Information processing in a simple one-step cascade

Abstract

Using the formalism of information theory, we analyze the mechanism of information transduction in a simple one-step signaling cascade S→X representing the gene regulatory network.Approximating the signaling channel to be Gaussian, we describe the dynamics using Langevin equations. Upon discretization, we calculate the associated second moments for linear and nonlinear regulation of the output by the input, which follows the birth-death process. While mutual information between the input and the output characterizes the channel capacity, the Fano factor of the output gives a clear idea of how internal and external fluctuations assemble at the output level. To quantify the contribution of the present state of the input to predict the future output, transfer entropy is computed. We find that higher amount of transfer entropy is accompanied by the greater magnitude of external fluctuations (quantified by the Fano factor of the output) propagation from the input to the output. We notice that low input population characterized by the number of signaling molecules S, which fluctuates in a relatively slower fashion compared to its downstream (target) species X, is maximally able to predict (as quantified by transfer entropy) the future state of the output. Our computations also reveal that with increased linear nature of the input-output interaction, all three metrics of mutual information, Fano factor and, transfer entropy achieve relatively larger magnitudes. *

Information transmission in a two-step cascade: interplay of activation and repression

“…In consequence, information content I(s; y) becomes less information transmission along a network deciphers the propagation of the fluctuations. We note here that these fluctuations capture the knowledge of the concentration changes at the signal level Nandi et al (2018). Hence, net synergy increases for both AA and AR.…”

Information restriction in two-step cascade: role of fidelity and fluctuations

“…Using equations ( 30)-( 32), the RI for sTSC, +TSC and −TSC motifs are calculated and presented later. In our previous investigation [38], we have seen that, RI depends on both I(s; x) and I(s; y) + τ s→y . Such a dependency may misinterpret about the nature of X and hence we have adopted a normalization strategy, which gave us a new scale free term in percentage domain, namely restricted efficiency E R .…”

“…It is important to mention here that, the Langevin approximation that we adopt in our study, is well established and has been used in many recent studies involving stochastic dynamics [20,23,[38][39][40][41][42]. We use equations ( 8)-( 10) as our primary dynamical equations using which we do further analytical calculations and computations.…”

“…In Gaussian framework (where the system components follow Gaussian distribution [20,23,38]), the information theoretic terms (MI's and the TE) can be defined in terms of variances and covariances associated with the system components as,…”

“…Such a dependency may misinterpret about the nature of X and hence we have adopted a normalization strategy, which gave us a new scale free term in percentage domain, namely restricted efficiency E R . E R measures the efficiency of intermediate X to restrict information transduction from S to Y [38]. In the present manuscript, we take resort to use E R , defined as,…”