Predictability and randomness of paw choices are critical elements in the behavioural plasticity of mouse paw preference

Animal Behaviour 98 (2014) 167e176

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Predictability and randomness of paw choices are critical elements in the behavioural plasticity of mouse paw preference Andre S. Ribeiro a, *, Brenda A. Eales b, Jason Lloyd-Price a, Fred G. Biddle b a b

Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, Tampere, Finland Department of Medical Genetics, Faculty of Medicine and Department of Biological Sciences, Faculty of Science, University of Calgary, Calgary, AB, Canada

a r t i c l e i n f o Article history: Received 11 June 2014 Initial acceptance 4 August 2014 Final acceptance 22 September 2014 Available online 11 November 2014 MS. number: 14-00476 Keywords: adaptability information entropy learning and memory mouse paw preference predictability randomness

Lateralized paw usage of mice, Mus musculus, is a learned behaviour, based on a gradual reinforcement of randomly occurring weak asymmetries in paw choice early in training. The reinforcement relies on strain-dependent, short-term and long-term memory. We characterized the skills of information accumulation by quantifying the predictability of each reach of initially naïve mice from past behaviour in two training sessions of 50 reaches, separated by a 1-week interval. We studied six mouse strains, including 9XCA and BTBR with absent corpus callosum and severely reduced hippocampal commissure, and compared them to a null model with random, unbiased paw preference. We found that each paw choice was based on a limited, strain-specific number of previous choices. Also, there was a limited, strain-specific degree of predictability of each choice. Consequently, there was a strain-specific degree of randomness that was not lost with training. After 1 week for consolidation of memory of learned biases, paw choices became more predictable and made use of fewer previous choices, except in 9XCA and BTBR; nevertheless, a degree of randomness remained. We conclude that paw choices are regulated by short-term memory of a small number of previous choices and by long-term memory that affects future behaviour patterns and decreases, but does not remove, the usage of short-term memory. Both shortterm and long-term memory skills are strain dependent. Importantly, a degree of randomness is not removed by training and this may be a critical element for behavioural plasticity in paw preference in changing environments, supplying constant adaptability in paw preferences. © 2014 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

Paw preference behaviour in mice, Mus musculus, has the feature of symmetry at the level of the population, but strong asymmetries at the level of individuals. Laboratory strains of mice have characteristically different patterns of paw preference that have remained consistent across many generations and in different laboratories, since the initial description of the behaviour in a single-paw reaching test (Collins, 1968, 1969). Studies in right- and left-biased test chambers demonstrated that mice learn a direction of paw preference as they reach for food with their forepaws (Biddle & Eales, 1999). Therefore, the differences in patterns of paw preference must arise from strain differences in a genetically regulated system of learning and memory. The challenge for genetic analysis of paw preference behaviour has been to understand the mechanism of learning and memory in different strains and to identify measurable elements that are genetically regulated and, hence, that give rise to different patterns of paw (or hand)

* Correspondence: A. S. Ribeiro, Office TC336, Department of Signal Processing, Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland. E-mail address: andre.ribeiro@tut.fi (A. S. Ribeiro).

preference (McManus, et al., 1988; Palmer, 2002, 2003, 2012; Rogers, 2009). Early assessments of the learning and memory of paw preference behaviour have been reviewed in Biddle and Eales (2013). Briefly, kinetic analysis in right- and left-biased test chambers uncovered the learning response to the number of training reaches, the decay of memory between tests, the importance of memory by blocking memory consolidation with a protein synthesis inhibitor, and the range of phenotypic, hence, genotypic differences in paw preference learning ability between mouse strains (Biddle & Eales, 2006). Subsequently, agent-based simulations reproduced the dynamic patterns of paw preference between strains by using ‘learning rate’ as the heritable trait (Ribeiro, Lloyd-Price, Eales, & Biddle, 2010). From this, it was determined that several strains, previously identified as ‘nonlearners’, actually have significant learning ability. Further, the simulations allowed a definition of the expected behaviour of nonlearner model mice and a prediction of the limits of paw preference learning in unbiased test chambers (Ribeiro, Eales, & Biddle, 2011). Finally, studies showed that the acquisition of biases is severely hampered, particularly in the longterm, in strains with absent corpus callosum and severely reduced

http://dx.doi.org/10.1016/j.anbehav.2014.10.008 0003-3472/© 2014 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

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hippocampal commissure, which suggests that memory is essential in the generation and consolidation of biases in paw preference in mice (Ribeiro, Eales, & Biddle, 2013). Ribeiro et al. (2011) characterized long-term learning and memory of paw preference in unbiased test chambers by comparing the biases in paw preference in two tests that were separated by a 1-week interval. Most mice exhibited heavier biases in the second test and in the same direction as the weaker biases in their first test. This was evidence that paw preference is an adaptive behaviour, based on learning. Moreover, mouse strains differed in degree of bias. Namely, in some strains (e.g. C57BL/6J) most mice were heavily biased and the number of ‘heavily biased’ mice increased in the second test, whereas in other strains (e.g. CDS/Lay) many mice remained unbiased in both tests and, more importantly, the fraction of heavily biased mice increased only weakly from the first to the second test. This result was strong evidence that the degree of learning of paw preference is genetically regulated and it is detectable in tests using unbiased chambers. We also characterized strain-dependent short-term memory skills in the system of learning and memory in paw preference behaviour (Ribeiro et al., 2011). A positive autocorrelation for any lag between two paw choices in the test session demonstrated that the reaching behaviour of mice was not fully random; rather, it was based on previous events. Also, this positive autocorrelation decreased with increasing lag between successive paw reaches within a test session, which demonstrated that mice gradually learned a direction of paw preference from reach to reach, during a session. For this, mice ought to pay more attention to their recent paw choices than to their distant past choices. Finally, mouse strains differed in both mean positive autocorrelation and rate of decrease in autocorrelation with increasing lag between reaches (Ribeiro et al., 2011), which further established that there were heritable differences in short-term memory skills in a test session as well as in the long-term memory skills between sessions. These observations might reflect a reciprocal and antagonistic relationship between short-term and long-term memory acquisitions. Whereas long-term memory skills are required to make use of past learning in future reaching events, individuals that retain more information from immediate past reaches than from distant past reaches can adapt their behaviour more rapidly to changing environments. Rates of adaptation to changing environments are being studied in many biological systems. A recent study on genetic networks suggests that sensing changes in the environment provides evolutionarily selective advantages in rapidly fluctuating environments (Ribeiro, 2008). In the case of paw preference behaviour, we suggested that a probabilistic paw choice creates a wide distribution of right-paw and left-paw usage among genetically identical individuals of an inbred mouse strain and differences in the patterns of paw preference between different genotypes of mice, such as from different inbred strains, could provide mice with more robustness to environmental changes and create a selective advantage for some strains in specific environments (Ribeiro et al., 2010). Further, different rates of adaptation of paw preference would lead to different fitness, depending on the rate of fluctuation of the environment, as discussed in other systems (Acar, Mettetal, & van Oudenaarden, 2008; Eldar & Elowitz, 2010; Hill & Zhang, 2004). In the context of probabilistic paw preference behaviour, different rates of adaptation are manifest in the variance of the phenotypic distributions of paw preference of different genotypes (i.e. differences in patterns of right- and left-paw preference), rather than as changes in mean values of right- or left-paw usage (Biddle & Eales, 2011; Ribeiro et al., 2010). Autocorrelation analysis of successive paw reaches (Ribeiro et al., 2011) provided the first clear evidence for heritable

differences in short-term memory of paw preference learning between strains as well as for the occurrence of behavioural modification from reach to reach, during a training session. Namely, it showed that the positive autocorrelation that is found between successive paw reaches decreases with increasing lag between the reaches (Ribeiro et al., 2011). Nevertheless, so far, there is no method to determine how many previous reaches influence the decision of which paw to use at each reach (and, thus, the predictability of the choices), nor is there a means to quantify the degree of influence that these past choices have on each paw choice during the course of a test session. These quantities would allow us to measure and evaluate the system of short-term memory processes associated with learning a paw preference and, thus, to compare the genetically regulated, short-term and long-term learning abilities of different mouse strains. They may also help us meet the challenge of genetic analysis of paw preference behaviour with identified measurable elements of the system that are genetically regulated. We confronted this issue in the present study by analysing the information entropy in the time series of paw choices that were made by previously untested, naïve mice of various inbred strains in unbiased U-world or UW test chambers. We asked three questions concerning the behaviour of naïve mice during their first training session. (1) How many previous reaches are used in decision making? (2) How predictable is each paw choice, given the knowledge of all past paw choices? (3) What is the magnitude of the strain differences in these two properties? With the data from the second training session of these mice, 1 week after their first session, we asked the following questions. (1) How much are the properties of paw choice in the second training session modified by the information from the first session? (2) How much do the strains differ in degree of behaviour modification between sessions? (3) Are the effects of both short- and long-term memory of previous reaches visible in the behaviour in the second session? From the answers, we quantify the amount of paw preference learning that occurs during a training session and provide a measure of the maximum degree of predictability of paw choice and, consequently, of the remaining degree of stochasticity (i.e. uncertainty) in paw preference. Finally, we also quantify the number of previous reaches that are required to achieve maximum predictability, which can be used as a measure of the number of previous reaches used by the short-term memory mechanisms to affect subsequent decisions. We used an unbiased test chamber because it has several advantages compared to biased ones. First, there is no physical or other reason for a bias in paw choice to appear where none existed, other than the existence of procedural learning from previous choices. Second, it allowed us to show that there are no biases at the population level, which suggests absence of constitutive biases. Third, we expected that the speed of learning a bias in paw preference in the absence of a physical reason for preferring a paw would be slower than in a biased test chamber, which may facilitate its detection in the case of strong learners. METHODS As in our previous work, we use the word ‘memory’ to mean ‘implicit memory’ or an unconscious form of memory (Roediger, 1990; Schacter, 1987) and ‘learning’ to imply ‘procedural learning’ or a behavioural change by an acquisition of implicit memory (Nissen & Bullemer, 1987). Mouse Strains, Housing and Husbandry We studied paw preference in the inbred strains C57BL/6JBid, C3H/HeSnJ.PafBid, DBA/2JBid and CBA/FaCamBid. We also used the

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9XCA/WahBid and BTBR Tþ Itpr3tf/J strains, whose paw preference learning is strongly hampered by short-term and long-term memory deficits, owing to their total absence of the corpus callosum and severely reduced hippocampal commissure (Ribeiro et al., 2013). BTBR is a historically inbred mouse strain, maintained at the Jackson Laboratory (Bar Harbor, ME, U.S.A.) and discovered in a strain survey to exhibit these neurological deficits (Wahlsten, Metten, & Crabbe, 2003). The originating sources for 9XCA and BTBR mice to our laboratory are described in Ribeiro et al. (2013). Noncomplementation previously demonstrated the genetic identity of the recessive forebrain commissural trait in the 9XCA and BTBR strains (Wahlsten et al., 2003). 9XCA is a recombinant inbred strain, which was derived from a mating between 129P1/ReJ and BALB/cWah1 strains and selectively bred because it lacked a corpus callosum and had a more severely reduced hippocampal commissure than either of its progenitor strains (MacPherson, McGaffigan, Wahlsten, & Nguyen, 2008; Schimanski, Wahlsten, & Nguyen, 2002). The hippocampal commissure was described as, quantitatively, approximately three times smaller in 9XCA than in C57BL/6J, in which it was considered of normal size within the strains that were assessed. Variability in the size of this commissure is small in both 9XCA and C57BL/6J (Wahlsten et al., 2003). We note that the 9XCA and BTBR strains do not have any special housing or maintenance requirements. Under our husbandry conditions, the natural behaviour and breeding performance of these mice is indistinguishable from those of the mice of strains with normal intercerebral commissural structures; hence, there are no welfare implications in their use (as an aside, because these strains are indistinguishable, the agenesis of the corpus callosum in all BTBR was unnoticed by mouse biologists for well over half a century after its introduction in laboratories). All strains are registered inbred strains and are maintained as genetic reference strains with continued sisterebrother inbreeding. The strain names are simplified to the following: C57BL/6J, C3H/ HeSnJ, DBA/2J, CBA/FaCam, 9XCA, BTBR. The mice are cared for in accordance with the Guide to the Care and Use of Experimental Animals of the Canadian Council on Animal Care (CCAC, approval number AC13-0118). The Animal Care Committee of the University of Calgary approved the experimental procedures. After weaning from our breeding colony, the mice for paw preference testing were housed in groups of up to five per cage; males (one or two) were usually caged with females, to prevent fighting. These cages were clear polycarbonate (29.5  19.0 cm and 13 cm high) ‘shoebox’ type cages, with stainless steel wire-grid lids that held feed and a water bottle; bedding material was aspen wood chip and virgin unbleached ‘crinkle cut’ paper for nesting. A 10 cm length of 3.8 cm ABS piping was used as cage enrichment to aid cage changing of our breeding and experimental mice. These cages were deemed appropriate and approved for usage for these experiments by the Animal Care Committee of the University of Calgary, in accordance with the CCAC Guidelines on Laboratory Animal Facilities. Food (rodent formula 5020, PMI Nutrition International, www. labdiet.com) and water were available ad libitum. The conditions of the mouse rooms were under control (20 ± 1  C, relative humidity 40%) with a 14:10 h light cycle (lights on at 0800 hours). Paw preference testing was conducted in the second half of the light period in the same colony room. Mice were raised specifically for this experiment and tested usually at 10e12 weeks of age. Following the test period, the mice were euthanized by cervical dislocation (according to SOP E1, General Euthanasia, Animal Health Unit, University of Calgary). We tested 100 C57BL/6J mice, 51 C3H/HeSnJ mice, 100 DBA/2J mice and 100 CBA/FaCam mice. We also tested 100 9XCA mice and 100 BTBR mice whose absent corpus callosum and reduced

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hippocampal commissure severely hamper the acquisition of paw preference biases with training (Ribeiro et al., 2013). Finally, we simulated random unbiased choices of 100 null model mice (see Table 1). Previous analyses of empirical and simulated paw preference behaviour demonstrated that comparing behaviours of populations of approximately fewer than about 50 mice leads to inconsistent results (Ribeiro, et al., 2010). Therefore, to ensure a robust comparative analysis, we used sample sizes of 100 mice. For the C3H/HeSnJ strain, only 51 mice were available for testing. Nevertheless, it was possible to robustly detect consistent differences in behaviour from the other genetic strains. As such, we included the sample of 51 C3H/HeSnJ mice in the present study. Finally, we note that previous studies have not revealed a difference in behaviour between males and females in any strain, in either unbiased or biased test worlds (Biddle, Coffaro, Zeihr, & Eales, 1993; Biddle & Eales, 1999). Therefore, here we combined the data from both sexes. Measurements of Paw Preference Each mouse was previously untrained and considered to be naïve at the beginning of the first test session. Each mouse performed two sessions of 50 reaches in unbiased (UW) test chambers that were separated by a 1-week interval. All results are extracted from these two tests alone. Paw usage was assessed in UW (unbiased-world) test chambers (Biddle & Eales, 1999) where reaching with the right or left paw involves identical effort and is equally rewarded. Previously untested mice are called ‘naïve’ and we observed the behaviour of mice when naïve and 1 week after the first test. Adult mice between 10 and 20 weeks of age were fasted for 12e24 h and placed in a test chamber (Fig. 1). Tests using shorter fasting periods (or other, more preferred foods) showed that the mice were not motivated to reach for the food and simply sat in the test chamber. At 12e24 h of fasting, the mice exhibited normal in-cage activity, similar to nonfasted individuals, but when placed in the test chamber they reached for the tube, without much delay. Their reaching was slow and steady and neither frenetic (which would hamper the counting in paw usage) nor reluctant. This fasting period is in agreement with the 24 h fasting period that has been used in other recent assessments of mouse paw preference (Ribeiro et al., 2011; RibeiroCarvalho, Abreu-Villaca, Paes-Branco, Filgueiras, & Manhaes, 2010). Dimensions of the test chambers are described in Collins (1975, p. 184) and are repeated here for completeness: ‘The test apparatus was fabricated of Plexiglass and consisted of five in-line testing cubicles whose inside dimensions were 3.8 cm wide by 5.5 cm deep by 11.5 cm high. A 9 mm glass feeding tube was attached to the front wall of each cubicle 5.75 cm from the floor.’ We used a Plexiglas feeding tube, instead of glass. In UW chambers, the tube is equidistant from the left and right side of the cubicle. The food was placed into the feeding tube with a small spatula and, depending on the enthusiasm of the mouse to reach for it, was either commercial diet Purina Mouse Diet 9F ground into a coarse powder, humanTable 1 Improvement of individual biases (IR) between paw preference behaviours in two tests of 50 reaches in unbiased test chambers, separated by 1 week Strain

No. of mice tested

IR

C57BL/6J C3H/HeSnJ DBA/2J CBA/FaCam BTBR 9XCA Null model

100 51 100 100 100 100 100

0.74 0.75 0.70 0.64 0.46 0.36 0.33

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mutual information, IN, between all choices and the N choices preceding these choices. We assume that the present choice is affected only by the fraction of times a given paw was used in the N previous reaches, rather than the specific temporal order of these reaches. To calculate IN, we calculate the fraction of times (from here on referred to as ‘probability’) that the ‘present’ choice is ‘right paw’ (PR). Next, we calculate the probability that in the N previous reaches there were M right-paw reaches (PM), for all M (i.e. for 0  M  N). Finally, we calculate the probability of both the right paw being chosen in the present reach and having M right-paw reaches in the previous N reaches (PM,R), for all M. All probabilities are calculated from all reaches made by mice of a given strain for which N previous reaches are available. From these, we calculate the entropy of the present choices, Hpresent, the entropy of N past choices, Hpast, and the joint entropy of present and past N choices, Hpp, for all N:

      Hpresent ¼ PR  log2 PR  1  PR  log2 1  PR

Hpast ¼ 

N X

½PM  log2 ðPM Þ

(2)

(3)

M¼0

Hpp ¼ 

N  X M¼0

  PM;R  log2 PM;R      PM  PM;R  log2 PM  PM;R

(4)

Finally, we calculate IN between present choices and N past choices as follows: Figure 1. Mouse using its right paw to reach for food in an unbiased-world test chamber. The food tube is equidistant from the left and right sides. From Biddle et al. (1993) and reproduced with permission, © Canadian Science Publishing or its licensors.

grade, natural rolled oat cereal (unflavoured) ground into a coarse powder or a diet supplement called ‘Love Mash’, used in our mouse breeding colony (Ribeiro et al., 2013). Sufficient food was placed in the tube so that the mouse reached carefully without digging frenetically. The sequence of right- and left-paw entries to retrieve food was recorded for a total of 50 reaches per mouse. Model of Unbiased Nonlearner Mouse in an Unbiased World The behaviour of a model, unbiased, nonlearner mouse in a test chamber can be described by an unbiased binomial distribution. The probability PR(k) that an unbiased nonlearner mouse uses its right paw k times in N reaches is given by equation (1), where p is 0.5:


PR ðkÞ ¼


  N X N N PR ðkÞ ¼ 1 pk ð1  pÞNk ¼ 0:5N ; with k k k¼0

(1) The behaviour of a population of M unbiased nonlearner mice can either be deduced from equation (1) or be numerically sampled. This provides an objective ‘metric of learning and memory ability’; also, it aids in determining whether differences between strains are significant (Ribeiro et al., 2011, 2013). Information that is Predictable from Past Choices To determine the fraction of information in a given paw choice that is predictable given N past choices, we first calculate the

IN ¼ Hpresent þ Hpast  Hpp

(5)

We are interested in the fraction of information regarding the present choice that is predictable given N past choices. In other words, we are interested in the uncertainty coefficient (UN), which can be obtained by dividing IN by Hpresent:

UN ¼

IN Hpresent

(6)

This quantity represents the predictability of any reach, given the knowledge of the N past reaches. Thus, this quantity characterizes mouse strains, rather than individual mice. For example, let us assume that we want to calculate the predictability of the next reach of mice of strain X, given the knowledge of N ¼ 2 previous reaches. For this, we would collect one data point for every reach after the second reach made by a mouse of strain X. In one session, we would collect 48 such data points (e.g. reach 8 with previous reaches 7 and 6, reach 9 with previous reaches 8 and 7, etc.) from each mouse of a strain. The probabilities PR, PM and PM,R, of a strain would then be estimated from these data points, and UN can be calculated according to equation (6). We calculate UN for all values of N from 1 to 25, from the measured sequences of choices of all mice of a strain in a session. Since each session consists of 50 reaches, using higher values of N, greater than 25, compromises reliability, owing to the lack of samples. UN is limited between 0 and 1. If UN is equal to 0, present choices are not affected by N past choices (as the past does not inform the present). This would occur if the mice have no shortterm memory of previous reaches or if previous choices are not considered in subsequent decision making. If UN is equal to 1, all choices are fully determined by the N preceding choices, and thus by knowing these, it would be possible to predict the next choice with complete certainty.

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Number and Predictability of Previous Choices To extract quantities from the measurements, we fitted an exponential curve of the form c  (1  el$N) by least squares to the measured values of U(N) for N ¼ 1, …, 25. For N infinite, this formula reduces to c, which is the maximum value of U(N), for any N. We calculated the coefficient of determination (R2) to test the goodness of fit of the exponential curve. This quantity will have a value of at most 1. A value of x indicates that (1  x) of the variance in the data is not explained; that is, it is not captured by the model. From the values of U(N ¼ 1, …, 25), we estimated two properties of the learning process of paw preference in each strain: the number of previous choices used in decision making and the maximum degree of predictability of the choices. Note that, from the difference between the maximum degree of predictability and the maximum possible value of U, one can further quantify the degree of unpredictability of the choices in a session. The number of previous choices significantly affecting present decisions is obtained from the exponential curve of the form c  (1  el$N) that was fitted to U(N). Once c and l were known for a given strain, we equated this function to 0.95  c and solved for N, to estimate NU(max),, which is the value of N previous paw choices that is sufficient to reach 95% of the maximum U for that strain. In other words, we calculated how many previous reaches are needed to obtain 95% of the information of the next reach that can be predicted. This value (95%) was chosen arbitrarily, but we observed that selecting other values does not qualitatively alter the conclusions. If we selected another value, x, we could obtain the changes that the results would suffer by multiplying these by:

lnð1  xÞ lnð1  0:95Þ

(7)

We also extracted the value of c from the fitted curve, which is used as a measure of the maximum predictability (Umax) of the paw choices of a strain, given the knowledge of the previous reaches. Consequently, the quantity (1  Umax) is a measure of the ‘randomness’ (or stochasticity) in paw preference that is not removed by training during a test session. Finally, we also calculated U1, the predictability of the choices, given the knowledge of the immediately preceding choice alone. For this, we collected one data point for every reach after the first reach made by a mouse of a strain. In one session, we collected 49 such data points (e.g. reach 2 with previous reach 1, reach 3 with previous reach 2, etc.). The probabilities PR, PM, and PM,R were then estimated from these data points, and U1 was calculated from equation (6). From this, we could determine, for example, whether or not a strain with higher U1 than another strain necessarily has higher Umax as well. If not, that implies that there are at least two components of short-term memory: namely, the accuracy with which the preceding reach is remembered and the accuracy with which more past reaches are remembered (assuming that the accuracy with which a choice is remembered is directly related to the degree of influence it has on a subsequent choice). Degree of Reinforcement of Biases Between Training Sessions Previous studies showed that, when strains with long-term memory skills are given a 1-week interval between training sessions, individual biases are stronger in the second session than in the first (see e.g. Ribeiro, et al., 2011). Since all the strains used here are symmetric in numbers of right- and left-biased mice, we tested for the stronger bias in the second session with a Boolean variable that we named ‘bias improvement’ (b). This quantity is 1 if an

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individual's number of right-paw entries (RPE) in the first UW is 25 or less and the RPE in the second UW is equal to or less than the RPE in the first UW; otherwise, it equals 0. Similarly, b is 1 if an individual's RPE in the first UW is 25 or greater and the RPE in the second UW is equal to or greater than the RPE in the first UW; otherwise, it equals 0. The value of b for a mouse with an RPE of 25 in both the first and second UW is 0 by convention. The ‘bias improvement ratio’ (IR) is the average of the bias improvement of the mice of a strain, and quantifies how many mice increased their bias in the second session. Note that the value of IR for unbiased nonlearner model mice with random paw preference will equal 0.33, assuming two training sessions of 50 reaches each (Ribeiro et al., 2011). Therefore, if there is any behavioural modification with training, IR is expected to be higher than this value of 0.33 for spurious learning. (If the sessions were longer, i.e. with more reaches, this value would decrease.) Also, the maximum possible value of IR is 1 and it would be expected for mice with a deterministic paw preference that used the same paw, either right or left, for all reaches. We used the average IR of a population of mice of a given strain as a quantitative measure of their average degree of behavioural change between sessions. RESULTS From the paw preference tests, we extracted the RPE distributions of each strain, measured in the first and second test, respectively (Figs. 2 and 3). No strain exhibited a significant bias in the numbers of mice preferentially using the right or left paw, in either test. Namely, for each strain, we performed a binomial test to determine whether the number of mice preferentially using the right paw could have arisen from an unbiased binomial distribution. All P values were much greater than 0.05. From this we conclude that there is no evidence for a bias in any of the strains. However, in all strains, except 9XCA and BTBR, many mice exhibited strong biases, particularly in the second test. Finally, we note the similarity of the RPE distributions of 9XCA and BTBR and the RPE distributions of the null model mice. The increase in number of heavily biased mice in the second test is due, at least partially, to the retention of biases acquired in the first test (Ribeiro et al., 2010), followed by their further increase in the next test session. This is shown by the IR values of each strain (Table 1). Also shown in the Table is the spurious IR of 0.33 that is expected for nonlearner mice with random paw choices. Relevantly, the two strains, BTBR and 9XCA, that have absent corpus callosum and reduced hippocampal commissure, expressed an IR that was only slightly better than the null model. Meanwhile, the maximum IR of 1.0 would be expected for mice with a deterministic paw preference, but that behaviour was not found in the mice reported here or in any other mice that we have tested to date. Relevantly, both the fraction of mice retaining acquired biases and the degree of retained bias differed between strains. As mentioned above, such differences between strains result from both different short-term memory skills during the test sessions and different long-term memory skills between the sessions. The existence of procedural learning during test sessions, based on short-term memory, is detectable by autocorrelation analysis from the behaviour modifications that occur during these periods. Positive autocorrelations imply that paw choices are, to some extent, based on previous choices. It follows that each paw choice ought to be predictable, to some degree, from previous choices and its predictability should increase when increasing the number of previous reaches considered. Finally, since the positive autocorrelation decreases with increasing lag between successive paw reaches, the memory of previous reaches is expected to decrease with

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BTBR, UW1

C3H/HeSnJ, UW1

20

20

20

10

10

10

0

20

40

0

CBA/FaCam, UW1 Number of mice

C57BL/6J, UW1

20

40

0

DBA/2J, UW1 20

20

10

10

10

20

40

0

20

40

40

9XCA, UW1

20

0

20

0

20

40

Null, UW1 20 10

0

20 40 RPE score

Figure 2. Right-paw entry (RPE) distributions from the first test of 50 paw reaches made in an unbiased-world test chamber (UW1) by naïve mice of various strains and by nonlearner model mice. The 51 RPE scores (0, 1, 2, … 50) from individual mice are binned in 17 groups of three RPE scores.

BTBR, UW2

C3H/HeSnJ, UW2

20

20

20

10

10

10

0

20

40

0

CBA/FaCam, UW2 Number of mice

C57BL/6J, UW2

20

40

0

DBA/2J, UW2 20

20

10

10

10

20

40

0

20

40

40

9XCA, UW2

20

0

20

0

20

40

Null, UW2 20 10

0

20 40 RPE score

Figure 3. Right-paw entry (RPE) distributions from the retest of 50 paw reaches made in an unbiased-world test chamber (UW2), 1 week after an identical test by mice of various strains and nonlearner model mice. The 51 RPE scores (0, 1, 2, … 50) from individual mice are binned in 17 groups of three RPE scores.

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Uncertainty coefficient

0.7

BTBR C3H/HeSnJ C57BL/6J CBA/FaCam DBA/2J 9XCA Null

0.6 0.5 0.4

0.7 Uncertainty coefficient

increasing lag. Consequently, the predictability of a paw choice should increase for increasing number of previous reaches only up to a certain number, at which point considering additional reaches should no longer quantitatively affect the predictability. Long-term memory allows the bias in paw preference to increase with training, that is, to be higher in future sessions (compare Figs. 2 and 3). Thus, given two training sessions separated by a 1-week interval, we expected the predictability of the choices to be higher in the second session, owing to reduced randomness. For the same reason, in both training sessions, the behaviour of mice from strains exhibiting stronger biases should be more predictable than the mice of strains with weaker biases. To test these hypotheses, we calculated the uncertainty coefficient (U) for each strain as a function of the number (N) of previous reaches (for all N < 26) from the series of paw choices of each mouse. Results from the first and second sessions are shown in Figs. 4 and 5, respectively, along with their fitted exponentials. From Figs. 4 and 5, we can see, in general, that the uncertainty coefficient U(N) increased gradually with increasing number of previous reaches (N) in all strains, except the null model mice, and in both sessions. Also, the higher the number of previous reaches considered in each strain, the more predictable a choice became, but only up to a certain value of N. This result provides strong evidence that recent, previous choices are de facto used in decision making. Meanwhile, beyond a certain value of N, U(N) no longer increased significantly, suggesting that, as hypothesized, only a limited number of previous reaches are affecting decisions about paw choice in a test session. Also from Figs. 4 and 5, it is clear that all strains differed widely in behaviour. First, some strains differed in the value of U(N ¼ 1), which is the predictability of a paw choice, given the knowledge of the immediately previous choice alone (see also Table 2). Second, all strains differed in the maximum values of U(N). Third, the strains with identical values of U(N ¼ 1), namely DBA/2J and CBA/FaCam as well as BTBR and 9XCA, differed in their maximum values of U(N). Finally, the strains appeared to differ in how many reaches needed to be considered in order to reach the maximum values of U(N). From this, it is possible to conclude that, in general, the strains differ not only in how much the previous reach affects the next paw choice, but also in how much each reach depends on all previous reaches and in how many of these previous reaches influence the next choice. In addition, Figs. 4 and 5 show that the strains differed in the extent to which their behaviours changed from the first to the second test session. This implies that they differ in long-term

0.1 0

5

10 15 20 No. of previous reaches

25

Figure 4. Uncertainty coefficient as a function of the number of previous reaches considered in the first test in an unbiased-world test chamber with 50 consecutive reaches. The exponential curves of the form c  (1  el$N) are fitted to the values of U(N) of each strain.

BTBR C3H/HeSnJ C57BL/6J CBA/FaCam DBA/2J 9XCA Null

0.6 0.5 0.4 0.3 0.2 0.1 0

5

10 15 20 No. of previous reaches

25

Figure 5. Uncertainty coefficient as a function of the number of previous reaches considered in the second test in an unbiased-world test chamber with 50 consecutive reaches. The exponential curves of the form c  (1  el$N) are fitted to the values of U(N) of each strain.

memory skills, as suggested by the values of IR (Table 1). This is particularly evident when comparing CBA/FaCam with BTBR. Although these two strains behaved similarly in the first session, they behaved differently in the second. Whereas CBA/FaCam mice modified their behaviour based on long-term memory skills, BTBR mice (like 9XCA mice) did not, as we expected, given the absence of their corpus callosum and severely reduced hippocampal commissure. Finally, Figs. 4 and 5 show that the behaviour of the mice in the second session was determined by both short- and long-term memory of previous reaches. Short-term memory is evident in that increasing the number of previous reaches considered increased the uncertainty coefficient. Long-term memory is evident in that the uncertainty coefficient values in the second session differed from those in the first for all strains but BTBR and 9XCA. We fitted an exponential curve to the values of uncertainty U(N) in Figs. 4 and 5, in order to extract Umax, the maximum degree of predictability of choices, and NU(max), the number of previous reaches that are necessary to consider in order to achieve 95% of the value of Umax. Results are shown for each strain in Table 2 for the first and second training session, along with the results of the tests of goodness of fit of the exponential curves, which indicate that, with the exception of the null model, the exponential curve is a good fit to the data in a statistical sense. Also shown are the values of U1, that is, the degree of predictability of the next choice of paw, given the knowledge of the immediately previous choice alone. From Table 2, it is clear that the values of U1, Umax and NU(max) are strain dependent. In general, strains with higher maximum Table 2 Values of NU(max) and predictability Umax extracted from the first and second test Strain

0.3 0.2

173

C57BL/6J C3H/HeSnJ DBA/2J CBA/FaCam BTBR 9XCA Null model

UW1

UW2

NU(max)

Umax

R2

U1

NU(max)

Umax

R2

U1

3.63 7.68 8.69 15.99 10.67 11.12 3417.9

0.59 0.31 0.24 0.21 0.19 0.15 0.00

0.98 0.98 0.97 0.99 0.94 0.95 1.60

0.35 0.08 0.04 0.04 0.00 0.00 0.00

3.13 5.01 5.55 6.84 12.03 13.41 2639.5

0.66 0.50 0.38 0.30 0.24 0.14 0.00

0.95 0.92 0.98 0.97 0.94 0.96 1.9

0.43 0.25 0.14 0.12 0.00 0.00 0.00

Values of NU(max) and predictability Umax extracted from the results shown in Fig. 4 (first test in an unbiased-world chamber, UW1) and in Fig. 5 (second test, UW2) by fitting an exponential curve to the measured values of U(N) by least squares. Also shown is the goodness of fit, i.e. the coefficient of determination (R2) and the value of U(N ¼ 1) of the immediately previous reach, indicated as U1.

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predictability (Umax) used relatively fewer previous reaches to achieve 95% of their maximum predictability (NU(max)) in both the first and second training session. In other words, if the 9XCA and BTBR strains are excluded for the moment, stronger learners in general required fewer training reaches than poor learners to achieve their maximum predictability in the first test session and they required even fewer training reaches to achieve a greater maximum predictability in the second session. This is expected if the higher predictability results from stronger biases in paw choice, rather than, for example, from nonrandom sequences of choices. In particular, as the variability in paw preference decreases with the degree of bias of the choices, the number of previous choices necessary to predict the next choice is also expected to decrease. In the limit of a fully biased mouse, its choices could be predicted with absolute precision from a single past reach. However, if the mean value of U1 of two strains is identical, reaching higher values of Umax appears to require remembering more previous reaches. This is also expected since, if one previous reach can only influence the next choice to some extent, in order to obtain greater influence of past choices on subsequent ones, an individual may need to consider more previous choices when making the next decision. Interestingly, in no strain did the maximum predictability Umax reach values close to 1, even in the second session, indicating that paw preference behaviour remained stochastic to a considerable degree when the mice were given the amount of training in the present study. The quantity (1  Umax) is a measure of the remaining randomness. In this regard, when the time series of paw choices was inspected, no mouse exhibited a nonrandom sequence of choices (e.g. cycles of repeated alternating left and right paw reaches, cycles of three left paws followed by one right paw, etc.). Rather, training (or reaching) biases the paw choice, but it does not alter the stochastic nature of the choices. This is the likely reason for the accuracy in fitting the values of uncertainty U(N) with exponential curves (Figs. 4 and 5). Regarding 9XCA and BTBR mice, it is important to note that their paw choices were not totally random, indicating that the shortterm memory skill of these strains is weak but not null, as we had previously suggested from an autocorrelation analysis (see above). Nevertheless, 9XCA and BTBR mice exhibited little or no increase in their maximum predictability Umax between the two test sessions (Table 2). All of the other tested strains increased or improved their maximum predictability in the second test session and they improved their maximum predictability with fewer previous reaches. In contrast, both 9XCA and BTBR mice used the same or slightly more previous reaches in the second test session to achieve a low maximum predictability that is similar to what they expressed in their first test session (Table 2). This suggests that 9XCA and BTBR mice have virtually no long-term memory of any weak biases in paw preference that were acquired in their first unbiased-world test session. This is probably associated with their genetically identical (noncomplementing), completely absent corpus callosum and severely reduced hippocampal commissure. Finally, the values of Umax and NU(max) changed between the two tests in all strains, except in 9XCA and BTBR (Table 2). Such changes indicate the existence of long-term memory skills. Relevantly, the degree of change differed between strains, suggesting that the long-term memory skills are strain dependent. The relatively smaller changes in the values of Umax and NU(max) in stronger learners of paw preference, such as C57BL/6J, may be due to these mice achieving biases in the first test session that are close to the limit in the degree of biasing that is possible in tests with 50 paw reaches. In this regard, the degree of learning in the first test is here measured by Umax. This quantity ought to detect the degree of

behavioural change between tests (along with the degree of loss of memory during the week between the tests). Since the degree of behavioural change between tests was also assessed by IR, we computed the Kendall's tau (t) correlation (Kendall, 1938) between Umax and IR of each strain. We found a positive correlation of 0.9 (P ¼ 0.003). From this, we conclude that there is a statistically significant positive correlation between the two quantities, as expected. DISCUSSION The source of behavioural plasticity in mouse paw preference has remained elusive from the time of its first description (Collins, 1968, 1969) to the present (Biddle & Eales, 2013). Previous studies showed that paw preferences in the mouse emerge from a constant reinforcement of weak biases, generated at random early in training and this reinforcement relies on learning from previous experiences (Ribeiro et al., 2011). Thus, the process of biasing paw preference ought to involve extraction, integration, storage and retrieval of information, which we assume to be key tasks of the brain. Study of the learning process in mouse paw preference might therefore provide a better understanding of how short-term and long-term memories regulate behaviours in general. In this study, we first defined measurable properties of the learning and memory process from the patterns of paw preference of different mouse strains. First, we observed a gradual increase in predictability of paw choices with number of previous choices considered, but only up to a small number of previous choices and, second, we observed that this increased predictability decreased with lag between reaches and the addition of another previous reach. Therefore, in our opinion, the uncertainty coefficient and, consequently, the number of previous reaches affecting a choice are good quantitative measures of how short-term memory of past choices affects subsequent paw choices. These quantities ought to provide a framework to assess the developmental and functional genetic regulation of this complex adaptive behaviour, such as the heritable elements that regulate and produce the characteristic patterns of paw preference of selected mouse strains (as in Figs. 2 and 3). Moreover, if a genetic analysis were successful with the mouse behaviour, mouse genes might provide an entry into the biology and evolution of asymmetry of hand usage, and perhaps of learning processes, in other species as well. Our observations suggest that all tested mice used short-term memory of previous reaches in order to make their next paw choice during a test session because the choices were predictable from past choices to some extent, rather than random. Also, all strains but 9XCA and BTBR (as expected; Ribeiro et al., 2013), appeared to exhibit long-term memory of the bias in the acquired paw preference because, in the second test, most mice exhibited an even more pronounced bias in the same direction than before. In this regard, our observations suggest that long-term memory of past behaviour resulted in a ‘constant bias’ in paw choice in the subsequent session whereas short-term memory generated a ‘dynamic bias’ that changed (usually increased) during the sessions. When deciding which paw to use during a subsequent session, all previously tested strains, except 9XCA and BTBR, appeared to combine long-term memory of previously acquired biases with short-term memory of the bias in a small number of immediately previous choices. The evidence for this is the strong positive correlation between biases exhibited in the first and second session and the increase in that bias in the second session. Further evidence is the decrease in the number of reaches considered in order to make each next decision during the second session, even though the maximum predictability of each choice was higher than in the first session.

A. S. Ribeiro et al. / Animal Behaviour 98 (2014) 167e176

We quantified four properties of short-term memory: (1) how much the preceding choice (U1) influences the next paw choice; (2) how many previous choices (NU(max)) influence the next choice; (3) how much the next choice is influenced by all previous choices (Umax); and, finally, (4) the randomness in paw choice (1  Umax) that is not removed by training. All mouse strains were found to exhibit unique behaviours in that they differed in at least a few of these four properties of short-term memory, in agreement with previous studies (Ribeiro et al., 2013). Probably, these quantities also differ slightly between mice of the same strain, given the stochastic nature of the choices and small differences in learning skills between individuals of the same strain. Unfortunately, there were too few sample reaches from each individual in the present study for statistical comparison of individuals. Our results also suggest that at least some of the strains differ in long-term memory skills. For example, the behaviour of DBA/2J mice appeared to differ more from CBA/FaCam mice in the second than in the first session. Also, although CBA/FaCam and BTBR behaved almost identically in the first session, they differed widely in the second (no doubt due to the neurological deficits in the latter strain). This suggests that long-term and short-term memory processes are somewhat independent from one another, even though the outcome of the long-term memory process is limited by the outcome of the short-term memory process. Overall, we suggest that the clear differences in behaviour within a training session and differences in changes in behaviour between sessions are direct evidence that genetics play an important role in the regulation of paw preference behaviour and that there are separable genetic roles in the regulation of the short-term and long-term learning and memory processes. In any case, it is worth stressing that, without exception, all four normal strains studied here (C57BL/6J, C3H/HeSnJ, DBA/2J and CBA/ FaCam) showed increased values of Umax in the second training session. This provides strong evidence that long-term memory of previously acquired biases takes place and influences future behaviours. Also, in these strains, in both test sessions, those with less effective short-term memory (i.e. weaker degree of influence of the immediately preceding choice (U1) and of all previous choices on the next choice) exhibited more previous choices with a detectable influence on each choice (NU(max)). We believe that this does not imply that mouse strains with lesser certainty of past choices ‘compensate’ for this uncertainty by recollecting more past choices. Instead, we expect that, if a mouse is more ‘certain’ of the immediately preceding choice (which is always appropriate in an unbiased chamber), then it is likely that it will make less effort to recollect more past choices, although it could. As an aside, even though an autocorrelation analysis has shown that, in mice with stronger biases, each choice is more strongly correlated with a larger number of previous choices within a test session (Ribeiro et al., 2011), this is not in disagreement with our present results, since autocorrelation does not imply usage of memory of a larger number of previous choices to make the next paw choice. The numbers of previous choices that appear to influence subsequent choices also appear to be sufficient to maintain strong biases in the strains we have analysed, but the numbers are also sufficiently small so that, if the environmental conditions change, the mouse is likely to be able to quickly invert its paw preference within a few reaches. This is particularly the case for naïve mice because, by inspection, we observed such inversions in some mice, even in the absence of changes in the environment. In general, three or four consecutive reaches, in the direction opposite to the preferred one, suffice in unbiased test chambers. Also, we expect fewer to be required, if the direction of the environment had actually changed. We have tested this before and, in particular, such inversions were most visible in a previous study using left- and

175

right-biased test chambers. In biased test chambers, strong learner mice, such as C57BL/6J, were more left-biased in left-biased test chambers than poor learner mice, but they quickly became more right-biased than poor learner mice in right-biased chambers (Biddle & Eales, 1999, 2006). This demonstrates that paw preference is an adaptive behaviour and that long-term memory plays a strong role only if the conditions of the environment remain unchanged. Nevertheless, we expect such inversions of paw preference to be less likely, and slower, as long-term memory of usage of one of the paws accumulates in stable environmental conditions. In contrast to the normal mouse strains, both 9XCA and BTBR with completely absent corpus callosum and severely reduced hippocampal commissure had a low maximum predictability of paw choice, but this was clearly not null when compared to nonlearner model mice (Figs. 4 and 5). Nevertheless, neither strain had a significant improvement in their predictability in the second session. This is objective evidence that both 9XCA and BTBR mice had little or no long-term memory of the training in the first session and, thus, we suggest that these results may be direct evidence for a disruption of this genetically regulated learning function by the genetically identical (noncomplementing) absence of corpus callosum and severely reduced hippocampal commissure in these mice (Wahlsten et al., 2003). Also, we hypothesize that the small differences in maximum predictability and in number of previous reaches to achieve maximum predictability between 9XCA and BTBR mice in both test sessions are the result of minor background genetic differences between them that also regulate the learning and memory system in paw preference behaviour. In any event, the obvious qualitative difference in long-term memory of paw preference learning behaviour may be a useful screening tool to functionally assess mice for potential intercerebral commissural deficiencies (Bohlen, Bailoo, Jordan, & Wahlsten, 2012; Wahlsten, Bishop, & Ozaki, 2006; Wahlsten et al., 2003). We expect that the ability to adaptively bias paw choices would be evolutionarily advantageous, perhaps by making the process of reaching either faster and/or less energy consuming. An ability to constantly change the bias in paw choice, based on a degree of randomness, or to become biased differently for different tasks, rather than inheriting a fixed bias (or task-based fixed biases), should be advantageous, particularly in changing environments. Hence, we suggest that critical elements in paw preference behaviour are not only the ability to learn a preference from a paw reach in the short term of a training session and to consolidate this preference in the long term provided that conditions do not change, but also the ability to maintain a degree of randomness that is not removed by training. This is an important component of the paw preference behaviour since it provides the ability for constant adaptation to changing environments, even in heavily biased individuals. Finally, we do not know why mouse strains differ in their learning ability of paw preference. Probably, it is a consequence of different short-term and long-term memory skills in general, rather than memory skills that were evolved specifically for this task. Future direct genetic analysis should allow the identification of the heritable (genomic) causes of the differences. In the meantime, our study supports a simple reason for why normal mouse strains may differ in degree of paw preference learning and it provides an evolutionary importance for proceeding with genetic analysis of this trait. Different mouse strains were derived historically from different wild populations (Beck et al., 2000) and, during their inbreeding, genetically different elements that regulate behavioural plasticity were fixed in a homozygous state in the different inbred strains. So far, no mouse strain has been found to be unable to learn and, hence, to express either a random or a deterministic paw preference. Therefore, in the case of paw preference behaviour, any suggestion for a selective advantage of mutually exclusive,

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phenotypic alternatives in direction of paw preference may be a distraction. Instead, we should be searching for which genes regulate the ‘strength’ of short- and long-term memory in the system of its learning and memory and which may have provided a foundation for an evolutionary adaptive advantage of its behavioural plasticity in individual mice. Conclusions In summary, we calculated information entropy as a means to characterize and quantify the amount of paw preference learning that occurred when mice reached for food with their forepaws in unbiased test chambers in two test sessions that were separated by a 1-week interval. From the sequences of probabilistic right- and left-paw reaches, we measured the number of previous reaches that needed to be considered to achieve a maximum predictability of the next paw choice in each strain and we compared the results to simulated nonlearner model mice. We also measured this degree of maximum predictability. All tested mice, including BTBR and 9XCA with absent corpus callosum and severely reduced hippocampal commissure, had short-term memory skills because, by knowing their previous choices, one could predict, to some extent, their next choice. The mice maintained a degree of randomness that was not removed during the training session. These skills were strain specific since the maximum predictability and thus the degree of randomness not removed by training, as well as the number of previous reaches necessary to achieve it, were strain dependent. Interestingly, normal mouse strains achieved a greater maximum predictability of paw choice with inversely fewer numbers of previous reaches. Also, these normal strains expressed a long-term memory of their first test session because they increased their maximum predictability of paw choice with still fewer previous reaches in their second test session. Two independent mouse strains with genetically identical absent corpus callosum and severely deficient hippocampal commissure showed no evidence for long-term memory of paw preference training, as previously shown, because they both required more previous training reaches in their second test session to achieve a low maximum predictability of paw choice. More importantly, we have shown here that these deficiencies also affected their short-term memory since their paw choices in the first session were much more random, i.e. less determined by previous reaches than in other strains. We conclude that, during a test session, mice continuously stored information from the sequence of right- and left-paw choices, which they then used to affect their next paw choice when they reached for food in unbiased test chambers; however, an amount of randomness in paw choice did not appear to be removed by training. Regardless of the cause of this limitation, we suggest that a degree of randomness in paw choice provides mice with an advantage of adaptive plasticity in changing environments. We believe that our study may assist the assessment of genetic regulation of the elements of the learning and memory process that underlies the adaptive plasticity of paw preference behaviour in the mouse model system. Acknowledgments A.S.R. thanks the Academy of Finland for support (grant no. 257603). J.L.-P. thanks the President's graduate programme of TUT. F.G.B. thanks anonymous funding sources to the University of Calgary and both the Department of Biological Sciences and the Life and Environmental Science Animal Resource Centre for accommodating this work within the Faculty of Science of the University of Calgary. We thank the referees for their constructive criticism and the Editorial Office for skilful guidance and for improving the presentation of our manuscript.

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