Energetic costs of cellular computation

Abstract

Cells often perform computations in order to respond to environmental cues. A simple example is the classic problem, first considered by Berg and Purcell, of determining the concentration of a chemical ligand in the surrounding media. On general theoretical grounds, it is expected that such computations require cells to consume energy. In particular, Landauer's principle states that energy must be consumed in order to erase the memory of past observations. Here, we explicitly calculate the energetic cost of steady-state computation of ligand concentration for a simple two-component cellular network that implements a noisy version of the Berg-Purcell strategy. We show that learning about external concentrations necessitates the breaking of detailed balance and consumption of energy, with greater learning requiring more energy. Our calculations suggest that the energetic costs of cellular computation may be an important constraint on networks designed to function in resource poor environments, such as the spore germination networks of bacteria.T he relationship between information and thermodynamics remains an active area of research despite decades of study (1-4). An important implication of the recent experimental confirmation of Landauer's principle, relating the erasure of information to thermodynamic irreversibility, is that any irreversible computing device must necessarily consume energy (2, 3). The generality of Landauer's argument suggests that it is true regardless of how the computation is implemented. A particularly interesting class of examples relevant to systems biology and biophysics is that of intracellular biochemical networks that compute information about the external environment. These biochemical networks are ubiquitous in biology, ranging from the quorumsensing and chemotaxis networks in single-cell organisms to networks that detect hormones and other signaling factors in higher organisms.A fundamental issue is the relationship between the information processing capabilities of these biochemical networks and their energetic costs (5-8). It is known that energetic costs place important constraints on the design of physical computing devices as well as on neural computing architectures in the brain and retina (9-11), suggesting that these constraints may also influence the design of cellular computing networks.The best studied example of a cellular computation is the estimation of the steady-state concentration of a chemical ligand in the surrounding environment (12)(13)(14). This problem was first considered in the seminal paper by Berg and Purcell who showed that the information a cell can acquire about its environment is fundamentally limited by stochastic fluctuations in the occupancy of the membrane-bound receptor proteins that detect the ligand (12). In particular, they considered the case of a cellular receptor that binds ligands with a concentration-dependent rate k off 4 and unbinds particles at a uniform rate k off 4 (see Fig. 1). They argued that cells could estimate the ambient che...

Thermodynamics of Statistical Inference by Cells

“…We focus on long time intervals, T 1, with many binding events, where the receptor dynamics can be modeled by nonequilibrium steady states (NESS). The entropy production of the Markov process is the energy per unit time (power) required to maintain this NESS, and therefore calculating the entropy production is equivalent to calculating the energy consumed by the biochemical network [10,22]. The entropy production is given by [26] …”

“…Given that energetic costs place important constraints on the design of physical computing devices [8] and neural computing architectures [9], one may conjecture that thermodynamic constraints also influence the design of cellular information processing networks. This raises interesting questions about the relationship between the information processing capabilities of biochemical networks and energy consumption [10][11][12][13][14]. Indeed, we will show that thermodynamics places fundamental constraints on the ability of biochemical networks to perform statistical inference.…”

“…We find that in order to learn more information (decrease its uncertainty), the receptor must always expend more energy (increase entropy production). Note that, in this paper, we restrict ourselves to modeling the receptor and ignore the downstream signaling network that converts the signal from the receptor into a cellular response [10,13]. Thus, the energies computed here represent lower bounds on the total energy consumed by the statistical estimation network.…”

Cooperators trade off ecological resilience and evolutionary stability in public goods games

“…Additionally, we note that we have not included a cost for being facultative in the model. For example, these cells must pay a metabolic cost associated with sensing the number of cooperators around them [30]. Here, we chose to investigate the effects of a facultative investment strategy with negligible costs for being facultative to establish how facultative strategies can outperform unconditional ones in principle.…”

The Case for Absolute Ligand Discrimination: Modeling Information Processing and Decision by Immune T Cells

“…Other examples include cellular commitment to a given fate in response to dynamical signaling pathways [11], or decision to take action in the case of immune responses, characterized by binary Erk phosphorylation, cytokine release, and cell proliferation [2]. The later decisions are irreversible, indicating that computation is accompanied by information erasure and thus energy dissipation [48]. Additionally, information processing may be multi-tiered in order to retrieve different features of the input stimuli: rapid decision could discriminate between ligands of different nature, while slower decision could report the quantity of ligands.…”