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Modelling and simulation

Modelling and simulation

How well can biological cells sense their environment?

22 Nov 2019 Isabelle Dumé
New models could shed light on how bacteria like these move in response to chemical stimuli.

Biological cells adapt to chemical changes in their environment by sensing certain molecules as they bind to specific receptors on the cell surface. Previous work to measure this sensing ability typically assumed that concentrations of these binding molecules, known as ligands, remain constant or change at steady rates over time. Now, researchers in France and the US have developed a mathematical model for a cell’s sensitivity that better reflects real-world conditions. Their work could shed light on dynamic processes within biological systems, such as rapid cell growth in an embryo or the motion of bacteria in response to chemical stimuli.

The new model was developed by Thierry Mora of the ENS in Paris and Ilya Nemenman of Emory University in Georgia, and it describes the rapid shifts in a cell’s chemical environment with a non-linear randomly changing numerical field. This formulation allows the researchers to apply techniques from stochastic field theory that are routinely employed to solve problems in quantum and statistical physics.

Calculating the smallest fluctuations

Cells sense chemical concentrations by binding external ligands to specific receptors on their surface. Mora and Nemenman’s model derives the probability of a ligand binding to a cell within a given time period to calculate the smallest fractional fluctuations of concentrations that the cell can detect.

They found that the cell can sense smaller fractional fluctuations as the overall concentration of a biochemical increases, or as a receptor’s binding rate increases. In previous calculations that assumed a constant, non-fluctuating, environment, the cell’s sensitivity – expressed as an error in the concentration, c – was related to the biochemical concentration and the receptor binding rate by a ½ power law known as the Berg and Purcell bound.

In the new model this sensitivity changes more slowly with the concentration and binding rate and obeys a ¼ power law. Indeed, it scales as δc/c ∼ (Dacτ) -1/4. In this equation, D is ligand diffusivity, a is the linear size of the receptor, and τ is the ligand fluctuation time scale.

Model works for a real-world situation

The researchers, who have reported their work in Physical Review Letters, say they have already applied their model to a real-world situation in which an external chemical drives a network of signals inside the cell after it binds with the cell’s receptors. Their computer simulations showed that under these circumstances, the cell can detect the molecule within the fundamental limit they derived.

Robert Endres of Imperial College London, who was not involved in this research, says that the problem of sensing a fluctuating ligand concentration by a receptor is certainly relevant for biology. He adds that deriving the sensing limit via a field-theoretic approach, as Mora and Nemenman did, is “very elegant”. However, he also downplays the degree to which their findings differ from earlier work.

“Although a great result, I would not say that it is a radically different limit from the usual Berg and Purcell limit,” Endres says. The Berg and Purcell limit, he explains, is a lower limit, a kind of “noise floor”, while Mora and Nemenman’s new limit is higher due to a fluctuating ligand concentration. Second, as the researchers explain themselves, the new limit can be reconciled with the Berg and Purcell limit using an optimal averaging time – that is, by making the measuring time interval as long as possible to better average the results obtained, and short enough for the concentration of a ligand to vary less.

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