Logical Description of Bovine Herpesvirus Type 1 Latent Infection

Transcription

1 J, gen. Virol. (1986), 67, Printed in Great Britain 885 Key words: bovine herpesvirus type 1/log&al analysis/latent injection Logical Description of Bovine Herpesvirus Type 1 Latent Infection By P.-P. PASTORET,* E. THIRY AND R. THOMAS 1 Virology Department, Faculty of Veterinary Medicine, University of LiOge, Rue des VktOrinaires, 45, B-1070 Brussels and 1Department of Molecular Biology, Faculty of Sciences, Free University of Brussels, Rue des Chevaux, 67, B-1640 Rhode-St-Genkse, Belgium (Accepted 24 January 1986) SUMMARY Description of the interactions between bovine herpesvirus type 1 (BHV-1) and cattle was performed by the method known as kinetic logic. This logical formalization uses variables with two possible values, 1 and 0, which tell whether an element is present or not at a significant level. To each variable is associated a function which tells if the element is being produced at a significant rate. The temporal relation between a variable and its associated function is given by specific time delays. The BHV-1 infection system is described by a set of five logical equations which tell in what conditions each function is on or off. The five functions are : V, development of viral multiplication; R, development of reactivation of the latent virus; A, development of an immune response; G, establishment of the viral genome; M, development of a memory of a first immune response. Several examples are detailed in a dynamic analysis, in connection with known experimental data. INTRODUCTION The infection of cattle with bovine herpesvirus type 1 (BHV-1) provokes two major diseases, infectious bovine rhinotracheitis and infectious pustular vulvovaginitis (Gibbs & Rweyemamu, 1977). After recovery from primary infection, the virus persists in the animal in a latent form so that it can no longer be detected by conventional virological assay procedures. Latency, a biological property of great epidemiological importance, is shared by other members of the Herpesviridae (Honess & Watson, 1977). In latently infected animals, the virus is occasionally reactivated; it can be re-excreted without any clinical sign and, in this way, transmitted silently to previously unexposed animals. Latency also allows BHV-1 to persist in a closed herd without introduction of exogenous virus. BHV-1 latency is well-documented and it is a good model for the study of latency for several reasons: the phenomenon of latency can be studied in the proper species where it appears and in a naturally fixed situation (Pastoret et al., 1984). In addition, BHV-1 can be experimentally reactivated by the use of glucocorticoids (dexamethasone). The re-excretion of BHV-1 is modulated by the level of specific immunity, and, when this level is above a certain threshold, reactivation can occur without re-excretion of infectious viral particles (Pastoret et al.,1980). The aim of this work is not to provide a detailed model of BHV-1 latent infection since at present not enough is known about the mechanisms. More modestly, we wish to present a formal description of our current view of the system, with special emphasis on the conditions contributing to viral re-excretion. A first justification is that, as in many other fields, the steady accumulation of facts makes it increasingly difficult to have a global view of the subject; a formal description may help although by necessity it is over-simplified. The main objective, however, is to provide a way of checking the consistency of the views we may have on such a complex system. Besides the essential point of self-consistency, models are usually built to account for a small number of selected features of a system, but formal analysis almost invariably shows up implications which SGM

2 886 p.-p. PASTORET, E. THIRY AND R. THOMAS had not been considered during the modelling. Some of them will be consistent with already known facts. Others are 'predictions' which wilt have to be tested experimentally. As in many other instances, a quantitative description of the situation would only serve to imply that we know more about the system than we actually do. We would be very satisfied with a qualitative, if coherent, description. Thus, we turned to a logical formalization, i.e. a description which uses variables with a limited number of values (typically, two only: 0 and 1). More specifically, we use the method described by Thomas (1973, 1979). It has become apparent that the essential dynamic aspects of complex systems are preserved by a proper logical description, in spite of its apparently caricature-like nature. The pathology of BHV-I infection is largely due to respiratory infection. The virus is usually transmitted by direct contact from animal to animal. After a primary infection, virus replicates in epithelial cells of the anterior respiratory tract. Thus, during a primary infection, when virus is replicating extensively, a large number of virions are present in nasal exudates (Pastoret et al., 1979). During this period, the animal is highly contagious for its surroundings over a period of several days. Nevertheless, animals recover within 2 weeks, except when bacterial superinfection occurs (Gibbs & Rweyemamu, 1977). After recovery from primary infection, BHV-1 infectious particles are no longer detected in nasal mucus and, moreover, the animal is now immune. As already mentioned, the virus can persist in the host in a latent form. The conditions required for the establishment of latency are still under investigation. In particular, it is not known whether the dose of virus to which the animal was exposed during primary infection and the extent of its subsequent multiplication are important for the establishment of latency. Neither is it known to what extent the immune status of the animal following a primary infection influences the ability of another strain to establish latency in the same animal. Nevertheless, the latency of BHV-1 has already been investigated in several model situations, the most extensively studied being attenuated vaccine strains. In this case, it has been established that: (i) attenuated strains can remain in a latent state (Nettleton et al., 1984; Pastoret et al., 1980), (ii) vaccination by attenuated or inactivated vaccines does not prevent the further establishment of a challenge wild virus in a latent form (Darcel le Q. & Dorward, 1975 ; Nettleton et al., 1984), and (iii) primary infection with a virulent strain seems to prevent latency of a re-infecting attenuated strain (Thiry et al., 1985 a). Thus, all animals carry virus in a latent form after primary infection; in addition, in spite of vaccination, a superinfecting virus will establish itself in a latent form if it is virulent. Reactivation of BHV-1 can occur by means of several stimuli, including the experimental injection of glucocorticoids, in particular dexamethasone (Sheffy & Davies, 1972). The mechanism of BHV-1 reactivation is still unknown. The reactivation of latent virus may be followed not only by re-excretion of infectious particles (Snowdon, 1965) but also of noninfectious particles (Pastoret et al., 1979). The re-excretion of reactivated BHV-1 appears to be modulated by the level of specific immunity, which is dependent in turn on the schedule of previous infections, reactivations or vaccinations, and on whether the immune response was induced by the multiplication of a wildtype or an attenuated virus (Straub & Wagner, 1977; Rossi & Kiesel, 1982). The sequence of events may be interpreted as follows (Pastoret et al., 1980, 1984). After a primary infection, the animal is able by the response of its immune system to prevent the clinical effects of re-infection with a virulent strain, but cannot properly control an episode of reexcretion (Davies & Carmichael, 1973). The first viral reactivation with or without re-excretion produces a further increase of the specific immune status and of the efficiency of the various immune mechanisms. The animal is therefore more able to control a further reactivation so that there is a longer period during which no re-excretion occurs. Nevertheless, reactivation and reexcretion of BHV-1 can be provoked repeatedly in the same animal by dexamethasone treatment (Pastoret et al., 1979). The animals which, under experimental conditions (e.g. dexamethasone treatment), excrete the highest level of virus after reactivation are those with lower specific immune responses. This observation supports the view that re-excretion is influenced by the specific immune status of the animal (Pastoret et al., 1979, 1980).

3 Logical description of BHV-1 infection 887 The occurrence of spontaneous viral reactivation and re-excretion is not well-documented. It is indicated by the detection of re-excretion of BHV-1 virions and of a rise in specific antibodies. The spontaneous re-excretion of field strains of BHV-1 occurs in experimental animals and in closed herds for a period of at least 1 year after infection (Snowdon, 1965; Hyland et al., 1975). METHODOLOGY Kinetic logic The method known as kinetic logic (Thomas, 1973) has been described in detail elsewhere (Thomas, 1979, 1984). In short, to each of the elements whose description seems crucial to us we associate both a logical variable (a, b, c... ) whose value (1 or 0) tells whether the element is present or not at a significant level, and a logical function (A, B, C... ) which tells if the element is being produced at a significant rate. For instance, in a genetic system, the logical value of a variable tells whether the gene product is present, and the logical value of the corresponding function tells whether the gene is on. More generally, our logical variables usually describe concentrations while our functions describe rates of production. It must be emphasized that a = 0 (product 'absent') does not mean that the product is completely absent; it means that the product is below its threshold level. In our context, variable v (for instance) takes the value 1 when virions are actually present and the corresponding function V takes the value 1 when virions are being produced. In a steady state, v and V have the same value, i.e. virions have not been produced (V -- 0) for a prolonged period, and there are no more virions present (v = 0), or virions have been produced (V = 1) for a considerable period and are present (v = 1). However, when the value of V has recently changed, v and Vmay have different values, i.e. virions are being produced (V = 1) but they are not yet present at a detectable level (v = 0), or virions have stopped being produced (V = 0) but they are still present (v = 1) (Fig. 1). There is thus a rather simple temporal relation between a variable and the corresponding function. Let us start from a steady state in which a function and its variable have the same logical value. If a signal changes the value of the function (i.e. switches it on or off), the variable adopts the new value of the function, but only after a characteristic time delay; if function V has been switched on, one must wait from a time tv before virions appear; if function V has been switched off, one must wait for a time tv before virions disappear. There is no reason why the 'on' and 'off' delays should be the same; in practice, they are often very different. Note that during the transient period in which a function and the corresponding variable have different values, the logical value of the variable serves as a memory of the preceding value of the function. As shown in detail elsewhere (Thomas, 1984), we describe a system by a set of logical equations which relate the value of each function to the values of the relevant variables; more exactly, the logical equations tell in what conditions each function is on or off, depending on the presence or absence of the relevant elements. A logical equation of the form A = f (a, b, c... ) means that function A is on (A has the value 1) if the values of variables a, b, c... are such that f(a, b, c) = 1. We use the classical connectives: a. b (orab) means a and b (logical product); a + b means a or b (or inclusive; logical sum); a means not a (logical complement). For instance, A = a~ + c means that function A has the value 1 ifa (and not b) or c, or both, have the value 1. These logical equations resemble the differential equations used in chemical kinetics in the sense that both relate rate of synthesis to concentrations, and this is how time is included (implicitly) in our logical equations. From these logical equations, one can build a state table, which gives the values of the functions for each combination of values of the variables. Note that in addition to the internal variables described so far, one has to consider input variables. While, as already mentioned, the value of an internal variable is a delayed effect of the value of the corresponding function, the values of input variables can typically be changed at will. For instance, one can decide to submit a previously unexposed animal to infection with BHV-1 (i), or reactivate the latent virus using an appropriate stimulus (d); i and d are input variables. From the state tables, one can derive all the sequences of states (pathways) of the system. Which sequence(s) is(are) followed depends on the relative values of the time delays. Which

4 888 P.-P. PASTORET, E. THIRY AND R. THOMAS V=I Function V=O v=l v=o 1 I v=o [ v=o, I I I, j tv t~ Fig. 1. Logical value of variable v functions as a memory of the preceding value of function V. The arrows indicate that a signal has changed the value of V (more exactly, switched on or off the synthesis of virions). This operates as an order to change the value v (more exactly, to make virions appear or disappear, according to the case). However, this order is executed only after a suitable delay tv or t7 depending on whether the function is switched on or off. If a counter order takes place before the order has been executed, we reason as if the order had not been given. delays are involved in choices between the sequences of states, and how, is determined by a subsequent analysis. A formal description of the BHV-1 infection Various choices of functions and variables are conceivable. Those we finally chose are shown in Table 1. Function V represents viral multiplication. The associated variable v refers to the presence of mature virions. As regards the immune response, we chose to describe it simply by the presence of active specific immunity directed against the virus below (a) or above (a) a certain threshold, and by the presence (m) or absence (m) of a memory of an earlier response. The logical functions associated with these variables are respectively A, which refers to the development or maintenance of the response, and M, which refers to the establishment or maintenance of a memory of the response. It can be noticed that, in this symbolism, the immunity conferred by primary or secondary (or more generally anamnestic) response is represented by the same variable a. However, the value ofm tells whether one is dealing with a primary (m = 0) or a secondary (m = 1) response, and as a result, the time delays are very different (Table 2). In other words, instead of explicitly using distinct variables and functions to describe the primary and secondary responses, we distinguish between the two situations by the values of the time delays (a secondary response develops faster and persists longer). The reason for introducing variable m is that while the value, 0 or 1, of variable a indicates whether specific immunity is above or below a protective threshold now, we need a variable whose value tells whether it is or has been present. Clearly, if one wrote M = a, function M would take the value 1 some time after the appearance of immunity, but it would drop back to 0 after immunity has disappeared (see Fig. 1 for the time dependence between a function and its associated variable). However, if M = a + m (it means a or m), once m has taken the value 1, both M and m will keep this value. More generally, the simple logical structure X =... + x ensures that, once x has reached the value 1, both X and x are blocked for ever at this value. Similarly, we have to express the situation that once an animal has been successfully infected with BHV-1, the viral genome will persist indefinitely. This can be written: G = v + g. Most of the time, the virus will then remain latent, but following appropriate treatment, e.g. dexamethasone treatment (d), the virus is reactivated. When we write: R = gd, we implicitly assume that independently of the above-mentioned effect of immunity on viral multiplication, there is a mechanism which somehow keeps the

5 Logical description of BHV-1 infection 889 Table 1. Functions and variables Function V: development of viral multiplication R : development of reactivation of a latent virus A : development of an immune response G : establishment of the viral genome M: development of a memory of a first immune response Input variable i: infection with BHV-1 iv: infection with a virulent strain ia: infection with an attenuated strain vi: presence (after injection) of inactivated BHV-1 d: stimulus of reactivation (e.g. dexamethasone treatment) Variable v: presence of virions r: effective reactivation of the latent virus a: presence of specific active immunity g: presence and persistence of the viral genome m: presence of a memory of a first immune response Table 2. Time delays* iv=l ia=l m = 0 tal : t~l : m = 1 t~2 : 7 7 ta2: * The values of the time delays of appearance (t~) or disappearance (t~) of variable x are expressed in units of time delay (UD), which correspond roughly to days. t v = 1 ; t~ = 12; t r = 1 ; t~ = 1 ; tg = 0 ; t~ : no value; t m = 0; t~: no value. established genome in a latent state unless proper conditions are applied. Once these conditions are fulfilled, R = 1 and reactivation is effective (r = 1) after a delay tr. Now we are in a position to propose equations for V and A. V -- a (iv 4- ia 4- r) means that, provided the level of immunity against the virus is below a threshold (if), virus multiplication can take place following infection (i) or reactivation (r). Infections with virulent (iv) or with attenuated (ia) virus both result in virus development (V), but with different 'on' and 'off' delays of a (Table 2). A = v 4- vi 4- r means that the development of specific immunity against the virus is induced by successful multiplication of the virus (v) or by a massive injection of inactivated virus (vi) or by reactivation (r). We thus reach the following provisional description (Fig. 2): V= a(iv 4- ia + r) R = gd A = v 4- vi 4- r G=v4-g M=a4-m Note that iv, ia, vi and d are input variables; whether or not infection, injection of inactivated virus or an appropriate stimulus of reactivation occurs does not depend on the internal state of the system, but rather on a deliberate decision of the experimenter or on casual external circumstances. The other variables (v, r, a, g, m) are internal variables whose values are dependent on prior values. An essential point is that we do not try to include in the equation of a function all the variables which influence the value of this function, but rather those values which (rightly or wrongly) are considered to influence the function directly. For instance, variable v influences its own development, but only indirectly. This is why v is not seen in the equation of V. However, v directly influences the development of immunity (and it is thus present in the equation of A) and variable a in turn influences the multiplication of the virus (and

6 890 P.-P. PASTORET, E. THIRY AND R. THOMAS or(~ + + g-- and + + ~ + and~and r - i,. V ~ ~ r y d r +/ %or /Ji + + Fig. 2. Logical scheme of BHV-1 latent infection. it is thus present in the equation of V). Thus, v figures in the equation of A and a figures in the equation of V. This describes the indirect effect of v on its own later development. The values of the time delays are expressed in 'units of time delay' (UD), which correspond roughly to days. They represent the time required, under experimental conditions, to switch on or off the variables when the value of the corresponding function has changed. It is assumed, for example, that the level of neutralizing antibodies and of cell-mediated immunity has reached a protective threshold 10 days after primary infection. We therefore choose the value 10 for tal. Other values of time delays, such as t 7 value, cannot be deduced from experimental data, but we assume, in accordance with Blyth & Hill (1984), that reactivation persists only for the time required to induce virus multiplication at the site of latency; since t 7 must be short, it was therefore considered as equal to 1 (Table 2). From our set of logical equations, a state table (Table 3) can be derived which provides the values of the functions for each combination of values of the variables. Usually, each of the 2 n combinations of values of the n internal variables occupies a row. In the present case, however, instead of constructing a large table with 32 rows (corresponding to the combinations of values of the five internal variables), we give two sub-tables, one for m = 0 and one for m = 1. This is convenient because in practice one begins in the sub-table m = 0, and, as soon as there has been a primary response, one shifts to (and remains in) the sub-table m = 1. Each table (or sub-table) comprises columns corresponding to the various possible treatments (input variables). Here, we have considered columns corresponding to: no current treatment (0); injection of inactivated virus (vi); infection with a live virus (i); treatment with dexamethasone or a similar reactivating stimulus (d). We may also consider columns corresponding to simultaneous double or multiple treatments. In the dynamic analysis (see below) an example using a double treatment (id, simultaneous infection and reactivation stimulus) will be described. Note that each logical state of the system can be described by a logical vector listing the values of the variables and a second logical vector listing the corresponding values of the functions. Consider, for instance, a previously unexposed animal which has just been vaccinated with inactivated virus. In this situation, the state of the variables is (first line of Table 3, left column), but the state of the functions is (same line, column vi), indicating that function A (the development of specific immunity against the virus) is on. One can describe this state of the system by giving the vector of variables followed by the vector of functions: 00000/ However, it is more compact and more convenient to write 00000, in which the dash over the value of the third variable indicates that there is an order to change its value; indeed, specific immunity is not yet present, but it is being developed (as a result of vaccination). Note that a state without any dash is a stable state, as there is no order to change the value of any variable.

7 VP~ G M A d Table 3. Complete state table m=o m=l vragm [ 0 VRA G M A d vragm f... 0 ooooo ~ ~ b'6"66ti IO'O'OTol ~ ~ ~

8 892 P.-P. PASTORET, E. THIRY AND R. THOMAS Table 4. Compact state table m=0 m=l A A 0 v i i d 0 vi i d ~ F~J~3J ~)~ _ _ For example, see, state 00[ HI in the right part of Table 3, second row, column 0. This describes a carrier state in which there is neither mature virus nor a state of reactivation nor specific immunity, but the viral genome and a memory of an earlier immunization are present. It has been found convenient to re-write, in addition to a state table, a 'compact' state table in which each state is described by the logical vector of the variables, completed by the dashes which indicate which variables should change their value. In the present case, this gives Table 4, in which some states are surrounded by dashed lines. This simply means that these states would be stable if the system were blocked in the corresponding column; however, as we shall see in the next section, the system remains only for a short time within these columns. Dynamic analysis Let us start from ~, a stable state of column 0 (Table 4) which represents a previously unexposed animal free of BHV-1 infection and of any previous contact with BHV-1 antigen. Infection is seen in our formalism as a shift from column 0 to column i. Strictly speaking, the system should remain in this column only for the actual duration of exposure to exogenous virus. This could be described by ascribing to the process a specific time delay or by introducing an additional variable to memorize the exposure to virus. In practice, it appears more convenient and not too distorting to keep the system in a column other than column 0 only for the time required to switch on one variable; afterwards, the system goes back to the initial column (Fig. 3). The system is now in state T0000, in which three variables are asked to change their value; the change that will actually take place depends on the values of the time delays (Table 2). We assume that once the animal is successfully infected, the time required to establish the viral genome is short and at any rate shorter than the two other time delays, which we estimate to 10 UD for development of effectivespecific immunity, and at about 12 UD for the disappearance of mature viral particles. With these values for the delays, the pathway is as described in Fig. 4

9 Logical description of BHV-1 infection 893 [ tal : 10,,:0 0 ~. vragm tv: 1 t~: 12 Li01~6 ]0111 o0111 tm:o ta1:28 or 56 Fig. 3 Fig. 4 Fig, 3. Pathway followed after infection of a previously unexposed animal. Fig. 4. Pathway followed after infection of a previously unexposed animal (continued from Fig. 3). with as successive steps permanent establishment of the viral genome (g) and establishment of specific immunity (a). The state is now T0110; as soon as specific immunity is developed, m (which serves to indicate that there has been a primary response) takes the value 1 and we reach state TO 1! 1 (column 0 in the right section of Table 4, which corresponds to the situation m = 1). From now on, there is only one possible evolution: ]'0111 ~ 00T11 -~ ~ffb-]q], in which the virions and immunity disappear after some days and some weeks, respectively. The animal is now in a stable state ~ in which the viral genome is still present (latent) and there is a memory of a primary specific immune response. Starting from state ~, various stimuli (e.g. treatment with dexamethasone) can lead to column d, resulting in reactivation (Fig. 5). The system now goes back to column 0. The stimulus itself has disappeared, but the organism keeps for a while (1 UD) the memory of the stimulus, which is symbolized by function R (reactivation), but whose mechanism is still unknown. Virus is produced as early as 1 UD after the application of the stimulus followed by the development of a specific immune response; here, one is dealing with a secondary response (m = 1); therefore, the 'on' delay is much shorter (ta2 = 7) than the first time and the 'off' delay much longer (ta2 = 90 or i80) (Table 2). The sequence is shown in Fig. 6. At any time, it is possible to re-infect an animal, to inject inactivated virus or to reactivate latent virus. This is symbolized by a shift to column i, vi or d, respectively. For instance, reinfection may take place any time after a primary infection. The result will depend on the state of immunity at the time of re-infection. Ifa = 1 at the time of re-infection, neither the sequence of logical states nor the time schedule will be altered by re-infection (Fig. 7 a, b); the situation in Fig. 7 (b) was encountered when re-infection with a temperature-sensitive (ts) vaccine strain was attempted in cattle previously infected with a virulent strain 8 weeks earlier (Thiry et al., 1985 a). The failure of the re-infecting virus to develop is accounted for by the slow decay of immunity (tax longer after infection with a virulent strain; Table 2). On the contrary, if immunity was no longer operative at the time of superinfection, the sequence is as shown in Fig. 7(c). This situation was encountered in cattle re-infected with a virulent strain 9 weeks after vaccination with ts vaccine virus (Nettleton et al., 1984). In this case, re-infection results in virus production because the decay of immunity (tal) is shorter after a primary infection with ts virus. Another possibility involves promoting reactivation very soon after primary infection, before a specific immune response has developed. According to our scheme, the evolution would be as described in Fig. 8. A characteristic feature of this scenario is that reactivation provides a counter-command to the command to stop virus production, and the new command to stop production occurs only after the state of reactivation has disappeared. Here, we would expect virus to persist 14-to 22 UD, in contrast withthe normal period of 12 UD. Although there are no documented experiments in which dexamethasone treatment has been applied soon after

10 894 P,-P. PASTORET, E. THIRY AND R. THOMAS o v ragm N~ ta2 : y d t~: ], ~r tr:l ~ tv:l te:l 6 6 t~2:90 or 180 Fig. 5 Fig. 6 Fig. 5. Application of a stimulus of reactivation. Fig. 6. Pathway followed after reactivation. (a) 0 i t~: " l ta~ _ l (b) " OOl I ta~ (c) t~: taz : 7 5 ta2:90 or 180,, tv: l Fig. 7. Pathways followed after re-infections occurring at different times after primary infection (see text).

11 Logical description of BHV-1 infection 895 (a) t~l : lo o i d (b~ vragm 0 ]OOLO I. 000oo I tv: 1 I ~ t~, : I lo01o tg:0! ]OOLO ti:l d t tr:l t~: 12 ~o110 ]Ollb tm:0 t~:12 ~ tm:0 lo oo]11 oo]11 t~1:28 or 56 ~ t~:28or 56 Fig. 8. Pathway followed after reactivation induced very soon after primary infection. primary infection, somewhat similar experiments have been performed in which, 10 days after primary infection, animals have been infested with the lungworm, Dictyocaulus viviparus, which also induces reactivation (Msolla et al., 1983 ; Thiry et al., 1985 b). Virus was indeed found up to 3 weeks after the primary infection. This formal analysis allows us to describe epizootiological situations not yet experimentally encountered. We will consider the case of simultaneous reactivation of latent BHV-1 and reinfection with exogenous BHV-!., in the same animal. To deal with this situation, it is necessary to enlarge the state table (Table 4) by adding a new column, id (Table 5). The predicted evolution of the system is detailed in Fig. 9; it is similar to that observed after re-infection or reactivation, except that the period of virus excretion (v = 1) would be expected to be slightly longer. In this case, viral excretion is described as a combination of excretion after infection and re-excretion after reactivation. According to the model, re-excretion of latent virus begins 1 UD after the onset of excretion of re-infecting virus and finishes 1 UD after the end of the excretion period of the superinfecting virus. This possibility has prompted us to design new experiments, which are currently underway. DISCUSSION The logical description of BHV-1 infection is the first attempt to adapt the method of kinetic logic to the concepts of animal virology. The mechanisms of BHV-1 latency and reactivation still remain largely unknown. The description was therefore built upon current understanding and so far ignores molecular mechanisms. Nevertheless, even from an epizootiological point of view, the formal analysis is a good tool for different purposes. It allows us to represent in simple terms a complex system which is difficult to grasp in purely verbal terms: each state is defined by the values of five variables and the passage of one state to another is expressed simply by changing the value of one or two variables. The pathway followed can be defined by a sequence of states more easily than by a verbal explanation. The representation, even though schematic, gives a picture of events which is in agreement with the already known facts: The pathways followed after primary infection, or after reactivation, represent what is observed experimentally. The logical description of re-infection is in accordance with the experimental results obtained by Nettleton et al. (1984) and Thiry et al. (1985a), as detailed in the dynamic analysis. Moreover, the dynamic analysis has suggested answers for results difficult to interpret. For example, the early reactivation and re-excretion of BHV-1 after infestation by D. viviparus have been more easily understood by logical formalization. The logical description can also suggest an evolution of the system for each proposed epizootiological situation. The initial state is defined by the history of the animal, i.e. previous infection(s) or vaccination(s), previous reactivation(s), and by current circumstances, i.e. stimulus of reactivation, (re-)infection, (re)vaccination, etc. When

12 896 p.-p. PASTORET, E. THIRY AND R. THOMAS Table 5. Compact state table when id = 1 id m = 1 vragm O i o,,"_o);ff_ij vragm I'5"5"b"~ , i t~:l ta2:7 i [ t~: too ta~:90 or Fig. 9. Pathway followed infection and reactivation. id tv:l after simultaneous re- tr:l this state is defined, the logical description will indicate the pathway to be followed to attain a stable state. In the same way, formal analysis can also help in determining an experimental schedule. Designing the logical pathway corresponding to the proposed experimental schedule allows the experimenter to assess, for example, the period when reactivation or re-infection has to be induced after primary infection, or the expected effect of a treatment, such as delayed hypersensitivity test. Apart from providing a global and coherent view of complex systems, such formal treatments are of little help unless they generate predictions which can be subjected to the verdict of experimentation. Thomas et al. (1976) have shown previously how formal analysis of control of immunity in bacteriophage 2 can allow new predictions suggesting experiments whose results can be used to formulate a better model. Our method has been used in other fields within and outside biology (see for instance Kaufman et al., 1985), on each occasion providing clear-cut ways to test models by experiment. Agreement between prediction and results is a success for the model, not for the method. In fact, the method is often more useful when it permits modification (or even rejection) of a model than when it merely confirms it. One of the experiments suggested by the analysis of our present model is simultaneous reactivation of latent BHV-1 and re-infection with exogenous BHV-1, in the same animal. Biological experiments of this type are lengthy and the model is useful in the economical design of experiments. Whether or not the results fit with the model proposed, the exercise will have been useful, if only to modify or reject the model, and suggest new experiments. The logical analysis presented here confines itself to a panoramic description of the interactions between BHV-1 and its host. This kind of formalization can certainly be used to treat other aspects of virus infections: interactions of virus and cells at the tissue level, for example, or the regulation of the expression of viral genes within the cellular environment, as

13 Logical description of BHV-1 infection 897 already described by Thomas & Van Ham (1974) and Thomas et al (1976) in the case of bacteriophage 2. Moreover, it will be interesting to test the validity of logical formalization in the building of epidemiological models in which interactions are studied at a population level, and to evaluate whether such models are sufficient to propose rational prophylaxis. We thank Dr J. Saliki and Dr A. Schwers for their help in revising the manuscript. This work was carried out with the help of 'Actions de Recherche concert6es' and of 'Fonds de la Recherche Fondamental collective'. REFERENCES BLYTH, W. A. & HILL, T. J. (1984). Establishment, maintenance, and control of herpes simplex virus (HSV) latency. In Immunobiology of Herpes Simplex Virus Infection, pp Edited by B. T. Rouse & C. Lopez. Florida: CRC Press. DARCEL LE Q., C. & DORWARD, W. J. (1975). Recovery of infectious bovine rhinotracheitis virus following corticosteroid treatment of vaccinated animals. Canadian Veterinary Journal 16, DAVIES, D. H. & CARMICHAEL, I. E. (1973). Role of cell-mediated immunity in the recovery of cattle from primary and recurrent infections with infectious bovine rhinotracheitis. Infection and Immunity 8, GIBBS, E. P. J. & RWEYEMAMU, M. M. (1977). Bovine herpesviruses. Part 1. Bovine herpesvirus 1. Veterinary Bulletin 47, HONESS, R, W. & WATSON, D. H. (1977). Unity and diversity in the herpesviruses. Journal of General Virology 37, HYLAND, S. J., EASTERDAY, B. C. & PAWLISCH, R. (1975). Antibody levels and immunity to infectious bovine rhinotracheitis virus (IBR) infections in Wisconsin dairy cattle. Developments in Biological Standardization 28, KAUFMAN, M., URBAIN, J. & THOMAS, R. (1985). Towards a logical analysis of the immune response. Journal of Theoretical Biology 114, l. MSOLLA, P. M., ALLAN, E. M., SELMAN, I. E. & WISEMAN, A. (1983). Reactivation and shedding of bovine herpesvirus 1 following Dictyocaulus viviparus infection. Journal of Comparative Pathology 93, NETTLETON, p. F., SHARP, J. M., HERRING, A. J. & HERRING, J. A. (1984). Infectious bovine rhinotracheitis virus excretion after vaccination, challenge and immunosuppression. In Latent Herpesvirus Infections in Veterinary Medicine, pp Edited by G. Wittmann, R. M. Gaskell & H.-J. Rziha. The Hague: Martinus Nijhoff. PASTORE'F, P.-P., AGUILAR-SETIEN, A., BURTONBOY, G., MAGER, J., JETTEUR, P. & SCHOENAERS, F. (1979). Effect of repeated treatment with dexamethasone on the re-excretion pattern of infectious bovine rhinotracheitis virus and humoral immune response. Veterinary Microbiology 4, PASTORET, P.-P., BABIUK, L. A., MISRA, V. & GRIEBEL, P. (1980). Reactivation of temperature-sensitive and nontemperature-sensitive infectious bovine rhinotracheitis vaccine virus with dexamethasone. Infection and Immunity 29, PASTORET, P.-P., THIRY, E., BROCHIER, B., DERBOVEN, G. & VINDEVOGEL, H. (1984). The role of latency in the epizootiology of infectious bovine rhinotracheitis. In Latent Herpesvirus Infections in Veterinary Medicine, pp Edited by G. Wittmann, R. M. Gaskell & H.-J. Rziha. The Hague: Martinus Nijhoff. ROSSl, c. R. & I~IESEL, G. K. (1982). Effect of infectious bovine rhinotracheitis virus immunization on viral shedding in challenge-exposed calves treated with dexamethasone. American Journal of Veterinary Research 43, SHEFFY, B. E. & DAVIES, D. H. (1972). Reactivation of a bovine herpesvirus after corticosteroid treatment. Proceedings of the Society for Experimental Biology and Medicine 140, SNOWDON, W. A. (1965). The IBR-IPV viruses: reaction to infection and intermittent recovery of virus from experimentally infected cattle. Australian Veterinary Journal 41, 135~142. STRAUB, O, C. & WAGNER, K. (1977). Die sanierung einer Besammungstation von IBR-IPV Virusausscheidern durch einen Einsatz von IBR-IPV-lebend Impstoff. Deutsche tierorztliche Wochenschrift 84, THIRY, E., BROCHIER, B., SALIKI, J., PIRAK, M. & PASTORET, P.-P. (1985a). Excretion and reexcretion of thermosensitive and wild-type strains of infectious bovine rhinotracheitis virus after co-infection or two successive infections. Veterinary Microbiology 10, THIRY, E., SAL1KI, J., LAMBERT, A.-F., BUBLOT, M., POUPLARD, L. & PASTORET P.-P. (1985b). Studies on conditions necessary for bovine herpesvirus 1 reactivation. In Immunity to Herpesvirus Infections of Domestic Animals, pp Edited by P.-P. Pastoret, E. Thiry & J. Saliki. Luxembourg: Office for Official Publications of the European Communities. THOMAS, R. (1973). Boolean formalization of genetic control circuits. Journal of Theoretical Biology 42, THOMAS, R. (editor) (1979). Kinetic logic: a boolean approach to the analysis of complex regulatory systems. Lecture Notes in Biomathematics, vol. 29. Berlin: Springer-Verlag. THOMAS, R. (1984). Logical description, analysis and synthesis of biological and other networks comprising feedback loops. Advances in Chemical Physics 55, TrtOMAS, R. & VAN HAM, P. (1974). Analyse formelle de circuits de r~gulation g~netique: le contr61e de l'immunit~ chez les bacteriophages lambdoides. Biochimie 56, THOMAS, R., GATHOYE, A. M. & LAMBERT, L. (1976). A complex control circuit. Regulation of immunity in temperate bacteriophages. European Journal of Biochemistry 71, (Received 1 July 1985)