Difusão numa matriz monolítica – Droga dissolvida em carreador polimérico

Uma matriz monolítica é a forma mais simples e mais barata de controlar a liberação de fármacos. Para fabricá-la, um polímero ou outro material é homogeneamente distribuído com a droga por mistura da droga com o material polimérico. Os interstícios controlam a liberação da droga. O grau do controle da difusão da droga pela matriz é determinado pelas propriedades do polímero e do fármaco.

Ou a droga está totalmente dissolvida no polímero ou dispersa como partículas sólidas na matriz. A última condição prevalece quando a concentração da droga é muito maior que sua solubilidade no polímero. A cinética de liberação nestes dois estados é diferente.

Aqui será descrita a liberação para o caso da droga dissolvida na matriz. Quando a matriz entra em contato com o solvente, a droga começa a se difundir para fora dos interstícios da estrutura polimérica. A expressão matemática que rege a difusão pela matriz é uma equação diferencial parcial, a segunda lei de Fick:

Iremos analisar uma situação em que a matriz polimérica seja esférica. Em coordenadas esféricas, esta expressão é modificada para:

Considerado a difusão como radial, a equação se reduz a:

(1)

onde D é o coeficiente de difusão, C é a concentração da droga e r é a distância do centro da esfera.

Podemos então determinar as condições iniciais e de fronteira. Ao colocar a forma farmacêutica em contato com a água, a concentração da droga na superfície da esfera é zero, enquanto que a concentração dentro da esfera é única para todos os pontos. Se a esfera tem raio a, segue que:

, (2)

, (3)

Podemos resolver este problema por separação de variáveis. Podemos primeiro fazer uma substituição que facilitará a resolução:

(4)

Perceba que:

Isolando ,

(5)

Perceba também que:

Assim:

(6)

Substituindo (5) em (6) em (1), assim como (2) e (3) em (4), chegamos ao PVIF (cuja EDP é análoga a conhecida equação do calor em uma dimensão):

(7)

, ( 8 )

, (9)

Podemos resolver por separação de variáveis:

(10)

Substituindo (10) em (7):

Chegamos, então, a duas EDO’s com as condições determinadas por (8) e (9)

(11)

(12)

(13)

Se multiplicarmos a equação (11) por A(r) e fizermos uma integração de 0 a a:

Usando integração por partes na primeira integral:

Chegamos a conclusão que só temos autofunções para autovalores :

Se , e, pelas condições em (11), não há autofunções.

Se ,

Pela condição ,

Pela condição , , que só produz autofunções para:

e, portanto:

, (14)

(15)

Substituindo (14) em (13):

Logo, (16)

Através de (10), (15) e (16), e pelo princípio da superposição, chegamos à solução geral:

(17)

Falta agora, determinar os coeficientes . Usaremos a condição (9)

Assim,

(18)

E, finalmente, usando (4), (17) e (18):

Referências:

C.-J Kim. Controlled release dosage form design. Technomic, Lancaster PA, 2000, 301 pp.

J. Crank. The mathematics of diffusion, Second Edition, Claremdon Press, Oxford, 1975.

Fármacos usados no tratamento da AIDS

Há cinco categorias de fármacos usados no combate do HIV:

1. Inibidores nucleosídicos/nucleotídicos da transcriptase reversa
2. Inibidores não-nucleosídicos da transcriptase reversa
3. Inibidores da protease
4. Inibidores da fusão do HIV com as células do hospedeiro
5. Inibidores da Integrase

Seguem alguns vídeos do youtube ilustrando a ação destes fármacos (não repare na propaganda que alguns vídeos fazem)

Inibidores Nucleosídeos/Nucleotídicos da Transcriptase Reversa (NRTIs – Nucleoside Reverse Transcriptase Inhibitors; NTRTIs – Nucleotide Reverse Transcriptase Inhibitors)

NRTIs and NTRTIs are antiretroviral drugs which following absorption into the body must be metabolized in the affected cell in order to become active. The NRTI metabolism involves three steps, while NTRTIs require only two steps. NRTIS are analogs of DNA building blocks. NRTIs work by imitating natural DNA building blocks. When building a new viral DNA chain, reverse transcriptase enzyme binds to NRTIs instead of binding to the natural occurring DNA building blocks. Because the structure of the NRTIs, there is no allowed attachment to the next DNA building block. DNA chain growth is terminated. HIV has developed two drug resistance mechanisms to NRTIs. Mechanism number one is decreased binding of the enzyme reverse transcriptase to NRTIs. ?(The remaining mutations that have this sort of impact on the binding affinity). The second mechanism to NRTI resistance is the increased removal of the NRTI from the elongating DNA chain.

AZT

Inibidores não-nucleosídicos da transcriptase reversa (NNRTIs – Non-nucleoside reverse transcriptase inhibitors)

Instead of competing with naturally occurring DNA building blocks as do the NRTIs, NNRTIs bind tightly to the enzyme reverse transcriptase thereby preventing viral RNA from being converted to DNA. In contrast to the NRTIs mutations, drug resistance to NNRTIs is normally associated with mutations that are proximal to the drug binding site on reverse transcriptase. And that distortion of this binding pocket is the mechanism of resistance.

HIV1 is a virus with a high replication rate. Within infected CD4 cells the viral nucleocapsid breaks open releasing two RNA strands and essential replication enzymes such as HIV1 reverse transcriptase. It is a heterodimer with a p51 subunit and a p66 subunit. The p66 subunit contains a finger upon and a thumb region resembling a (____ hand?). Reverse transcriptase has two catalytic domains, the ribonuclease H active site and the polymerase active site. Here single stranded viral RNA is transcribed into a RNA-DNA double helix. Ribonuclease H breaks down the RNA. The polymerase then completes the remaining DNA strand to form a DNA double helix. This proviral DNA contains the genetic material of HIV1. Therapeutical suppression of viral replication slows down the decline of CD4 cells and the disease progression. Nucleoside reverse transcriptase inhibitors (NRTIs) inhibit the polymerase active site. After metabolism to non function nucleotides their incorporation causes chain termination. The non-nucleoside reverse transcriptase inhibitors (NNRTIs) form another class of powerful antiretroviral agents. They inhibit reverse transcriptase by reducing its conformational flexibility. The thumb region of reverse transcriptase is flexible. It opens and closes like a hand. Only the closed position allows transcription of RNA. The base of the thumb has a hydrophobic pocket-like binding site. This is the target of NNRTIs. Nevirapine is an important representative of this class. It does not need to be metabolized. In its native form, nevirapine binds in the pocket. This locks the thumb in the open position and prevents the transcription of RNA. Thus nevirapine stops viral replication. Due to this mechanism, nevirapine is a potent partner in the combination therapy of HIV1 infection.

Inibidores da Protease (PIs – Protease Inhibitors)

Protease inhibitors slow down HIV replication of the viruses integrated into the host cells DNA in acutely and chronically infected cells. During the maturation process of new virions, the HIV protease enzyme cuts newly produced elements of virus (____)? polyproteins into essential functional protein products. This critical process occurs as each new virion grows from the membrane of an HIV infected cell and continues after the immature virus is released from the cell. The host cell is eventually destroyed in the process. If the polyproteins are not cut the new virus fails to mature and is incapable of infecting a new cell. Protease inhibitors are able to interfere with the functioning of the native protease enzyme. They disable the enzyme before it can cleave the new viral polyprotein into its essential protein products thereby (_____)? the new virion immature and non infectious. The mechanism of resistance to protease inhibitors may be more complex than originally thought and is not as well understood as NRTI and NNRTI resistance. When PI resistance occurs, PI interference with mutant protease is no longer adequate.

The ability of HIV to infect cells is essential to its replication. Infection of a suitable host cell such as a CD4+ T lymphocyte leads to integration of the proviral DNA into the host cell genome. It now contains the genetic information for the building blocks of new HIV virus including two viral RNA strands and three viral enzymes, one of which is the HIV protease. The protease plays a key role in the formation of infectious virus. Activation of the cell induces transcription of a proviral DNA into a messenger RNA. The viral messenger RNA migrates into the cytoplasm where components of a new virus are synthesized. Some of these components have to be processed by the virus protease which cleaves longer proteins into smaller core proteins. This step is crucial to create an infectious virus. Two viral RNA strands, the viral enzymes and core proteins are assembled. This immature viral particle leaves the cell, acquiring a new (envelope?) host and viral proteins. The virus matures and becomes ready to infect other cells. Inhibition of HIV protease can stop this replication cycle. The introduction of peptidic protease inhibitors represented a milestone in treatment of HIV infection. These types of protease inhibitors bind to protease via an extensive network of hydrogen bonds resulting in the drug being attached to the active site. This blocks the action of the protease preventing HIV replication. Unfortunately mutations in HIV protease occur frequently and may limit the use of current protease inhibitors. A change in even a few amino acids can prevent these drugs binding to protease leading to broad cross resistance. Therefore there is a need for novel protease inhibitors with high potency and improved ability to overcome the diversity of mutations in the protease. Tipranavir is a novel non-peptidic protease inhibitor that displays the essential features of such an improved inhibitor. Unbound tipranavir displays the bioactive conformation more often than current protease inhibitors. Therefore less energy is required for tipranavir to adapt its overall conformation to the requirements of the binding site. Tipranavir establishes a strong network ()? energy bond interactions with conserved elements of the protease active site that cannot be mutated without the enzyme losing its function. In addition, tipranavir makes a direct hydrogen bond with the backbone atoms of the isoleucine amino acids at position 50 on each subunit of the protease. All current protease inhibitors make this interaction indirectly through a water molecule expending energy to immobilize it. The release of this water molecule by tipranavir is an energetic favorable event. The direct bond to this conserved regions results in an improved binding of tipranavir to the protease. Finally, for current protease inhibitor mutations in the protease generally weaken the bonding interactions. Tipranavir compensates for the impact of mutations in a thermodynamically unique manner by conserving and even enhancing these important contacts. As a result of these important features tipranavir retains entire ()? even against HIV strains with extensive resistance to current protease inhibitors. In summary, tipranavir has an improved ability to overcome the diversity of mutations in the protease by adopting the bioactive conformation more frequently; by estabilishing a strong network hydrogen bonds with conserved elements of the protease;  By binding directly to isoleucine 50; and by compensating for the impact of mutations by enhancing important contacts. These characteristics contribute to tipranavir’s unique resistance profile and make tipranavir an innovative option for the treatment of HIV disease.

Inibidores da fusão do HIV com as células do hospedeiro

Occuring after attachment and co-receptor binding the third step in HIV cell entry, fusion, also represents a target for anti-viral drug development. One model of fusion requires gp41 to undergo extensive structural reorganization in order to destabilize the viral and cell membranes. Compounds that bind gp41 and interfere with this process have the potential to prevent HIV cell entry. Drug candidates that block gp41, known as fusion Inhibitors, are currently in clinical development.

Inibidores da Integrase

Integrase is an essential enzyme that allows HIV to integrate its proviral DNA into the host cell cromossomes. Integrase Inhibitors are on the development as a new class of anti-HIV drugs.

Nota: Existem inibidores da fusão e da integrase que são comercializados.