Engineering Basal Cognition: Minimal Genetic Circuits for Habituation, Sensitization, and Massed-Spaced Learning
However, if either the number of pulse repetitions or the interpulse delay is excessively large, the peak response decreases. This reduction arises because an excessive number of pulses (large N) allocates insufficient time within each pulse for the accumulation of the intermediate activator, while a prolonged interpulse delay (large Δt) allows the activator concentration to decay significantly before the next pulse arrives.
To gain further insight into how the spacing of input pulses affects memory accumulation and downstream output, we consider a simplified version of the presented model, in which each input pulse fully saturates the receptor response and the output protein G is produced in an all-or-nothing manner, driven by a step activation threshold.
This can be modeled by the following simplified system: dAdt=αΔτonN∑k=0N−1δ(t−tk)−γA,dGdt=βH(A(t)−1)−γG 14 where δ(t – t k ) denotes the Dirac delta function representing an impulsive input at discrete times t k = k Δτoff. Consequently, the memory variable A exhibits instantaneous integration of each input pulse, followed by an exponential decay in the interval before the next input arrives. The expression of output G is governed by a Heaviside transfer function H(A(t)−1) , which acts as an abrupt switch that yields 1 when memory is above a normalized threshold , A(t) ≥ 1, and 0 otherwise. Thus, production halts when the memory decays below the threshold.
Let N identical pulses be delivered instantly at equally distant intervals of size Δτ ≈ Δτoff, with total input strength α Δτon. The state of A immediately after the k-th pulse, denoted A k , follows from the balance between input and decay: Ak=αΔτonN1−e−(k+1)γΔτoff1−e−γΔτoff 15
The duration of output production during the k-th interval, denoted lk , is determined by how long A(t) remains above the threshold, bounded by the arrival of the next pulse for all but the final interval.
Let t k * = γ–1 log(A k ) be the time expected for A k > 1 to decay to the threshold. Then lk≔{H(Ak−1)tk*,ifk=N−1,H(Ak−1)min(tk*,Δτoff),otherwise 16 Thus, output dynamics are given by the addition of individual pulse contributions. G(t)=βγ∑k=0N−1(1−e−γτk+(t))e−γτk−(t)H(t−tk) 17 The duration of output production from the k-th pulse up to time t, denoted τ k +(t), and the time elapsed since production halted, denoted τ k –(t), are respectively defined as τk+(t)≔min(t−tk,lk),τk−(t)≔max(0,t−tk−lk) The Heaviside function H(t−tk) ensures that each component contributes only after its onset time t k .
With β > γ, the output increases during each production interval and peaks at the end of each pulse tk+lk . Given equally spaced pulses and zero initial output in the first interval, each subsequent pulse starts with a positive baseline due to incomplete decay from previous inputs. This leads to a nondecreasing sequence of peak outputs. Hence, the global maximum must be at the end of the final pulse, t=tN‐1+lN‐1 , since no prior peak can be higher due to the cumulative effect of residual output from earlier pulses.
Under the restriction that the input added in a single pulse is strong enough to sustain output production for the full relaxation phase. That is, if log(αΔτonN)≥γΔτoff 18 then, splitting the input into N equally spaced pulses will yield a higher total output than a single, massed pulse. This assumption simplifies the following analysis, though it should be noted that it defines a strict subset of the parameter space where spaced pulses are advantageous. For a more detailed analysis, see Supporting Information (Subsection S6.1).
For a massed pulse (N = 1), the output production halts when A(t 0 *) = 1, giving an output production duration: t0*=l0=γ−1log(αΔτon) which yields a maximum output: maxtG(t)|N=1=βγ(1−1αΔτon)
When, instead, the input is split into two equal pulses (N = 2), the first half-strength pulse decays for Δτoff until the second pulse arrives (per the assumption in eq ), after which the memory jumps to A1=αΔτon2(1+e−γΔτoff) Production then halts at: t1*=Δτoff+l1,l1=γ−1log(A1) Thus, the combined active phases produce: maxtG(t)|N=2=βγ(1−2e−γΔτoffαΔτon(1+e−γΔτoff))
Under the previous assumptions, the region where spaced pulses are strictly better than a massed pulse is maxtG(t)|N=2>maxtG(t)|N=1 which simplifies algebraically to the condition: 2e−γΔτoff1+e−γΔτoff<1 This holds when γ Δτoff > 0, ensuring that e–γΔτoff < 1. Results showing that this property also holds for the general case N ≥ 2 under the same assumptions are provided in the Supporting Information (Subsection S6.1).
Cognition can be defined as the acquisition, processing, storage, and use of information to generate or modulate behavior. Some single-cell organisms, from bacteria to protozoans or Physarum molds, are known to be able to perform a diverse range of computational tasks, including simple forms of learning. The study of basal cognition has deeply enlarged our comparative analysis of possible cognitions and raises some deep questions: How common is cellular cognition? How complex can it be? If cognition is defined narrowly in terms of neural representations, it is necessarily rare at the cellular level. However, if instead it is defined operationally as the capacity to modify responses based on stimulus history, then cognition-like behavior is likely widespread in bacterial and unicellular systems. Many regulatory networks naturally integrate past inputs over time via slow protein turnover, transcriptional delays, and molecular memory, making forms of nonassociative learning an intrinsic consequence of cellular regulation rather than an exceptional specialization. From this perspective, the synthetic circuits explored here do not introduce cognition into cells but isolate, formalize, and amplify mechanisms that are already common, highlighting how basal cognitive functions can emerge from minimal biochemical dynamics.
A central tenet in defining cognitive complexity has to do with how organisms cope with time. When dealing with the fundamental components of basal cognition, one first aspect of this problem is how to respond to potential sources of information (from the environment or other individuals) using previous experiences. In neural systems, many of these issues are resolved at the synaptic level, whereas aneural agents have to deal with time and timing using other design principles. Circadian rhythms, for example, define a very important innovation in unicellular organisms, which internalizes night–day cycles and allows anticipation. −
In this paper, we have considered a relevant problem regarding the minimal complexity necessary for nonassociative learning based on designed genetic circuits. The regulatory circuits presented, while implemented using components from Gram-negative bacteria, are based on abstract and modular control motifssuch as incoherent feed-forward loops for habituation and double-repression cascades for sensitizationthat arise from general principles of transcriptional regulation. These motifs are therefore not intrinsically tied to bacterial physiology and, in principle, can be ported to other biological systems, including yeast or mammalian cells, by replacing organism-specific elements (e.g., transcription factors, promoters, and degradation or inhibition mechanisms) while preserving the underlying regulatory logic. By exploring this within the context of habituation, sensitization, and mass-spaced learning, we aimed to rigorously define the key conditions that allow for their efficient implementation. A central component common to all our circuits is a memory element that provides the way to keep time and modulate the final response, directly or by means of repressor elements. Moreover, habituation and sensitization responses, as well as their combination, have been designed by means of very minor changes in transcription motifs. This suggests a high accessibility among diverse learning circuits, including potential combinations.
Our pursuit of minimal circuits centers on a transcription factor–based genetic toolkit; however, this choice of genetic motifs does not preclude alternative approaches to studying and engineering cognition through other components of cellular networks. Theoretical research in systems biology has demonstrated that biochemical networks involved in cell signaling can generate context-dependent dynamic behaviors. More broadly, computational circuits have also been shown to be embeddable within metabolic networks. −
Within this broader landscape, an important open question emerging from our findings is whether the circuit motifs investigated here might already be presentalbeit implicitlywithin natural regulatory networks. Indeed, while core topological elements like incoherent feed-forward loops and double-repression cascades are ubiquitous in bacterial networks, topology alone does not ensure learning-like behavior. Such implementation of nonassociative learning demands specific dynamical properties, most critically a “molecular memory” that decays slowly enough to span multiple stimuli. In natural systems, such persistence is constrained by factors including dilution due to cell division, and evolutionary trade-offs that prioritize metabolic efficiency over the costs of maintaining high protein concentrations required for an analog memory, especially when a simpler, switch-like response suffices. While synthetic circuits may overcome these limitations through tunable, high-level expressionoften with little regard for metabolic costsuch energetically expensive states are seldom sustainable within native cellular networks. Consequently, if such learning motifs occur naturally, their functional expression is likely context-dependent and restricted to specific ecological regimes. Cells may instead exploit alternative memory mechanismssuch as genetic mutations or DNA methylationwhereas microbial communities can encode past environmental exposures through ecological shifts; these forms of memory typically outlast transient, inheritance-based memories mediated by metabolites or proteins. Moreover, in complex environments, adaptive behaviors can also emerge through population-level strategies that favor probabilistic solutionssuch as stochastic phenotype switching , thereby rendering cellular-level “memory” unnecessary.
By using synthetic biology to engineer cognitive functions, we also gain a powerful lens to investigate cellular complexity and its potential constraints. A long-term objective in this endeavor is to map the structure of the “cognitive space” in which various types of cognitive agents may reside. , This raises a fundamental question: to what extent can individual cells, whether existing independently or as part of a multicellular organism, perform cognitive tasks such as learning or anticipation? The role of gene networks in these processes may differ substantially between prokaryotic and eukaryotic systems. For example, a Stentor cell is approximately ∼105 times larger than an E. coli cell, with a reproduction time of τr ≈ 2–3 days under optimal laboratory conditions, compared to the ∼2 h replication cycle of the bacterium when grown in minimal medium. More generally, protozoan life cycles span 1 to 3 orders of magnitude longer than those of E. coli , allowing molecular mechanismsincluding gene networkssufficient time to influence behavior throughout the life cycle of the organism. In contrast, bacterial replication occurs on a time scale comparable to that of the expression dynamics of candidate synthetic circuits, which significantly constrains the integration of such mechanisms into cellular behavior. Understanding how circuit complexity and organismal complexity are intertwined will be essential for charting the limitsand possibilitiesof cellular cognition.