Living cells can sense their environment with high precision. Yet, the resources required for sensing with high precision is an open question. Here we address this question for both equilibrium and non-equilibrium systems. We find that in equilibrium systems the precision of sensing is fundamentally limited by the number of receptors; the signaling network that transmits the information from the receptors to the interior of the cell can never increase the precisionof sensing. We show that this limit arises from a fundamental trade-off between the removal of the extrinsic noise in the receptor state and the suppression of the intrinsic noise in the signaling network. We next prove that only non-equilibrium systems can lift this trade-off : They can integrate the receptor state over time while suppressing the intrinsic noise by using energy to store the receptor state into stable modification states of the readout molecules. We explicitly calculate the resources required for a canonical signaling motif, a push-pull network . We arrive at an analytical expression that shows that storing the state of the bound receptor over time requires at least one readout molecule to store the state and at least 4 kT of energy to store it reliably. Thus, each of the resources -- time, protein copy numbers, and energy -- limits sensing, and it is the limiting resource which places the fundamental limit on sensing .
Living cells deploy many resources to sense their environments, including receptors, downstream signaling molecules, time and fuel. However, it is not known which resources fundamentally limit the precision of sensing, like weak links in a chain, and which can compensate each other, leading to trade-offs between them. We show by modeling that in equilibrium systems the precision is limited by the number of receptors; the downstream network can never increase precision. This limit arises from a trade-off between the removal of extrinsic noise in the receptor and intrinsic noise in the downstream network. Non-equilibrium systems can lift this trade-off by storing the receptor state over time in chemical modification states of downstream molecules. As we quantify for a push-pull network , this requires i) time and receptors; ii) downstream molecules; iii) energy (fuel turnover) to drive modification. These three resource classes cannot compensate each other, and it is the limiting class which sets the fundamental sensing limit. Within each class, trade-offs are possible. Energy allows a power-speed trade-off, while time can be traded against receptors .
R
can sense their environment with high precision. Yet, the resources required for sensing with high precision is an open question. Here we address this question for both equilibrium and non-equilibrium systems. We find
deploy many resources to sense their environments, including receptors, downstream signaling molecules, time and fuel. However, it is not known which resources fundamentally limit the precision of sensing, like weak links in a chain, and which can compensate each other, leading to trade-offs between them. We show by modeling
R
of sensing is fundamentally
is
R
signaling network that transmits the information from the receptors to the interior of the cell
downstream network
R
the precisionof sensing. We show that this
precision. This
D
fundamental
D
the
R
state and the suppression of the
and
R
signaling network. We next prove that only non-equilibrium
downstream network. Non-equilibrium
R
: They can integrate
by storing
R
while suppressing the intrinsic noise by using energy to store the receptor state into stable
in chemical
R
the readout molecules. We explicitly calculate the resources required for a canonical signaling motif, a
downstream molecules. As we quantify for a
R
. We arrive at an analytical expression that shows that storing the state of the bound receptor over time requires at least one readout molecule to store the state and at least 4 kT of energy to store it reliably. Thus, each of the resources -- time, protein copy numbers, and energy -- limits sensing, and
, this requires i) time and receptors; ii) downstream molecules; iii) energy (fuel turnover) to drive modification. These three resource classes cannot compensate each other, and
R
resource which places the fundamental limit on sensing
class which sets the fundamental sensing limit. Within each class, trade-offs are possible. Energy allows a power-speed trade-off, while time can be traded against receptors