Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting

In this paper we study lifted inference for the Weighted First-Order Model Counting problem (WFOMC), which counts the assignments that satisfy a given sentence in first-order logic (FOL); it has applications in Statistical Relational Learning (SRL) and Probabilistic Databases (PDB). We present several results. First, we describe a lifted inference algorithm that generalizes prior approaches in SRL and PDB. Second, we provide a novel dichotomy result for a non-trivial fragment of FO CNF sentences, showing that for each sentence the WFOMC problem is either in PTIME or #P-hard in the size of the input domain; we prove that, in the first case our algorithm solves the WFOMC problem in PTIME, and in the second case it fails. Third, we present several properties of the algorithm. Finally, we discuss limitations of lifted inference for symmetric probabilistic databases (where the weights of ground literals depend only on the relation name, and not on the constants of the domain), and prove the impossibility of a dichotomy result for the complexity of probabilistic inference for the entire language FOL

The RCK2 domain of the human BKCa channel is a calcium sensor

Large conductance voltage and Ca2+-dependent K+ channels (BKCa) are activated by both membrane depolarization and intracellular Ca2+. Recent studies on bacterial channels have proposed that a Ca2+-induced conformational change within specialized regulators of K+ conductance (RCK) domains is responsible for channel gating. Each pore-forming α subunit of the homotetrameric BKCa channel is expected to contain two intracellular RCK domains. The first RCK domain in BKCa channels (RCK1) has been shown to contain residues critical for Ca2+ sensitivity, possibly participating in the formation of a Ca2+-binding site. The location and structure of the second RCK domain in the BKCa channel (RCK2) is still being examined, and the presence of a high-affinity Ca2+-binding site within this region is not yet established. Here, we present a structure-based alignment of the C terminus of BKCa and prokaryotic RCK domains that reveal the location of a second RCK domain in human BKCa channels (hSloRCK2). hSloRCK2 includes a high-affinity Ca2+-binding site (Ca bowl) and contains similar secondary structural elements as the bacterial RCK domains. Using CD spectroscopy, we provide evidence that hSloRCK2 undergoes a Ca2+-induced change in conformation, associated with an α-to-β structural transition. We also show that the Ca bowl is an essential element for the Ca2+-induced rearrangement of hSloRCK2. We speculate that the molecular rearrangements of RCK2 likely underlie the Ca2+-dependent gating mechanism of BKCa channels. A structural model of the heterodimeric complex of hSloRCK1 and hSloRCK2 domains is discussed

Global parameter search reveals design principles of the mammalian circadian clock

Background: Virtually all living organisms have evolved a circadian (~24 hour) clock that controls physiological and behavioural processes with exquisite precision throughout the day/night cycle. The suprachiasmatic nucleus (SCN), which generates these ~24 h rhythms in mammals, consists of several thousand neurons. Each neuron contains a gene-regulatory network generating molecular oscillations, and the individual neuron oscillations are synchronised by intercellular coupling, presumably via neurotransmitters. Although this basic mechanism is currently accepted and has been recapitulated in mathematical models, several fundamental questions about the design principles of the SCN remain little understood. For example, a remarkable property of the SCN is that the phase of the SCN rhythm resets rapidly after a 'jet lag' type experiment, i.e. when the light/ dark (LD) cycle is abruptly advanced or delayed by several hours. Results: Here, we describe an extensive parameter optimization of a previously constructed simplified model of the SCN in order to further understand its design principles. By examining the top 50 solutions from the parameter optimization, we show that the neurotransmitters' role in generating the molecular circadian rhythms is extremely important. In addition, we show that when a neurotransmitter drives the rhythm of a system of coupled damped oscillators, it exhibits very robust synchronization and is much more easily entrained to light/dark cycles. We were also able to recreate in our simulations the fast rhythm resetting seen after a 'jet lag' type experiment. Conclusion: Our work shows that a careful exploration of parameter space for even an extremely simplified model of the mammalian clock can reveal unexpected behaviours and non-trivial predictions. Our results suggest that the neurotransmitter feedback loop plays a crucial role in the robustness and phase resetting properties of the mammalian clock, even at the single neuron level

Calcium-activated chloride current amplifies the response to urine in mouse vomeronasal sensory neurons

The vomeronasal organ (VNO) is an odor detection system that mediates many pheromone-sensitive behaviors. Vomeronasal sensory neurons (VSNs), located in the VNO, are the initial site of interaction with odors/pheromones. However, how an individual VSN transduces chemical signals into electrical signals is still unresolved. Here, we show that a Ca2+-activated Cl− current contributes ∼80% of the response to urine in mouse VSNs. Using perforated patch clamp recordings with gramicidin, which leaves intracellular chloride undisrupted, we found that the urine-induced inward current (Vhold = −80 mV) was decreased in the presence of chloride channel blockers. This was confirmed using whole cell recordings and altering extracellular chloride to shift the reversal potential. Further, the urine-induced currents were eliminated when both extracellular Ca2+ and Na+ were removed. Using inside-out patches from dendritic tips, we recorded Ca2+-activated Cl− channel activity. Several candidates for this Ca2+-activated Cl− channel were detected in VNO by reverse transcription–polymerase chain reaction. In addition, a chloride cotransporter, Na+-K+-2Cl− isoform 1, was detected and found to mediate much of the chloride accumulation in VSNs. Collectively, our data demonstrate that chloride acts as a major amplifier for signal transduction in mouse VSNs. This amplification would increase the responsiveness to pheromones or odorants

Symmetric Weighted First-Order Model Counting

The FO Model Counting problem (FOMC) is the following: given a sentence $\Phi$ in FO and a number $n$, compute the number of models of $\Phi$ over a domain of size $n$; the Weighted variant (WFOMC) generalizes the problem by associating a weight to each tuple and defining the weight of a model to be the product of weights of its tuples. In this paper we study the complexity of the symmetric WFOMC, where all tuples of a given relation have the same weight. Our motivation comes from an important application, inference in Knowledge Bases with soft constraints, like Markov Logic Networks, but the problem is also of independent theoretical interest. We study both the data complexity, and the combined complexity of FOMC and WFOMC. For the data complexity we prove the existence of an FO$^{3}$ formula for which FOMC is #P$_1$-complete, and the existence of a Conjunctive Query for which WFOMC is #P$_1$-complete. We also prove that all $\gamma$-acyclic queries have polynomial time data complexity. For the combined complexity, we prove that, for every fragment FO$^{k}$, $k\geq 2$, the combined complexity of FOMC (or WFOMC) is #P-complete.Comment: To appear at PODS'1