Linear rate response functions and quantities for the cascade models.

<p>Linear rate response functions of EIF neurons subject to white noise input for modulations of the input mean around <i>μ</i> with constant <i>σ</i>: <i>R</i>_<i>μ</i>(<i>t</i>; <i>μ</i>, <i>σ</i>) in kHz/V (<b>A</b>, gray) and for modulations of the input standard deviation around <i>σ</i> with constant <i>μ</i>: <i>R</i>_<i>σ</i>(<i>t</i>; <i>μ</i>, <i>σ</i>) in ) (<b>B</b>, gray). These functions are calculated in the Fourier domain for a range of modulation frequencies [ in 1/V and in )] (insets, gray; absolute values are shown), and fit using an exponential function exploiting asymptotic results for (<b>A</b>, red dashed), as well as considering a range of frequencies (<b>A</b> and <b>B</b>, red solid). In addition, is fit using a damped oscillator function (<b>A</b>, violet). The details of the fitting procedures are described in the text. <b>C</b>: quantities (<i>τ</i>_<i>μ</i>, <i>τ</i>_<i>σ</i>, <i>τ</i> and <i>ω</i>) from the linear filter approximations (cf. <b>A</b>, <b>B</b>), required for the LN_exp and LN_dos model variants (Eqs (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005545#pcbi.1005545.e288" target="_blank">85</a>), (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005545#pcbi.1005545.e297" target="_blank">87</a>) and (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005545#pcbi.1005545.e302" target="_blank">89</a>)), as a function of <i>μ</i> and <i>σ</i>.</p

Network-generated oscillations.

<p>Oscillatory population spike rate and mean adaptation current of 50,000 excitatory coupled aEIF neurons and each of the derived models (for constant external input moments) generated by the interplay of recurrent excitation/adaptation current (<b>A</b>) and by delayed recurrent inhibition (<b>B</b>). In addition, the limit cycle of the LN_exp model is shown in terms of the (quantity) steady-state spike rate <i>r</i>_∞ as a function of effective input moments <i>μ</i>_eff, (<b>A</b>, top) and for the spec₂ model in dependence of the total input moments (<i>μ</i>_tot, (<b>A</b>, bottom). The phase of the cycle is visualized by grayscale color code (increasing phase from black to white). The values for the input, adaptation and coupling parameters were <i>μ</i>_ext = 1.5 mV/ms, , <i>a</i> = 3 nS, <i>b</i> = 30 pA (<b>A</b>, top), <i>μ</i>_ext = 1.275 mV/ms, , <i>a</i> = 3 nS, <i>b</i> = 60 pA (<b>A</b>, bottom), <i>K</i> = 1000, <i>J</i> = 0.03 mV, <i>τ</i>_<i>d</i> = 3 ms (<b>A</b>, both). In <b>B</b> adaptation was removed (<i>a</i> = <i>b</i> = 0) and delays were identical <i>d</i>_<i>ij</i> = <i>d</i>; input and coupling parameter values were <i>μ</i>_ext = 1.5 mV/ms, , <i>K</i> = 1000, <i>J</i> = −0.0357 mV, <i>d</i> = 10 ms (top) and <i>μ</i>_ext = 3 mV/ms, , <i>K</i> = 1000, <i>J</i> = −0.087 mV, <i>d</i> = 5 ms (bottom).</p

Steady-state spike rate and mean membrane voltage for a population of EIF neurons.

<p><i>r</i>_∞ and 〈<i>V</i>〉_∞ for an uncoupled population of EIF neurons (aEIF with <i>a</i> = <i>b</i> = 0) as a function of (generic) input mean <i>μ</i> and standard deviation <i>σ</i>, calculated from the (steady-state) Fokker-Planck equation, shown in two different representations (left and right, each).</p

Example of aEIF network response and output of derived models for varying input.

<p>From top to bottom: Mean input <i>μ</i>_ext (black) together with input standard deviation <i>σ</i>_ext (gray, visualized for one neuron by sampling the respective white noise process <i>ξ</i>_ext,i). 2^nd row: Membrane voltage <i>V</i> of one neuron (gray, with spike times highlighted by black dots) and membrane voltage statistics from the excitatory coupled aEIF population of 50,000 neurons (red) and from the FP model (blue dashed): mean ± standard deviation over time, as well as voltage histograms (gray) and probability densities <i>p</i>(<i>V</i>, <i>t</i>) (blue dashed) at three indicated time points. 3^rd row: Adaptation current <i>w</i> of one neuron (gray) and mean adaptation currents of all models ± standard deviation for the aEIF network (shaded area). Note that differences in the mean adaptation currents of the different models are hardly recognizable. 4^th row: Spike times of a subset of 25 neurons randomly chosen from the network. Below: Spike rate <i>r</i> of the LN cascade based models (LN_exp, LN_dos) and the spectral models (spec₁, spec₂) in comparison to the FP model and the aEIF network (<i>r</i>_<i>N</i>). The values of the coupling parameters were <i>J</i> = 0.05 mV, <i>K</i> = 100, <i>τ</i>_<i>d</i> = 3 ms.</p

Protein–DNA Chimeras for Nano Assembly

In synthetic biology, “understanding by building” requires exquisite control of the molecular constituents and their spatial organization. Site-specific coupling of DNA to proteins allows arrangement of different protein functionalities with emergent properties by self-assembly on origami-like DNA scaffolds or by direct assembly <i>via</i> Single-Molecule Cut & Paste (SMC&P). Here, we employed the ybbR-tag/Sfp system to covalently attach Coenzyme A-modified DNA to GFP and, as a proof of principle, arranged the chimera in different patterns by SMC&P. Fluorescence recordings of individual molecules proved that the proteins remained folded and fully functional throughout the assembly process. The high coupling efficiency and specificity as well as the negligible size (11 amino acids) of the ybbR-tag represent a mild, yet versatile, general and robust way of adding a freely programmable and highly selective attachment site to virtually any protein of interest