Editorial overview:new protein production tools for structural biology

Full text: The idea of producing proteins from recombinant DNA hatched almost half a century ago. In his PhD thesis, Peter Lobban foresaw the prospect of inserting foreign DNA (from any source, including mammalian cells) into the genome of a λ phage in order to detect and recover protein products from Escherichia coli [ 1 and 2]. Only a few years later, in 1977, Herbert Boyer and his colleagues succeeded in the first ever expression of a peptide-coding gene in E. coli — they produced recombinant somatostatin [ 3] followed shortly after by human insulin. The field has advanced enormously since those early days and today recombinant proteins have become indispensable in advancing research and development in all fields of the life sciences. Structural biology, in particular, has benefitted tremendously from recombinant protein biotechnology, and an overwhelming proportion of the entries in the Protein Data Bank (PDB) are based on heterologously expressed proteins. Nonetheless, synthesizing, purifying and stabilizing recombinant proteins can still be thoroughly challenging. For example, the soluble proteome is organized to a large part into multicomponent complexes (in humans often comprising ten or more subunits), posing critical challenges for recombinant production. A third of all proteins in cells are located in the membrane, and pose special challenges that require a more bespoke approach. Recent advances may now mean that even these most recalcitrant of proteins could become tenable structural biology targets on a more routine basis. In this special issue, we examine progress in key areas that suggests this is indeed the case. Our first contribution examines the importance of understanding quality control in the host cell during recombinant protein production, and pays particular attention to the synthesis of recombinant membrane proteins. A major challenge faced by any host cell factory is the balance it must strike between its own requirements for growth and the fact that its cellular machinery has essentially been hijacked by an expression construct. In this context, Bill and von der Haar examine emerging insights into the role of the dependent pathways of translation and protein folding in defining high-yielding recombinant membrane protein production experiments for the common prokaryotic and eukaryotic expression hosts. Rather than acting as isolated entities, many membrane proteins form complexes to carry out their functions. To understand their biological mechanisms, it is essential to study the molecular structure of the intact membrane protein assemblies. Recombinant production of membrane protein complexes is still a formidable, at times insurmountable, challenge. In these cases, extraction from natural sources is the only option to prepare samples for structural and functional studies. Zorman and co-workers, in our second contribution, provide an overview of recent advances in the production of multi-subunit membrane protein complexes and highlight recent achievements in membrane protein structural research brought about by state-of-the-art near-atomic resolution cryo-electron microscopy techniques. E. coli has been the dominant host cell for recombinant protein production. Nonetheless, eukaryotic expression systems, including yeasts, insect cells and mammalian cells, are increasingly gaining prominence in the field. The yeast species Pichia pastoris, is a well-established recombinant expression system for a number of applications, including the production of a range of different membrane proteins. Byrne reviews high-resolution structures that have been determined using this methylotroph as an expression host. Although it is not yet clear why P. pastoris is suited to producing such a wide range of membrane proteins, its ease of use and the availability of diverse tools that can be readily implemented in standard bioscience laboratories mean that it is likely to become an increasingly popular option in structural biology pipelines. The contribution by Columbus concludes the membrane protein section of this volume. In her overview of post-expression strategies, Columbus surveys the four most common biochemical approaches for the structural investigation of membrane proteins. Limited proteolysis has successfully aided structure determination of membrane proteins in many cases. Deglycosylation of membrane proteins following production and purification analysis has also facilitated membrane protein structure analysis. Moreover, chemical modifications, such as lysine methylation and cysteine alkylation, have proven their worth to facilitate crystallization of membrane proteins, as well as NMR investigations of membrane protein conformational sampling. Together these approaches have greatly facilitated the structure determination of more than 40 membrane proteins to date. It may be an advantage to produce a target protein in mammalian cells, especially if authentic post-translational modifications such as glycosylation are required for proper activity. Chinese Hamster Ovary (CHO) cells and Human Embryonic Kidney (HEK) 293 cell lines have emerged as excellent hosts for heterologous production. The generation of stable cell-lines is often an aspiration for synthesizing proteins expressed in mammalian cells, in particular if high volumetric yields are to be achieved. In his report, Buessow surveys recent structures of proteins produced using stable mammalian cells and summarizes both well-established and novel approaches to facilitate stable cell-line generation for structural biology applications. The ambition of many biologists is to observe a protein's structure in the native environment of the cell itself. Until recently, this seemed to be more of a dream than a reality. Advances in nuclear magnetic resonance (NMR) spectroscopy techniques, however, have now made possible the observation of mechanistic events at the molecular level of protein structure. Smith and colleagues, in an exciting contribution, review emerging ‘in-cell NMR’ techniques that demonstrate the potential to monitor biological activities by NMR in real time in native physiological environments. A current drawback of NMR as a structure determination tool derives from size limitations of the molecule under investigation and the structures of large proteins and their complexes are therefore typically intractable by NMR. A solution to this challenge is the use of selective isotope labeling of the target protein, which results in a marked reduction of the complexity of NMR spectra and allows dynamic processes even in very large proteins and even ribosomes to be investigated. Kerfah and co-workers introduce methyl-specific isotopic labeling as a molecular tool-box, and review its applications to the solution NMR analysis of large proteins. Tyagi and Lemke next examine single-molecule FRET and crosslinking following the co-translational incorporation of non-canonical amino acids (ncAAs); the goal here is to move beyond static snap-shots of proteins and their complexes and to observe them as dynamic entities. The encoding of ncAAs through codon-suppression technology allows biomolecules to be investigated with diverse structural biology methods. In their article, Tyagi and Lemke discuss these approaches and speculate on the design of improved host organisms for ‘integrative structural biology research’. Our volume concludes with two contributions that resolve particular bottlenecks in the protein structure determination pipeline. The contribution by Crepin and co-workers introduces the concept of polyproteins in contemporary structural biology. Polyproteins are widespread in nature. They represent long polypeptide chains in which individual smaller proteins with different biological function are covalently linked together. Highly specific proteases then tailor the polyprotein into its constituent proteins. Many viruses use polyproteins as a means of organizing their proteome. The concept of polyproteins has now been exploited successfully to produce hitherto inaccessible recombinant protein complexes. For instance, by means of a self-processing synthetic polyprotein, the influenza polymerase, a high-value drug target that had remained elusive for decades, has been produced, and its high-resolution structure determined. In the contribution by Desmyter and co-workers, a further, often imposing, bottleneck in high-resolution protein structure determination is addressed: The requirement to form stable three-dimensional crystal lattices that diffract incident X-ray radiation to high resolution. Nanobodies have proven to be uniquely useful as crystallization chaperones, to coax challenging targets into suitable crystal lattices. Desmyter and co-workers review the generation of nanobodies by immunization, and highlight the application of this powerful technology to the crystallography of important protein specimens including G protein-coupled receptors (GPCRs). Recombinant protein production has come a long way since Peter Lobban's hypothesis in the late 1960s, with recombinant proteins now a dominant force in structural biology. The contributions in this volume showcase an impressive array of inventive approaches that are being developed and implemented, ever increasing the scope of recombinant technology to facilitate the determination of elusive protein structures. Powerful new methods from synthetic biology are further accelerating progress. Structure determination is now reaching into the living cell with the ultimate goal of observing functional molecular architectures in action in their native physiological environment. We anticipate that even the most challenging protein assemblies will be tackled by recombinant technology in the near future.

Igazolható-e az üzleti ciklus az iparágak viselkedésével? = Can business cycles be proved with the behavior of enterprises?

A dolgozat alapja egy olyan Leontief-típusú gazdaság, ahol minden egyes ágazatban egy vállalat termel, tehát monopóliumokból áll a gazdaság. A vállalatok termelnek, és a termékeiket a piacon értékesítik. A gazdaság mozgásegyenleteit a vállalati mérleg összefüggések, valamint a piaci csere után a gazdaságban, a termékek készletváltozása írja le. Az így létrejött mozgásegyenletekből arra következtethetünk, hogy a ciklusok egy ilyen modellben szükségszerűen kialakulnak, tehát az üzleti ciklus a gazdaság működéséhez hozzátartozik. Journal of Economic Literature (JEL) kód: D46, E32. = The aim of the paper is to analyze a Leontief-type economy, i.e. all firms produce only one product and only one technology. The firms sell the products on a monopolistic market. The move of this economy is controlled by the balance sheet expressions and the inventory level fluctuations. The differential equations of the move of this economy show a cyclical movement of the economy along the balanced growth path. Journal of Economic Literature (JEL) kód: D46, E32.

Cooperation in supply chains: A cooperative game theoretic analysis = Együttműködés ellátási láncokban: Egy kooperatív játékelméleti elemzés

A cikkben a kooperatív játékelmélet fogalmait alkalmazzuk egy ellátási lánc esetében. Az ostorcsapás-hatás elemeit egy beszállító-termelő ellátási láncban ragadjuk meg egy Arrow-Karlin típusú modellben lineáris készletezési és konvex termelési költség mellett. Feltételezzük, hogy mindkét vállalat minimalizálja a fontosabb költségeit. Két működési rendszert hasonlítunk össze: egy hierarchikus döntéshozatali rendszert, amikor először a termelő, majd a beszállító optimalizálja helyzetét, majd egy centralizált (kooperatív) modellt, amikor a vállalatok az együttes költségüket minimalizálják. A kérdés úgy merül fel, hogy a csökkentett ostorcsapás-hatás esetén hogyan osszák meg a részvevők ebben a transzferálható hasznosságú kooperatív játékban. = In this paper we apply cooperative game theory concepts to analyze supply chains. The bullwhip effect in a two-stage supply chain (supplier-manufacturer) in the framework of the Arrow-Karlin model with linear-convex cost functions is considered. It is assumed that both firms minimize their relevant costs, and two cases are examined: the supplier and the manufacturer minimize their relevant costs in a decentralized and in a centralized (cooperative) way. The question of how to share the savings of the decreased bullwhip effect in the centralized (cooperative) model is answered by transferable utility cooperative game theory tools.

Fenntartható fejlődés = Sustainability issues in purchasing and supply management

A fenntarthatóság kérdését a vállalati működésben számos kutatás elemzi. A vizsgálatokat azonban érdemes kiterjeszteni a vállalatokat beszállítóikkal összekötő kapcsolatrendszerre és az annak menedzseléséért felelős beszerzésre is, hiszen a nagy vállalatok beszerzési döntései jelentős értékükön keresztül fontos motiváló erőt jelentenek a beszállító vállalatok egy sokkal szélesebb hálózata számára. Tanulmányunk célja áttekinteni a fenntarthatóság három pillérjének beszerzési értelmezésének lehetőségeit, ehhez kapcsolódva bemutatni azokat a motivációs tényezőket, amelyek biztosíthatják azt, hogy a beszerzés a gyakorlatban is kezelni tudja a fenntarthatóság szempontjait. A bemutatott eredmények az irodalom feltérképezésén alapszanak, és egy olyan kutatás részét képezik, melynek során vállalati beszerzési szakembereket kérdezünk a fenntartható beszerzéssel kapcsolatos vállalati gyakorlatról és tapasztalataikról. A kutatás a Budapesti Corvinus Egyetemen folyó „Versenyben a világgal” kutatási program keretében készült. = Sustainability issues in literature are getting more and more attention. In this study the focus is extended to purchasing and supplier relationships as companies influence their supply base by the priorities of their sourcing decision. This paper addresses sustainability in purchasing in a comprehensive way including green, social responsibility and corporate growth issues. The results of a research project which aims to reveal and structure the meaning of sustainable purchasing and the motivating forces leading companies to make efforts in purchasing for sustainability and means applied to attain achievements at some fields of sustainability. After presenting the results of literature review, some theory development was done to create a framework in which it is possible to describe the sustainability means applied and the motivating force behind. This framework serves as a basis of an empirical investigation among Hungarian companies. The empirical results validated the theoretical framework: the number and the characteristics of sustainability activities were determined by the type of motivation (to avoid negative effects, compliance to expectations, to attain positive effects). Our research project was part of the research project “In Global Competition”.

Analysis of purchasing activity with discounted cash flow inventory models = Beszerzési tevékenység elemzése diszkontált pénzáramlású készletmodellel

A klasszikus tételnagyság probléma két fontosabb készletezési költséget ragad meg: rendelési és készlettartási költségek. Ebben a dolgozatban a vállalatok készpénz áramlásának a beszerzési tevékenységre gyakorolt hatását vizsgáljuk. Ebben az elemzésben a készpénzáramlási egyenlőséget használjuk, amely nagyban emlékeztet a készletegyenletekre. Eljárásunkban a beszerzési és rendelési folyamatot diszkontálva vizsgáljuk. A költségfüggvény lineáris készpénztartási, a pénzkiadás haszonlehetőség és lineáris kamatköltségből áll. Bemutatjuk a vizsgált modell optimális megoldását. Az optimális megoldást egy számpéldával illusztráljuk. = The classical economic order quantity model has two types of costs: ordering and inventory holding costs. In this paper we try to investigate the effect of purchasing activity on cash flow of a firm. In the examinations we use a cash flow identity similar to that of in inventory modeling. In our approach we analyze the purchasing and ordering process with discounted costs. The cost function of the model consists of linear cash holding, linear opportunity cost of spending cash, and linear interest costs. We show the optimal solution of the proposed model. The optimal solutions will be presented by numerical examples.

Buyback and return policies for a book publishing firm = Egy könyvkiadó vállalat visszavásárlási stratégiája

A dolgozat célja egy vállalati gyakorlatból származó eset elemzése. Egy könyvkiadót tekintünk. A kiadó kapcsolatban van kis- és nagykereskedőkkel, valamint a fogyasztók egy csoportjával is vannak kapcsolatai. A könyvkiadók projekt rendszerben működnek. A kiadó azzal a problémával szembesül, hogy hogyan ossza el egy frissen kiadott és nyomtatott könyv példányszámait a kis- és nagykereskedők között, valamint mekkora példányszámot tároljon maga a fogyasztók közvetlen kielégítésére. A kiadóról feltételezzük, hogy visszavásárlási szerződése van a kereskedőkkel. A könyv iránti kereslet nem ismert, de becsülhető. A kis- és nagykereskedők maximalizálják a nyereségüket. = The aim of the paper is to analyze a practical real world problem. A publishing house is given. The publishing firm has contacts to a number of wholesaler / retailer enterprises and direct contact to customers to satisfy the market demand. The book publishers work in a project industry. The publisher faces with the problem how to allocate the stocks of a given, newly published book to the wholesaler and retailer, and to hold some copies to satisfy the customers direct from the publisher. The publisher has a buyback option. The distribution of the demand is unknown, but it can be estimated. The wholesaler / retailer maximize the profits. The problem can be modeled as a one-warehouse and N-retailer supply chain with not identical demand distribution. The model can be transformed in a game theory problem. It is assumed that the demand distribution follows a Poisson distribution.

Initial inventory levels for a book publishing firm = Kezdőkészletek egy könyvkiadó vállalatnál

Egy könyvkiadó vállalatot vizsgálunk. A kiadó kiadványait a szokásos értékesítési láncon (kis- és nagykereskedelem) keresztül értékesíti. A kérdés az, hogy egy új könyv példányait hogyan allokálja az értékesítési láncban. Feltételezzük, hogy a kereslet ismert, Poisson-eloszlású. A készletezés költségeit szintén ismertnek tételezzük fel. Cél a költségek minimalizálása. = The aim of the paper is to analyze a practical real world problem. A publishing house is given. The publishing firm has contacts to a number of wholesaler / retailer enterprises and direct contact to customers to satisfy the market demand. The book publishers work in a project industry. The publisher faces with the problem to allocate the stocks of a given, newly published book to the wholesaler and retailer, and to hold some copies to satisfy the customers direct from the publisher. The distribution of the demand is unknown, but it can be estimated. The costs consist of inventory holding and shortage, backorder costs. The decision maker wants to minimize these relevant costs. The problem can be modeled as a one-warehouse and N-retailer supply chain with not identical demand distribution. The problem structure is similar that of a newsvendor model. It is assumed that the demand distribution follows a Poisson distribution.

Ellátási lánc kapcsolatok modellezése = Modeling of supply chain relationships

A dolgozatban az ellátási láncokban meglévő diadikus kapcsolatok minőségét állítjuk a vizsgálatok középpontjába. Az irodalomban számtalan megközelítés ismert az ellátási lánc kapcsolatok fejlődésének leírására. Ezen fejlődési elméletek inkább elméleti szinten írják le a diadikus kapcsolatok változását, annak empirikus tesztelhetőségét nem vizsgálják. Dolgozatunkban kísérletet teszünk az ellátási lánc kapcsolatok fejlődésének empirikus vizsgálatára. Arra próbálunk választ találni, hogy az életciklus hipotézis az üzleti kapcsolatok időbeli fejlődésére alkalmazható-e. = Our paper combines two approaches using data of an internet based questionnaire and applying quantitative analysis it tests the hypothesis business relationship development in time can be described with the concept of life cycle. The concept of life cycle is widely used in business research. Among others the diffusion of innovation is described using this concept, or the concept of product life cycle just to name a few. All of these researches analyze the life cycle along a specific variable (for example the volume of sales or revenue in case of the product life cycle) which (except the last stage of the cycle, the decline) has a cumulative character resulting in the widely known specific shape of a life cycle. Consequently testing a life cycle hypothesis inevitably means the acceptance of some type cumulativity in the development.

Cooperation in an HMMS-type supply chain: A management application of cooperative game theory = Kooperáció egy HMMS-típusú ellátási láncban: A kooperatív játékelmélet egy menedzsment alkalmazása

We apply cooperative game theory concepts to analyze a Holt-Modigliani-Muth-Simon (HMMS) supply chain. The bullwhip effect in a two-stage supply chain (supplier-manufacturer) in the framework of the HMMS-model with quadratic cost functions is considered. It is assumed that both firms minimize their relevant costs, and two cases are examined: the supplier and the manufacturer minimize their relevant costs in a decentralized and in a centralized (cooperative) way. The question of how to share the savings of the decreased bullwhip effect in the centralized (cooperative) model is answered by the weighted Shapley value, by a transferable utility cooperative game theory tool, where the weights are for the exogenously given “bargaining powers” of the participants of the supply chain. = A cikkben a kooperatív játékelmélet fogalmait alkalmazzuk egy Holt-Mogigliani-Muth-Simon-típusú ellátási lánc esetében. Az ostorcsapás-hatás elemeit egy beszállító-termelő ellátási láncban ragadjuk meg egy kvadratikus készletezési és termelési költség mellett. Feltételezzük, hogy mindkét vállalat minimalizálja a releváns költségeit. Két működési rendszert hasonlítunk össze: egy hierarchikus döntéshozatali rendszert, amikor először a termelő, majd a beszállító optimalizálja helyzetét, majd egy centralizált (kooperatív) modellt, amikor a vállalatok az együttes költségüket minimalizálják. A kérdés úgy merül fel, hogy a csökkentett ostorcsapás-hatás esetén hogyan osszák meg a részvevők ebben a transzferálható hasznosságú kooperatív játékban a költség megtakarítást, exogén módon adott tárgyalási pozíció mellett.

The calculation of dynamic ecological footprint on the basis of the dynamic input-output model

The Leontief input-output model is widely used to determine the ecological footprint of consumption in a region or a country. It is able to capture spillover environmental effects along the supply change, thus its popularity is increasing in ecology related economic research. These studies are static and the dynamic investigations are neglected. The dynamic Leontief model makes it possible to involve the capital and inventory investment in the footprint calculation that projects future growth of GDP and environmental impacts. We show a new calculation method to determine the effect of capital accumulation on ecological footprint. Keywords: Dynamic Leontief model, Dynamic ecological footprint, Environmental management, Allocation method

Dinamikus optimalizálás és a Leontief-modell (Dynamic optimization and the Leontief model)

A tanulmány a variációszámítás gazdasági alkalmazásaiból ismertet hármat. Mindhárom alkalmazás a Leontief-modellen alapszik. Az optimális pályák vizsgálata után arra keressük a választ, hogy az Euler–Lagrange-differenciálegyenlet rendszerrel kapott megoldások valóban optimális megoldásai-e a modelleknek. Arra a következtetésre jut a tanulmány, hogy csak pótlólagos közgazdasági feltételek bevezetésével határozhatók meg az optimális megoldások. Ugyanakkor a megfogalmazott feltételek segítségével az ismertetett modellek egy általánosabb keretbe illeszthetők. A tanulmány végső eredménye az, hogy mind a három modell optimális megoldása a Neumann-sugárnak felel meg. /===/ The study presents three economic applications of variation calculations. All three rely on the Leontief model. After examination of the optimal courses, an answer is sought to whether the solutions to the Euler–Lagrange differential equation system are really opti-mal solutions to the models. The study concludes that the optimal solutions can only be determined by introducing additional economic conditions. At the same time, the models presented can be fitted into a general framework with the help of the conditions outlined. The final conclusion of the study is that the optimal solution of all three models fits into the Neumann band.

Ütemvakság

A gazdaság növekedés felgyorsulása hosszú távon először szükségszerűen csak egy rövid helyreállítási perióduson keresztül valósulhat meg, amelynek során a növekedés ütemét a válságok miatt elmaradt vagy más okból elmulasztott növekedés pótlása gyorsítja fel. Ez azonban messze nem jelenti a hosszú távú növekedési ütem felgyorsulását. A jelenséget először Jánossy Ferenc írta le, akinek megállapításai ma is érvényesek: egy jelentős visszaesés, majd stagnálás után a növekedési ütem 2005 után visszaállt az 1980 óta kialakult 1,5 százalékos hosszú távú ütemre. A Jánossy-féle szakmastruktúra-tényező nem más, mint a tudástőke: a munkaképes lakosság személyes tudása, jártassága és motivációja. Ezek az összetevők egy újrafogalmazott termelési függvény emberi elemei számos új és már korábban is ismert tényező mellett. Az emberi erőforrások nyilvántartása nem kompetenciaalapú, és emiatt a hosszú távú növekedési ütem alacsony szintjét sem tudjuk megmagyarázni. A növekedési ütem ingadozásai mögött elsősorban gazdaságpolitikai hibákat, érdemeket keresünk, holott az emberi beruházások elégtelen szintje jelenti a problémát, amely a múlt örökségnek és a jelen terheinek súlya alatt nem oldódik meg automatikusan. A magyar gazdaság egy újabb helyreállítási periódus előtt áll, s a gazdasági átalakítás alapvető feladata a foglalkoztatható lakosság aktivizálása, enélkül minden növekedési gyorsulás csak átmeneti helyreállítási periódus marad. JEL kód: B23, C22, E01, O11. /===/ Acceleration of economic growth in the long term can primarily be achieved only through a short period of consolidation, in which the growth rate of growth by recession or made up for by growth potential neglected for other reasons. But this is far from equivalent to an acceleration of the long-term growth rate. The phenomenon was described first by Ferenc Jánossy, whose conclusions remain valid to this day: after a substantial slump and a period of stagnation, the growth rate recovered after 2005 the long-term rate of 1.5 per cent that had set in after 1980. Jánossy's trade structure factor amounts to capital in knowledge: the personal know-how, expertise and motivation of the able-bodied population. These factors are the human constituents of a newly formulated production function, along with numerous new and previously known factors. The registration of human resources is competence- based and so it cannot explain the low level of the long-term growth rate either. People tend primarily to see failures and achievements of economic policy behind the failures and achievements of economic policy, when the real problem is inadequate human investment, which will not resolve itself automatically under the weight of the past and present burdens. The Hungarian economy is on the brink of a new period of recovery, and the basic task of economic transformation is to activate the employable population, without which any acceleration of growth will amount only to a temporary period of recovery.

The efficiency of remanufacturing in a dynamic input–output model

For industrialised economy of ourdays, remanufacturing represents perhaps the largest unexploited resource and opportunity for realising a greater growth of the economy in an environmental-conscious manner. The aim of this paper is to investigate of the impact of remanufacturing in the economy from an economic-efficiency point of view. In static context this phenomenon was analysed in the literature. We use the multi-sector input–output framework in a dynamic context to study intra-period relationships of the sectors of economy. We extend the classical dynamic input–output model taking into consideration the activity of remanufacturing .We try to answer the question, whether the remanufacturing/reuse increases the growth possibility of an economy. We expose a sufficient condition concerning the effectivity of an economy with remanufacturing. By this evaluation we analyse a possible sustainable development of the economy on the basis of the product recovery management of industries.

The resource conservation effect of recycling in a dynamic Leontief model

The aim of the paper is to investigate the impact of recycling on the use of non-renewable resources in the economy. The paper tries to generalize the classical dynamic input–output model. In this regard we extend the standard Leontief model with the balance equation of recycled products, and we establish some properties of this augmented model. We investigate how recycling extends the availability of non-renewable natural resources for the next generations in an inter-industry framework. Supposing a balanced growth both for production and consumption, we examine the existence of the balanced growth path of this model and compare the results to the classical Leontief model. We try to answer the question whether recycling/reuse increases the growth possibility of an economy. Finally, we illustrate our results with a simple numerical example. Thus, we analyze a possible sustainable development of the economy on the basis of the product recovery management of industries.