The department of Mathematics and Statistics at the University of Limerick invites you to a seminar by **Dr Mohit Dalwadi (University of Nottingham):**

**Title:** Multiscale problems in synthetic biology

**Abstract:** Multiscale problems in synthetic biology Synthetic biology is a fast-growing, interdisciplinary science whereby biological systems are designed or modified for useful purposes. In this talk, we explore two multiscale problems that arise in synthetic biology. The first problem involves nutrient delivery to bacteria, and the second problem involves growing artificial body tissue within a rotating bioreactor. While the mathematical equations that govern nutrient delivery to bacteria are known, there is a significant separation between bioreactor and bacterial lengthscales. Thus, it is prohibitively expensive to include small bacterial regions in a computational model of bacterial uptake over the length of a bioreactor. To bypass this expense, the bacterial uptake is often modelled as an effective sink over the domain. However, it is not immediately clear how to relate properties on the bacterial scale with this effective result. For example, one may intuitively expect the effective uptake to scale with bacterial volume for weak uptake, and with bacterial surface area for strong uptake. In this talk, we quantify when each of these scalings is valid, obtain the correct form of the effective uptake when neither of these scalings is appropriate, and characterize the smooth transition between these canonical forms of the effective uptake as a function of the system parameters. We also consider a mathematical model of an experiment used to grow artificial body tissue. In this experiment, a tissue construct is placed inside a petri-dish-shaped bioreactor to grow. This high aspect ratio vessel bioreactor is filled with a nutrient-rich fluid, and the cylindrical bioreactor is rotated around its axis at a constant angular velocity, with gravity acting perpendicular to the axis of rotation. The consequence of this rotation is the coupled movement of the construct and the fluid, motivated by enhancing nutrient delivery to the porous construct via advection. We investigate the coupled flow and construct movement problem, and show how a weak inertia can cause the long-time behaviour that experimentalists often attribute to tissue growth.

This seminar will take place on **Friday , March 24 ^{th} , at 4pm, in Room A2-002**.

If you have any questions regarding this seminar, please direct them to Iain Moyles (061 233726, iain.moyles@ul.ie).

A full list of upcoming seminars can be found at http://www.ulsites.ul.ie/macsi/node/48011

Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie), centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.