Biomixing by Chemotaxis and Enhancement of Biological Reactions

By Alexander V. Kiselev, Lenya Ryzhik. 2011

146 citations recorded by the source corpus.

Many phenomena in biology involve both reactions and chemotaxis. These processes can clearly influence each other, and chemotaxis can play an important role in sustaining and speeding up the reaction. However, to the best of our knowledge, the question of reaction enhancement by chemotaxis has not yet received extensive treatment either analytically or numerically. We consider a model with a single density function involving diffusion, advection, chemotaxis, and absorbing reaction. The model is motivated, in particular, by studies of coral broadcast spawning, where experimental observations of the efficiency of fertilization rates significantly exceed the data obtained from numerical models that do not take chemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes) into account. We prove that in the framework of our model, chemotaxis plays a crucial role. There is a rigid limit to how much the fertilization efficiency can be enhanced if there is no chemotaxis but only advection and diffusion. On the other hand, when chemotaxis is present, the fertilization rate can be arbitrarily close to being complete provided that the chemotactic attraction is sufficiently strong. Moreover, an interesting feature of the estimates on fertilization rate and timescales in the chemotactic case is that they do not depend on the amplitude of the reaction term.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/0fdd8df382f3843d1c48d6c22212f311032dfffc

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Citations in the corpus

How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? (2015, background): “This may become substantially different in situations when different types of boundary conditions are considered, possibly accounting for signal influx, or when signal absorption is replaced with mechanisms of signal production by cells, as recently proposed and studied in contexts involving fluid i”
Suppression of Chemotactic Explosion by Mixing (2015, background): “The problem of chemotaxis in fluid flow has been studied before; for example, in a setting similar to ours [21], [22] studied the effect of chemotaxis and fluid advection on the efficiency of absorbing reaction.”
Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid system (2015, methodology): “In particular, the system (1.1) thereby includes the outcomes of the modeling approaches for biomixing recently presented by Espejo and Suzuki ([5]) on the basis of an original work by Kiselev and Ryzhik ([13], [14]).”
Blow-up prevention by quadratic degradation in a two-dimensional Keller–Segel–Navier–Stokes system (2016, background): “For instance, in the modeling context addressed in [18] the number r was chosen to be zero according to the natural assumption that there is no production of eggs and sperm at the considered stage of coral fertilization.”
Global existence and boundedness in a 3D Keller–Segel–Stokes system with nonlinear diffusion and rotational flux (2017, unknown): “Motivated by the modeling background [18,26], Wang and the second author [34,36] recently established the global existence and boundedness of solutions to the following Keller–Segel–Stokes system in a bounded domain Ω ⊂ R (d = 2, 3): ⎧ ⎪⎪⎨ ⎪⎪⎩ nt + u · ∇n = Δn − ∇ · ( nS(x, n, c)∇c, x ∈ Ω, t > 0, ct”
A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization (2019, background): “also the particular chemotaxis-fluid model introduced in [28]) we assume the underlying mechanisms to be of essentially (self-)competition type, thus leading to standard quadratic absorption.”
Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation (2018, background): “1), inter alia accounting for nonlinear cell diffusion ([51], [6], [41], [55], [58]), for variants in the cross-diffusive interaction ([53], [20], [4], [39], [57]) or also in the signal evolution, or even containing couplings to further mechanisms and components such as haptotactic cues ([5], [40], ”
Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity (2018, background): “also the related setting addressed in [28], and [3] for a concise derivation of chemotaxis-fluid systems of the considered type).”
Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity (2015, unknown): “Related mechanisms of chemotaxis-fluid interaction also arise in different biological contexts such as biomixing-based fertilization strategies of certain benthic invertebrates [14,15].”
Stabilization in a two-dimensional chemotaxis-Navier–Stokes system (2013, unknown): “2) involving signal production by cells and a quadratic death term in the cell evolution, as proposed in a different modeling context in [15].”