A tunable population timer in multicellular consortia

•We propose a chemical wire architecture for distributed biological computation•Our model predicts how input signals can be restored or modulated in the output•Chemical wires store temporal information and system act as timer•Digital periodic filtered by altering strain ratios Processing time-dependent requires cells to quantify duration of past regulatory events program time span future signals. At single-cell level, timer mechanisms implemented with genetic circuits. However, such systems are difficult implement single due saturation molecular components stochasticity limited intracellular space. In contrast, multicellular implementations outsource some information-processing circuits extracellular space, potentially escaping these constraints. Here, we develop theoretical framework, based on trilinear coordinate representation, study collective behavior populations composed three cell types under stationary conditions. This framework reveals that distributing different processes (in our case production, detection degradation time-encoding signal) across distinct strains enables implementation timer. Our analysis also shows circuit easily tunable varying cellular composition consortium. One defining features is their ability process information, way sensing internal external generating response. paradigm, while serving an inspiration development synthetic biology (Andrianantoandro et al., 2006Andrianantoandro E. Basu S. Karig D.K. Weiss R. Synthetic biology: new engineering rules emerging discipline.Mol. Syst. Biol. 2006; 2: 2006.0028https://doi.org/10.1038/msb4100073Crossref PubMed Scopus (780) Google Scholar), has guided search gene protein responsible all kinds functions (Alon, 2019Alon U. An Introduction Systems Biology: Design Principles Biological Circuits. CRC press, 2019Crossref Scholar). 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We consider simplicity population not structured space well (corresponding liquid culture) phase (i.e. do proliferate), although conditions strictly required, will argue discussion. Additionally, stationarity limiting assumption biochemical point view, since shown Escherichia coli able respond stimuli (Gefen 2014Gefen Fridman Ronin Balaban N.Q. Direct observation stationary-phase surprisingly period production activity.Proc. 111: 556-561https://doi.org/10.1073/pnas.1314114111Crossref (90) establishes restrictive environment relative growth rates involved play relevant role operation system. earlier proposal growing cells, but result required use type, output was dominated (Koseska 2009Koseska Zaikin Kurths Timing decision making via communication.PLoS 4: e4872https://doi.org/10.1371/journal.pone.0004872Crossref (40) present analyze three-strain quantitatively. constructs 1B), located defined above: emitter, receiver, sink. chimeric parts order accomplish desired tasks. communicating bbit, stands bit, biobit. candidate molecule must stable enough negligible abiotic rate. bbit AHL. take any value [0,1] depending signal, see duration. emitter construct contains minimum set synthesize at comprises induce expression promoter medium concentration above/below (depending whether activates represses its target gene, respectively). Finally, sink consists genes, constitutively expressed, degrade bbit. goal communicate each other, frequencies affect communication. assume B, linearly proportional density strain. supposed following Michaelis-Menten dynamics, 1A):dBdt=KEE−DmBKS+BS(Equation 1) term equation above represents arises B becomes large saturate quantified maximum rate Dm, starts manifested biobit surpasses Michaelis KS. last depends affinity degrading enzyme, turn expressed Also, plays total “enzime” kinetics, appears multiplying Dm. equation, E represent below R receptor concentrations cells/mL directly optical units (which could more convenient designing experimental system). For simplicity, conceived phase, condition still means alive dividing growing, there no dilution intrinsic scales considered here. define frequency population: ε=E/P, σ=S/P, ρ=R/P, where P provided phase). By definition, ε+σ+ρ=1. now bijection possible inside equilateral triangle 1C). vertex corresponds strains, ε, σ ρ distance representing side opposite corresponding (the equal sides obey constraint sum distances lying constant, 1 case, seen above). called graphical explore intuition behind geometrical representation simple: closer vertex, represented Since none change density, describing fixed triangle. Δ triangle). Any correspond unique population, sections. calculate points Equation (1) obtain explicit equilibrium, fractions ε respectively:Beq=KEKSεDmσ−KEε(Equation 2) pairs (ε,σ) make denominator Beq zero divide two regions (see dashed line left panel Figure 2A). When Dmσ>KEε (region line, covered dots), reaches equilibrium (2). convergence region (represented C below). Solving differential traces converge (green lines middle situation balanced strain, bottom inset right 2A. values terms inset) (production larger than smaller it) ensure DmσDmKEPropertyBeq=KEKSεDmσ−KEε(σ,ε,ρ)=(kσˆ,kεˆ,1−k)vˆ=P(Dmσ−KEε)σˆ=KEDm+KE εˆ=DmDm+KE 0 being 0, k arbitrary real number 1. Open table tab σˆ=KEDm+KE Within along straight radiating top hitting σε¯ side, reach same value. noting (2) rewritten Beq=KEKSDmσ/ε−KE. Thus, only ratio σ/ε. geometric similarity straightforward σ/ε belonging To this, lines, characterized, abundance (relative frequencies) (σ1,ε1) (σ2,ε2), 2B. Let h1 h2 vertex. triangles delimited ε-h σ-h to:ε1ε2=h1h2=σ1σ2⇒σ1ε1=σ2ε2⇒Beq,1=Beq,2(Equation 3) dots center panels 2C depict isolines B(t) them. culture-point characterized asymptotic vˆ grows Considering grown KS, linear, leading tovˆ=P(KEε−Dmσ)(Equation 4) ask values. Geometric considerations segment parallel speed (4). growth-rate (purple dots). There simple gain about regions. instance, isoline divergence, greater associated be. And vˆ=0. here provides intuitive understanding examine modulation activity significant portion form So far, As discussed induces protein, fluorescent protein. relating follows activating sigmoidal described Hill function:F=BnKn+Bn(Equation 5) plotted plot 3A entails assuming fast comparison other timescale dynamics. normalize (0,1). thresholds response, T5 T95, 5% 95% respectively. measured precisely quantifying heterogeneity existing individual contribute chosen bbit) averaged heterogeneity. above, allow domain according induction level 3A, right): (i) uninduced named U, Beq≤T5 so measurable output; (ii) I, Beq≥T95 maximal readout; (iii) variable between, V, Beq∈(T5,T95). domain, keeps goes on, contrast I