A Model for Population Reproducing by Fission

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained.

show abstract

“…Equation (1.1) was derived in detail by Sinko & Streifer [1,2]. The cell division problem was studied by Hall & Wake [3].…”

Section: Introductionmentioning

confidence: 99%

Solutions to an advanced functional partial differential equation of the pantograph type

2015

View full text Add to dashboard Cite

show abstract

“…These models describe the temporal evolution of the distribution of the population over a state variable. The latter can include the cell mass (Sinko and Streifer, 1971;Subramanian and Ramkrishna, 1971), the age and/or volume of the cell (Bell and Anderson, 1967;Sinko and Streifer, 1967;Bell, 1968;Anderson et al, 1969;Sinko and Streifer, 1969), and also the molar contents of intracellular components (Ataai and Shuler, 1985;Mantzaris et al, 2001a;Mantzaris et al, 2001b;Mantzaris et al, 2001c;Henson et al, 2002). More recently Fredrickson and Mantzaris (2002) and Fredrickson (2003) expanded the CPB formulation to account for the transitions between the different phases of the cell cycle.…”

Section: Introductionmentioning

confidence: 99%

Cell population balance and hybrid modeling of population dynamics for a single gene with feedback

Stamatakis¹

2013

Computers & Chemical Engineering

View full text Add to dashboard Cite

Latest research on biological systems is steadily shifting from isolated single cells to entire cell populations. The latter are inherently heterogeneous, and their modeling requires approaches that explicitly account for this property. A comprehensive such approach is the cell population balance (CPB), which, however, is computationally expensive and becomes intractable for multivariable models.In this work, we demonstrate the use of model-reduction to efficiently simulate cell population heterogeneity in a genetic network of a single gene with feedback. Starting from a 4-species model we use singular perturbation analysis to derive a single equation for the intracellular protein concentration. We subsequently incorporate this equation to a hybrid model consisting of a CPB for the cell volume, and a continuum equation for the protein concentration. We finally compare the results obtained with the hybrid model with those of the full CPB, demonstrating the accuracy and computational efficiency of the hybrid methodology.

show abstract

“…In their paper "A model for populations reproducing by fission" [19], J. W. Sinko and W. Streif er presented a deterministic model decribing the dynamics of single species populations of organisms reproducing by binary fission. Starting from the assumption that the important physiological characteristics of these organisms can be described by their size alone, they derived a complicated nonlinear evolution equation which they solved numerically (moreover, the model is applied to populations of the planarian worm Dugesia tigrina and theory and experiments are compared with each other).…”

Section: Introductionmentioning

confidence: 99%

On the stability of the cell size distribution

Diekmann¹,

Heijmans²,

1984

View full text Add to dashboard Cite

Abstract. A model for the growth of a size-structured cell population reproducing by fission into two identical daughters is formulated and analysed. The model takes the form of a linear first order partial differential equation (balance law) in which one term has a transformed argument. Using semigroup theory and compactness arguments we establish the existence of a stable size distribution under a certain condition on the growth rate of the individuals. An example shows that one cannot dispense with this condition.

show abstract

A Model for Population Reproducing by Fission

Cited by 67 publications

References 3 publications

Solutions to an advanced functional partial differential equation of the pantograph type

Solutions to an advanced functional partial differential equation of the pantograph type

Cell population balance and hybrid modeling of population dynamics for a single gene with feedback

On the stability of the cell size distribution

Contact Info

Product

Resources

About