In this chapter, we explain how the SLG model (Schmajuk et al., 1996; Schmajuk & Larrauri, 2006; Schmajuk, 2002) introduced in Chapter 2 describes the multiple properties of latent inhibition (LI). We also discuss alternative approaches to LI.

Simulation procedures

In all the simulations presented in this chapter, different measures of conditioning were simulated as follows. When a conditioned emotional response paradigm was simulated, CR strengths were transformed into suppression ratios. Suppression ratios were calculated with the equation A/(A + B), where A represents the appetitive responding (e.g. bar pressing for food, water licking) when the CS is present, and B represents the appetitive responding during the preceding non-CS period of equal duration. We assume that responding during the CS period is given by β − CR(CS), and responding during the preceding non-CS period is given by β − CR(CX), where β is proportional to the intensity of the appetitive behavior. Therefore, the suppression ratio was calculated by (β − CR(CS))/((β − CR(CX)) + β − CR(CS)) = (β − CR(CS))/(2β − CR(CS) − CR(CX)). In order to avoid unrealistic negative suppression ratios, the value of β was arbitrarily set to the maximum value of the CR(CS). Notice that when V(CX,US) is close to or smaller than 0, then the suppression ratio is well approximated by (β − CR(CS))/(2β − CR(CS)).

Buhusi and Schmajuk (1999) presented a neural network model of conditioning that combines the SD/SLH configural model presented in Chapter 11, with a timing model offered by Grossberg and Schmajuk (1989). The Grossberg and Schmajuk (1989) timing model incorporates a mechanism by which a CS can predict the time when the US is presented. In this timing model, stimuli evoke multiple traces of different duration and amplitude, that peak at different times after CS presentation. In the “configural–timing” model offered by Buhusi and Schmajuk (1999), these traces compete to become associated directly and indirectly (through hidden units) with the US, as described in Chapter 11. The output of the system predicts the value, moment and duration of presentation of reinforcement.

Most interestingly, and in contrast to the SD/SLH model, in the configural–timing neural network described in this chapter, a stimulus may assume different roles (simple CS, occasion setter, or both) at different time moments. Moreover, while in the SD/SLH model competition between CSs is purely associative, in the configural–timing model competition between CSs is both associative and temporal. CSs compete to predict not only the presence and the intensity of the US, but also its temporal characteristics: time of presentation and duration. The configural–timing model is able to address both the temporal and associative properties of simple conditioning, compound conditioning and occasion setting.

Following the ideas proposed in Chapter 4, this chapter applies the “conceptual nervous system” provided by the SLG model in order to establish brain–behavior relationships during latent inhibition. Here (a) we describe possible neural substrates for some of the variables in the SLG model; (b) based on those assumptions we use of the model to explain the effects of manipulations of the dopaminergic [DA] system, the hippocampus and the nucleus accumbens on LI; and (c) we apply the model to the description of some of the positive symptoms of schizophrenia.

The neural substrates of latent inhibition

In order to extend the application of the SLG model from the purely behavioral domain to the neurophysiological domain, we defined a mapping function between psychological and neurophysiological spaces that establishes where psychological variables are represented in the brain. Schmajuk, Cox and Gray (2001; Schmajuk et al.,2004) mapped nodes and connections in the SLG network onto the brain circuit, as shown in Figure 6.1. The participation of the brain regions in this circuit in LI, a combination of those proposed by Gray et al. (1997) and Weiner and Feldon (1997), was later confirmed by Puga et al. (2007) using cytochrome oxidase histochemistry in mice. Importantly, in line with our approach, according to Puga et al. (2007) their data suggest that LI is the consequence of a reduced processing of the CS.

This book analyzes attentional, associative, configural and timing mechanisms that are embedded in different computational, neural network theories of ­classical conditioning.

Part I serves as an introduction to the problem and possible solutions. Chapter 1 briefly introduces a number of well-known conditioning paradigms and describes both theories and computational models that have been proposed to describe and explain them.

Part II concentrates on attentional and associative mechanisms. Chapters 2, 3, 5, 7, 8 and 9 describe an attentional–associative model and apply it to the description of excitatory and inhibitory conditioning, compound conditioning, latent inhibition, overshadowing, blocking, backward blocking, recovery from overshadowing, recovery from blocking, recovery from backward blocking, extinction and creative processes. Chapters 4, 6, 7 and 10 describe the neurobiological mechanisms involved in fear conditioning, latent inhibition, creative processes and extinction.

Part III is devoted to configural mechanisms. Chapters 11 and 12 describe a configural model and apply it to the description of occasion setting. The model provides a very precise description of under what conditions a CS functions as a simple CS or an occasion setter, and how these different functions are mechanistically achieved. In the model, direct and indirect CS–US associations compete, through the same rule that governs blocking, overshadowing and conditioned inhibition, to decide the role of the CS as a simple CS or as an occasion setter. Chapter 13 analyzes the neurobiological bases of occasion setting.

We have previously shown (Schmajuk, 1997), that the SLG model addresses different basic conditioning paradigms, including (a) simultaneous, delay and trace conditioning, and the effect of varying the interstimulus interval (Smith, 1968); (b) the effect of increasing US duration (Burkhardt & Ayres, 1978); (c) backward conditioning (Siegel & Domjan, 1971; Heith & Rescorla, 1973); (d) second-order excitatory (Kamil, 1969) and inhibitory conditioning (Rescorla, 1976); (e) sensory preconditioning (Brogden, 1939); and (f) partial reinforcement with different percentages of reinforced trials (Gormezano & Moore, 1969). According to the model, interstimulus interval (ISI, see Figure 2.3) effects are explained in terms of the shape of the trace τCS (see Figure 2.3 and Equation [2.1]), the effect of increasing US duration in terms of the increase in the size of the temporal overlap between XCS and λUS (see Equation [2.9a]), backward conditioning in terms of the combination (chaining) of CS–CX and CX–US associations (see Equation [2.3]), second-order conditioning and sensory preconditioning in terms of the combination (chaining) of CS1–CS2 and CS2–US associations. The model correctly describes the competition between the excitation due to chaining and the conditioned inhibition (see below), produced by the alternated presentations of CS–CX (or CS1–CS2) and CX–US (or CS2–US) trials, present in backward conditioning, second-order conditioning and sensory preconditioning.

Recent simulations show that the SLG model also describes the effect of massed vs. spaced trials (e.g. Spence & Norris, 1950) in terms of the increased CX–US associations (that compete with CS–US associations) when massed trials are used.

Dendrites as electrical systems with distributed parameters differ from electrical systems with lumped parameters in an important aspect: any dendritic site can be considered as either input or output or both. In that sense, we deal with an electrical system such that the inputs and outputs are distributed in space, over the whole dendritic space.

The voltage is a standard and direct indicator of electric states. Similarity or dissimilarity of voltages reflects similarity or dissimilarity of electric states at different locations in space. The sign and magnitude of the voltage, that is the difference in the transmembrane potential between the sites, determines what electrically communicates with what and the intensity of the sent/received signals. The sites communicate by sending/receiving charges, i.e. by currents. The current flows in the direction of the voltage drop. Hence, considering the path profiles of the transmembrane voltage, one can see from where and to where the current flows in the given domain. Given the core resistance of the dendritic cable, the current between neighbouring sites is proportional to the voltage difference. Since one cannot ‘observe’ the path map of resistances, the path map of the voltages is informative, however not exhaustively. For an exhaustive characterization of the electric states and of the electric communication between sites over the dendritic space, a complementary map of the membrane currents is required (see Chapter 6).

Dendritic cables in the steady state

In the steady state, there are no temporal changes in voltage, voltage-sensitive conductance and current. The time derivatives of all values are zero. Therefore the capacitive current is zero.

After the single dendritic path analyzed in the preceding chapter, an elementary bifurcation introduces the simplest case of a second discrete dimension for navigating over the dendrites. A set of elementary bifurcations forms the so-called binary tree, which is most typical for dendritic arborizations of neurons. Obviously, the bifurcation, also named binary branching or dichotomic branching is topologically symmetrical but most often metrically asymmetrical, due to differences in lengths and/or diameters of the sister branches.

In this chapter, we study the proximal-to-distal electrical relationship in two sister paths by comparing sites situated at the same path distance from their common origin but on different paths. The path length of the shorter branch determines the path distance extent of the domain in which we can compare equidistant sites, since it is obvious that the most distal sites on the longer branch do not have equidistant counterparts on the shorter one! Remaining at the same path distance from the origin in the first continuous dimension and ‘jumping’ from one branch to the other in the second discrete dimension, we can compare electrical states of equidistant sites (Figure 8.1). Such a structure is most convenient for studying the impact of the metrical asymmetry of branching on the electrical structure of the paths. The difference in the electrical states reveals the critical impact of metrical asymmetry.

Theory for different configurations

Consider a simple example of metrical asymmetry: two branches of the same diameter d and different lengths, shorter l and longer l′ = l + Δl (Δl > 0) arising from the common origin.