Telling time with an intrinsically noisy clock

Intracellular transmission of information via chemical and transcriptional networks is thwarted by a physical limitation: the finite copy number of the constituent chemical species introduces unavoidable intrinsic noise. Here we provide a method for solving for the complete probabilistic description of intrinsically noisy oscillatory driving. We derive and numerically verify a number of simple scaling laws. Unlike in the case of measuring a static quantity, response to an oscillatory driving can exhibit a resonant frequency which maximizes information transmission. Further, we show that the optimal regulatory design is dependent on the biophysical constraints (i.e., the allowed copy number and response time). The resulting phase diagram illustrates under what conditions threshold regulation outperforms linear regulation.Comment: 10 pages, 5 figure

Optimizing information flow in small genetic networks. II: Feed forward interactions

Central to the functioning of a living cell is its ability to control the readout or expression of information encoded in the genome. In many cases, a single transcription factor protein activates or represses the expression of many genes. As the concentration of the transcription factor varies, the target genes thus undergo correlated changes, and this redundancy limits the ability of the cell to transmit information about input signals. We explore how interactions among the target genes can reduce this redundancy and optimize information transmission. Our discussion builds on recent work [Tkacik et al, Phys Rev E 80, 031920 (2009)], and there are connections to much earlier work on the role of lateral inhibition in enhancing the efficiency of information transmission in neural circuits; for simplicity we consider here the case where the interactions have a feed forward structure, with no loops. Even with this limitation, the networks that optimize information transmission have a structure reminiscent of the networks found in real biological systems

Control of quantum interference in molecular junctions: Understanding the origin of Fano and anti- resonances

We investigate within a coarse-grained model the conditions leading to the appearance of Fano resonances or anti-resonances in the conductance spectrum of a generic molecular junction with a side group (T-junction). By introducing a simple graphical representation (parabolic diagram), we can easily visualize the relation between the different electronic parameters determining the regimes where Fano resonances or anti-resonances in the low-energy conductance spectrum can be expected. The results obtained within the coarse-grained model are validated using density-functional based quantum transport calculations in realistic T-shaped molecular junctions.Comment: 5 pages, 5 figure

Optimizing information flow in small genetic networks. I

In order to survive, reproduce and (in multicellular organisms) differentiate, cells must control the concentrations of the myriad different proteins that are encoded in the genome. The precision of this control is limited by the inevitable randomness of individual molecular events. Here we explore how cells can maximize their control power in the presence of these physical limits; formally, we solve the theoretical problem of maximizing the information transferred from inputs to outputs when the number of available molecules is held fixed. We start with the simplest version of the problem, in which a single transcription factor protein controls the readout of one or more genes by binding to DNA. We further simplify by assuming that this regulatory network operates in steady state, that the noise is small relative to the available dynamic range, and that the target genes do not interact. Even in this simple limit, we find a surprisingly rich set of optimal solutions. Importantly, for each locally optimal regulatory network, all parameters are determined once the physical constraints on the number of available molecules are specified. Although we are solving an over--simplified version of the problem facing real cells, we see parallels between the structure of these optimal solutions and the behavior of actual genetic regulatory networks. Subsequent papers will discuss more complete versions of the problem

Switch‐1 instability at the active site decouples ATP hydrolysis from force generation in myosin II

Myosin active site elements (i.e., switch-1) bind both ATP and a divalent metal to coordinate ATP hydrolysis. ATP hydrolysis at the active site is linked via allosteric communication to the actin polymer binding site and lever arm movement, thus coupling the free energy of ATP hydrolysis to force generation. How active site motifs are functionally linked to actin binding and the power stroke is still poorly understood. We hypothesize that destabilizing switch-1 movement at the active site will negatively affect the tight coupling of the ATPase catalytic cycle to force production. Using a metal-switch system, we tested the effect of interfering with switch-1 coordination of the divalent metal cofactor on force generation. We found that while ATPase activity increased, motility was inhibited. Our results demonstrate that a single atom change that affects the switch-1 interaction with the divalent metal directly affects actin binding and productive force generation. Even slight modification of the switch-1 divalent metal coordination can decouple ATP hydrolysis from motility. Switch-1 movement is therefore critical for both structural communication with the actin binding site, as well as coupling the energy of ATP hydrolysis to force generation

Entanglement and Tensor Product Decomposition for Two Fermions

The problem of the choice of tensor product decomposition in a system of two fermions with the help of Bogoliubov transformations of creation and annihilation operators is discussed. The set of physical states of the composite system is restricted by the superselection rule forbidding the superposition of fermions and bosons. It is shown that the Wootters concurrence is not proper entanglement measure in this case. The explicit formula for the entanglement of formation is found and its dependence on tensor product decompositions of the Hilbert space is discussed. It is shown that the set of separable states is narrower than in two-qubit case. Moreover, there exist states which are separable with respect to all tensor product decompositions of the Hilbert space.Comment: 8pp, published versio

Destruction of states in quantum mechanics

A description of destruction of states on the grounds of quantum mechanics rather than quantum field theory is proposed. Several kinds of maps called supertraces are defined and used to describe the destruction procedure. The introduced algorithm can be treated as a supplement to the von Neumann-Lueders measurement. The discussed formalism may be helpful in a description of EPR type experiments and in quantum information theory.Comment: 14 pp, 1 eps figure, LaTeX2e using iopart class. Final version, will be published in J. Phys. A: Math. Ge

The linear ubiquitin chain assembly complex regulates TRAIL-induced gene activation and cell death.

The linear ubiquitin chain assembly complex (LUBAC) is the only known E3 ubiquitin ligase which catalyses the generation of linear ubiquitin linkages de novo LUBAC is a crucial component of various immune receptor signalling pathways. Here, we show that LUBAC forms part of the TRAIL-R-associated complex I as well as of the cytoplasmic TRAIL-induced complex II In both of these complexes, HOIP limits caspase-8 activity and, consequently, apoptosis whilst being itself cleaved in a caspase-8-dependent manner. Yet, by limiting the formation of a RIPK1/RIPK3/MLKL-containing complex, LUBAC also restricts TRAIL-induced necroptosis. We identify RIPK1 and caspase-8 as linearly ubiquitinated targets of LUBAC following TRAIL stimulation. Contrary to its role in preventing TRAIL-induced RIPK1-independent apoptosis, HOIP presence, but not its activity, is required for preventing necroptosis. By promoting recruitment of the IKK complex to complex I, LUBAC also promotes TRAIL-induced activation of NF-κB and, consequently, the production of cytokines, downstream of FADD, caspase-8 and cIAP1/2. Hence, LUBAC controls the TRAIL signalling outcome from complex I and II, two platforms which both trigger cell death and gene activation