cell retrieval by xMD for improved diagnostics of cancer and other diseases.