Alisa S. Vadasz

On the Distinction Between Lag and Delay in Population Growth

The analysis and results presented in this paper provide conclusive evidence to distinguish between the delay effect and the lag as two biologically distinct phenomena. It therefore dispels the incorrect notion that delay effects represented by delay differential equations are the biological reason behind the lag phase in microorganism growth. The resulting consequence so far is that the only other reason for the lag phase is the existence of unstable stationary states. The latter are a result of accounting for the microbial metabolic mass transfer in the population growth process.

Metabolic Mass Transfer in Monotonic Growth of Microorganisms

Microorganism growth and reproduction have been traditionally modeled independently of the direct effect of the metabolic process. The latter caused inconsistencies between the modeling results and experimental data. A major inconsistency was linked to the experimentally observed lag phase in the growth process. Attempts to associate the lag phase to delay processes have been recently proven incorrect. The only other alternative is the existence of unstable stationary states resulting from the explicit inclusion of the metabolic mass transfer process via the resource consumption and utilization. The proposed theory that accounts for the latter is presented, analyzed, and compared with experimental data both qualitatively as well as quantitatively.

WEAK NONLINEAR ANALYSIS OF THE NEOCLASSICAL GROWTH MODEL AT SPATIALLY HOMOGENEOUS CONDITIONS

The neoclassical growth model is being analyzed subject to spatially homogeneous perturbations by using the weak nonlinear method of solution and comparing its results to the numerical solution. The latter expands the analytical tools beyond the investigation of Turing instability. The results identify a Hopf bifurcation at a critical value of a controlling parameter, and their comparison to direct numerical solutions show an excellent match in the neighborhood of this critical value and for amplitudes of oscillations that are not too large.

ON THE GOMPERTZ LIMIT OF THE MONOTONIC NEOCLASSICAL GROWTH MODEL

The burden of proof of any theory aiming to represent a physical or biological reality by demonstrating its unifying properties is applied in the present paper in relation to the Neoclassical growth model and its ability to reproduce Gompertz growth. The Neoclassical growth model derived from first biological and physical principles was shown to capture all qualitative features that were revealed experimentally, including the possibility of a Logarithmic Inflection Point (LIP), the possibility of a LAG, concave as well as convex curves on the phase diagram, the Logistic growth as a special case, growth followed by decay, as well as oscillations. In addition, quantitative validation demonstrated its ability to reproduce experimental data in a few tested cases. This paper demonstrates that the Neoclassical growth model can reproduce a Generalized version of Gompertz growth too.

LINEAR STABILITY ANALYSIS OF THE NEOCLASSICAL GROWTH MODEL TO SPATIALLY HOMOGENEOUS PERTURBATIONS

A linear stability analysis of the stationary solutions for growth of populations with respect to Spatially Homogeneous Perturbations (SHoP) is presented. The Neoclassical growth theory is extended to apply to spatially heterogeneous populations. The latter includes the metabolic mass transfer effects and allows for the recovery of substantial and distinct phenomena observed experimentally, such as the mechanism controlling the LAG phase, a result that holds impressive future potential in diverse applications. The stability conditions are expressed explicitly in terms of the primitive parameters of the original nonlinear system. The results are necessary when undertaking a corresponding linear stability analysis for growth of populations with respect to Spatially Heterogeneous Perturbations (SHeP).

Impact of Metabolic Mass Transfer on Monotonic Growth of Micro-Organisms

A proposed Neoclassical growth theory of micro-organisms is shown to apply in a much wider variety of cases, from micro-level organisms via animal and human cell growth and up to the macro-level populations encountered in ecology. Including the metabolic mass transfer effects, that are an essential ingredient of the Neoclassical Theory, allows for the recovery of substantial and distinct phenomena observed experimentally. The proposed theory identifies the mechanism controlling the Lag phase, a result that holds impressive future potential in diverse applications. Different theoretical results are presented and compared with experimental data to substantiate the claim that the model based on the Neoclassical Growth Theory is the only available model that produces results, which are consistent with all experimental evidence.Copyright