Many biological processes are regulated by molecular devices that respond in an ultrasensitive fashion to upstream signals. A wide variety of biological processes are controlled by switchlike sensors that are highly sensitive to specific stimuli. For example chemotaxis is driven by multiple flagellar motors which spin clockwise or counterclockwise under the regulation of CheY-P. Recent experiments revealed that bacterial motors exhibit an ultrasensitive response (with a Hill coefficient of ~10) to CheY-P concentrations [1]. Another example is the mitogen-activated protein kinase (MAPK) cascade a well-conserved signaling module controlling cell fate decisions [2 3 For instance the MAPK pathway in oocytes converts the concentration of specific hormones into an all-or-none response (oocyte maturation) with a Hill coefficient of at least 35 as estimated in Ref. [3]. Obviously this ultrasensitivity allows small changes in the input cues to induce dramatic functional effects. As biochemical signals often fluctuate over time due to inherent stochasticity signaling noise poses a limit to the capacity of concentration sensing. Does ultrasensitivity help the system to read out the input signal? Or does it amplify the input noise to the extent that it corrupts the precision of concentration measurement? What are GSK1070916 the general constraints for biochemical sensing? These are the key questions we attempt to address here. There has been significant interest to understand how signaling noise limits the accuracy of biochemical sensing [4-16]. In 1977 Berg and Purcell argued that the physical limit to concentration measurements is set by the dynamics of their random arrival at target locations [4]: For a single sensor of linear size is the concentration of the molecules interacting with the sensor is the diffusion constant of the molecules and is the measurement time. The Berg-Purcell limit was later generalized to an array of sensors [5 6 and the precision GSK1070916 of biochemical sensing was again found to be limited by the molecular counting noise independent of the number or the sensitivity of sensors. More recent studies have extended the problem of concentration sensing to more sophisticated tasks such as spatial and temporal gradient sensing [8-12] and have explored possible mechanisms that beat the Berg-Purcell limit [14 15 The interplay between ultrasensitivity and noise is intriguing as small variations in the input may cause large output differences. However the nonlinearity of ultrasensitive systems makes theoretical progress difficult. Previous studies usually assume that the fluctuation is small such that one can linearize the input noise in the chemical Langevin equation [17-19] or in the fluctuation-dissipation analysis [20]. This small noise approximation allows for analytical treatment but may not correctly capture the impact of noise or the sensing capacity of ultrasensitive systems. In this paper we present a simple model consisting of multiple ultrasensitive sensors that measure a (noisy) input signal. We explicitly derive the upper and lower bounds for the output sensory noise. In contrast to the additive noise rule derived earlier [17 18 20 our result shows that the output noise is strictly bounded. We further show that the apparent sensitivity of the system is also constrained by the input signal-to-noise ratio. As a result we find a fundamental limit to biochemical sensing for arbitrarily ultrasensitive systems. This new limit is strictly tighter than the Berg-Purcell limit and can be applied to GSK1070916 both Poisson and non-Poisson input signals. II. MODEL The input of our model refers to a biochemical signal sets the time scale over which the input signal reverts to its mean level ? ≡ 2≡ 2/(and GSK1070916 thus the Fano factor is simply (the scale parameter). By tuning or = 1) and non-Poisson (≠ 1) fluctuations. We also observe that can be interpreted as the signal-to-noise ratio. For most biological Rabbit Polyclonal to NOTCH4 (Cleaved-Val1432). systems it is expected that ? 1 and hence the zero point is inaccessible i.e. = 0) = 0 by Eq. (2). As a common example the input signal = 1 (Poisson noise) such that = identical receptors which independently bind the chemical ligands and switch between the on and off states. As a first step we assume that these receptors are so close to each other in space that they experience the same local concentration. In this scenario the effect of ligand diffusion is negligible. Since all the receptors are regulated by the same noisy input.